assessment of potential fuel saving benefits of hybrid

Assessment of Potential FuelSaving Benefits of Hybrid-Electric Regional Aircraft

Joris Van Bogaert

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ASSESSMENT OF POTENTIAL FUEL SAVINGBENEFITS OF HYBRID-ELECTRIC REGIONAL

AIRCRAFT

by

Joris Van Bogaert

in partial fulfillment of the requirements for the degree of

Master of Sciencein Aerospace Engineering

at the Delft University of Technologyto be defended publicly on Thursday December 17 2015

Supervisor Drir Mark VoskuijlDr Arvind G Rao

Thesis committee Dr Hans Mulder TU DelftSimon Tayler Fokker Elmo

This thesis is confidential and cannot be made public until December 31 2015

An electronic version of this thesis is available at httprepositorytudelftnlThesis registration number 06815MTFPP

PREFACE

This thesis presents the research done in investigating the potential reduction in fuel consumptionthat can be achieved by utilizing a hybrid-electric power plant in aircraft It has been written tofulfill the requirements for the degree of Master of Science in Aerospace Engineering at the DelftUniversity of Technology The research described herein was conducted under the supervision ofDrir Mark Voskuijl and Dr Arvind G Rao

First and foremost I would like to thank my supervisors for their excellent guidance supportand feedback during this process Thanks also to my friends and colleagues at the TU Delft it wasalways helpful to discuss ideas about my research with you Finally I take this opportunity to expressmy gratitude to my family and girlfriend for their love unfailing encouragement and support

Joris Van BogaertDelft December 2015

iii

SUMMARY

Both NASA and the EU have set ambitious goals in terms of aircraft emission reduction Previousstudies have indicated that these goals can not be met with evolutionary improvements of conven-tional technologies For this reason there is a need for revolutionary aircraft concept andor radicalinnovative systems One such concept is the use of a hybrid-electric propulsion system

The aim of this project is to investigate the potential improvements in fuel consumption of ahybrid-electric regional aircraft which uses both batteries and conventional fuel as power sourceSince no comprehensive design studies of such a concept have been performed so far the designspace is explored as well

All designs considered in this project are constructed for the year 2035 because the currentlevel of technological progress is not adequate for a hybrid-electric aircraft to be feasible By theyear 2035 it is expected that lithium-air battery technology will mature and a battery specific energyof 750 Whkg to 1500 Whkg can be expected Also high-temperature superconducting technologyin wiring electric motors and other electronics are predicated to be viable The study is limited toregional aircraft because the required range of larger aircraft can not be met even with the expectedtechnological improvements

Many different power train architectures are possible using both batteries and conventional fuelmost notably the series-hybrid architecture and the parallel-hybrid architectures It is chosen to usethe parallel-hybrid architecture in all designs due to its potential for a lower weight and versatilityin operating modes Using this architecture two operating modes are considered the power splitoperating mode and the constant gas turbine power operating mode The power split operatingmode requires a certain power split as input for each flight phase which determines how the gasturbine and electric motor are used during that flight phase The constant gas turbine operatingmode requires a maximum continuous gas turbine power as input This gas turbine is then usedas efficiently as possible during the mission and the electric motor is used when more power isrequired

Since several designs have to be generated in order to explore the design space a program isneeded which can generate a preliminary aircraft design based on a set of input parameters in arelatively short time span For this purpose a (mostly) physics-based preliminary design programcalled Initiator is used This program is heavily adapted in order to be able to generate regionalhybrid-electric aircraft designs Especially the mission analysis is heavily modified First of all thisadapted program is used to generate a reference aircraftbased upon the ATR 72-600 The refer-ence aircraft is subsequently compared to its real-life counterpart in order to validate some of thechanges made to the Initiator program It is found that the reference aircraft is a very close matchto the ATR 72-600 in terms of mass breakdown geometry and performance The changes pertain-ing to the hybrid-electric aircraft can not be validated since no comparable design studies have beenperformed so far

Subsequently the effect of making a design more hybrid (increasing the degree of hybridizationor the supplied power ratio) is investigated for multiple battery specific energies It is found thatfor a range of 1528 km the fuel weight decreases with an increasing supplied power ratio for anybattery specific energy between 750 Whkg and 1500 Whkg At the same time the MTOM increasesThis holds true for a range up to around 5000 km (depending on the chosen battery specific energy)After which either no benefit can be achieved from using a hybrid-electric aircraft or there exists anoptimum in the supplied power ratio This is because after a certain point more energy is required

v

vi PREFACE

to transport the batteries than the energy stored in the batteries itself There is also a limit to themaximum achievable supplied power ratio for most battery specific energyrange combinationsAfter a certain point the MTOM (and thus also the energy requirement) increases to such a levelthat no more feasible design is possible

Comparing both operating modes shows that the constant gas turbine operating mode givesmore optimal results compared to using a constant power split over the entire mission There is aslight decrease in fuel weight for the same MTOM and battery weight due to the lower average SFCUsing a constant power split over the entire mission might not be optimal however no optimalpower split has been found so far This might be a topic for further study

Lastly one final regional hybrid-electric aircraft is selected from the design space using a batteryspecific energy of 1000 Whkg and a supplied power ratio of 034 This was chosen as being a fea-sible realistic design point which does not require too large technological improvements in orderto be feasible This design point results in fuel weight reduction of 28 compared to the referenceaircraft while having an increase in MTOM of 14 From this it can be concluded that significantfuel weight reduction can be achieved by using the hybrid-electric aircraft concept However theexact figure of how much benefit can be achieved is highly dependent on the level of technologicalprogress between now and 2035 In particular the battery specific energy has a large influence

CONTENTS

List of Figures ix

List of Tables xiii

1 Introduction 1

2 Project Description 321 Configuration and Requirements 3

22 Technology Overview 5

221 Battery Technology 5

222 Electric Motor Technology 9

23 Power plant Architecture 10

231 Architecture Possibilities 10

232 Selected Architecture 11

24 Control Strategies 13

25 Important Parameters 14

3 Methodology 1531 Initiator 15

32 Reference Aircraft Design 17

321 Engine and Propeller Sizing 17

322 Gas turbine power and fuel consumption variation 19

323 Other Modifications 23

33 Class 2 Battery and Fuel Sizing 23

331 Battery Sizing 23

332 Fuel 25


341 Take-off 32

342 Climb 36

343 Cruise 39

344 Descent 42

345 Landing 44

346 HoldLoiter 46

35 Comparison between Class 2 and Class 25 sizing 48

351 Mission analysis results 48

352 Comparison 51

36 Electric Motor Sizing 52

37 Wiring 53

38 Other Components 54

39 Component Placement 55

310 Implementation 56

311 Limitations 56

vii

viii CONTENTS

4 Results 5941 Reference Aircraft 5942 Hybrid Aircraft 62

421 Inputs 62422 Supplied Power Ratio 63423 Operating Modes 68424 Optimal Power Split 74

43 Sensitivity Analysis 77431 Range 77432 Battery specific energy 79

44 Final Design 79

5 Conclusion amp Recommendations 8351 Conclusion 8352 Recommendations 84

A Derivation of hybrid-electric range equation 85

Bibliography 87

LIST OF FIGURES

21 Impression of the EuroFlyer aircraft concept [1] 422 Critical temperature of superconducting materials [2] 923 Series hybrid architecture 1024 Parallel hybrid architecture 1125 Architecture of the power plant 12

31 Simplified flow chart showing the basic workings of the initiator program 1632 Example of a power loading diagram of an aircraft comparable to the ATR72-600 1833 Power variation as a function of velocity and altitude [3] 20

34 Slope of PP0

compared to the slope of(ρρ0

)075for a velocity of 250 knots 20

35 Fuel flow as a function of velocity and altitude [3] 2136 SFC as a function of velocity and altitude [3] 2137 SFC variation with power setting for a typical cruise condition with V = 200 knots and

h = 20000 ft (= 6096 m) [3] 2238 Results of the adapted Brequet range equation for a variable fuel weight and power split 2739 Example of a typical mission profile that can be used to determine the battery and fuel

weight 28310 Activity diagram of the flight phases of the Mission Analysis module 31311 Altitude speed and flight path angle of an arbitrary hybrid-electric aircraft during

take-off 34312 Flow chart of the take-off phase 35313 Graph of the shaft power gas turbine power and electric motor power during the climb

phase with a power split of 05 37314 Altitude speed and flight path angle of an arbitrary hybrid-electric aircraft during the

climb phase 37315 Flow chart of the climb phase 38316 Altitude speed and flight path angle of an arbitrary hybrid-electric aircraft during the

cruise phase 40317 Flow chart of the cruise phase 41318 Altitude speed and flight path angle of an arbitrary hybrid-electric aircraft during the

descent phase 43319 Flow chart of the descent phase 43320 Altitude speed and flight path angle of an arbitrary hybrid-electric aircraft during

landing 44321 Flow chart of the landing phase 45322 Flow chart of the loiter phase 47323 State of an arbitrary hybrid-electric aircraft during the entire mission including devi-

ation and loiter 49324 Shaft - gas turbine - and electric motor power during the entire mission for a constant

power split of 05 50325 Battery- and fuel weight used during the entire mission for a constant power split of 05 50

ix

x LIST OF FIGURES

326 Variation of the electric motor and cryocooler weight with respect to the maximumelectric motor power 53

327 Cable weight as a function of current for a cable rated at 6 kV 54

41 Front view of the ATR72-600 compared to the reference aircraft 6042 Side view of the ATR72-600 compared to the reference aircraft 6043 Top view of the ATR72-600 compared to the reference aircraft 6144 Battery mass vs supplied power ratio for multiple battery energy densities 6445 Fuel mass vs supplied power ratio for multiple battery energy densities 6546 Maximum take-off mass vs supplied power ratio for multiple battery energy densities 6547 Maximum electric motor power vs supplied power ratio for multiple battery energy

densities 6648 The mass of the components making up the electrical part of the powertrain (minus

the batteries) vs supplied power ratio for a battery energy density of 1500 Whkg 6649 mass of the gas turbine vs supplied power ratio for multiple battery energy densities 67410 The maximum continuous gas turbine power vs the supplied power ratio for battery

energy densities of 750 1000 and 1500 Whkg 68411 Shaft - electric motor - and gas turbine power during the entire mission for a constant

power split resulting in a supplied power ratio of 025 using a battery specific energyof 1000 Whkg 69

412 Shaft - electric motor - and gas turbine power during the entire mission for a certaininput gas turbine power resulting in a supplied power ratio of 025 using a batteryspecific energy of 1000 Whkg 69

413 Difference in fuel mass for the constant gas turbine power operating mode comparedto the power split operating mode using a battery specific energy of 750 1000 and 1500Whkg 71

414 Difference in battery mass for the constant gas turbine power operating mode com-pared to the power split operating mode using a battery specific energy of 1000 and1500 Whkg 71

415 Difference in maximum electric motor power for the constant gas turbine power op-erating mode compared to the power split operating mode using a battery specificenergy of 750 1000 and 1500 Whkg 72

416 Difference in gas turbine mass for the constant gas turbine power operating modecompared to the power split operating mode using a battery specific energy of 7501000 and 1500 Whkg 72

417 Difference in MTOW for the constant gas turbine power operating mode compared tothe power split operating mode using a battery specific energy of 750 1000 and 1500Whkg 73

418 Optimum power split using model predictive control [4] 74419 Optimum power split input variation 1 75420 Optimum power split input variation 2 75421 Fuel and battery mass vs supplied power ratio for designs with constant power split

and the optimum power split according the Perullo et al 76422 Fuel and battery mass vs supplied power ratio for designs with constant power split

and the optimum power split according the Perullo et al 76423 MTOW vs supplied power ratio for designs with constant power split and the optimum

power split according the Perullo et al 77424 Variation of fuel mass with supplied power ratio for multiple ranges 78425 Variation of maximum take-off mass with supplied power ratio for multiple ranges 78426 Fuel mass vs battery specific energy for multiple supplied power ratios 79

LIST OF FIGURES xi

427 Isometric view of the hybrid-electric aircraft 81428 Front view of the hybrid-electric aircraft 81429 Side view of the hybrid-electric aircraft 81430 Top view of the hybrid-electric aircraft 82

LIST OF TABLES

21 Estimation of battery parameters by the year 2035 8

31 Parameters the state matrix rsquoSrsquo keeps track of 2932 Comparison between the class 2 and class 25 sizing methods for constant power splits

ranging from 000 to 100 5133 Comparison between the class 2 and class 25 sizing methods for input gas turbine

powers ranging from 01 MW to 3 MW 5234 New input parameters that are needed in the Initiator program when designing a hybrid-

electric aircraft 58

41 Requirements of the ATR 72-600 which are also used as input for the reference aircraftdesign 59

42 Parameters comparing the ATR 72-600 to the reference aircraft 6243 Input values that are used for each design considered in this chapter 6244 Parameters comparing the hybrid-electric aircraft to the reference aircraft 8045 Parameters comparing the geometry of the hybrid-electric aircraft to the reference air-

craft 80

xiii

NOMENCLATURE

Acronyms

ACARE Advisory Council for Aviation Research and Innovation in Europe

AVL Athena Vortex Lattice

FF Fuel fraction

HTS high-temperature super-conducting

IEEE Institute of Electrical and Electronics Engineers

KEAS Knots equivalent airspeed [kts]

LTS Low-temperature super-conducting

MEA More-Electric-Aircraft

MTOM Maximum take-off mass [kg]

SFC Brake specific fuel consumption [gKWh]

SOC State of charge

SRIA Strategic Research and Innovation Agenda

UAV Unmanned Aerial Vehicle

Subscripts

bat Battery

el ec Electrical wiring and inverter

em Electric motor

0 Sea-level condition

avg Average

cable Cable

climb State during the climb phase

cryo Cryocooler

disk Propeller disk

endcruise State at the end of the cruise phase

gasturb Gas turbine

precruise State at the beginning of the cruise phase

xv

xvi LIST OF TABLES

prop Propeller

take-off State during the take-off phase

tot total

Symbols

∆ Change in [-]

Q Heat transfer rate [W]

η Efficiency [-]

γ Flight path angle [deg]

Φ Supplied power ratio [-]

ρ Density [ kgm3 ]

A Area [m2]

e Specific energy [Whkg]

p power density [kWkg]

v Power to volume ratio [kWl]

vol Volumetric energy density [Whl]

a Speed of sound [ms]

b Wing span [m]

D Drag [N]

d Diameter [m]

E Energy [Wh]

f Frequency [Hz]

g Gravitational acceleration [ ms2 ]

H Degree of hybridization [-]

h Altitude [m]

L Lift [N]

l Length [m]

m Mass [kg]

N number

P Power [W]

Q Heat energy [J]

LIST OF TABLES xvii

R Range [km]

S Power split [-]

T Thrust [N]

t time [sec]

U Voltage [V]

V Speed [ms]

1INTRODUCTION

The Strategic Research and Innovation Agenda (SRIA) of ACARE [5] as well as the NASA N+3 [6]goals have set ambitious targets in terms of emission reduction for the aviation industry WithinSRIA 2035 it is recommended that 51 CO2 emission reduction should result from improvementsof propulsion systems and airframes while NASA N+3 sets a goal of a 60 fuel burn reduction by2025 [7]

Continuous improvements of conventional technologies will not be enough to fulfil these ambi-tious requirements The project SELECT [8] (contracted by Northrop Grumman for NASA) demon-strated that the NASA N+3 goals could not be met with evolutionary improvements of conventionaltechnologies For this reason there is a need for revolutionary aircraft concepts andor radical inno-vative systems

One such concept is to use a hybrid-electric propulsion system This propulsion system usesboth batteries (or some other source of electric energy such as fuel cells) and conventional fuel topower the aircraft This has the possibility of significantly reducing emissions and fuel burn

The aim of this project is to investigate the potential fuel saving (and thus also emission reduc-tion) hybrid-electric regional aircraft can achieve by the year 2035 No comprehensive design studyof hybrid-electric aircraft have been performed so far all previous design studies were either verylimited in scope or performed for small UAVrsquos As such in order to find out what the potential fuelsaving is the design space is explored as well This is done by adapting an existing physics-basedconceptual design program in order for it be able to design hybrid-electric aircraft The scope ofthis project is limited to regional aircraft since the technology in the year 2035 is not expected to besufficient for larger aircraft with a longer range to be achievable

First of all in Chapter 2 the project is further explained in particular what kind of configurationand technologies will be used in the hybrid-electric aircraft designs as well as what control strategiescan be employed The methodology of how a design is generated is explained in Chapter 3 and inChapter 4 the results of the design study are expanded upon Finally in Chapter 5 the conclusionand recommendations for future work are presented

1

2PROJECT DESCRIPTION

In this chapter the aim of the project is further explained as well as an investigation into what tech-nological advancement can be expected by the year 2035 Some different power plant architecturesare discussed and one of the architectures is selected as a baseline Subsequently the used operat-ing modes are briefly explained (ie how it is determined when how much of what power source isused) and the most important parameters are presented

21 CONFIGURATION AND REQUIREMENTSThe aim of this project is to investigate the decrease in fuel consumption a hybrid-electric aircraftconcept could have as compared to a conventional aircraft by the year 2035 Since almost no com-prehensive design studies pertaining to hybrid-electric aircraft have been performed so far the de-sign space is explored as well The design studies that were performed are limited in scope or onlyapplicable for small UAVs [9] [10] [11] [12]

A hybrid-electric propulsion system is defined as a propulsion system in which the energy forpropulsion is carried in two or more kinds or types of energy sources or converters and at leastone of them can deliver electrical energy [13] In this project we only consider two power sourcesone conventional gas turbine and one electric motor powered by batteries Using these two powersources many different power plant architectures are possible which are discussed in Section 23

The configuration of the hybrid-electric concept under investigation is based upon the Euroflyer[1] a novel aircraft configuration developed during the 2013 Design Synthesis Exercise at the DelftUniversity of Technology Figure 21 shows an artistrsquos impression of the final Euroflyer design Thehybrid-electric aircraft configuration is meant to incorporate the same basic elements

bull Boundary layer ingestion due to push-prop located at the rear of the fuselage which ingestspart of the boundary layer around the fuselage in order to reduce drag

bull Contra-rotating propellers which not only offset the torque created by the propeller but alsohave the possibility of increasing the efficiency of the propeller at the cost of extra noise gen-eration 1 and added mechanical complexity

In this project however only the impact of the hybrid-electric propulsion system is examined Theimpact of the contra-rotating propeller and boundary layer ingestion will not be taken into accountsince this is outside the scope of the project and would need to be investigated in further studies

1The extra noise generation can be cancelled out by adding a shroud around the propellers as is done in the Euroflyerconcept

3

4 2 PROJECT DESCRIPTION

Figure 21 Impression of the EuroFlyer aircraft concept [1]

In order to compare the performance of a hybrid-electric aircraft to a conventional aircraft abaseline aircraft is developed as well This reference aircraft will be based upon the ATR-72-600To be able to make a good comparison the requirements for the hybrid-electric design will be thesame as those for the ATR-72-600 These requirements are also similar to those for the Euroflyer [1]

These requirements are as follows

bull Range 1528 km

bull Number of passengers 68

bull Payload weight 7500 kg

bull Cruise Mach 045

bull Cruise altitude 7500 m

The reason for designing a regional aircraft and not a larger aircraft with longer range is because thetechnology in 2035 is not expected to be adequate for a larger aircraft with such a propulsion systemto be feasible However the influence on range will also be examined to determine what the rangelimit of a hybrid-electric regional aircraft is as well as what factors influence it

22 TECHNOLOGY OVERVIEW 5

22 TECHNOLOGY OVERVIEWIn this section a brief overview is given of the technologies that are required in order for a hybrid-electric aircraft to be feasible as well as the expected technological progress between now and 2035This mainly pertains to the battery technology and the electric motor technology While it is ex-pected that other technology such as the gas turbine technology will also improve between nowand 2035 this is not taken into account during the course of this project

221 BATTERY TECHNOLOGY

One of the main hurdles to overcome before hybrid regional aircraft become feasible is the batterytechnology The energy density of todayrsquos batteries is simply not high enough to make hybrid elec-tric propulsion viable for anything larger than ultra-light aircraft or UAVrsquos Luckily there is a lot ofresearch being done in this field (which will be discussed later) especially with the growth in theelectric car market

Although specific energy is probably the most important criteria for evaluating battery perfor-mance in aircraft it is certainly not the only criterion Below is a list of the main performance metricsnecessary for a good evaluation and comparison

bull Specific energy (ebat ) [Whkg]

bull Volumetric energy density (volbat ) [Whl]

bull Power density (pbat ) [Wkg]

There are also other metrics that have to be considered such as safety and charging perfor-mance as well as any other possible systems that have to be implemented such as battery cooling

Safety entails everything from explosion hazard to overheating hazard It is very hard to make anestimation of the magnitude of such hazards for technology that is still in its infancy For this reasonthis performance metric has not been investigated any further Charging performance is also animportant metric for which no accurate prediction can be done at this time

In this section an overview of the most important battery technologies currently under devel-opment is given Their respective advantages and disadvantages are also listed as well as the futureprospects of the battery technologies Since the aircraft under consideration is being developedfor a 2035 timeframe it is necessary to make an estimation of how battery technology will evolveand mature To make a hybrid-electric aircraft viable a certain battery specific energy density willbe needed which is much higher than todayrsquos Boeing determined the specific energy density ofbattery systems would need to be 750 Whkg or greater in order for a hybrid aircraft to be a realis-tic option [7] Battery energy density increases every year with about 6 [14] however sometimesthere are big jumps when new technology becomes available This means that it is very hard or evenimpossible to make accurate predictions for where battery technology will be by 2035 As such inthis project a wide range of battery specific energies is examined

LITHIUM ION

Lithium ion is the main battery technology used for high performance applications such as vehiclesor portable electronic devices Although this technology is already mature every year there is stillan increase in energy density of about 6 [14] This increase is mainly due to improvements infabrication using lighter cases (such as aluminium instead of stainless steel) or by optimization ofthe cell design [15] This trend is expected to continue for the foreseeable future until an energydensity of around 250 Whkg is reached [14]

Some companies such as Envia Systems state that they have achieved lithium-ion batteries witha specific energy of 400 Whkg [16] However the author could not find reliable sources for theseclaims and no additional information is available


Since lithium-ion technology is already very mature compared to the other technologies notmuch improvement in energy density is possible for this technology In the not so distant future aspecific energy 250 Whkg can be achieved [15] How it will evolve further is not known Most au-thors expects this technology to not be capable of higher energy densities than around 350 Whkgmost likely not enough to make a hybrid regional aircraft viable Based on trends of existing lithium-ion batteries the volumetric energy density is about 17 times higher than the specific energy forlithium-ion batteries This technology while cutting edge at the moment will probably be obsoleteby 2035 for high performance applications

LITHIUM SULPHUR

An emerging battery technology is Lithium-sulphur batteries This is at the time of writing the mostresearched emerging battery technology with more than 450 papers published on this topic in lessthan 2 years [17] In lithium-sulphur cells the following reaction takes place

2Li + S mdashgt Li2S

This reaction results in a theoretical specific energy of 3730 Whkg Almost an order of magnitudehigher than that of common lithium-ion battery cells [18] Of course the practical specific energywill be far less because of the added mass of the housing and other components Sulphur also hasthe added benefit of being cheap and abundant thus also promising a major improvement in notonly specific energy but also cost [17] Nevertheless there are still some major issues to be overcomebefore this battery technology can become mainstream [18]

bull The discharge process of Lithium-sulphur cells proceeds through the sequential formation ofpolysulphides (Lix Sy ) which easily dissolve in the liquid carbonate electrolyte solutions andeventually diffuse to the lithium anode resulting in severe corrosion effects This results inthe loss of active materials low overall efficiency and large capacity decay after a number ofcycles

bull The low electronic conductivity of S Li2S and the intermediate Li-S products severely affect-ing the charge rate capability of the battery

bull The use of lithium metal as the anode which can cause serious safety risks due to unevendeposition upon charge and can result in a short circuit in the cell which in turn can resultin thermal runaway and eventually fires or explosions

However many breakthroughs have happened in a very short timespan These developments re-sulted in Lithium-sulphur batteries being used in practical applications not only laboratory ex-periments One such example is the long endurance UAV Zephyr which set the record for longestunmanned flight by staying aloft for 54 hours This was partially possible due to the lithium-sulphurbatteries it carries These batteries have a specific energy of 350-380 Whkg much higher than anylithium-ion battery available today Although these batteries are extremely high performance thenumber of recharge cycles is still limited (exact figures are not available) [19] In a lab environmentlithium-sulphur batteries with a specific energy of 500 Whkg have been demonstrated On top ofthat they had a cycle performance of up to 1500 cycles [20]

The main RampD focus for lithium-sulphur batteries lies on improving the cycle life performanceBased on development goals of Sion Power it is expected that batteries with an acceptable cycle life(gt1000 cycles) will be commercially available by 2020 [21] [14] Sion power also states that specificenergies of around 550-650 Whkg at cell level would be available by then [21] This is considerablyhigher compared to for lithium-ion batteries Specific power is expected to be at least 400 Wkg[14]


LITHIUM AIR

Another novel battery technology is lithium-air batteries This technology is still in its infancy yetlab prototypes show promising results Lithium-air uses oxygen as oxidizer so it does not have totake the oxidizer with it This results in much higher theoretical energy densities up to 11680 Whkg[22] However practical energy densities for Li-air batteries will be far less Existing metal-air bat-teries such as Znair typically have a practical energy density of about 40-50 of their theoreticaldensity However one can safely assume that even fully developed Li-air cells will never achievesuch an excellent ratio because lithium is very light and therefore the overhead of the battery struc-ture electrolytes and so forth will have a much larger impact [22] But using air as the oxidizer alsomeans that during discharge the batteries actually increase in weight The reaction for non-aqueouslithium-air batteries is as follows

2Li + O2 mdashgt Li2O2

Considering the chemistry of this reaction the increase in weight can be estimated as follows [19][22]

bull Reaction Potential Li2O2 31 V

bull Faraday constant 96485 Cmol

bull Specific mass O2 0016 kgmol

∆m = 0016 kgmol middot3600 C

Ah

31V middot96485 Cmol

= 192 middot10minus4 kg

W h(21)

Lithium-air technology is still in the early developmental stages with practical results falling farshort of theoretical calculations The best reported lab cell has achieved a specific energy of only363 Whkg [23]

As mentioned before quite a few challenges remain before lithium-air batteries can be a viablepower source The most important research topics that still remain are [23] [22]

bull Better understanding of the electrochemical reactions and their relationship to the dischargechargecurrents This is vital for demonstrating chemical reversibility and understanding the effi-ciency of the battery

bull Development of oxidation-resistant electrolytes and cathodes This is also very important forchemical reversibility and efficiency in the battery cycling

bull Understanding the nature of electrocatalysis for Li-air batteries and the development of cost-effective catalysts This is key to enhancing power density in discharge and electrical effi-ciency in a discharge-charge cycle

bull Development of new air cathodes that optimize transport of all reactants to the active catalystsurfaces and provide appropriate space for solid lithium oxide products This is required tomaintain capacity at higher power densities

bull Development of a lithium metal or lithium composite electrode capable of repeated chargingand discharging at higher current densities

bull Development of high throughput air-breathing system that separates O2 from ambient air inorder to avoid H2O CO2 and other environmental contaminants from limiting the lifetime ofLi-air batteries


bull Understanding the origin of the temperature dependencies in Li-air batteries and minimizingtheir adverse effects

There is no scientific consensus on if or when the above mentioned problems might be resolvedand what the expected gravimetric energy density might be in a 2035 timeframe Below is a list ofsome of the most important authors and what their predictions are in terms of energy density by2035

bull Kuhn et al 1000-1500 Whkg [24] [25]

bull S Stuumlckl et al 750ndash2000 Whkg [19]

bull L Johnson 2000 Whkg [26]

bull K Rajashekara 2000 to 3500 Whkg [27]

The wide discrepancy between the figures demonstrates that the uncertainty is very large and thereare still many unknowns However figures given by K Rajashekara seem too optimistic The vol-umetric energy density can also be expected to lie within approximately the same range Johnsonalso predicts the power density to be in the range of 400 to 640 Wkg [26] There is also no scientificconsensus whether this technology will achieve market readiness by 2035 While NASA states thatbased on past development cycles it is unlikely that the technology will be mature by the N+3 timeframe [28] IBM states that the technology is expected to be consumer ready by 2030 [22]

OVERVIEW AND CONCLUSION

Table 21 gives an overview of the parameters for each of the technology options discussed in thissection All of the values are rough estimations for the year 2035 and will most likely not be veryaccurate However they can provide a good basis for comparison of the various technologies

The last column represents the technology readiness level (TRL) This is a metric for how maturethe technology is at this time It is represented in a scale from 1 to 9 with 1 being where just thetheoretical principles are observed and 9 being a system that is proven in extensive operation Inthis case the definition by NASA is used [29]

Table 21 Estimation of battery parameters by the year 2035

Type Specific energy[Whkg]

Volumetric energydensity [Whl]

Power density [Wkg] TRL

Lithium-Ion 350 590 400-450 (rough esti-mation)

9

Lithium-Sulfur gt 650 gt 460 gt 400 5Lithium-Air 750-2000 750-2000 400-640 3

If the conclusion by Boeing that an energy density of at least 750 Whkg is needed is correct thanit would appear that lithium-air batteries are the only option except if lithium-sulphur batteriesachieve a greater energy density than is currently expected The main problem with lithium-airbatteries is whether the technology will be ready by 2035 Since lithium-ion batteries took at least20 years to achieve TRL 9 it is likely that lithium-air will need approximately the same amount oftime to achieve maturity [28]

For the designs considered in this study a wide range of battery specific energies is used be-tween 750 Whkg and 1500 Whkg Since most sources agree that this is a realistic range for lithium-air batteries A sensitivity study is also performed to figure out the behaviour of the design withchanging energy density (Section 432)


222 ELECTRIC MOTOR TECHNOLOGY

Current electric motors are mainly used in vehicles such as cars not in aircraft For aircraft propul-sion the required shaft power is an order of magnitude higher than the high power density motors inuse today Scaling up these motors leads to unfavourable trends related to physical sizing laws Withgrowing motor size the ratio of outer (cooling-) surface to internal motor volume gets worse this isdetrimental for efficient heat dissipation In ground based applications such as power plant gener-ators this problem is addressed by using oversized conductor cross sections to minimize heat lossBecause this requires very heavy and bulky motor layouts this design is not practical for aerospaceapplications [19]

This problem can be solved by using high-temperature super-conducting (HTS) motors [30]Superconducting materials have the unique property of being able to carry current with almost noresistive losses This property only occurs when the superconducting material is below a certaincritical temperature magnetic field and current density level [2]

In the past reaching these critical temperatures was extremely expensive and thus not practicalHowever more recently high-temperature superconducting materials have been discovered whichhave a much higher critical temperature above the boiling point of liquid nitrogen (77 K) Figure 22shows the critical temperature of superconducting materials and their respective date of discovery

Figure 22 Critical temperature of superconducting materials [2]

These superconducting motors can eliminate many of the problems related to upscaling con-ventional motors A study was carried out comparing a 4480 KW HTS motor to a conventional in-duction motor It was found that the load loss (heat produced) at full power amounted to 40 thatof the conventional motor which leads to much higher efficiency On top of that the HTS motor hada 50 volume reduction and it was found that the HTS motor would weigh around 70 that ofthe conventional motor resulting in a much higher power density [2] [28] Current superconductingmotors have a power density comparable to turbine engines while fully developed superconductingengines have the potential of being 3 times lighter [31]

Supercooling a motor takes power For a low temperature superconducting motor it takes about12 of the rated power to run the cryocooler while for a HTS motor this cryocooler only uses 016 of the rated power This is due to the much lower temperatures that must be sustained to reachthe LTS critical temperature [2] [28] Another disadvantage of HTS motors is the added complexityof the system Other systems have to be added such as a cryocooling system and an inverter [28]

There are still challenges that remain before this technology is ready for use in commercial air-craft The main hurdle that needs to be overcome is the insufficient power to weight ratio for thetechnology to be practical The cold heads for the cryocooling system currently have an energy den-sity of around 3 kgkW-input and the compressor has an energy density of about 15 kgkW-input


[28] It would be desirable to reduce the combined cold head and compressor weight to around 3kgkW-input [28] [31] This may be possible for aircraft entering into service around 2035 [31] It hasalso been estimated that the needed power to weight ratio for the electric motor would be around25 kWkg and around 50 kWkg for the generators [31]

Another issue is that the latest generation of HTS wiring is not yet available in long lengths andthe first generation wiring is extremely expensive (around 40 of the total motor cost) [2] Anotherproblem that has to be overcome is that DC HTS motors meet the low loss requirement however ithasnrsquot been demonstrated yet that low loss AC conductors can be developed in the future Expertspredict that a loss of less than 10 WA-m is needed [28]

The cryogenic cooling system also provides some challenges namely cryogenic pipe leakagethe Carnot efficiency and a higher reliability of the system A reliability of 998 needs to beachieved [32]

When these challenges are solved HTS engines can be used in aerospace applications Althoughthese challenges are substantial (especially the large jump in power to weight ratio required) NASAis confident that we will see this technology in commercial aircraft by 2035 [28]

23 POWER PLANT ARCHITECTURE

231 ARCHITECTURE POSSIBILITIES

Many distinct power plant architectures are possible for a hybrid electric propulsion system Themost commonly used are the series-hybrid architecture and the parallel-hybrid architecture

The series powertrain configuration shown in Figure 23 is the simplest of all the possible con-figurations The propeller shaft is only driven by the electric motor The gas turbine is used to eithercharge the batteries or provide auxiliary power to drive the electric motor [33] This means the gasturbine can continuously operate at its most efficient point thereby reducing fuel consumption andemissions For commercial ground vehicles this configuration even has the lowest fuel consump-tion of all the configurations mentioned in this section [34]

Power converter

Electric motor

Gas turbineGas turbine

Generator

Figure 23 Series hybrid architecture

Another advantage is that the gas turbine can generally be sized smaller because it only needs tomeet average power demands However in order to meet peak power demands the electric motorand battery need to be sized larger than in other configurations This combined with the needfor a generator results in a significant weight penalty compared to the parallel configuration [12][35] This is not such a big problem for ground vehicles but for aircraft this can be a major issueAdditionally because the mechanical energy from the gas turbine is first converted to electricalenergy then passed to the electric motor and converted once again to mechanical energy to drive

23 POWER PLANT ARCHITECTURE 11

the propeller there exist large conversion losses between the mechanical and electrical systems [35]In the parallel-hybrid configuration both the mechanical power output and the electrical power

output are connected in parallel to drive the transmission as shown in Figure 24 An advantage ofthis configuration is that it requires only two propulsion devices where either the electric motorandor the gas turbine can be downscaled without a loss in maximum power [12] This result in thesmallest weight especially important for aerospace applications Another advantage is that it ben-efits from redundancy because of the two separate powertrains This is a major advantage for thecertification process [35] However according to some regulations it is not allowed to have any extraclutch This means there can be no clutch between the electric motor and the gas turbine Thiswould result in electric motor only mode not being possible and an extra loss in gas turbine onlymode when the battery is fully charged due to the extra drag in the electric motor [12] However theauthor could find no evidence of such regulation in CS-25 or FAR-25 [36] [37] Regardless studieshave shown that even without a clutch this configuration still results in the least fuel consumptionand a highest efficiency for aircraft [12] although all studies performed so far have only been donefor light aircraft (lt 1000 kg) The biggest drawback of this configuration is the increased complex-ity of the mechanical coupling [12] and the significant increase in control complexity [38] becausepower flow has to be regulated and blended from two power sources

In the most common control strategy (although mostly for electric cars) the gas turbine is almostalways on and operates at constant power output at its peak efficiency point [34] The electric engineis used when the power required is larger than the power delivered by the gas turbine (such as duringtake-off) If the power needed for the propeller is less than the power delivered by the gas turbinethe remaining power can be used for charging the batteries by using the electric motor as generator

Power converter

Electric motor

Gas turbine

Figure 24 Parallel hybrid architecture

The are other architectures such as the series-parallel hybrid and complex-hybrid architecturehowever they arenrsquot commonly used because of their inherent complexity These types of architec-tures combine the advantages and disadvantages of both the series hybrid and parallel hybrid ar-chitectures They are not suited for aerospace applications because they come with a severe weightpenalty when compared to the series - and parallel-hybrid configurations

232 SELECTED ARCHITECTURE

Ultimately the most suited architecture for a hybrid electric regional aircraft is the parallel-hybridarchitecture The versatility in operating modes combined with the potential for the smallest weightmake this the better choice for aerospace applications Whether this assessment is entirely cor-rect is impossible to know at this stage not enough design studies comparing both power plants


in aerospace applications (especially aircraft over 1000 kg) were performed to really get conclusiveevidence that one architecture is more optimal than the other The level of technological progressbetween now and 2035 also has a large impact on what configuration is more feasible For examplethe series-hybrid architecture requires a much more powerful electric motor which might not befeasible if certain technological progress is not achieved (such as high temperature superconduct-ing) The weight of a certain architecture also depends on many other factors such as the chosencontrol strategy type of mission etc

Figure 25 shows the chosen architecture with all relevant parameters and symbols Since thebattery delivers direct current (DC) and the electric motor requires alternating current (AC) an in-verter is needed between the battery and electric motor which transforms the power from DC to ACThis inverter also greatly increases the voltage coming from the batteries This is needed to reducethe required thickness (weight) of the cables see Section 37

ηbat ηEM

ηgasturb

InverterElectric motor

Gas turbine

Pbat

PbatOffTake

Pem

Pgasturb

Pshaft

ηprop

Pfuel

ηelec

Figure 25 Architecture of the power plant

With the technological development of reliable solid-state high power-density power-relatedelectronics it would be beneficial in the not-so-far future to move towards a More Electric Aircraft(MEA) [39] The MEA uses electrical power to replace the hydraulic pneumatic and mechanicalpower in order to optimize the performance and life cycle cost of the aircraft It would make thesubsystems easier to maintain more durable lower in cost and higher in performance An addi-tional advantage is that no air off-take in the gas turbine is needed which increases performance

The downside is that it requires a highly reliable fault tolerant electrical power system and pro-grammable solid-state devices in order to have adequate load management fault isolation and di-agnostic health monitoring [39] However such systems are already needed for the hybrid-electricpropulsion system [40] This would also minimize the increase in weight the MEA concept wouldbring It might thus be beneficial to use such a concept for a hybrid-electric aircraft

24 CONTROL STRATEGIES 13

As can be seen in Figure 25 there is the factor PbatO f f Take which represents the power that isdiverted from the battery to power other electrical systems (which would be relatively large whenusing the MEA concept) However for the designs considered here the MEA concept is not usedbecause that would go beyond the scope of the project as well as introduce additional difficultiesin terms of estimating the power and weight requirements such a concept would bring For thesereasons all subsystems are sized using the same methods as for a conventional aircraft and the factorPbatO f f Take is zero for all designs

24 CONTROL STRATEGIESDeciding how and when to use the electric motor andor gas turbine throughout the mission alsohas a very large impact on the amount of batteries and fuel to be taken on board Since there are twopower sources present many different design variables are introduced which represent how muchof what power source is used at what time In order to keep the number of design variables as low aspossible a new variable is introduced the power split (Si ) This variable can vary between 0 and 1during the entire mission with 0 representing the use of only the gas turbine and 1 representing theuse of only the electric motor at that specific point in time

Si =Pemi

Psha f ti

(22)

For example a power split of 06 means that 60 of the power delivered to the propeller shaft comesfrom the electric motor and the other 40 from the gas turbine

To reduce the complexity the power split is chosen to be constant for each mission phase apartfrom the cruise phase Since the cruise phase is much longer than other flight phases it is chosento make the power split variable during this phase A certain power split has to be selected for thebeginning of the cruise phase and one for the end of the cruise During this flight phase the powersplit will vary linearly between the two chosen power splits During the descent no power splitis defined since not much power is required and the gas turbine usually idles during these flightphases for more information see Section 344 Whether there is an optimal power split for eachflight phase is a difficult question to answer Intuitively one might think that it would be beneficialto have a large power split (more gas turbine power than electrical power) in the beginning of themission in order to burn more fuel and get a lighter aircraft and later on use more electrical powerin order to reduce the total fuel burn This effect is even magnified when using lithium-air batteriessince these gain weight during usage thus it being more beneficial to use them as late in the missionas possible Whether this assessment is correct is investigated in Section 424

Choosing a certain power split for each flight phase might not always be the most intuitive wayof choosing how hybrid an aircraft is It is also very hard to specify a good power split beforeanything about the design is known For these reasons another control strategy is introduced Theso-called constant gas turbine power operating mode When using this operating mode a certain(max-continuous) gas turbine power is chosen in stead of a power split During take-off and climbthe maximum available gas turbine power is used and if needed supplemented with power fromthe electric motor2 During the cruise phase the gas turbine is used at its most fuel efficient powersetting3 and again the electric motor is used to provide the extra power that might be needed Thebenefit of this control strategy is that the gas turbine can generally be sized smaller compared to thepower split operating mode4 and is operated at a more efficient point resulting (in theory) in a moreoptimal design which requires less fuel for the same mission In theory it might be possible to select

2When the power delivered by the gas turbine is less than the required shaft power3Smallest SFC4Dependent on the chosen power split


power splits such that the resulting design is exactly the same as for the constant gas turbine poweroperating mode In Section 423 the comparison is made between both operating modes

An additional advantage of the constant gas turbine power control strategy is that if the requiredshaft power is less than the delivered gas turbine power the excess power could be used for chargingthe batteries during flight which could result in the aircraft landing with partially (or completely)charged batteries potentially reducing cost and turnaround time In that case the electric motor isused as a generator

25 IMPORTANT PARAMETERSSince many designs are generated using different operating modes some parameters have to beintroduced which can be used to compare different designs Also a certain measure of how hy-brid a certain design is has to be introduced Most commonly used in literature are the degree ofhybridization for energy (HE ) and power (HP ) [41] defined as

HP = Pemmax

Psha f tmax

(23)

and

HE = Ebat

Etot(24)

However the degree of hybridization of power is not really a good parameter to measure howhybrid a design is For example having a large electric motor that is only used for a short whilewill results in a large degree of hybridization of power while only a very small part of the mission ishybrid In that regard the degree of hybridization of energy is a better parameter However it isalso not ideal since the specific energy of fuel is much larger compared to the battery specific energyand the efficiency of the electrical systems much higher than that of the gas turbine This results invalues of HE being generally quite low (lt 02) even though the total supplied electric motor energy(Eem) might be higher than the total supplied gas turbine energy (Eg astur b) For this reason anotherparameter is introduced the supplied power ratio (Φ) [41] This is defined as the total electric motorpower over the entire mission in relation to the total shaft power over the entire mission

Φ= Eemtot

Esha f ttot

(25)

The advantage of this parameter is that it is more intuitive than the degree of hybridization ofenergy A value of Φ = 0 represents a conventional aircraft while a value of Φ = 1 represents a fullyelectric aircraft When using a constant power split over the entire mission the supplied power ratiowill be approximately the same as this constant power split

3METHODOLOGY

In this chapter the methodology for sizing the different components and ultimately leading to a cer-tain design for a hybrid-electric aircraft is presented This design process is completely automatedin the Initiator program [42] That is why first a short description of the Initiator program is providedin order to better understand the design process that is used Later the sizing of different compo-nents including the batteries and electric motor is explained Next a brief description is given ofthe implementation of the methods into the Initiator And lastly the limitations of the presentedmethodologies are given

31 INITIATORThe Initiator is a (mostly) physics-based conceptual aircraft design program developed at the TU-Delft It is implemented in MATLAB [43] and allows for the generation of a preliminary aircraftdesign based on a set of (basic) input parameters Creating such a design takes about 20 minutesIt is capable of generating very diverse aircraft designs from conventional aircraft to three-surfaceaircraft to blended wing bodies

What makes this program ideal for the purpose of designing a hybrid-electric aircraft is twofoldFirst of all it is modular in nature which allows for the easy addition and modification of new mod-ules and parts Secondly because generating a design takes a relatively short time the influence ofchanging certain input parameters on the design is easy to determine This is especially useful in thecase of a hybrid-electric aircraft where the value of various input parameters (such as the expectedbattery specific energy) can not be known for sure and a certain range of values has to be examined

To better understand the design process a short explanation is given of how the Initiator pro-gram works as well as what kind of inputs are required Figure 31 shows the basic structure of theprogram Keep in mind that this is a very simplified structure and many modules are omitted forthe sake of clarity and other modules are bundled together into one module Nevertheless it doesgive a good overview of how the Initiator achieves a new design

The input file contains the basic requirements the aircraft needs to achieve such as range pay-load passenger amount etc as well as some basic geometry parameters such as wing location(low- mid- or high wing) and tail type This file is read in the beginning of the run and the valuesremain constant during the entire design process The settings file contains all other input param-eters that are not present in the input file This a an extensive list of hundreds of constants that areused during the design process Almost all modules use certain parameters from this settings fileSection 310 contains a list of settings that are added to be able to achieve a hybrid-electric aircraftdesign

After the input file is read a database of reference aircraft is used together with a class 1 weightestimation to achieve a first estimate of the basic aircraft parameters such as MTOM Afterwards

15

16 3 METHODOLOGY

Class 1

Weight

Estimation

Wing- and

power

loading

Geometry

design

modules

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis

Performance

Estimation

Modules

Design

converged

Reference

aircraft

database

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis

Class 25 weight estimation

Converged

No

Yes

No

Design

Yes

Input fileSettings file

All modules

Figure 31 Simplified flow chart showing the basic workings of the initiator program

based on requirements and regulations (FAR 25 or 23) a wing- and power loading diagram (in caseof turboprop aircraft) is constructed which results in a design point Figure 32 shows an example ofsuch a diagram

Next geometry design modules are ran which estimate the basic components of the aircraftsuch as the wing fuselage engines and control surfaces Afterwards a class 2 weight estimation ispreformed which estimates the mass of all components as well as sizes some components (landinggear fuel tanks) which were not sized in the geometry design modules

When the weight estimation is completed multiple aerodynamic analysis modules are run AVLC Lmax estimation and parasite drag estimation The aerodynamic forces determined by AVL arealso used to determine the wing weight The next module that is used is the mission analysis mod-ule this module determines the fuel (and battery) mass needed for the mission It also runs AVLagain as part of the mission analysis in order to determine the drag polar

Subsequently a class 25 weight estimation is performed This weight estimation runs multiplemodules in a certain order It uses inputs from the mission analysis such as fuel and battery massto perform a more accurate class 2 weight estimation Next the aerodynamic analysis modules arerun again as well as another mission analysis The class 25 weight estimation keeps running thosemodules in that specific order until the difference in MTOM between 2 iterations is below a certainmargin

Finally after the class 25 weight estimation is converged the performance estimation moduleis run which evaluates the performance of the design constructs a manoeuvre loading diagram andpayload-range diagram When this is finished the program starts the entire design loop again fromthe wing- and power loading module until the difference between 2 subsequent iterations is belowa certain margin

32 REFERENCE AIRCRAFT DESIGN 17

The aircraft geometry is defined in so called parts Parts are objects such as the wings landinggear fuselage etc These objects not only store geometrical data of each part but also other impor-tant parameters These parts are a convenient way of keeping track of certain variables and passingit between modules

The Initiator program as explained above is only capable of designing aircraft which use turbo-fan engines Many changes had to be made in order for it to design aircraft with turboprop enginesnot to mention hybrid-electric aircraft Many modules had to be modified what these modifica-tions are will be explained in the next sections Also new parts had to be added batteries electricmotor wiring and inverter

32 REFERENCE AIRCRAFT DESIGNAs mentioned previously modifications have to be made to the initiator in order to make it possiblefor the program to design a turboprop aircraft This has to be done before additional modificationscan be applied which would allow the initiator to design a hybrid-electric aircraft This section givesa brief overview of the changes made to the initiator in order for it to be able to design a turbo-prop aircraft However since this is not the main focus of the project only the general changes areexplained and unnecessary details have been avoided

In order to validate the changes made a reference aircraft will be constructed based upon theATR 72-600 Later in Section 41 this newly constructed reference aircraft is compared to the ATR72-600 in terms of performance mass geometry and fuel burn

321 ENGINE AND PROPELLER SIZING

Since the initiator is only able to design aircraft with turbofan engines the engine geometry siz-ing (and placement) module as well as the class 2 weight estimation (and subsequently class 25)module need to be modified to able to cope with turboprop engines

The geometry of the engines is determined based on the maximum power they have to deliverThis maximum power is either determined using the power loading found from the power loadingdiagram see Figure 32 or from the mission analysis 1 depending on how far the program is in thedesign iteration From the maximum power the length and diameter and mass of the gas turbine isdetermined using respectively Equation 31 32 and 33 derived by Raymer [44] based on empiricaldata

dg astur b = 025lowast(

Pg astur b

1000

)012

(31)

lg astur b = 012lowast(

Pg astur b

1000

)0373

(32)

mg astur b = 096lowast(

Pg astur b

1000

)0803

(33)

The installed engine mass is equal to 13lowastmg astur b Other engine parts which are taken into accountare the engine controls engine starter and nacelle as well as the mass of the propeller The propellerdiameter is based on the maximum propeller tip speed determined using Equation 34 derived byRoskam [45] Where Mt i p is the maximum propeller tip Mach number by default 08

dpr op =radic

a2

π2 lowast f 2 lowast (Mt i p minusM 2) (34)

1Taking into account the number of engines

18 3 METHODOLOGY

Since no propeller model is present in the Initiator program and implementing such a modelwould be outside the scope of this project some other method has to be used for determining thepropeller efficiency under multiple conditions During the class 2 sizing process the propeller effi-ciency is assumed as a constant This approach is not accurate enough during the mission analysissince a large variation in the propeller efficiency exists during the entire mission For this reason theideal propeller efficiency (Equation 35) is used during the Class 25 sizing process Since this equa-tion represent the maximum theoretically obtainable propeller efficiency it is scaled with a factorof 09 in order to achieve more realistic values

ηpr opi deal =2

1+(

TAdi sklowastV 2lowast ρ

2+1

)12(35)

Figure 32 Example of a power loading diagram of an aircraft comparable to the ATR72-600


322 GAS TURBINE POWER AND FUEL CONSUMPTION VARIATION

During any mission there is a large variation in velocity and altitude Since the maximum powerand fuel consumption of a gas turbine are not constant with velocity and altitude large variationin SFC will occur during the flight A model to calculate the variation of SFC and maximum thrustfor a turbofan engine is already implemented in the Initiator program However no such model ispresent for turboprop engines Implementing such a model from scratch would go far beyond thescope of this project however assuming a constant maximum power and SFC would result in largeerrors Therefore data was taken from the Fokker 50 engine (Pratt amp Whitney PW125 2) [3] in orderto construct a model based on that data Later on this model can then be scaled with the enginepower (since the used maximum engine power is not necessary the same as for the PW125) to findthe maximum power and fuel consumption variation with speed and altitude Since dependingon the chosen operating mode large variations in power setting can also occur (which can have avery large effect on the SFC) the variation of SFC with power setting for the same engine is alsoincorporated into the model

Since data is only available for a velocity range between 130 KEAS (6688 ms) and 200 KEAS(10289 ms) and an altitude range of 10000 ft (3048 m) to 30000 ft (9144 m) some inter- and ex-trapolation has to be performed This is generally inadvisable since extrapolation can lead to largeerrors however since during the mission the velocity and altitude lie mostly within the aforemen-tioned range any errors will not have a large influence on the final result It is worth mentioningthat this model is not meant to be very accurate for all engines but merely to give reasonable resultsfor SFC and power variation That being said it is expected that this model is more than adequatefor the purpose of this project

Figure 33 shows the variation of maximum continuous power with altitude and velocity Thereis an upper limit to to maximum continuous power of around 16 MW for this particular engineThis maximum power is later on scaled with the maximum power of the current design so thatthe variation is exactly the same for all engines (but the maximum power differs) According toaircraft performance theory the equivalent shaft power of the turboprop at any given altitude maybe related to its sea-level value by the relationship

P

P0=

(ρ

ρ0

)n

(36)

where in the troposphere (up to an altitude of approximately 11 km) the exponent n has a valueof approximately 075 [46] However since the power has a certain maximum value at which themaximum power curves become flat (at around 16 MW in figure 33) the above relationship is onlyvalid for the slope of the curve (ie as if there was no maximum value to the power) see Figure 34In this graph only the curve for a velocity of 250 knots (asymp 129 ms)is shown however the relation isalso valid for any other velocity

For the fuel flow variation (see Figure 35) the upper limit of the fuel flow is not the same for allvelocities For example for V = 300 kts the upper limit is approximately 123 gs while for V = 200 ktsit is around 130 gs Dividing the fuel flow by the power (and doing some unit manipulation) yieldsthe SFC variation see Figure 36 As can be seen this graph does not always have the smoothestcurves This is due to the inter- and extrapolation of both the fuel flow and the power variationgraphs However as mentioned before it does give figures accurate enough for the purpose of thisproject It can be clearly seen that there is little variation in SFC with altitude while a larger variationexists for velocity

The SFC not only varies with speed and altitude but also with power setting Figure 37 showsthe variation of the SFC with powersetting for a typical cruise condition (V asymp 103 ms and h = 6096m) For the sake of clarity only the values for power settings between 02 and 1 are shown since for

2This engine is also used in the ATR72-600

20 3 METHODOLOGY

lower power settings the SFC increases rapidly It is assumed the same variation holds for differentvelocities and altitudes

This model is implemented into the Initiator program by normalizing all values and scaling itwith the maximum power of the gas turbine For the electric motor it is assumed there is no variationin power or power consumption with altitude velocity or power setting

0 01 02 03 04 05 06 07 08 09 1middot104

04

06

08

1

12

14

16

18middot106

Altitude [m]

Max

co

nti

no

us

pow

er[W

]

V = 0 ktsV = 100 ktsV = 200 ktsV = 300 kts

Figure 33 Power variation as a function of velocity and altitude [3]

0 01 02 03 04 05 06 07 08 09 1middot104

04

05

06

07

08

09

1

11

Altitude [m]

( ρ ρ0

) n [-]

PP0(ρρ0

)n n=075

Figure 34 Slope of PP0


)075for a velocity of 250 knots


0 01 02 03 04 05 06 07 08 09 1middot104

60

80

100

120

140

Altitude [m]

Fuel

flow

[gs

]V = 0 ktsV = 100 ktsV = 200 ktsV = 300 kts

Figure 35 Fuel flow as a function of velocity and altitude [3]

0 01 02 03 04 05 06 07 08 09 1middot104

260

280

300

320

340

Altitude [m]

SFC

[g

kW

h]

V = 0 kts V = 100 kts V = 200 kts V = 300 kts

Figure 36 SFC as a function of velocity and altitude [3]

22 3 METHODOLOGY

02 03 04 05 06 07 08 09 1280

300

320

340

360

Power setting [-]

SFC

[g

kW

h]

Figure 37 SFC variation with power setting for a typical cruise condition with V = 200 knots and h = 20000 ft (= 6096 m)[3]

33 CLASS 2 BATTERY AND FUEL SIZING 23

323 OTHER MODIFICATIONS

Some other modifications also had to be made in order to be able to design a turboprop aircraft Forexample at the end of each design iteration there is a check whether all the passengers fit into thefuselage if not the fuselage length is increased This was necessary because the Initiator programoften underestimates the fuselage length for regional aircraft

Large changes are also made to the mission analysis modules which will not be expanded uponhere since the complete explanation of the mission analysis modules can be found in Section 34

33 CLASS 2 BATTERY AND FUEL SIZINGIn this section the methodologies are presented that are used to determine the amount of batteriesand fuel that have to be taken on board As mentioned before the Initiator program uses both aclass 2 and a class 25 weight estimation in this section only a class 2 method is discussed Section34 contains the class 25 sizing process The class 2 methods discussed here are based on manyassumptions and are not accurate in all cases However this is not a problem as the Initiator pro-gram only uses the Class 2 methods for determining the battery and fuel weight as a first guess andlater on the found values are overwritten by the values found in the class 25 sizing process (missionanalysis) As such the accuracy of these methods only affects the time it takes for the program toconverge and not the final design

331 BATTERY SIZING

Since there are two distinct operating modes implemented for hybrid-electric aircraft the sizingprocess will also differ for these two operating modes First the method used for class 2 sizing of thebatteries for the power split operating mode is presented and afterwards the methodology for theconstant gas turbine power operating mode

POWER SPLIT OPERATING MODE

As mentioned before a certain power split is defined for each phase of the mission For estimatingthe battery amount needed for the take-off and climb phase the same method is used First theamount of energy for those phases are estimated using the fuel fractions (of the non-hybrid aircraft)For example for the climb phase

m f uelcl i mb =mpr ecr ui se

1F Fcl i mb minus1(37)

From which the energy for the entire climb phase can be determined using the specific fuel con-sumption (SFC)

Ecl i mb = m f uelcl i mb lowast1000lowast1000

SFC(38)

Knowing the total energy that needs to be delivered by the engine the battery energy can bedetermined using the corresponding power split for each phase as well as the relevant efficienciesFor example for the climb phase

Ebatcl i mb =Ecl i mb lowastScl i mb

ηel ec lowastηem lowastηbat(39)

With ηel ec being the efficiency of the wiring and inverter ηem the efficiency of the electric motorand ηbat the discharging efficiency of the battery From the battery energy the battery mass is foundusing the battery specific energy

24 3 METHODOLOGY

For the cruise phase two different splits are defined one at the beginning of the cruise phase(Spr ecr ui se ) and one at end of the cruise phase (Sendcr ui se ) From these splits an average split for theentire mission is defined

Sav g = Spr ecr ui se +Sendcr ui se

2(310)

This is valid because the power split changes linearly over the entire cruise phase For the class2 weight estimation this average split (Sav g ) is taken over the entire mission range so not just thecruise phase Another assumption that is made is that D V is constant during the cruise phase Thisis an assumption that in some cases might lead to errors however as mentioned before this is notreally a problem since later on in the design iteration a more accurate method for determining thebattery mass is used which overrules the method here Any inaccuracies in this method will resultin a longer convergence time but will not affect the final design

From these simplifications it follows that the power the electric motor (thus also the batteries)have to deliver is constant for the entire cruise phase This power of the electric motor is given by

Pem = D lowastVcr ui se lowastSav g lowast 1

ηpr op(311)

From which the battery power can be determined taking into account the efficiencies

Pbat =Pem


Since this power is constant over the entire cruise phase it can be multiplied by the time of the cruisephase ( R

Vcr ui se) to find the total electrical energy needed for the entire cruise phase From which

using the battery specific energy and volumetric energy density the battery weight and volume re-quired for the cruise phase can be determined It would also be possible to determine the batteryweight during the cruise phase by using the hybrid-electric range equation which is discussed inSection 332

During the descent phase the electric motor is switched off meaning the battery mass requiredfor this phase is always zero regardless of operating mode After summing the battery mass andvolume required for each phase the total battery mass and volume is found An extra 10 is addedto the battery mass and volume to have a buffer so the battery doesnrsquot discharge completely3

CONSTANT GAS TURBINE POWER OPERATING MODE

Using this operating mode means that the power of the gas turbine is predefined and this engineruns at its most efficient point during the majority of the mission The rest of the power required isdelivered by the electric engine No power splits are used during this operating mode which meansthe above method is not applicable for this operating mode First of all the energy required for eachflight phase (apart from cruise and descent) is determined using the same method as for the powersplit operating mode (Equation 38)

The total take-off power is found from the power loading diagram an example of which can beseen in figure 32 Subsequently the total take-off energy of the gas turbine can be determined usingthe following relation

Eg astur bt akeo f f =Et akeo f f lowastPg astur bt akeo f f

Pt akeo f f(313)

From which the battery take-off energy (and mass) can be determined

3Which might result in damage to the battery pack


Ebatt akeo f f =Et akeo f f minusEg astur bt akeo f f


For the climb phase the contribution of the gas turbine to the total energy can be known becausethe required time-to-climb is known from the mission requirements So the battery energy requiredfor the climb phase can be found

Ebatcl i mb =Ecl i mb minusPg astur bcl i mb lowast tcl i mb

ηel ec lowastηbat lowastηem(315)

For this operating mode the gas turbine is run at its most efficient point during the cruise phaseFor the class 2 sizing the SFC variation with power setting (Figure 37) is not known yet For thisreason a certain constant power setting during cruise is selected by the designer Using this powersetting the power of the gas turbine (Pg astur bcr ui se ) is determined and the power of the electric motoris then given by

Pem = D lowastVcr ui se

ηpr opminusPg astur bcr ui se (316)

From which the total energy of the battery can be determined using the same method as wasused for the power split operating mode (Equation 312 and beyond) Again during the descentphase the electric motor is turned off so no battery mass is needed for that phase The total batterymass is determined by summing all the contributions of all the flight phases and adding a certainbuffer (by default 10 )

LIMITATIONS

When using the constant power operating mode and selecting a gas turbine power which is largerthan the power required during a certain flight phase it results in a negative battery energy Inreality this would mean the battery can be charged during the flight using the excess gas turbinepower Implementing battery charging would require the program to keep track of the state-of-charge during the mission to know when the batteries are full as well as when they are empty andmore battery needs to be added This would require a more detailed mission analysis (class 25)and as such is not implemented in the class 2 sizing of the batteries When the battery energy foundis negative zero battery mass is added instead of the batteries being charged For this reason theremight be some errors when selecting a large power for the gas turbine

When using Lithium-Air batteries the battery mass increases by approximately 0000192 kgWhduring discharging see Section 221 This again is not implemented in the class 2 sizing of thebatteries

The calculation of the battery mass needed during the cruise phase is based upon the assump-tion that D V is constant during cruise This simplification may lead to errors and as such it wouldbe better to use the new hybrid-electric range equation discussed in the next section However atthe time of writing this is not implemented

332 FUEL

A class 2 method for determining the fuel weight was already implemented into the Initiator Thismethod is modified to be able to deal with hybrid-electric aircraft

For the power split operating mode the fuel weight for the take-off and climb phase is deter-mined by scaling the fuel fractions with their respective power split For the constant power operat-ing mode the fuel needed for take-off and climb is found from the total gas turbine energy neededduring each phase For the take-off phase Equation 313 is used While for the climb phase the gasturbine power is multiplied with the time-to-climb

26 3 METHODOLOGY

Eg astur bcl i mb = Pg astur bcl i mb lowast tcl i mb (317)

The fuel weight is subsequently determined from the gas turbine energy as follows

m f uel =SFC lowast Eg astur b

1000

1000(318)

For the descent phase the fuel fraction is used for both operating modes since there is no differ-ence in control strategy for each operating mode during this phase The fuel fraction is not scaledsince no electric motor power is used during the descent

The fuel weight during the cruise phase for an ordinary turboprop aircraft is determined usingthe Brequet range equation

R = ηpr op1000lowast1000

SFC

L

Dln

(mpr ecr ui se

mendcr ui se

)(319)

From the above equation the fuel weight can be found since the range is known as well as mpr ecr ui se However this equation is not valid for hybrid-electric aircraft since not only fuel is used as energybut also batteries (of which the weight at end of the cruise phase is not lower than at the beginning)As such a new equation has to be derived which is also valid for hybrid-electric aircraft This newhybrid-electric range equation is

R = 1Sηel

+ (1minusS)lowastSFC lowaste f uellowast CL

CDlowastηpr op lowast 1

ecombi nedlowast l n

(ecombi ned lowastEpr ecr ui sse +mempt y

mempt y

)(320)

With ηel being the total electrical efficiency from the battery to the electric motor output

ηel = ηbat lowastet ael ec lowastηem (321)

The factor ecombi ned is the combined specific energy of both the batteries and the fuel and is definedas

ecombi ned = x lowaste f uel + (1minusx)lowastebat

e f uel lowastebat(322)

Where rsquoxrsquo is

x = Ebat

Etot= S

S + (1minusS)lowastSFC lowaste f uel lowastηel(323)

The derivation of this equation can be found in Appendix A This equation is only valid for aconstant power split (S) As such if the power split varies during the cruise phase the average powersplit is used Also a constant SFC is assumed as well as a constant propeller efficiency and CL

CD Using

this equation for a given range and power split the required energy (Epr ecr ui se ) can be found Fromthis energy the battery and fuel weight can be calculated as follows

mbat =Epr ecr ui se lowastx

ebat(324)

m f uel =Epr ecr ui se lowast (1minusx)

e f uel(325)

For a conventional aircraft (S=0) the results of Equation 320 will correspond exactly to the orig-inal Brequet range equation Figure 38 shows the results of this equation for a variable power splitand a range of 1528 km as well as the following inputs


bull SFC = 300 [gkWh]

bull ebat = 1000 [Whkg]

bull e f uel = 12778 [Whkg]

bull ηel = 095 [-]

bull ηpr op = 08 [-]

bull CLCD

= 20 [-]

bull mempt y = 15000 [kg]

For the above set of inputs the fuel and battery weight varies almost linearly with power splitFigure 38 is constructed using a constant empty mass in reality the empty mass will increase withan increasing power split since the total aircraft mass increases and as such also the structural massIn the next chapter this is discussed in more detail

0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

Power Split [-]

Mas

s[k

g]

Fuel WeightBattery Weight

Figure 38 Results of the adapted Brequet range equation for a variable fuel weight and power split

For the constant power operating mode the approach described above is not used Since the gasturbine power during the cruise phase is known this power is multiplied with the cruise time to findthe fuel weight

28 3 METHODOLOGY

34 CLASS 25 BATTERY AND FUEL SIZINGThe class 25 method for determining the fuel and battery weight as well as the maximum powerthat the electric motor and gas turbine have to deliver involves performing a mission analysis Thismission analysis performs an analysis of each flight phase and determines all relevant parametersat each time step This time step varies for each mission segment For example during the cruisephase a longer time step is taken than during take-off or landing since the parameters during cruisewill not change much from one time step to the nextBelow all the mission segments are listed and in Figure 39 an example of a typical mission profileis shown Although the take-off and landing phase are present in this mission profile they can notbe seen in the figure since the duration of those segments is very short

1 Standard Mission

bull Take off

bull Climb 1

bull Cruise 1

bull Descent 1

bull Landing 1

2 Extended Mission

bull Climb 2

bull Cruise 2

bull Descent 2

bull HoldLoiter

bull Descent 3

bull Landing 2

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 24000

02

04

06

08

1

12

14middot104

Clim

b1

Cruise 1

Des

cen

t1

Clim

b2

Cru

ise

2

Des

cen

t2

Loit

erD

esce

nt3

range (m)

alti

tud

e(m

)

Figure 39 Example of a typical mission profile that can be used to determine the battery and fuel weight


For the Class 25 sizing the extended mission is used since enough fuelbatteries have to betaken on board to abort the landing divert to another airport as well as loiter at that airport forsome time (30 minutes)

In this section the mission analysis for each flight segment is explained Some segments (such asdescent) occur multiple times during one (extended) mission Although for each of these segmentsdifferent inputs are given the implementation of each repeated segment is identical and as suchare only explained once The focus of this section lies on the changes made to the mission analysismodule That being said a short description of the workings of the original module is also given inorder to better understand the modifications that are made

The activity diagram of the flight phases the mission simulation goes through is shown in Figure310 The simulation consists of an iteration loop which starts by setting the initial conditions ofthe state matrix (S) The state matrix stores the state of all the variables being tracked at each pointin time It is also handed from each flight phase to the next to keep track of the state of the aircraftTable 31 shows the variable the state matrix handles Many other variables such as the propeller ef-ficiency are also included in the state matrix yet not shown in the table since they are only includedto be able to plot them

Table 31 Parameters the state matrix rsquoSrsquo keeps track of

Parameter Description Unitt Time that has passed up un-

til that certain point in themission

sec

h Altitude mR Distance travelled up until

that point in the missionm

V Airspeed msm f uel Fuel burned up to that point

in the missionkg

mbat Battery mass used up untilthat point in the mission

kg

Ebat Battery energy used up untilthat point in the mission

kg

γ Flight path angle degPem Electric motor power WPg astur b Gas turbine power WPsha f t Shaft power WT Thrust ND Drag N

All the initial conditions are set to 0 except for the aircraft weight which is set to the MTOM Thesimulation then passes the state matrix to the first flight phase the take-off which in turn passes itto the next phase after the conditions to end of the respective phase are met The diversion startswith an alternate climb which continues on with the state matrix from the descent as a go-aroundis performed The diversion is only simulated if the extendedmission input is set to 1 which is thecase during the Class 25 sizing process The fuel burn and battery weight calculated at the end ofthe simulation is fed back to determine the new MTOM The iteration loop runs until the calculatedfuel and battery mass are the same as the input fuel and battery mass within a certain margin Tospeed up this process the variables W f br est and Rr est have been created These variables track the

30 3 METHODOLOGY

fuel burn and range from the end of cruise to the landing and are fed back into the cruise phase Inthis way the descent can be started at the correct point in time to reach the required range or fuelburn at the end of the landing The same can not be done for the battery weight since the batteryweight does not decrease during the flight it actually increases (if using lithium-air batteries) Forthe mission analysis the batteries are treated as being part of the empty weight and the increase inbattery mass counteracts the decrease in fuel mass during flight

This entire process was originally only implemented for non-hybrid aircraft with turbofan en-gines The mission analysis module is first modified in order for it to be able to determine the fuelweight for turboprop aircraft In practice this meant completely rewriting the each flight phasemodule such that there are two versions of each One that is used in case turbofan engines are usedand one for when turboprop engines are used Here only the version used for turboprop aircraft isdiscussed with the modifications made for hybrid-electric aircraft


Start

Set initial

conditions of state

matrix S

Take-off

Climb 1

Cruise 1

Extended CruiseDescent 1

Extended

cruise time

Extended

mission

Landing 1Landing 2

Calculate total fuel

burn and battery

weight

Descent 3

Loiter

Descent 2

Cruise 2

Climb 2

Calculate diversion

Rrest Wfbrest

Calculate Rrest

Wfbrest

Fuel weight

converged

End

No

No

Yes

Yes

No

Yes

Figure 310 Activity diagram of the flight phases of the Mission Analysis module

32 3 METHODOLOGY

341 TAKE-OFF

Figure 312 shows the flow diagram of how the take-off phase is calculated First the initial statematrix (S) is loaded This is 0 for all parameters apart from the weight which is the MTOM Allsettings that are needed for this phase are loaded as well these include constants such as the landinggear drag increase and efficiencies of the battery electric motor etc

Next the take-off power is determined from the power loading diagram (see Figure 32 for anexample) This is the shaft power and is assumed constant for the entire take-off phase since thisis only a short flight phase with little variation in altitude A power setting is also selected Thepower setting is 1 for the entire take-off phase regardless of operating mode Although this is notthe most efficient operating point a power setting of 1 is also taken for the constant gas turbinepower operating mode This is because choosing a lower power setting with a lower specific fuelconsumption will result in a much heavier electric motor since during the take-off (and climb) phasethe power requirement is generally the maximum of the entire mission On top of that the increasein fuel mass will be almost negligible because there is only a slight increase in SFC while the take-offphase has a relatively short duration

Next the propeller efficiency has to be determined However as mentioned before no propellermodel is currently implemented in the Intitiator and implementing such a model would go beyondthe scope of the project especially for contra-rotating propellers (as would be used on the designedhybrid aircraft) For this reason it was chosen to use the ideal propeller efficiency and scale it with afactor of 09

As can be seen in Equation 35 determining the propeller efficiency requires that the thrust isknown but the thrust also depends on the propulsive efficiency So for the very first time step thisbecomes a problem and the thrust is determined using the static thrust equation 326 [46]

Tst ati c = Pt akeo f f23 lowast

(4lowastρlowastπlowast

(Dpr op

2

)2)13

(326)

Even if this equation does not result in an accurate thrust value it will have a negligible effect on thedesign since it is only used for the first time step (01 sec) after which Equation 332 is used

From the CL and CD relation during take-off the lift and drag at the time step are determinedthe ground effect as well as the drag increase because of the landing gear are taken into account Ifduring the current time step the aircraft is still on the ground an extra drag component is also addedthe ground friction drag (Dg )

Next some derivatives of the state matrix are calculated namely the change in flight path angle

( dγd t ) the change in pitch angle ( dθ

d t ) the change in speed ( dVd t ) height ( dh

d t ) and range ( dRd t ) These are

calculated using the lift drag weight speed and flight path angles at the current time step Usingthe relations found in Section 32 the specific fuel consumption is determined based on the currentspeed altitude and power setting The SFC is the same regardless of operating mode since the powersetting for both operating modes is the same Until this point there is no difference in calculationsfor both operating modes however now a differentiation is made First the power split operatingmode is discussed

Since the shaft power (Psha f t ) is known (equal to pt akeo f f ) the power the electric motor has todeliver (Pem) can easily be found according to Equation 327

Pem = Psha f t lowastSt akeo f f (327)

With St akeo f f being the power split during the take-off phase not to be confused with statematrix rsquoSrsquo With Pem known the power the batteries have to deliver (Pbat ) is found using the relevantefficiencies (See Equation 312) The power of the gas turbine (Pg astur b) is found in an analogous

way as Pem From their respective power change in battery energy ( dEbatd t ) and mass ( dmbat

d t ) as wellas the change in fuel mass the change in fuel weight per time step can be found


dEbat

d t= Pbat

3600(328)

dmbat

d t=

dEbatd t

ebat(329)

dm f uel

d t= SFC lowastPg astur b

1000lowast1000lowast3600(330)

For the constant power operating mode the same parameters are determined using a slightlydifferent method As per the definition of this operating mode Pg astur b is constant Since the powerthat is input is not the take-off power but the maximum continuous power Pg astur b during the take-

off phase has to be scaled with the maximum continuous power setting After whichdm f uel

d t can bedetermined using Equation 330 and Pem can be found by

Pem = Psha f t minusPg astur b (331)

From which the battery energy and mass can be found using Equations 328 and 329 Using thisoperating mode adds one extra complication It is possible that during a flight phase the selected gasturbine power is larger than the required shaft power If that is the case the batteries can be chargedusing the excess power and dEbat

d t lt 0 So adding battery mass ( dmbatd t gt 0) is only done when the

battery energy is larger or equal to the maximum battery energy needed so far during the mission(ie when there is no more battery energy left from the already present battery mass) and dEbat

d t ispositive

Subsequently the total change in aircraft weight is determined taking into account the decreasein fuel weight and the increase in battery weight (when using lithium-air batteries) The emissionsthe aircraft produces during the time step are also calculated These emissions are CO2 H2O andNOX and are determined taking into account the fuel burned as well as the altitude of the aircraft

Lastly the new state matrix is calculated using the derivatives calculated during the iterationloop If the screen height is reached (end of take-off) the iteration stops and the program moveson to the next flight phase climb If the screen height is not yet reached a new thrust is calculatedusing Equation 332 and a new iteration at the next time step is started

Tt akeo f f =Pt akeo f f lowastηpr op

V(332)

During the take-off phase each time step is only 01 seconds because large changes in the aircraftstate occur in a relatively short time Figure 311 shows the result of this iteration in terms of aircraftaltitude speed and flight path angle for an arbitrary aircraft with the same requirements of the ATR72-600

34 3 METHODOLOGY

0 01 02 03 04 05 06 07 08 09 10

5

10

15

alti

tud

e(m

)

0 01 02 03 04 05 06 07 08 09 10

20

40

60

spee

d(m

s)

0 01 02 03 04 05 06 07 08 09 102468

10

range (km)

γ(d

eg)

Figure 311 Altitude speed and flight path angle of an arbitrary hybrid-electric aircraft during take-off


Aircraft on

ground

Determine

take-off

power

Initial aircraft

state

Relevant

settings

Select power

setting (1)

Calculate

static thrust

Calculate

propeller

efficiency

Calculate lift

and drag

Calculate

ground

friction drag

Yes

Determine

derivatives

No

Calculate

SFC

Constant power

operating mode

Calculate Pem Pbat

Pgasturb based on

the power split

No

Determine change

in battery and fuel

energy and weight

Calculate Pem Pbat

based on selected

Pgasturb

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Screen height

reached

Calculate

new thrust

No

End Yes

Figure 312 Flow chart of the take-off phase

36 3 METHODOLOGY

342 CLIMB

The flow chart of the climb phase is shown in Figure 315 First the maximum gas turbine powerat sea level (and V =0) is determined (take-off power) Next an iteration time step is chosen Whenthe aircraft has an altitude of under 200 meter the time step is 01 seconds afterwards a time stepof 1 second is used until an altitude of 3048 meter (10000 feet) is reached after which the time stepincreases again to 5 seconds Using this method increases the step size whenever a relatively steadystate has been reached in order to reduce computation time

Next the drag polar is loaded (previously determined using AVL) and recalculated every fewminutes based on the shift in center of gravity due to fuel burn and battery mass increase Thepropeller efficiency is determined again using the ideal propeller efficiency equation (Equation 35)from which subsequently the thrust can be determined (Equation 332)

The lift and drag are then calculated using the aircraft weight thrust speed flight path angledrag polar etc The increase in lift and drag from the take-off flap configuration (up to an altitudeof 3000 feet) is also taken into account The derivatives for speed flight path angle altitude anddistance can then be determined using the thrust drag lift γ speed and weight as well as factorssuch as the percentage of excess power that is used for climbing vs accelerating to cruise speed Theexact strategy of when to climb and when to accelerate will not be expanded upon further becauseit is of little relevance to the project and was already implemented in the original Initiator program

For the calculation of battery mass and fuel burn (as well as gas turbine power (Pg astur b) andelectric motor power (Pem)) a differentiation is again made between the constant power operatingmode and the power split operating mode

First the power split operating mode is discussed The shaft power is assumed equal to the take-off power (potentially scaled with a certain factor if maximum power is not required for climb) Thegas turbine power is then determined using the power split during the climb phase If the requestedgas turbine power is larger than the maximum gas turbine power (based on speed and altitude) thegas turbine power is taken to be equal to the maximum gas turbine power If the same power split isselected for take-off and climb this is the case almost immediately resulting in the selected powersplit being valid only for the first time step as can be seen in Figure 313 The slight dip in gas turbinepower in the beginning of the climb phase is due to inaccuracies in the maximum gas turbine powermodel (Section 322) however such anomalies are expected to have negligible effect on the overalldesign

The electric motor power does not vary with speed and altitude and as such can be taken con-stant for the entire climb phase The shaft power is than determined as the sum of the Pg astur b andPem With Pg astur b as well as Pg astur bmax known the power setting is determined (1 for the case inFigure 313) The SFC is subsequently calculated based on the power setting speed and altitudewhile the change in battery mass is determined from Pbat

For the constant power operating mode first a power setting is chosen (1 appears to be the bestchoice for the same reasons as were discussed in the previous section) Then based on the powersetting the maximum gas turbine power altitude and speed the gas turbine power is determinedas well as the SFC Next after checking whether or not the battery energy is depleted the changein battery energy and mass is calculated Now the change in fuel and aircraft weight is again deter-mined Subsequently the state matrix is calculated and a new iteration is started until the requiredcruise altitude and mach number is reached

Figure 314 shows the state of the aircraft during the climb phase The peak that can be seen inthe flight path angle is due to the derivative of a certain state that can momentarily become verylarge when a sudden change in state occurs (in this case when the aircraft stops accelerating andonly climbs) However peaks like that only occur for 1 time step and as such will have a negligibleeffect on the overall results although as a result a slight dip in aircraft velocity can be seen in Figure314


0 20 40 60 80 100 120 140 1601

15

2

25

3

35

4middot106

Range [km]

Pow

er[W

]

Shaft PowerElectric Motor PowerGas Turbine Power

Figure 313 Graph of the shaft power gas turbine power and electric motor power during the climb phase with a powersplit of 05

0 20 40 60 80 100 120 140 1600

02040608

1middot104

alti

tud

e(m

)

0 20 40 60 80 100 120 140 1606080

100120140

spee

d(m

s)

0 20 40 60 80 100 120 140 1600

5

10

15

20

range (km)

γ(d

eg)

Figure 314 Altitude speed and flight path angle of an arbitrary hybrid-electric aircraft during the climb phase

38 3 METHODOLOGY

Determine

maximum

power (take-

off power)

Aircraft state

at end take-off

Relevant

settings

Select

iteration

time step

Determine

drag polar

Calculate

propeller

efficiency

Calculate

thrust

Constant power

operating mode

Determine Pgasturb

based on power

splitNo

Scale max gas

turbine power

based on altitude

and speed

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

End

Calculate lift

and drag

Determine

derivatives

Pgasturb is maximum

gas turbine power

Pgasturb

more than max

turboprop

power

Yes

No

Determine power

setting

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Select power setting

Scale max gas

turbine power

based on altitude

and speed

Determine Pgasturb Calculate SFC

Determine Pem and

Pbat

Cruise altitude

and speed

reachedYes

No

Figure 315 Flow chart of the climb phase


343 CRUISE

Firstly before the cruise phase iteration is started the drag polar is loaded (constructed using AVL)Also if using the constant power operating mode a power setting is chosen that results in the lowestSFC In the current SFC model this will result in a power setting of around 0885 for the entire cruisephase This search for the lowest SFC can be done outside the iteration loop because the variationof SFC with power setting is assumed constant for the entire cruise phase in accordance with Figure37

Once the iteration is started the drag polar is retrimmed based on the fuel burned (and thebattery mass increase in case of lithium-air batteries) Next the lift drag and thrust are determinedafter which the propeller efficiency as well as the aircraft state derivatives can be calculated Thesederivatives depends on the cruise strategy that is chosen There are 3 different strategies possible

bull Cruise climbThe aircraft climbs during the cruise phase as more fuel is burned For the case of hybrid-electric aircrafta cruise descent can take place if the increase in battery mass (due to thelithium-air batteries) is more than the decrease in fuel mass

bull Step climbSimilar to cruise climb but the change in altitude occurs is steps with a certain interval

bull Constant altitudeAs the name suggest there is no change in altitude during the cruise phase and also nochange in velocity

For all the designs and results shown in this thesis the cruise climb strategy is used since this is themost common strategy The shaft power is determined using

Psha f t =T lowastV

ηpr op(333)

So for the cruise phase the thrust is calculated first and afterwards the shaft power while forall other flight phases (except holdloiter) this is done the other way around For the power splitoperating mode the electric motor power (Pem) battery power (Pbat ) power setting and the changein battery and fuel weight are calculated using a very similar method as was employed for the climbphase The only difference is that for the cruise phase the power split is not constant The user canselect a power split for the beginning and the end of the cruise phase and the split will vary linearlyduring the entire flight phase As a result the derivative of the power split during cruise also has tobe calculated

For the constant gas turbine power operating mode the power setting has already been deter-mined before the iteration started After the maximum gas turbine power is calculated the powersetting is used to determine Pg astur b From there on out Pem Pbat as well as the SFC 4 can be cal-culated using the same method as was used for the climb phase The change in battery energy andmass is also determined using the same method as before taking into account whether the batteryis being charged or not

Next the change in fuel weight and subsequently aircraft weight is determined as well as theemissions The new state matrix is calculated using the previously determined derivatives and theiteration is started all over again until the required range is reached It is also possible to run themission analysis with a certain fuel mass as input and the range will be calculated In that case theiteration runs until a certain amount of fuel is burned 54The calculation for the SFC can be moved outside the iteration for an increase in computational speed as the cost of a

very slight decrease in accuracy since there is little variation in speed and altitude during the cruise phase and the powersetting is constant

5This mode has not been tested for hybrid-electric aircraft

40 3 METHODOLOGY

Again figure 316 shows the state of an arbitrary hybrid-electric aircraft during the cruise phaseAs is expected the flight path angle and velocity is almost constant while the altitude gradually in-creases

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 14007500

7600

7700

7800

alti

tud

e(m

)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400139

1392139413961398

140

spee

d(m

s)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400minus05

0

05

1middot10minus2

range (km)

γ(d

eg)

Figure 316 Altitude speed and flight path angle of an arbitrary hybrid-electric aircraft during the cruise phase


Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

lift drag and

thrust

Calculate

propeller

efficiency

Constant power

operating mode

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Determine

derivatives

No

No

Determine

power

setting for

minimal SFC

Yes

Determine

Pshaft

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Scale max gas

turbine power

based on altitude

and speed

Determine Pgasturb

Battery not

charging and

battery energy

depleted

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Range reached

Yes

End Yes

Figure 317 Flow chart of the cruise phase

42 3 METHODOLOGY

344 DESCENT

As mentioned before for the descent phase no power split is used The gas turbine produces idlepower The idle power is defined as a certain percentage of the maximum power So for a smaller gasturbine the idle power will be small compared to a larger gas turbine At the same time the powerof the electric motor during this flight phase is always zero (the electric motor is turned off) Thereason for this is that an electric motor can instantly deliver power when requested and does notneed to spool up Since a gas turbine does need to spool up this engine is left on for safety reasonsShould the maximum power of the electric motor be relatively large compared to the maximumpower of the gas turbine it would in theory be possible to switch the gas turbine completely offduring descent and use the power of the electric motor when for some emergency more power isrequired The gas turbine could then be spooled up while the electric motor is already providingadequate power to climb again However at this time no regulations exist for such a case thus thegas turbine idles during the entire descent It might also be possible to use the idle power to chargethe batteries Finding out exactly what the best and safest descent strategy is for a hybrid-electricaircraft could be a subject of a further study

Because of the chosen control strategy there is no difference in fuel and battery calculationduring this phase for any operating mode Figure 319 shows the flow chart of how the Initiatordetermines the battery and fuel weight during this phase

First before the iteration is started the power setting is selected In this case this is the idlepower setting 6 Next like in the climb phase an iteration time step is selected By default this is 5seconds but it reduces to 1 second once an altitude of 607 meter 7 is reached since in this part thedescent is more dynamic and a better accuracy is required

Based on the current altitude and speed the maximum gas turbine power is determined fromwhich using the power setting the idle power (Pi dl e ) is found With the power known the thrustcan be calculated from which again the propeller efficiency can be known Subsequently the liftdrag and the derivatives of the state matrix are determined

The specific fuel consumption during the descent phase will be very high because running thegas turbine at idle is not very efficient However since the power is so low the overall fuel con-sumption is also relatively low Since the electric power is not used Pem = 0 and Pg astur b = Pi dle From these values the change in battery and fuel weight is determined as well as the new state ofthe aircraft Once the required altitude is reached the iteration stops and the next phase is started

Figure 318 shows the state of an arbitrary hybrid-electric aircraft during the descent Again asis the case during the climb phase the peak in the flight path angle is due to a sudden change instate of the aircraft resulting in a very large value for certain derivatives for one time step

6This is a setting that can be changed by default the value is 00272000 feet


1360 1380 1400 1420 1440 1460 1480 1500 1520 15400

02040608

1middot104

alti

tud

e(m

)

1360 1380 1400 1420 1440 1460 1480 1500 1520 15406080

100120140

spee

d(m

s)

1360 1380 1400 1420 1440 1460 1480 1500 1520 1540minus15

minus10

minus5

0

range (km)

γ(d

eg)

Figure 318 Altitude speed and flight path angle of an arbitrary hybrid-electric aircraft during the descent phase

Power setting = idle

Aircraft state

at end cruise

Relevant

settings

Select iteration time

step

Scale maximum

Pgasturb based on

altitude and speed

Determine Pidle Calculate thrust

Determine change

in aircraft weight

Calculate emissionsCalculate new state

matrix

End

Calculate propeller

efficiency

Determine

derivatives

Descent altitude

reached

Yes

No

Calculate lift and

dragCalculate SFC

Determine Pem and

Pbat (= 0)

Determine Pgasturb

(= Pidle)

Determine change

in fuel weight (no

change in battery

weight)

Figure 319 Flow chart of the descent phase

44 3 METHODOLOGY

345 LANDING

Figure 321 shows the flow chart of how the landing phase is calculated Before the iteration isstarted the landing drag polar is determined The effect of the high lift devices is also taken intoaccount Next as in all the other flight phases the propeller efficiency is determined and after-wards the lift and drag is calculated Again the effect of the landing gear and high lift devices istaken into account as well as the ground effect when below a certain altitude ( h

b lt 01) Afterwardsa check is made whether the aircraft is on the ground or not If so the ground friction drag (basedon the brake coefficient) as well as the reverse thrust (if applicable) is added to the total drag After-wards the derivatives are determined based on the previously calculated parameters as well as thestate and location of the aircraft The thrust and shaft power are determined next also dependenton whether the aircraft is on the ground or not (reverse thrust or idle thrust)

When using the power split operating mode the gas turbine power is determined using theinput power split for the landing phase From which all other remaining parameters are determinedusing a similar method as was previously discussed For the constant gas turbine power operatingmode it is chosen to only use the gas turbine power for the landing phase apart from when therequired power would be more than the maximum gas turbine power 8 As such no charging of thebatteries will occur during this flight phase One could also choose to use the gas turbine powerdifferently during this flight phase however as this phase is extremely short compared to the otherflight phases (apart from the take-off phase) any change in control strategy for the landing phasewill have negligible effect on the overall battery and fuel weight

Figure 320 shows the state of an arbitrary hybrid-electric aircraft during this flight phase as canbe seen no flare is present The aircraft descents at constant velocity until the altitude is zero afterwhich it will brake and slow down

15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

5

10

15

alti

tud

e(m

)

15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

20

40

60

spee

d(m

s)

15272 15273 15274 15275 15276 15277 15278 15279 1528 15281minus3

minus2

minus1

0

range (km)

γ(d

eg)

Figure 320 Altitude speed and flight path angle of an arbitrary hybrid-electric aircraft during landing

8This is almost never the case except when choosing a very small gas turbine power


Determine

landing drag

polar

Aircraft state

at end take-off

Relevant

settings

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Calculate lift

and drag

No

Determine

Pshaft and

thrust

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Pgasturb = Pshaft

Scale max gas

turbine power

based on altitude

and speed

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Speed and

altitude = 0

Yes

End Yes

Aircraft on

ground

Determine

derivatives

Calculate ground

friction drag and

reverse thrust if

applicable

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Calculate SFC

Yes

No

Yes

Figure 321 Flow chart of the landing phase

46 3 METHODOLOGY

346 HOLDLOITER

The hold or loiter phase is used when the extended mission is calculated It takes place when theaircraft has to hold for a certain amount of time before landing Figure 322 shows how this flightphase is determined Since during the entire phase the altitude and speed are constant some pa-rameters can be calculated outside the iteration loop improving computation time Firstly the dragpolar and secondly the maximum - and idle gas turbine power calculations are moved outside theiteration loop Once the iteration is started the propeller efficiency is determined based on thethrust at the previous time step and the drag polar is retrimmed based on the burnt fuel and batteryweight increase Next the lift and drag are determined in order to have the highest possible LDSince for the loiter phase it would be beneficial to fly using the CLCD that results in the maximumendurance (minimum power required) flying at maximum LD is actually not the best strategy for

the loiter phase It would be better to fly at maximum C32

L CD however this is not implemented in

the current version of the Initiator Making the change from maximum CLCD to maximum C32

L CD

will have little effect on the overall result of the mission analysisBased on this lift and drag a target velocity is calculated If the aircraft is flying faster than this

target velocity the shaft power is set to idle gas turbine power (and Pem = 0) Should the aircraft beflying slower than this target speed the power is increased to half the total maximum power If theaircraft is flying at the target velocity the shaft power is determined in accordance to Equation 3339

When using the power split operating mode the rest of the iteration is very similar as to whatwas used for the cruise phase For the constant gas turbine power operating mode there are a fewdifferences It was chosen to let the gas turbine provide all of the shaft power for the entire phase(except when the gas turbine power can not provide the necessary power) This was chosen becausefor a normal mission this flight phase would not take place and as such it would be much moreefficient to bring the necessary reserve fuel instead of providing a lot of extra batteries due to themuch higher specific energy of fuel Also since the power requirement for this phase is generallysmaller compared to the cruise phase it would not be beneficial in terms of SFC to let the gas turbineonly provide part of the total power requirement

From this gas turbine power the power setting is determined from which in turn the SFC iscalculated Next the electric motor - and battery power are determined and the change in batteryand fuel mass Once the required loiter time is achieved the iteration stops and the final descentphase is started (from loiter altitude to landing altitude) Since flight path angle as well as speedand altitude are constant during this flight phase no figure of the aircraft state is presented

9If the aircraft isnrsquot flying at the target velocity the lift and drag polars are determined for the correct aircraft velocity notthe target velocity


Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Determine

CLCD for

max LD

No

Determine

max Pgasturb

and Pidle

Determine Pshaft

based on target

velocity

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Loiter time

reached

Yes

End Yes

Determine Pgasturb

Determine power

setting

Figure 322 Flow chart of the loiter phase

48 3 METHODOLOGY

35 COMPARISON BETWEEN CLASS 2 AND CLASS 25 SIZINGNo validation of the above methods is possible due to the lack of comparable design studies forhybrid-electric aircraft For this reason it is interesting to compare the results of the class 2 andclass 25 methods to check whether they correspond or not First it is shown what kind of data isgenerated by the class 25 method All results shown in this Section are generated by running therelevant modules once with a certain set of inputs They are not the result of a design iteration sothey will not correspond with the results presented in Chapter 4

351 MISSION ANALYSIS RESULTS

Although the class 2 sizing will result in just one number for the fuel and battery sizing of the entiremission the mission analysis allows for a more detailed look at the entire mission and each flightphase to see what happens during each phase In this section an overview is given of these resultsof the mission analysis in order to paint a better picture of the kinds of results that can be expectedfrom the module as well as to check whether logical and realistic results are achieved 10 All datashown here is generated for a hybrid-electric aircraft using a constant power split of 05 over theentire mission apart from the descent phases where no power split is used The battery energydensity is 1000 Whkg The requirements are the same as for the ATR72-600 and all other inputsare as shown in Table 43 No data is shown for the constant gas turbine power operating mode Insection 423 the comparison between the operating modes is made

Figure 323 shows the state of the aircraft during the entire mission including deviation andloiter Since the required deviation range is only 300 km the aircraft does not complete the climbto cruise altitude before descent has to be set in again For this reason no secondary cruise phaseis present for this particular mission Although the take-off and landing phase are present they cannot be seen in Figure 323 because they occur for a very small part of the mission The reason for thespikes in the graph especially for γ is because when the aircraft changes state (for example whendescent sets in) the derivatives become very large momentarily resulting in the peaks visible in thegraph These peaks only last for 1 time step and as such will not have an effect on the overall result

Since a constant split of 05 is used the power of the gas turbine and electric motor are equalduring the entire mission apart from the descent phase However since the required gas turbinepower during the climb phase is more than the maximum gas turbine power the split of 05 is onlyvalid for the beginning of the climb phase afterwards the power split decreases slightly since theelectric motor power remains constant see Figure 324

Figure 325 shows the battery and fuel mass that is used during the mission Any point alongthe graph shows the battery and fuel mass used up until that point in the mission The same graphcould be made for battery and fuel energy which would show exactly the same trends As one wouldexpect during the climb phases the battery and fuel mass increase the fastest although the largestcontribution is still from the cruise phase

10Ggain since no real validation is possible

35 COMPARISON BETWEEN CLASS 2 AND CLASS 25 SIZING 49

0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2middot104

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

alti

tud

e(m

)

0 200 400 600 800 1000 1200 1400 1600 1800 20000

50

100

150

spee

d(m

s)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus20

minus10

0

10

range (km)

γ(d

eg)

Figure 323 State of an arbitrary hybrid-electric aircraft during the entire mission including deviation and loiter

50 3 METHODOLOGY

0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2

25

3

35

4

45

5

middot106

Cli

mb

1Cruise

Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]

Shaft Power Electric Motor Power Gas Turbine Power

Figure 324 Shaft - gas turbine - and electric motor power during the entire mission for a constant power split of 05

0 200 400 600 800 1000 1200 1400 1600 1800 20000

1000

2000

3000

4000

5000

Clim

b1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

range [km]

Mas

s[k

g]

Battery Fuel

Figure 325 Battery- and fuel weight used during the entire mission for a constant power split of 05


352 COMPARISON

In this section the comparison is made in terms of fuel and battery mass for the entire mission fora range of different inputs It is very important to note that the results shown here are generatedby running both sizing methods only once with the same inputs not for an entire design loop Theresults will therefore not necessarily correspond with the result shown in the next chapter All theresults are generated with the requirements shown in Table 41 and the inputs shown in Table 43and for a battery energy density of 1500 Whkg

First the results for the power split operating mode are compared and are shown in Table 32For all results a constant power split over the entire mission is used Four different power splits areexamined 1 (purely electric) 066 033 and 0 (only gas turbine)

Table 32 Comparison between the class 2 and class 25 sizing methods for constant power splits ranging from 000 to100

Class 2 method Class 25 method Difference

S = 100mfuel[kg] 0 0 00 mbat[kg] 5317 5635 + 60

S = 066mfuel[kg] 709 661 ndash 68 mbat[kg] 3602 3428 ndash 48

S = 033mfuel[kg] 1209 1248 + 32 mbat[kg] 1835 1645 ndash 103

S = 000mfuel[kg] 1735 1804 + 40 mbat[kg] 0 0 00

As can be seen both methods correspond adequately in terms of the battery and fuel weightfound The difference is at most around 10 for the battery weight at a constant power split of066 When using a variable power split over the entire mission the differences might become largersince especially the class 2 methods for certain flight phases are only rough estimations Howeverany inaccuracies in the class 2 methods will not have an influence on the final design since thoseoutputs are only used to have a first estimation and are overruled later on in the design loop by theoutput of the class 25 sizing method More accurate results for the battery mass might be foundwhen using the hybrid-electric range equation to determine the battery mass as well as the fuelmass for the cruise phase

Since there are distinct differences in the methods used for determining the battery - and fuelmass for the two different operating modes the same comparison as before also has to be made forthe constant gas turbine power operating mode Table 33 shows the results of this comparison formultiple input gas turbine powers The gas turbine powers that are compared vary from 01 MW to3 MW The reason a gas turbine power of 0 is not used (which should give about the same result asfor S = 100) is that the Initiator program does not converge for a very low gas turbine power (lessthan 10 kW) for the chosen input parameters

From table 33 it is clear that there are more significant differences between the class 2 and class25 sizing methods for this operating mode compared to the constant power split operating modeEspecially the fuel weight is consistently overestimated in the Class 2 sizing method This is becausethe decrease in SFC that results from using this operating mode can not be accurately determined inthe class 2 method as well as general inaccuracies that result from using a less complex and simplermethod

The class 2 battery weight estimation on the other hand shows slight better correspondence tothe class 25 method apart from large differences when the maximum gas turbine power becomes

52 3 METHODOLOGY

large (asymp 3 MW) When the gas turbine power is that large the batteries can be charged during thecruise phase using the excess power This mechanism can not be implemented in the class 2 method11 and as such the battery weight required will be overestimated in the class 2 method

Table 33 Comparison between the class 2 and class 25 sizing methods for input gas turbine powers ranging from 01MW to 3 MW

Pgasturbmax [MW] Class 2 method Class 25 method Difference

01mfuel[kg] 127 72 ndash 433 mbat[kg] 4518 5146 + 139



3mfuel[kg] 2559 1870 ndash 270 mbat[kg] 682 129 ndash 811

Although the class 2 method for the constant gas turbine power operating mode is not as accu-rate as the method for the power split operating mode this will not have an adverse effect on theultimate design(s) As mentioned before the class 2 method is only used to have a first guess in thebeginning of the design loop and is later on overwritten with more accurate results from the class 25sizing process This means that for the constant gas turbine power operating mode the programwill take slightly longer to converge to a design since the first guess is not as accurate

36 ELECTRIC MOTOR SIZING

The electric motor consists of not only the motor itself but also the cryocooler which is requiredto have superconducting properties The size and weight of the electric motor is dependent on themaximum power it has to deliver This power is either found from the take-off power loading (takinginto account the power split or the gas turbine power) or from the mission analysis depending onthe location in the design iteration A certain electric motor power density is chosen by default avalue of 15 kWkg is used This is a conservative estimate based upon predictions by NASA IEEEand others [47] [30] [28] However as mentioned before the contribution of the crycooler also hasto be taken into account This cryocooler not only adds weight but also requires power to functionThis power is dependent on the maximum rated power of the electric motor NASA states that sucha cryocooler is expected to have a power requirement of 016 of the maximum rated power of theelectric motor [28] However this seems a very optimistic number when compared to todayrsquos stateof the art cryocoolers For this reason a default value of 045 of the maximum electric motor poweris chosen With the power of the cryocooler known the weight is determined by the chosen inputpower density By default 3 kgkW [28] is used for the cryocooler power density (without the electricmotor) The volume of the engine is determined by the volumetric power density Figure 326 showsthe variation of the electric motor weight including the crycooler with the maximum rated electricmotor power

11Because a mission analysis is required to keep track of the SOC of the batteries during the entire mission

37 WIRING 53

0 05 1 15 2 25 3middot106

0

50

100

150

200

250

Maximum electric motor power [W]

Ele

ctri

cm

oto

r+

cryo

coo

ler

wei

ght[

kg]

Figure 326 Variation of the electric motor and cryocooler weight with respect to the maximum electric motor power

37 WIRING

The wiring encompasses everything that is needed to make the connection between the batterypack(s) and the electric motor Since high temperature superconducting motors used for aerospaceapplications require AC power [30] and batteries deliver DC power an inverter has to be present aswell This inverter not only changes the current from DC to AC but is also able to transform thevoltage from the battery output voltage to the electric motor input voltage Since it was chosennot to use high temperature supercooling for the wiring the wiring weight can be estimated moreaccurately based on real cable data For a given voltage and cable length the wiring weight will onlydepend on the current running through the cable This current in turn will depend on the power(for again a fixed voltage) To keep the cable diameter (and thus also the weight) as low as possiblethe voltage has to be quite high This voltage has to be chosen first for all designs considered inthis project a voltage of 6000 V AC is chosen Based on the power that has to run through the cablea certain current is obtained (I = P

U ) It was chosen to use aluminium wiring over copper wiringsince aluminium wiring has a lower weight for the same voltage and current 12 Using cable dataobtained from Synergy Cables Ltd [48] a graph can be constructed which plots the current vs thecable weight per unit length for a cable carrying 6 kV see Figure 327 This cable data also includesthe weight of the insulation

12Although it has a larger diameter due to aluminium having more resistance than copper

54 3 METHODOLOGY

100 150 200 250 300 350 400 4501

2

3

4

5

6

7

8

17703lowastAminus622451000

Cable current [A]

Cab

lew

eigh

t[kg

m]

Figure 327 Cable weight as a function of current for a cable rated at 6 kV

In the above figure the red line represents the trend line constructed from the data This trend-line is used in the Initiator program Should the calculated current lie outside the range shown inFigure 327 a different cable voltage should be chosen At this time however only one cable voltageis implemented namely 6 kV

Using the length of the cable the total mass of a cable can be known This length is determinedby the location of the battery pack and the electric motor The shortest distance between these twocomponents is taken and multiplied with a factor of 15 in order to account for the path the cablehas to take 13 The found mass also has to be multiplied with the number of cables For redundancyby default 2 cables are chosen

As mentioned previously an inverter also has to be present Using todays technology this in-verter would be too heavy and large For this reason it is chosen to also use HTS technology for thiscomponent The weight is dependent on the maximum power it has to handle Based on literaturea constant power density of 20 kWkg is chosen [47] This number includes the cryocooler as wellThe efficiency of the inverter including the cryocooler are estimated to be as high as 995 [47] [49]The efficiency at take-off would be about 025 lower [49] But since the take-off phase is short thisdifference is neglected

38 OTHER COMPONENTSIn this section a brief discussion is given of some other small changes to the Initiator namely thebattery cooling the implementation of the configuration and the fuselage weight estimation

Batteries can produce a lot of heat The amount of heat produced is dependent on the powerthe batteries deliver and the efficiency As such a battery cooling system should be incorporatedin the hybrid-electric aircraft design Finding the best method to cool the batteries and designinga cooling system is a topic for a more detailed design study Possibilities include using air coolingusing the cryocooler that is needed for the inverter and electric motor etc Although designing thiscooling system is not performed in this design study the added weight of such a cooling system hasto be taken into account As such a simple method for estimating the battery cooling weight has tobe found

13The wiring will not follow the shortest route from the battery to the electric engine since the cable would have to passthrough the cabin floor and obstruct many other components such as landing gear stowage see Section 39

39 COMPONENT PLACEMENT 55

The maximum heat the batteries produce is given by

Qbat = Pbat lowast (1minusηbat ) (334)

A method for determining the air conditioning weight is already present in the Initiator This isbased on the number of people that are present in the cabin The average human produces about120 Watt based on the average calorific intake of 2800 Kcal per day Using this fact the heat that thebatteries emit can be equated to a certain amount of extra passengers that are taken on boardAnd as such using the same method for the calculation of the air conditioning weight the batterycooling weight can be estimated This is a very rough estimation that might not be very accurateand can only be used to have a ballpark figure

Some major changes also had to be made in order to change the configuration to somethingthat represents the configuration shown in Figure 21 Changes include changing the wing locationthe fuselage shape and the gas turbine and propeller location

The fuselage weight estimation includes a calculation of the longitudinal loads on the fuselagebased on all the relevant components and their placement Obviously this has to be adapted inorder to include the contribution of the battery inverter wiring and the electric motor

39 COMPONENT PLACEMENT

The placement of all the components such as battery inverter wiring electric motor etc havea large influence on the final design For example it is beneficial to place the battery as close aspossible to the electric motor in order for the length of the wiring to be as short as possible Theelectric motor on the other hand has to be placed at the rear of the fuselage close to the gas turbinefor the mechanical coupling to not be too heavy As a result the optimal placement of all theelectrical components would be as far to the rear of the fuselage as possible However this is notpossible for two reasons Firstly the lack of space at the rear of the fuselage for all the componentsand more critically the position of the center of gravity of the aircraft would move too far to the rearmaking the aircraft unstable

For these reasons the battery which is often the heaviest component (depends on the factorof hybridization) is placed further to the front near the leading edge of the root of the wing (interms of x-location) Of course the batteries can not be placed inside the cabin so they are placedunderneath the floor of the cabin (no cargo is present there) The height of the battery pack isthus limited by the space underneath the cabin floor while the width is limited by the edges ofthe fuselage So the only variable (as a function of the battery volume) is the length of the batterypack Should the battery pack interfere with the space required for stowing the landing gear thebattery pack is moved forward such that there is still enough room for the landing gear This has theundesirable consequence that for very high hybridization factors (heavy battery pack) the batteryhas to be placed quite far to the front moving the total center of gravity of the aircraft also further tothe front than desired even sometimes exceeding the load limit of the front landing gear A possiblesolution to this problem is too split the battery pack in two placing one part in front of the landinggear and one part to the rear of landing gear However this is not implemented in the current versionof the program because on one hand it is impossible to automatically assess when this would bebeneficial to do but also if the center of gravity is too far to the front for this to occur the batterypack has to have such a large volume (and weight) that such a design is not a feasible design anyway(apart from the case where the battery gravimetric energy density is large and the volumetric energydensity is low) Figures 427 to 430 illustrate the component placement for a hybrid-electric aircraft

56 3 METHODOLOGY

310 IMPLEMENTATIONHow everything mentioned in this chapter is implemented in the Initiator is discussed in this sec-tion First and foremost some new parts are constructed the electric motor the batteries and thewiring + inverter The battery cooling is added as part of the aircraft systems as such no new partis constructed for this Each of these parts handles the properties of their respective part such asmass and center of gravity location but also maximum power for the electric motor or volume forthe batteries These properties can then be read by different modules when needed Both the bat-tery part and the electric motor part also have geometrical properties in order to be able to plot theirsize and location This is not the case for the wiring

For the class 2 weight estimation module some new sub-modules have been added to determinethe weight of the extra parts and some other sub-modules have been modified to be able to copewith turboprop aircraft (such as the engine weight module) A separate instance of the missionanalysis module is created which is used when either a turboprop or a hybrid-electric aircraft isused as input The original mission analysis module has been left (almost) unmodified and is usedfor turbofan aircraft

The input file with requirements remains largely unmodified whether the aircraft is hybrid-electric or not However many new inputs have been added to the settings file which are listedin Table 34

311 LIMITATIONSImplementing the above methods results in some limitations which are discussed here First andforemost since the design of a passenger transport aircraft with more than 19 seats and a MTOMof more than 8619 kg14 is considered one would expect to use far-25 requirements [37] These far-25 requirements are used for designing the reference aircraft however they can not be used fordesigning the hybrid-electric aircraft This is due to several requirements pertaining to the one-engine inoperative requirements which are impossible to take into account in the beginning ofthe design of the hybrid-electric aircraft If you consider one engine to be the electric motor andanother engine to be the gas turbine it might be possible in some configurations to meet theserequirements However a clutch would have to be present between these two engines and bothengines would have to have about the same maximum power which is not the case in the majority ofthe designs under consideration As of yet no certification process exists for hybrid-electric aircraftand since it is most likely impossible to meet the far-25 requirements in their current form the far-23 requirements [50] are used for all the hybrid-electric designs considered here

As discussed previously no power off-take from the batteries is considered All the power goesto the electric motor It might be possible to use the battery power to replace all the hydraulic me-chanical etc subsystems with electric system to increase reliability maintainability and possiblyeven decrease weight This is the so called more-electric-aircraft concept However this is not con-sidered in this design study as this would be outside the scope of the project as well as no reliablemethods exist for sizing such an aircraft

At the start of the design loop (but not part of the design iteration see Figure 31) a class 1 weightestimation is performed Since this weight estimation is entirely based upon a database of existingreference aircraft it does not take into account whether the to design aircraft is a hybrid-electricaircraft or not As such the first class 1 estimation is very inaccurate for hybrid-electric aircraftAfterwards a class 2 and 25 weight estimation is performed which overwrite the class 1 estimationwhich means a bad class 1 estimation will not have an effect on the ultimate design The designiteration might take a little longer because of the bad first guess The current implementation of theclass 2 weight estimation for the batteries and fuel produces inaccurate results in some cases (seeSection 352) The accuracy can be improved by implementing the hybrid-electric range equation

1419000 pounds

311 LIMITATIONS 57

to find both the battery and fuel weight and not just the fuel weight This adaptation will not havean effect on the ultimate design since later in the design iteration the mission analysis is performed(class 25 sizing)

There are also a few limitations pertaining to what range of inputs can be selected An erroroccurs when choosing a power split that would result in a fully electric cruise or hold phase (S =1) due to the hybrid-electric range equation (Equation 320) not finding a solution A workaroundis selecting a power split of 09999 The difference in the final design is negligible Also when thefound battery mass is very small (lt 50 kg) the longitudinal load on the fuselage is ignored Thisresults in a warning during the fuselage weight estimation however this has further no effect onthe design This does not occur when designing a non-hybrid aircraft since the battery part is nevercreated

When designing a hybrid-electric aircraft using the constant gas turbine power operating modethe calculation of the range at the end of the design iteration is not correct since this uses the hybrid-electric range equation (Equation 320) to estimate the range and this equation is only valid for thepower split operating mode (since the power split is included in the equation)

The design loop itself also takes longer for a hybrid-electric aircraft compared to a non-hybridaircraft This is mostly due to the extra variables that have to be calculated in the mission analysisAlthough it differs from design to design in general the design convergence takes about 5 minuteslonger when using the power split operating mode and 10 minutes (even up to 15 minutes in ex-treme cases) longer when using the constant gas turbine power operating mode The reason for thedifference between the two operating modes is the less accurate class 2 weight estimation for theconstant gas turbine operating mode (as was discussed in Section 352) Since the first guess (class2 estimation) isnrsquot always accurate the class 25 weight estimation requires more iterations beforeconverging For small input gas turbine powers approaching the infeasibility domain the entire de-sign loop can take significantly longer in some extreme cases even more than 1 hour The missionanalysis itself also takes slightly longer 2-3 seconds longer per mission analysis This is due to thedifference in implementation and the extra computing power required for for example searchingfor the optimal power setting during the cruise phase The above mentioned computing times areonly a ballpark figure and depend on the computing power available Although a lot of optimizationof the code is already performed the computation time can be further improved by optimizing thecode more

58 3 METHODOLOGY

Table 34 New input parameters that are needed in the Initiator program when designing a hybrid-electric aircraft

Parameter Description UnitHybrid Lets the program know whether or not a hybrid-

electric aircraft is being designed it influences theshape of the fuselage location of the gas turbinewhat parts are created and the mission analysis

-

ebat Specific energy of the battery pack Whkgvolbat Volumetric energy density of the battery pack By

default the same value as the specific energyWhl

∆mbat The increase in battery mass when battery energyis used This is non-zero for lithium-air batteries

kgWh

Reserve battery Factor of the total battery pack weight that is left asreserve in order for the battery pack to not fully de-plete at the end of the mission which could resultin permanent damage to the batteries

-

ηem Electric motor efficiency -ηel ec Efficiency of the wiring-inverter combination -ηbat Discharging and charging efficiency of the battery

pack-

ηpr op Propeller efficiency Used during the class 2 sizingprocess For the mission analysis this is calculatedusing the ideal efficiency (Equation 35)

-

pem Electric motor power to weight ratio kWkgvE M Electric motor power to volume ratio kWlem size ratio Electric motor lengthdiameter Used for con-

structing the electric motor with the correct di-mensions

-

Pcr yo Percentage of the maximum electric motor powerrequired to run the cryocooler of the electric motor

pcr yo Cryocooler power to weight ratio kWkgpi nv Inverter power to volume kWkgUcable Voltage running through the cables connecting the

batteryinverter to the electric motorV

Ncables Number of cables connecting the batteryinverterto the electric motor including those needed forredundancy

-

Mode Determines what operating mode is used 0 =power split operating mode and 1 = constant gasturbine operating mode

-

St akeo f f Power split during the take-off phase -Scl i mb Power split during the climb phase -Spr ecr ui se Power split at the start of the cruise phase -Sendcr ui se Power split at the end of the cruise phase -Sl andi ng Power split during the landing phase -Shol d Power split during the holdloiter phase -Pg astur b Maximum continuous gas turbine power used

when the constant gas turbine operating mode isselected

W

4RESULTS

In this chapter the results are presented Firstly the changes made to the Initiator in order to con-struct the reference aircraft are validated by comparing the reference aircraft to the ATR 72-600Next the results of the hybrid-electric aircraft are given starting with the effect of a change in thedegree of hybridization or supplied power ratio Subsequently a comparison is made between thetwo operating modes and an assessment is made whether there is an optimal power split that canbe used A sensitivity analysis with respect to battery specific energy and aircraft range is also per-formed And lastly one feasible design is investigated in more detail

41 REFERENCE AIRCRAFTIn this section the comparison is made between the reference aircraft that was designed using thechanges mentioned in Section 32 and the ATR 72-600 Table 41 shows the requirements of thisaircraft which are also used as input for the reference aircraft design The time to climb consists oftwo data points the time it takes (in minutes) to reach a specific altitude (in meter)

Parameter Value UnitPayload mass 7500 kgNumber of passen-gers

68 -

Range 1528 kmCruise Mach 045 -Cruise altitude 7500 mTake-off distance 1333 mLanding distance 1067 mTime to climb [175 5400] [min m]

Table 41 Requirements of the ATR 72-600 which are also used as input for the reference aircraft design

Figures 41 42 and 43 show the difference between the reference aircraft and the ATR in termsof geometry The grey aircraft represents the aircraft designed by the initiator while the black linesshow the geometry of the ATR 72-600 As can be seen both aircraft are very similar in terms ofgeometry showing only slight differences for the fuselage tail and wing The landing gear howeverappears to be quite a bit longer for the reference aircraft which suggest the landing gear designmodule might not give the most accurate results for this type of aircraft but this does not have alarge effect on the overall design It might be possible to design a reference aircraft which is an even

59

60 4 RESULTS

closer match to the ATR by tweaking some settings (such as wing kink location fuselage shape etc) However this would provide little added value

Figure 41 Front view of the ATR72-600 compared to the reference aircraft

Figure 42 Side view of the ATR72-600 compared to the reference aircraft

41 REFERENCE AIRCRAFT 61

Figure 43 Top view of the ATR72-600 compared to the reference aircraft

Table 42 shows the main parameters of the reference aircraft compared to the ATR 72-600 Ascan be seen the results for the reference aircraft are a very close match to those of the ATR 72-600 The largest difference is in the wing area with a difference of only 42 From this it canbe concluded that the changes made to the Initiator in order for it to be able to design a regionalturboprop aircraft are valid and provide results with sufficient accuracy for a preliminary design Itis worth noting however that although the MTOM of both aircraft are very similar the mass of theindividual components can differ a lot between the two aircraft This is partially due to differencein what is and what isnrsquot incorporated into each part 1

1For example the definition of what is included in electrical systems can differ between the ATR 72-600 and the refer-ence aircraft

62 4 RESULTS

Table 42 Parameters comparing the ATR 72-600 to the reference aircraft

Parameter ATR 72 -600 Reference aircraft DifferenceMax take-off mass[kg]

22800 22340 - 20

Mission fuel mass [kg] 2000 2050 + 24 Empty mass [kg] 13010 12780 - 18 Propeller diameter[m]

393 392 - 03

Wing Span [m] 2705 265 - 21 Wing Area [m2] 61 5854 - 42 Fuselage Length [m] 2717 27 - 06

42 HYBRID AIRCRAFTIn this section the results for the hybrid-electric aircraft are given First the values of various inputsthat are needed for creating the following designs are given Next the design space is exploredin terms of the supplied power ratio After which the difference between the operating modes isexamined and an attempt is made to find the optimum power split

421 INPUTS

Before the results of the hybrid aircraft are presented the used input values are discussed This isnecessary because these input settings have a large influence on the final design Table 43 showsthe inputs with their respectively chosen values Certain inputs such as battery specific energypower split or gas turbine power (depending on chosen operating mode) are not fixed but will varythroughout this chapter as these values have a very large influence on the results and their value cannot be known for sure

Table 43 Input values that are used for each design considered in this chapter

Parameter Value UnitHybrid 1 [-]∆Wbat 0000192 kgWhReserve battery 01 [-]ηem 098 [-]ηel ec 097 [-]ηbat 098 [-]ηpr op 085 [-]pE M 15 [kWkg]em size ratio 2 [-]Pcr yo 045 []pcr yo 033 [kWkg]pi nv 25 [kWkg]Ucable 6000 [V]Ncable 2 [-]

The description of the parameters in Table 43 can be found in Table 34 In the previous chapter

42 HYBRID AIRCRAFT 63

some more explanation is given as to why a certain value is used for certain parameters 2

422 SUPPLIED POWER RATIO

The effect that making the aircraft more hybrid is investigated here For this purpose the influenceof the supplied power ratio is examined One can also choose to examine the effect of the degreeof hybridization the results will be very similar The reason for choosing the supplied power ratioover the degree of hybridization is that it gives a better idea of how much total power and energy isdelivered to the propeller from both the electric motor and the gas turbine thus allowing for a bet-ter understanding of how hybrid a certain design is Also since the energy of the fuel is generallymuch larger than the energy contained in the batteries 3 the values for the degree of hybridizationtend to be much lower compared to the supplied power ratio Consequently the values for the de-gree of hybridization tend to be more clustered and do not give a very intuitive representation ofhow much electric motor - and gas turbine energy is actually used during the mission

In this section all hybrid designs under investigation have been constructed using the powersplit operating mode however all effects can also be observed for the constant gas turbine poweroperating mode In section 423 the difference between these two operating modes is examinedThe power split chosen for each design in this section is constant throughout the mission (Si =Si+1 = const ant ) In Section 424 it is examined whether there is a better alternative to using aconstant power split When using a constant power split the chosen power split is approximatelyequal to the supplied power ratio (Sconst ant asympΦ) Slight difference in both values might occur dueto the power split not being constant for the entire climb phase Pem gt S2 lowastPsha f t for most of theclimb phase

As mentioned before all parameters shown in Table 43 are fixed The only variables are thepower splits for each mission phase and the battery specific energy As discussed in Section 221the prognosis for battery specific energy in the year 2035 lies between 750 Whkg and 1500 WhkgAs a result in this section these two battery energy densities are chosen as well as 1000 Whkg Alldesigns with battery energy densities between 750 and 1500 Whkg will lie between the boundariesset by the aforementioned specific energies

First the battery and fuel mass are examined As one would expect the battery mass increaseswith increasing supplied power ratio see Figure 44 The slope of the battery mass highly dependson the battery specific energy While the slope is almost linear when ebat = 1500 Whkg it is almostexponential when ebat = 750 Whkg This is due to the snowball effect caused by the increase inMTOM see Figure 46 With an increase in battery mass comes an increase in MTOM which in turnincreases the total energy requirement which again increases the battery mass and so on For thisreason there is an upper limit to the achievable supplied power ratio 4 After a certain point theincrease in available energy of taking more batteries on board is less than the increase in requiredenergy that comes from taking these batteries on board As such after this point the MTOM willkeep increasing in every iteration and not converge to a solution

The decrease in fuel mass with supplied power ratio (Figure 45) appears to be more linear al-though with a different gradient for a different battery specific energy It is worth noting that thebenefits in terms of total fuel mass of having a higher battery specific energy for a low suppliedpower ratio (Φ lt 015) are almost non-existent due to the relatively small increase in MTOM Bothfor the decrease in fuel mass and the increase in battery mass the benefits of having a higher batteryspecific energy increase greatly when getting to higher supplied power ratios In Section 432 theinfluence of the battery specific energy is investigated in more detail

In Figure 45 and 46 the reference aircraft fuel mass and maximum take-off mass are also shown

2See Section 36 for most values3Due to the much higher specific energy of fuel compared to the battery pack4For a battery energy density less than 1500 Whkg

64 4 RESULTS

The reason the values for the reference aircraft do not correspond to the values for Φ = 0 is due tothe influence of the configuration itself Although the requirements are the same the fact that thereis only one engine (and no engine drag) as well as the different wing and center of gravity locationresult in a slightly lighter aircraft which uses less fuel The influence of boundary layer ingestion andcontra-rotating propellers are not taken into account

In Figure 47 the influence of the supplied power ratio on the maximum electric motor power isshown This is an important metric since not only the electric motor mass depends on this factorbut also the wiring mass inverter mass and the battery cooling mass Especially for the electric mo-tor power the influence of the battery specific energy at low supplied power ratios is negligible Thisis again due to the only slight increase in MTOM and the resulting small increase in take-off andclimb power required Nevertheless Figure 48 shows the variation of the mass of all componentswhich depend on Pem with supplied power ratio for a battery energy density of 1500 Whkg Thesame trends can be observed for all other battery energy densities The contribution of the batterycooling appears to decrease with an increase in supplied power ratio However as mentioned be-fore the battery cooling is very hard to size in the preliminary design phase and thus the values areonly a rough estimation

And finally in Figure 49 the variation of the gas turbine mass with supplied power ratio is shownSince the gas turbine mass depends on the maximum power the gas turbine has to deliver it standsto reason that the gas turbine mass variation is approximately inversely proportional to the electricmotor power variation (Figure 47)

It is important to note that not all designs in this section are feasible since some designs havestability issues due to the location of the center of gravity A low supplied power ratio results (ingeneral) in an aircraft with a light battery and a heavy gas turbine Since the configuration is fixedthis might result in a center of gravity which is too far to the rear This could be solved by placingthe batteries further to the front of the aircraft or moving the wing further to the rear etc On theother hand when the supplied power ratio becomes large the center of gravity can move too farto the front due to the heavy battery Where exactly this boundary of feasibility lies is very hardto predict because it depends heavily on the location of the various components which can bechanged relatively easily The battery specific energy also has a large influence on this range Ingeneral a supplied power ratio between 03 and 06 appears to be feasible

0 01 02 03 04 05 06 07 08 09 10

05

1

middot104

darr Reference aircraft fuel weight

Supplied Power Ratio [-]

Bat

tery

Mas

s[k

g]

ebat = 1500 Whkgebat = 1000 Whkgebat = 750 Whkg

Figure 44 Battery mass vs supplied power ratio for multiple battery energy densities


0 01 02 03 04 05 06 07 08 09 10

500

1000

1500

2000

2500



Fuel

Mas

s[k

g]


Figure 45 Fuel mass vs supplied power ratio for multiple battery energy densities

0 01 02 03 04 05 06 07 08 09 10

1

2

3

4middot104

uarr Reference aircraft MTOW


MT

OM

[kg]


Figure 46 Maximum take-off mass vs supplied power ratio for multiple battery energy densities

66 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

2

4

6middot106


Max

imu

mP

em


Figure 47 Maximum electric motor power vs supplied power ratio for multiple battery energy densities

0 01 02 03 04 05 06 07 080

200

400

600

800

1000

1200

1400


Mas

s[k

g]

TotalElectric MotorWiring and InverterBattery Cooling

Figure 48 The mass of the components making up the electrical part of the powertrain (minus the batteries) vs suppliedpower ratio for a battery energy density of 1500 Whkg


0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000


Gas

Turb

ine

Mas

s[k

g]


Figure 49 mass of the gas turbine vs supplied power ratio for multiple battery energy densities

68 4 RESULTS

423 OPERATING MODES

In this section it is examined whether there is a difference in designs using the power split operat-ing mode compared to the constant gas turbine power operating mode using otherwise the sameinputs To be able to compare these operating modes a certain measure for how hybrid a certaindesign is has to be introduced For this purpose the supplied power ratio is used again Figure 410shows the relation between the input gas turbine power and the supplied power ratio This rela-tion is approximately linear with a slope that depends on the chosen battery specific energy Thedifference is due to the lighter aircraft resulting from a larger battery specific energy A lighter air-craft will have a lower supplied power ratio for the same gas turbine power since less total energyis required but the gas turbine energy stays the same Again for all designs using the power splitoperating mode considered in this section a constant power split was used over the entire mission(Si = Si+1 = const ant ) This might not be the most optimal control strategy but more info on thattopic can be found in Section 424

0 01 02 03 04 05 06 07 08 09 10

05

1

15

2

25

3middot106


Max

imu

mC

on

tin

uo

us

Gas

Turb

ine

Pow

er[W

]


Figure 410 The maximum continuous gas turbine power vs the supplied power ratio for battery energy densities of 7501000 and 1500 Whkg

The reasoning behind the constant power operating mode is the decrease in SFC especiallyfor the cruise phase Figure 411 and 412 show the variation in Pem Pg astur b and Psha f t for twodesigns The first one is constructed using the power split operating mode and the second oneusing the constant gas turbine operating mode Both use exactly the same inputs (Table 43 andebat = 1000 Whkg) and have a resulting supplied power ratio of approximately 025 It can clearlybe seen that the constant gas turbine operating mode results in a design with less variation in thedelivered gas turbine power resulting in a lower SFC 5 It does have the downside that the electricmotor needs to compensate more for the peaks in the required shaft power The average SFC duringthe cruise phase is 291 gkWh for the constant gas turbine power operating mode compared to 300gkWh for the power split operating mode This might not seem like a large difference howeverover the entire cruise phase it does result in a non-negligible difference in fuel mass

5Since a larger power setting is used for the cruise phase


0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]Shaft Power Electric Motor Power Gas Turbine Power

Figure 411 Shaft - electric motor - and gas turbine power during the entire mission for a constant power split resultingin a supplied power ratio of 025 using a battery specific energy of 1000 Whkg

0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]


Figure 412 Shaft - electric motor - and gas turbine power during the entire mission for a certain input gas turbine powerresulting in a supplied power ratio of 025 using a battery specific energy of 1000 Whkg

70 4 RESULTS

When comparing the final designs of both operating modes in terms of fuel - and battery mass(Figure 413 and 414) it can be seen that for the same supplied power ratio the constant power op-erating mode results in a design with a slightly lower fuel mass and the same battery mass This canbe observed regardless of battery specific energy For a low supplied power ratio (approximatelyΦ lt015) the fuel mass of the constant gas turbine power operating seems to become larger comparedto the power split operating mode This is because for a low supplied power ratio the gas turbinepower becomes so large that Pg astur b gt Psha f t for the cruise phase As such the excess gas turbinepower is used for charging the batteries which has as result that the (partially) charged batteries canbe used for the subsequent flight phases and as such less battery mass needs to be taken on board

The variation in gas turbine power is less for the constant gas turbine power operating modeThis has as consequence that the electric motor needs to compensate more for the peaks in requiredshaft power (such as during take-off and climb) Figure 415 shows that the electric motor poweris significantly larger for the constant gas turbine power operating mode regardless of suppliedpower ratio (except for when Φ = 1 due to no gas turbine being present) Since the electric motormass wiring mass and battery cooling mass are all dependent on this factor their mass will also besignificantly more for the constant gas turbine power operating mode However for the same reasonthat the electric motor power is larger the gas turbine power and mass are significantly lower for theconstant gas turbine power operating mode (Figure 416)

All the previously mentioned effects appear to (partially) offset each other and as a conse-quence the MTOM of both operating modes is very similar (Figure 417) It might be the case thatfor some supplied power ratiorsquos the MTOM of the constant gas turbine operating mode is slightlylower however the used weight estimations are not accurate enough to conclude anything in thisregard

Ultimately it can be concluded that the constant power operating mode results in a slightlymore optimal design with less fuel mass for approximately the same battery mass and MTOM It isimportant to note that for most supplied power ratiorsquos a certain power split can be chosen such thatthe resulting design is exactly the same as the one found by using the constant gas turbine poweroperating mode Whether there is a certain combination of power splits that results in an even moreoptimal design is investigated in the next section


0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

2000


Fuel

Mas

s[k

g]

Power split op mode (ebat = 1500 Whkg)Constant Pg astur b op mode (ebat = 1500 Whkg)Power split op mode (ebat = 1000 Whkg)Constant Pg astur b op mode (ebat = 1000 Whkg)Power split op mode (ebat = 750 Whkg)Constant Pg astur b op mode (ebat = 750 Whkg)

Figure 413 Difference in fuel mass for the constant gas turbine power operating mode compared to the power splitoperating mode using a battery specific energy of 750 1000 and 1500 Whkg

0 01 02 03 04 05 06 07 08 09 10

02

04

06

08

1

12middot104


Bat

tery

Mas

s[k

g]


Figure 414 Difference in battery mass for the constant gas turbine power operating mode compared to the power splitoperating mode using a battery specific energy of 1000 and 1500 Whkg

72 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1

2

3

4

5

6middot106


Max

imu

mP

em[W

]Power split op mode (ebat = 1500 Whkg)Constant Pg astur b op mode (ebat = 1500 Whkg)Power split op mode (ebat = 1000 Whkg)Constant Pg astur b op mode (ebat = 1000 Whkg)Power split op mode (ebat = 750 Whkg)Constant Pg astur b op mode (ebat = 750 Whkg)

Figure 415 Difference in maximum electric motor power for the constant gas turbine power operating mode comparedto the power split operating mode using a battery specific energy of 750 1000 and 1500 Whkg

0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000


Gas

Turb

ine

Mas

s[k

g]


Figure 416 Difference in gas turbine mass for the constant gas turbine power operating mode compared to the powersplit operating mode using a battery specific energy of 750 1000 and 1500 Whkg


0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34

36

38

4middot104


MT

OM

[kg]


Figure 417 Difference in MTOW for the constant gas turbine power operating mode compared to the power split oper-ating mode using a battery specific energy of 750 1000 and 1500 Whkg

74 4 RESULTS

424 OPTIMAL POWER SPLIT

The above results using the power split operating mode are all generated using a constant powersplit over the entire mission However as one might imagine this might not yield the most optimaldesign Christopher Perullo and Dimitri Mavris [4] found that using model predictive control theoptimum power split varies from around 08 at the start of the mission to 0 at the very end of themission see Figure 418 This optimum power split results according to them in the largest rangefor a given fuel mass or the lowest fuel mass for a given range

Figure 418 Optimum power split using model predictive control [4]

The reasoning behind this is that it is optimal to burn as much fuel in the beginning of the mis-sion to achieve a lighter aircraft and use more batteries at the end of the mission which would thanrequire to deliver less power because of the lighter aircraft This effect is even magnified when usingLithium-air batteries because these batteries add mass during the course of their usage To see ifthis assertion is correct a similar power split was used as input into the modified Initiator programSince all phases of the mission (apart from the cruise) can only have a constant power split the ex-act variation as can be seen in Figure 418 can not be achieved using the current Initiator programHowever an approximation was achieved which can be seen in Figure 419 The deviation andholdloiter are also included since these mission phases have to be included when determining thefuel and battery mass However as is made clear in the subsequent plots the power split variationshown in Figure 419 does not result in a more optimal design point than a constant power splitThis is partially due to the large power requirement of both the gas turbine and the electric motorBecause multiple climb phases are included in the mission (first at the start of the mission and lateron during the deviation to a different airport) and the first climb phase requires mostly gas turbinepower and the second climb phase requires mostly electric motor power both the gas turbine andthe electric motor power have to be sized much larger resulting in a heavier aircraft offsetting anybenefit in aircraft mass that might result from burning more fuel in the beginning of the missionFor this reason a second power split variation is also investigated see Figure 420 Here the powerrequirement of the secondary climb phase (and subsequent flight phases) is mostly handled by thegas turbine eliminating the need for a much heavier electric motor Note that the power split is 1during the descent phase since no power split is used during this flight phase On the y-axis in Fig-ure 419 and 420 the power split is not shown but rather the parameter 1 - S in order to conformwith the definition of power split as used by Perullo et al in Figure 418

In subsequent figures the green dots represent the power split variation defined in Figure 419and the yellow dots the one defined in Figure 420 Which from this point on will be referred to aspower split variation 1 and power split variation 2 respectively These figures are constructed us-


0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]

Figure 419 Optimum power split input variation 1

0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]


ing a battery specific energy of 1000 Whkg However these effects can also be observed regardlessof battery specific energy

In Figure 421 it can be seen that neither power split variation result in a more optimal designcompared to a constant power split during the entire mission Both the fuel and battery mass appearto be slightly larger One reason for this effect is illustrated in Figure 422 For power split variation 1there is a very large increase in both the electric motor mass (including secondary systems) and gasturbine mass due to the reasons explained previously This results in a higher MTOM (Figure 423)requiring more battery and fuel mass For power split variation 2 the electric motor (and secondarysystems) is slightly lighter in comparison to using a constant power split however the gas turbinemass is again larger When combined this also leads to an increase in MTOM thus an increase infuel and battery mass

Notwithstanding the above reasoning does not give the full picture there is also a very impor-tant secondary effect at play that explains why these power split variation are not optimal Becausethe gas turbine has to be sized quite large in order to meet the power requirements for the climb andtake-off phase and later on in the mission the gas turbine power requirement is much smaller theSFC will keep increasing during the mission since the power setting will decrease 6 This effect willbe less for power split variation 2 due to the larger power setting in the deviation and loiter flightphases

Overall it is clear that Perullo et al [4] did not take into account several effects which have a verylarge impacts on the design resulting in their optimal power split not resulting in an optimal design

6And small power settings result in high SFC see Figure 37

76 4 RESULTS

The assumption made by Perullo et al of having no increase in empty mass for a hybrid-electricaircraft is an oversimplification which results in several effects being ignored

0 01 02 03 04 05 06 07 08 09 10

2000

4000

6000

8000


Mas

s[k

g]

Battery massFuel mass

Figure 421 Fuel and battery mass vs supplied power ratio for designs with constant power split and the optimum powersplit according the Perullo et al

0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400


Mas

s[k

g]

Electric motor + wiring + inverter + battery cooling massGas turbine mass


43 SENSITIVITY ANALYSIS 77

0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34middot104


MT

OM

[kg]

Figure 423 MTOW vs supplied power ratio for designs with constant power split and the optimum power split accordingthe Perullo et al

43 SENSITIVITY ANALYSISIn this section a sensitivity analysis is performed for range and battery specific energy It is chosento investigate the effect an increase in range (compared to the reference aircraft) has on the feasi-bility and benefit of a hybrid-electric aircraft in order to get a better understanding of what type ofmission a hybrid-electric aircraft could perform Since the battery specific energy has a very largeinfluence on the design (as is evident from the previously presented results) and the expected spe-cific energy can not be predicted accurately the influence of this parameter is investigated furtherOne could also perform a sensitivity analysis for other parameters such as the power density of theelectric motor (or other components) however the effect of these parameters on the design are verypredictable For example decreasing the electric motor power density will result in a slightly heavierdesign an as a result a slightly higher fuel and battery mass

431 RANGE

Figure 424 shows the variation of fuel mass with supplied power ratio for multiple mission rangesThis plot shows that the benefit in terms of fuel mass of having a hybrid-electric aircraft diminisheswith an increase in range For a range of more than 5000 km there appears to be no benefit at all Thisis because the larger the range the larger the increase in MTOM with supplied power ratio (Figure425) After a certain point the increase in MTOM of a hybrid-electric aircraft results in such a largeincrease in the total mission energy requirement that there is an increase in fuel requirement for themission compared to having a non-hybrid aircraft When looking at Figure 424 there appears to bean optimum of the supplied power ratio for a range of 5000 km This is not the case for lower rangesan increase in supplied power ratio will always lead to a decrease in fuel mass The reason for thisoptimum is that when the supplied power ratio becomes too large adding batteries will increasethe total energy requirement by an amount that is higher than the energy the batteries can deliverie it takes more energy to transport the batteries than the energy the batteries can deliver

78 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1000

2000

3000

4000

5000

6000


Fuel

wei

ght[

kg]

Range = 1528 kmRange = 3000 kmRange = 4000 kmRange = 5000 km

Figure 424 Variation of fuel mass with supplied power ratio for multiple ranges

0 01 02 03 04 05 06 07 08 09 12

25

3

35

4middot104


MT

OW

[kg]


Figure 425 Variation of maximum take-off mass with supplied power ratio for multiple ranges

44 FINAL DESIGN 79

432 BATTERY SPECIFIC ENERGY

Figure 426 shows the variation in fuel mass with the battery specific energy for a multitude of sup-plied power ratiorsquos (Φ) As can be seen the decrease in fuel mass between 750 and 1000 Whkg islarger than the decrease between 1000 and 1500 Whkg especially for larger supplied power ratiosObviously for Φ = 00 the data is just a flat line The difference between this line and the fuel massfor the reference aircraft is due to the different configuration resulting in a slightly lower fuel mass

700 800 900 1000 1100 1200 1300 1400 1500800

1000

1200

1400

1600

1800

2000

2200darr Reference aircraft fuel weight

Φ= 01

Φ= 02

Φ= 03

Φ= 04

Φ= 05

Φ= 06

Φ= 00

ebat [ W hkg ]

Fuel

Mas

s[k

g]

Figure 426 Fuel mass vs battery specific energy for multiple supplied power ratios

44 FINAL DESIGNNow that the design space is explored one particular design will be examined further First a designpoint has to be chosen The requirements (such as range) are the same as for the reference aircraftin order to be able to make a comparison between the two for the values see Table 41 The two pa-rameters that have the most influence on the design are the battery specific energy and the suppliedpower ratio (ie how hybrid the aircraft is) see section 422 From literature it was found that a bat-tery specific energy between 750 kWkg and 1500 kWkg can be expected from lithium-air batteriesby the year 2035 As was observed in Section 43 the benefit of increasing the specific energy from750 Whkg to 1000 Whkg is larger than the benefit of increasing it from 1000 Whkg to 1500 WhkgBased on this observation and the decrease in risk of choosing a relatively low specific energy abattery specific energy of 1000 Whkg is chosen for the design considered here

A certain degree of hybridization or supplied power ratio has to be chosen as well Several factorshave to be taken into account when selecting a certain value First of all the design should befeasible Choosing a too low supplied power ratio can result in a unstable aircraft since the centerof gravity can move too far to the rear because of the low battery mass A too high supplied powerratio on the other hand could result either in an infeasible design or in a design where the centerof gravity is moved too far to the front due to the large battery mass For the chosen configurationand a battery specific energy of 1000 Whkg a supplied power ratio between approximately 03 and065 results in a feasible design with no stability problems Another aspect that has to be accountedfor is the increase in cost with an increase in supplied power ratio Since the cost is not calculatedthe MTOM is taken as a metric of cost Because the MTOM increases rapidly with supplied powerratio the supplied power ratio has to be taken as low as possible to keep the cost low Of course thewhole point of designing a hybrid electric aircraft is to reduce the fuel mass as much as possible

80 4 RESULTS

thus requiring a supplied power ratio that is as large as possible It is the authors opinion that asupplied power ratio of around 035 provides an adequate balance between all those factors

As was concluded from section 423 the constant gas turbine operating modes result in a designwith slightly less fuel mass for about the same battery mass MTOM and supplied power ratio com-pared to a constant power split operating mode Thus a more optimal design and since no optimalvariable power split was found (Section 424) the constant gas turbine power operating mode ischosen for the design discussed here

Taking all of the above into account a battery specific energy of 1000 Whkg was chosen as wellas a constant maximum gas turbine power of 22 MW resulting in a supplied power ratio of approx-imately 034 Table 44 shows the comparison of the chosen design with the reference aircraft interms of mass breakdown and some performance parameters The climb rate shown is the maxi-mum climb rate that occurs during the mission and not necessarily the maximum achievable climbrate

Table 44 Parameters comparing the hybrid-electric aircraft to the reference aircraft

Parameter Reference aircraft Hybrid-electric air-craft

Difference

Max take-off mass[kg]

22340 25470 + 14

Mission fuel mass [kg] 2050 1470 ndash 28 Battery mass [kg] 0 2948 naEmpty mass [kg] 12780 13552 + 6 Maximum missionclimb rate [ms]

103 72 ndash 29

Total mission energy[MWh]

2619 2173 ndash 17

As can be seen in the above table using this hybrid-electric design results in an estimated 28 decrease in fuel mass compared to the reference aircraft at the cost of a 14 increase in MTOM Thisincrease in MTOM is largely due to the added battery mass but also due to the increase in emptymass This increase in empty mass is not only due to the added electric motor wiring inverter andbattery cooling mass but also due to the increase in needed structural mass caused by the increasein MTOM

In figure 45 some basic geometrical parameters of the hybrid-electric aircraft are shown andcompared to the reference aircraft The wings are obviously larger due to the increase in MTOMFigure 427 to 430 show the geometry of the hybrid-electric aircraft with the approximate size andlocation of the power plant components

Table 45 Parameters comparing the geometry of the hybrid-electric aircraft to the reference aircraft


Difference

Wing span [m] 265 288 + 87 Wing area [m2] 5854 691 + 18 Fuselage length [m] 27 271 + 04

44 FINAL DESIGN 81

510

1520

25

minus10minus5

05

10

2

4

6

8

Figure 427 Isometric view of the hybrid-electric aircraft

Figure 428 Front view of the hybrid-electric aircraft

Figure 429 Side view of the hybrid-electric aircraft

82 4 RESULTS

Figure 430 Top view of the hybrid-electric aircraft

5CONCLUSION amp RECOMMENDATIONS

51 CONCLUSIONThe aim of this project is to investigate the possible advantage of a hybrid-electric aircraft conceptcompared to a conventional aircraft for the year 2035 Since much uncertainty exists pertainingto the expected level of technological development between now and 2035 many designs are in-vestigated with multiple input parameters in particular the effect of the battery specific energy isinvestigated as well as the supplied power ratio It is found that for a range of 1528 km the fuelweight decreases with an increasing supplied power ratio for any battery specific energy between750 Whkg and 1500 Whkg At the same time the MTOM increases This holds true for a range upto around 5000 km (depending on the chosen battery specific energy) after which either no bene-fit can be achieved from using a hybrid-electric aircraft or there exists an optimum in the suppliedpower ratio This is because after a certain point more energy is required to transport the batter-ies than the energy stored in the batteries itself There is also a limit to the maximum achievablesupplied power ratio for most battery specific energyrange combinations After a certain point theMTOM (and thus also the energy requirement) increases to such a level that no more feasible designis possible

Two different operating modes are implemented the power split operating mode and the con-stant gas turbine power operating mode When comparing the power split operating mode usinga constant power split to the constant gas turbine power operating mode it is found that the lattergenerally results in a design with a lower mission fuel weight for approximately the same batteryweight and MTOM while using the exact same inputs and having the same supplied power ratioHence resulting in a slightly more optimal design

Of course using a constant power split over the entire mission might not be optimal and assuch it is investigated whether there is an optimal power split variation Perullo et al suggest usinga power split that decreases over the course of the mission (the aircraft uses more electrical energythe further in the mission) It was found that this power split variation is not optimal because ofthe resulting increase in gas turbine - electric motor - wiring - and battery cooling weight Anotherdisadvantage of this power split variation is the increase in SFC At this time no optimal power splitis found

Taking all these aspects into account one final design is considered using the constant gas tur-bine power operating mode with a battery specific energy of 1000 Whkg and a supplied power ratioof 034 This feasible design results in a fuel weight reduction of approximately 28 and an in-crease in MTOM of 14 From this it can be concluded that there is definitely the possibility ofdrastic fuel weight reduction by using the hybrid-electric aircraft concept (up to about 30 ) pro-vided that there is sufficient technological progress between now and 2035 particularly pertainingto battery specific energy density

83

84 5 CONCLUSION amp RECOMMENDATIONS

When designing a hybrid-electric aircraft great care has to be taken in selecting not only a suit-able power train architecture but also an operating mode These basic choices have to be taken intoaccount from the very start of the design process since they can have a very large impact on the finaldesign

52 RECOMMENDATIONSThere are some improvements which can be made in terms of the Initiator program itself in orderto get more reliable accurate results First of all the model of the power and fuel consumption vari-ation with speed altitude and power setting can be improved At the moment it is only valid for onespecific engine (PW 124B) and it is assumed all other engines show the exact same behaviour Theprogram is also limited to the parallel-hybrid power train It could be expanded relatively easily toalso include the series-hybrid architecture such that the user can select the appropriate architec-ture A comparison between those two (or more) architectures can also be made

Currently only a constant power split can be selected for all flight phases apart from the cruisephase It could be that that simplification results in non-optimal designs As such being able toinput a variable power split over the entire mission or a power split curve (such as constructed byPerullo et al see Figure 418) might provide better results

During descent it is chosen to keep the gas turbine at idle while the electric motor is switchedoff Since the electric motor does not need to spool up it could in theory be possible to switchthe gas turbine completely off when the available electric motor power is relatively large A furtherstudy could determine the optimal strategy that can be used during descent taking into accountany applicable regulations

The method for determining the battery cooling mass is very limited and most likely not veryaccurate A more detailed design study of a hybrid-electric aircraft will have to incorporate a bettermethod for sizing the battery cooling

No class 1 sizing method for hybrid-electric aircraft is implemented and the class 2 methodgives large errors in some cases (especially when using the constant gas-turbine operating mode)For this reason the time to converge for a hybrid-electric aircraft design is sometimes much longercompared to a conventional design Implementing a class 1 sizing method and updating the class2 method might improve this drastically although it will make no difference to the ultimate designIn order to further reduce the computational time required some more general optimization is alsopossible especially in the mission analysis

Since the power plant is such an important aspect of a hybrid-electric aircraft a more detailedstudy of the power plant should be done This would paint a better picture of the challenges op-portunities and limitations of such a power plant for aerospace applications It could also aid inproducing a more detailed sizing method

The used configuration for all hybrid-electric designs is based upon the Euroflyer [1] This con-figuration also incorporates boundary layer ingestion and contra-rotating propellers The benefits(and challenges) these aspects can provide are not taken into account Adding parts to the Initiatorwhich are able to compute the effects of the boundary layer ingestion and contra-rotating propellerswould take quite some time however it would be interesting to find out how much benefit can beachieved from this configuration

As is discussed in Section 424 no optimal split variation has been found so far It would bean interesting study to attempt to find such an optimum This would most likely include an opti-mization however since one design iteration can easily take more than 30 minutes either a lot ofcomputational power is required or some more optimization of the code has to occur

ADERIVATION OF HYBRID-ELECTRIC RANGE

EQUATION

The range is obtained from the following definite integralint t2

t1

V d t (A1)

usingdE

d t= Pbat +P f uel (A2)

Equation A1 becomes

R =int E f i nal

Est ar t

minus V

Pbat +P f ueldE

=int Est ar t

E f i nal

V

Pbat +P f ueldE

(A3)

Using

P f uel = Pg astur b lowastSFC lowaste f uel

= Psha f t lowast (1minusS)lowastSFC lowaste f uel(A4)

And

Pbat =S lowastPsha f t

ηel(A5)

The factor the range becomes

R =int Est ar t

E f i nal

V(Sηel

+ (1minusS)lowastSFC lowaste f uel

)lowastPsha f t

dE (A6)

During the cruise phase Psha f t is equal to

Psha f t =D lowastV

ηpr op(A7)

And

D = C D

C LlowastW (A8)

85

86 A DERIVATION OF HYBRID-ELECTRIC RANGE EQUATION

So VPsha f t

becomes

V

Psha f t= C L

C Dlowast ηpr op

W(A9)

As such Equation A6 becomes

R = 1Sηel

+ (1minusS)lowastSFC lowaste f uellowast C L

C Dlowastηpr op lowast

int Est ar t

E f i nal

1

WdE (A10)

Now we write the weight as a function of energy

W =Wempt y +Wbat +W f uel

=Wempt y + Ebat

ebat+ E f uel

e f uel

=Wempt y +Ebat lowaste f uel +E f uel lowastebat

e f uel lowastebat

(A11)

Now we introduce x = EbatEtot

So for S=1 x = 1 and for S=0 x=0

x = Ebat

Etot

= Ebat

Ebat +E f uel

=Eemηel

Eemηel

+Eg astur b lowastSFC lowaste f uel

(A12)

Using S = EemEsha f t

x = S lowastEsha f t

S lowastEsha f t + (1minusS)lowastEsha f t lowastSFC lowaste f uel lowastηel

= S

S + (1minusS)lowastSFC lowaste f uel lowastηel

(A13)

With x = EbatEtot

Equation A11 becomes

W =Wempt y +Ex lowaste f uel + (1minusx)lowastebat

e f uel lowastebat(A14)

The factorxlowaste f uel+(1minusx)lowastebat

e f uellowastebat(with x being defined in Equation A13) can be seen as the combined

specific energy of the batteries and fuel From now on this factor will be written as ecombi ned Assuch the range equation (Equation A10) becomes

R = 1Sηel



int Est ar t

E f i nal

1

Wempt y +E lowastecombi neddE (A15)

Since ecombi ned is constant for S = constant

R = 1Sηel


C Dlowastηpr op lowast 1


(ecombi ned lowastEst ar t +Wempt y

Wempt y

)(A16)

BIBLIOGRAPHY

[1] S Bosma A Eggermont R Heuijerjans F Kruijssen S Leest M Meijburg K Morias F v dOudenalder B Peerlings and K v Zomeren Euroflyer - an environmentally friendly regionalaircraft with a propulsive fuselage entering into service in 2035 Design Synthesis Exercise 2013- Delft University of Technology (2013)

[2] R Schiferl A Flory W C Livoti and S D Umans High-temperature superconducting syn-chronous motors Economic issues for industrial applications IEEE Transactions on IndustryApplications 44 1376 (2008) cited By 11 Export Date 8 January 2015

[3] Performance model Fokker 50 Report (Delft University of Technology 2010)

[4] C Perullo and D Mavris A review of hybrid-electric energy management and its inclusion invehicle sizing Aircraft Engineering and Aerospace Technology 86 550 (2014)

[5] Advisory Council for Aviation Research and Innovation in Europe (ACARE) Realising europersquosvision for aviation Strategic Research and Innovation Agenda 1 (2012)

[6] National Aeronautics and Space Administration Advanced concept studies for subsonic andsupersonic commercial transport entering service in 2030-35 period NASA Research Announce-ment Pre-Proposal Conference (2007)

[7] M K Bradley and C K Droney Subsonic ulta green aircraft research phase ii n+4 advancedconcept development NASA report NNL08AA16B (2012)

[8] S Bruner S Baber C Harris N Caldwell P Keding K Rahrig and L Pho Nasa n+3 subsonicfixed wing silent efficient low-emissions commercial transport (select) vehicle study NASA reportNNC08CA86C (2010)

[9] M K Bradley and C K Droney Subsonic ultra green aircraft research Phase 1 final reportBoeing Research amp Technology Huntington Beach California (2011)

[10] C Pornet C Gologan P C Vratny A Seitz O Schmitz A T Isikveren and M HornungMethodology for sizing and performance assessment of hybrid energy aircraft Journal of Aircraft 1 (2014)

[11] G E Bona M Bucari A Castagnoli and L Trainelli Flybrid Envisaging the future hybrid-powered regional aviation (2014) 10251462014-2733

[12] F Christian and A R Paul Design of hybrid-electric propulsion systems for light aircraft in 14thAIAA Aviation Technology Integration and Operations Conference AIAA Aviation (AmericanInstitute of Aeronautics and Astronautics 2014) doi10251462014-3008

[13] C C Chan A Bouscayrol and K Chen Electric hybrid and fuel-cell vehicles Architecturesand modeling Vehicular Technology IEEE Transactions on 59 589 (2010)

[14] S J Gerssen-Gondelach and A P C Faaij Performance of batteries for electric vehicles on shortand longer term Journal of Power Sources 212 111 (2012)

87

88 BIBLIOGRAPHY

[15] B Scrosati and J Garche Lithium batteries Status prospects and future Journal of PowerSources 195 2419 (2010)

[16] M Millikin Envia systems hits 400 whkg target with li-ion cells could lower li-ion cost to$180kwh Green Car Congress (2012)

[17] L F Nazar M Cuisinier and Q Pang Lithium-sulfur batteries MRS Bulletin 39 436 (2014)

[18] B Scrosati J Hassoun and Y K Sun Lithium-ion batteries a look into the future Energy ampEnvironmental Science 4 3287 (2011)

[19] S Stuckl J v Toor and H Lobentanzer Voltair - the all electric propulsion concept platform - avision for atmospheric friendly flight 28th international congress of the aeronautical sciences(2012)

[20] M-K Song Y Zhang and E J Cairns A long-life high-rate lithiumsulfur cell A multifacetedapproach to enhancing cell performance Nano Letters 13 5891 (2013)

[21] Y Mikhaylik I Kovalev R Schock K Kumaresan J Xu and J Affinito High energy rechargeableli-s cells for ev application status challenges and solutions Sion Power Corporation (2010)

[22] G Girishkumar B McCloskey A C Luntz S Swanson and W Wilcke Lithium-air batteryPromise and challenges The Journal of Physical Chemistry (2010) 101021jz1005384|J

[23] K Alexander and Y Ein-Eli Review on lindashair batteriesmdashopportunities limitations and perspec-tive Journal of Power Sources 196 886 (2011)

[24] H Kuhn A Seitz L Lorenz A Isikveren and A Sizmann Progress and perspectives of electricair transport 28th International congress of the aeronautical sciences (2012)

[25] H Kuhn and A Sizmann Fundamental prerequisites for electric flying Deutscher Luft- undRaumfahrtkongress 2012 (2012)

[26] L Johnson The viability of high specific energy lithium air batteries Symposium on ResearchOpportunities in Electrochemical Energy Storage - Beyond Lithium Ion Materials Perspectives(2010)

[27] K Rajashekara Present status and future trends in electric vehicle propulsion technologies Jour-nal of emerging and selected topics in power electronics 1 (2013)

[28] S W Ashcraft A S Padron K A Pascioni and G W Stout Review of propulsion technologiesfor n+3 subsonic vehicle concepts NASA report (2011)

[29] J C Mankins Technology readiness levels A white paper NASA (1995)

[30] P J Masson and C A Luongo High power density superconducting motor for all-electric aircraftpropulsion Applied Superconductivity IEEE Transactions on 15 2226 (2005)

[31] C A Luongo P J Masson T Nam D Mavris H D Kim G V Brown M Waters and D HallNext generation more-electric aircraft A potential application for hts superconductors AppliedSuperconductivity IEEE Transactions on 19 1055 (2009)

[32] M J Gouge J A Demko and B W McConnell Cryogenics assessment report Oak Ridge Na-tional Laboratory (2002)

BIBLIOGRAPHY 89

[33] K T Chau and Y S Wong Overview of power management in hybrid electric vehicles EnergyConversion and Management 43 1953 (2002)

[34] K Ccedilagatay Bayindir M A Goumlzuumlkuumlccediluumlk and A Teke A comprehensive overview of hybrid electricvehicle Powertrain configurations powertrain control techniques and electronic control unitsEnergy Conversion and Management 52 1305 (2011)

[35] J Y Hung and L F Gonzalez On parallel hybrid-electric propulsion system for unmanned aerialvehicles Progress in Aerospace Sciences 51 1 (2012)

[36] European Aviation Safety Agency Certification specifications for large aeroplanes cs-25(2007)

[37] Federal Aviation Administration Requisitos federal aviation regulations Part 25 - airworthi-ness standards Transport category airplanes ()

[38] F Christian and P Robertson Hybrid-electric propulsion for automotive and aviation applica-tions CEAS Aeronautical Journal 1 (2014)

[39] J A Rosero J A Ortega E Aldabas and L Romeral Moving towards a more electric aircraftAerospace and Electronic Systems Magazine IEEE 22 3 (2007)

[40] H Zhang C Saudemont B Robyns and M Petit Comparison of technical features between amore electric aircraft and a hybrid electric vehicle in Vehicle Power and Propulsion Conference2008 VPPC rsquo08 IEEE pp 1ndash6

[41] R Singh A T Isikveren S Kaiser C Pornet and P C Vratny Pre-design strategies and siz-ing techniques for dual-energy aircraft Aircraft Engineering and Aerospace Technology 86 525(2014)

[42] M Hoogreef Aircraft initiator manual

[43] MathWorksreg Matlab (httpnlmathworkscomproductsmatlab)

[44] D P Raymer Aircraft Design A conceptual Approach (American Institure of Aeronautics andAstronautics (AIAA) 1992)

[45] J Roskam Airplane Design Part II Preliminary Configuration Design and Integration of thePropulsion System (2013)

[46] J Ruijgrok Elements of airplane performance 2nd ed (VSSD Delft 2009)

[47] B Gerald Weights and efficiencies of electric components of a turboelectric aircraft propul-sion system in 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum andAerospace Exposition Aerospace Sciences Meetings (American Institute of Aeronautics and As-tronautics 2011) doi10251462011-225

[48] Synergy Cables Ltd Dataset of medium voltage power cables (2015)

[49] M J Hennessy Lightweight Efficient Power Converters for Advanced Turboelectric AircraftPropulsion Systems Report (NASA 2014)

[50] Federal Aviation Administration Part 23 ndash airworthiness standards Normal utility acrobaticand commuter airplanes ()

List of Figures

List of Tables

Introduction

Project Description

Configuration and Requirements

Technology Overview

Battery Technology

Electric Motor Technology

Power plant Architecture

Architecture Possibilities

Selected Architecture

Control Strategies

Important Parameters

Methodology

Initiator

Reference Aircraft Design

Engine and Propeller Sizing

Gas turbine power and fuel consumption variation

Other Modifications

Class 2 Battery and Fuel Sizing

Battery Sizing

Fuel


Take-off

Climb

Cruise

Descent

Landing

HoldLoiter

Comparison between Class 2 and Class 25 sizing

Mission analysis results

Comparison

Electric Motor Sizing

Wiring

Other Components

Component Placement

Implementation

Limitations

Results

Reference Aircraft

Hybrid Aircraft

Inputs

Supplied Power Ratio

Operating Modes

Optimal Power Split

Sensitivity Analysis

Range

Battery specific energy

Final Design

Conclusion amp Recommendations

Conclusion

Recommendations

Derivation of hybrid-electric range equation

Bibliography

ASSESSMENT OF POTENTIAL FUEL SAVINGBENEFITS OF HYBRID-ELECTRIC REGIONAL

AIRCRAFT

by

Joris Van Bogaert

in partial fulfillment of the requirements for the degree of

Master of Sciencein Aerospace Engineering

at the Delft University of Technologyto be defended publicly on Thursday December 17 2015

Supervisor Drir Mark VoskuijlDr Arvind G Rao

Thesis committee Dr Hans Mulder TU DelftSimon Tayler Fokker Elmo

This thesis is confidential and cannot be made public until December 31 2015

An electronic version of this thesis is available at httprepositorytudelftnlThesis registration number 06815MTFPP

PREFACE




iii

SUMMARY







v

vi PREFACE




CONTENTS

List of Figures ix

List of Tables xiii

1 Introduction 1

















332 Fuel 25


341 Take-off 32

342 Climb 36

343 Cruise 39

344 Descent 42

345 Landing 44

346 HoldLoiter 46



352 Comparison 51


37 Wiring 53




311 Limitations 56

vii

viii CONTENTS




44 Final Design 79



Bibliography 87

LIST OF FIGURES



34 Slope of PP0














ix

x LIST OF FIGURES


















LIST OF FIGURES xi


LIST OF TABLES








craft 80

xiii

NOMENCLATURE

Acronyms



FF Fuel fraction








SOC State of charge



Subscripts

bat Battery


em Electric motor


avg Average

cable Cable


cryo Cryocooler

disk Propeller disk


gasturb Gas turbine


xv

xvi LIST OF TABLES

prop Propeller


tot total

Symbols

∆ Change in [-]


η Efficiency [-]



ρ Density [ kgm3 ]

A Area [m2]






b Wing span [m]

D Drag [N]

d Diameter [m]

E Energy [Wh]

f Frequency [Hz]



h Altitude [m]

L Lift [N]

l Length [m]

m Mass [kg]

N number

P Power [W]

Q Heat energy [J]

LIST OF TABLES xvii

R Range [km]

S Power split [-]

T Thrust [N]

t time [sec]

U Voltage [V]

V Speed [ms]

1INTRODUCTION






1










3





bull Range 1528 km

















LITHIUM ION





LITHIUM SULPHUR










LITHIUM AIR








Ah



W h(21)

























9






















Power converter

Electric motor


Generator







Power converter

Electric motor

Gas turbine








ηbat ηEM

ηgasturb


Gas turbine

Pbat

PbatOffTake

Pem

Pgasturb

Pshaft

ηprop

Pfuel

ηelec







Si =Pemi

Psha f ti

(22)









HP = Pemmax

Psha f tmax

(23)

and

HE = Ebat

Etot(24)


Φ= Eemtot

Esha f ttot

(25)


3METHODOLOGY







15

16 3 METHODOLOGY

Class 1

Weight

Estimation

Wing- and

power

loading

Geometry

design

modules

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis

Performance

Estimation

Modules

Design

converged

Reference

aircraft

database

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis


Converged

No

Yes

No

Design

Yes


All modules
















Pg astur b

1000

)012

(31)


Pg astur b

1000

)0373

(32)


Pg astur b

1000

)0803

(33)


dpr op =radic

a2



18 3 METHODOLOGY


ηpr opi deal =2

1+(


2+1

)12(35)







P

P0=

(ρ

ρ0

)n

(36)





20 3 METHODOLOGY



0 01 02 03 04 05 06 07 08 09 1middot104

04

06

08

1

12

14

16

18middot106

Altitude [m]

Max

co

nti

no

us

pow

er[W

]



0 01 02 03 04 05 06 07 08 09 1middot104

04

05

06

07

08

09

1

11

Altitude [m]

( ρ ρ0

) n [-]

PP0(ρρ0

)n n=075





0 01 02 03 04 05 06 07 08 09 1middot104

60

80

100

120

140

Altitude [m]

Fuel

flow

[gs



0 01 02 03 04 05 06 07 08 09 1middot104

260

280

300

320

340

Altitude [m]

SFC

[g

kW

h]



22 3 METHODOLOGY

02 03 04 05 06 07 08 09 1280

300

320

340

360

Power setting [-]

SFC

[g

kW

h]







331 BATTERY SIZING








SFC(38)





24 3 METHODOLOGY



2(310)




ηpr op(311)


Pbat =Pem










Pt akeo f f(313)













LIMITATIONS




332 FUEL



26 3 METHODOLOGY




1000

1000(318)




SFC

L

Dln

(mpr ecr ui se

mendcr ui se

)(319)


R = 1Sηel





mempt y

)(320)







x = Ebat

Etot= S



CD Using



ebat(324)


e f uel(325)






bull ηel = 095 [-]


bull CLCD

= 20 [-]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

Power Split [-]

Mas

s[k

g]




28 3 METHODOLOGY


1 Standard Mission

bull Take off

bull Climb 1

bull Cruise 1

bull Descent 1

bull Landing 1

2 Extended Mission

bull Climb 2

bull Cruise 2

bull Descent 2

bull HoldLoiter

bull Descent 3

bull Landing 2

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 24000

02

04

06

08

1

12

14middot104

Clim

b1

Cruise 1

Des

cen

t1

Clim

b2

Cru

ise

2

Des

cen

t2

Loit

erD

esce

nt3

range (m)

alti

tud

e(m

)









sec




in the missionkg


kg


kg



30 3 METHODOLOGY




Start

Set initial

conditions of state

matrix S

Take-off

Climb 1

Cruise 1


Extended

cruise time

Extended

mission

Landing 1Landing 2


burn and battery

weight

Descent 3

Loiter

Descent 2

Cruise 2

Climb 2

Calculate diversion

Rrest Wfbrest

Calculate Rrest

Wfbrest

Fuel weight

converged

End

No

No

Yes

Yes

No

Yes


32 3 METHODOLOGY

341 TAKE-OFF







(Dpr op

2

)2)13

(326)














dEbat

d t= Pbat

3600(328)

dmbat

d t=

dEbatd t

ebat(329)

dm f uel










d t ispositive




V(332)


34 3 METHODOLOGY

0 01 02 03 04 05 06 07 08 09 10

5

10

15

alti

tud

e(m

)

0 01 02 03 04 05 06 07 08 09 10

20

40

60

spee

d(m

s)

0 01 02 03 04 05 06 07 08 09 102468

10

range (km)

γ(d

eg)



Aircraft on

ground

Determine

take-off

power

Initial aircraft

state

Relevant

settings

Select power

setting (1)

Calculate

static thrust

Calculate

propeller

efficiency

Calculate lift

and drag

Calculate

ground

friction drag

Yes

Determine

derivatives

No

Calculate

SFC

Constant power

operating mode

Calculate Pem Pbat

Pgasturb based on

the power split

No

Determine change

in battery and fuel

energy and weight

Calculate Pem Pbat

based on selected

Pgasturb

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Screen height

reached

Calculate

new thrust

No

End Yes


36 3 METHODOLOGY

342 CLIMB










0 20 40 60 80 100 120 140 1601

15

2

25

3

35

4middot106

Range [km]

Pow

er[W

]



0 20 40 60 80 100 120 140 1600

02040608

1middot104

alti

tud

e(m

)

0 20 40 60 80 100 120 140 1606080

100120140

spee

d(m

s)

0 20 40 60 80 100 120 140 1600

5

10

15

20

range (km)

γ(d

eg)


38 3 METHODOLOGY

Determine

maximum

power (take-

off power)

Aircraft state

at end take-off

Relevant

settings

Select

iteration

time step

Determine

drag polar

Calculate

propeller

efficiency

Calculate

thrust

Constant power

operating mode

Determine Pgasturb

based on power

splitNo

Scale max gas

turbine power

based on altitude

and speed

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

End

Calculate lift

and drag

Determine

derivatives

Pgasturb is maximum

gas turbine power

Pgasturb

more than max

turboprop

power

Yes

No

Determine power

setting

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight


Scale max gas

turbine power

based on altitude

and speed


Determine Pem and

Pbat

Cruise altitude

and speed

reachedYes

No



343 CRUISE







Psha f t =T lowastV

ηpr op(333)






40 3 METHODOLOGY


0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 14007500

7600

7700

7800

alti

tud

e(m

)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400139

1392139413961398

140

spee

d(m

s)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400minus05

0

05

1middot10minus2

range (km)

γ(d

eg)



Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

lift drag and

thrust

Calculate

propeller

efficiency

Constant power

operating mode

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Determine

derivatives

No

No

Determine

power

setting for

minimal SFC

Yes

Determine

Pshaft

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Scale max gas

turbine power

based on altitude

and speed

Determine Pgasturb

Battery not

charging and

battery energy

depleted

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Range reached

Yes

End Yes


42 3 METHODOLOGY

344 DESCENT









1360 1380 1400 1420 1440 1460 1480 1500 1520 15400

02040608

1middot104

alti

tud

e(m

)

1360 1380 1400 1420 1440 1460 1480 1500 1520 15406080

100120140

spee

d(m

s)

1360 1380 1400 1420 1440 1460 1480 1500 1520 1540minus15

minus10

minus5

0

range (km)

γ(d

eg)



Aircraft state

at end cruise

Relevant

settings


step

Scale maximum

Pgasturb based on

altitude and speed


Determine change

in aircraft weight


matrix

End

Calculate propeller

efficiency

Determine

derivatives

Descent altitude

reached

Yes

No

Calculate lift and

dragCalculate SFC

Determine Pem and

Pbat (= 0)

Determine Pgasturb

(= Pidle)

Determine change

in fuel weight (no

change in battery

weight)


44 3 METHODOLOGY

345 LANDING





15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

5

10

15

alti

tud

e(m

)

15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

20

40

60

spee

d(m

s)

15272 15273 15274 15275 15276 15277 15278 15279 1528 15281minus3

minus2

minus1

0

range (km)

γ(d

eg)




Determine

landing drag

polar

Aircraft state

at end take-off

Relevant

settings

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Calculate lift

and drag

No

Determine

Pshaft and

thrust

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Pgasturb = Pshaft

Scale max gas

turbine power

based on altitude

and speed

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Speed and

altitude = 0

Yes

End Yes

Aircraft on

ground

Determine

derivatives

Calculate ground

friction drag and

reverse thrust if

applicable

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Calculate SFC

Yes

No

Yes


46 3 METHODOLOGY

346 HOLDLOITER





L CD







Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Determine

CLCD for

max LD

No

Determine

max Pgasturb

and Pidle

Determine Pshaft

based on target

velocity

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Loiter time

reached

Yes

End Yes

Determine Pgasturb

Determine power

setting


48 3 METHODOLOGY









0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2middot104

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

alti

tud

e(m

)

0 200 400 600 800 1000 1200 1400 1600 1800 20000

50

100

150

spee

d(m

s)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus20

minus10

0

10

range (km)

γ(d

eg)


50 3 METHODOLOGY

0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2

25

3

35

4

45

5

middot106

Cli

mb

1Cruise

Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1000

2000

3000

4000

5000

Clim

b1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

range [km]

Mas

s[k

g]

Battery Fuel



352 COMPARISON





S = 100mfuel[kg] 0 0 00 mbat[kg] 5317 5635 + 60



S = 000mfuel[kg] 1735 1804 + 40 mbat[kg] 0 0 00





52 3 METHODOLOGY












37 WIRING 53

0 05 1 15 2 25 3middot106

0

50

100

150

200

250


Ele

ctri

cm

oto

r+

cryo

coo

ler

wei

ght[

kg]


37 WIRING




54 3 METHODOLOGY

100 150 200 250 300 350 400 4501

2

3

4

5

6

7

8


Cable current [A]

Cab

lew

eigh

t[kg

m]

















56 3 METHODOLOGY







1419000 pounds

311 LIMITATIONS 57





58 3 METHODOLOGY




-




kgWh


-


pack-


-



-





-


-



W

4RESULTS




68 -




59

60 4 RESULTS








62 4 RESULTS



22800 22340 - 20


393 392 - 03



421 INPUTS















64 4 RESULTS





0 01 02 03 04 05 06 07 08 09 10

05

1

middot104



Bat

tery

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

500

1000

1500

2000

2500



Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

1

2

3

4middot104



MT

OM

[kg]



66 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

2

4

6middot106


Max

imu

mP

em



0 01 02 03 04 05 06 07 080

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000


Gas

Turb

ine

Mas

s[k

g]



68 4 RESULTS

423 OPERATING MODES


0 01 02 03 04 05 06 07 08 09 10

05

1

15

2

25

3middot106


Max

imu

mC

on

tin

uo

us

Gas

Turb

ine

Pow

er[W

]






0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



70 4 RESULTS






0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

2000


Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

02

04

06

08

1

12middot104


Bat

tery

Mas

s[k

g]



72 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1

2

3

4

5

6middot106


Max

imu

mP

em[W



0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000


Gas

Turb

ine

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34

36

38

4middot104


MT

OM

[kg]



74 4 RESULTS







0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]


0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]







76 4 RESULTS


0 01 02 03 04 05 06 07 08 09 10

2000

4000

6000

8000


Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34middot104


MT

OM

[kg]



431 RANGE


78 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1000

2000

3000

4000

5000

6000


Fuel

wei

ght[

kg]



0 01 02 03 04 05 06 07 08 09 12

25

3

35

4middot104


MT

OW

[kg]



44 FINAL DESIGN 79



700 800 900 1000 1100 1200 1300 1400 1500800

1000

1200

1400

1600

1800

2000


Φ= 01

Φ= 02

Φ= 03

Φ= 04

Φ= 05

Φ= 06

Φ= 00

ebat [ W hkg ]

Fuel

Mas

s[k

g]




80 4 RESULTS






Difference


22340 25470 + 14


103 72 ndash 29


2619 2173 ndash 17





Difference


44 FINAL DESIGN 81

510

1520

25

minus10minus5

05

10

2

4

6

8




82 4 RESULTS







83












EQUATION


t1

V d t (A1)

usingdE


Equation A1 becomes

R =int E f i nal

Est ar t

minus V

Pbat +P f ueldE

=int Est ar t

E f i nal

V

Pbat +P f ueldE

(A3)

Using



And


ηel(A5)


R =int Est ar t

E f i nal

V(Sηel


)lowastPsha f t

dE (A6)


Psha f t =D lowastV

ηpr op(A7)

And

D = C D

C LlowastW (A8)

85


So VPsha f t

becomes

V

Psha f t= C L

C Dlowast ηpr op

W(A9)


R = 1Sηel



int Est ar t

E f i nal

1

WdE (A10)



=Wempt y + Ebat

ebat+ E f uel

e f uel


e f uel lowastebat

(A11)



x = Ebat

Etot

= Ebat

Ebat +E f uel

=Eemηel

Eemηel


(A12)




= S


(A13)

With x = EbatEtot







R = 1Sηel



int Est ar t

E f i nal

1



R = 1Sηel





Wempt y

)(A16)

BIBLIOGRAPHY















87

88 BIBLIOGRAPHY



















BIBLIOGRAPHY 89



















List of Figures

List of Tables

Introduction

Project Description


Technology Overview

Battery Technology





Control Strategies


Methodology

Initiator




Other Modifications


Battery Sizing

Fuel


Take-off

Climb

Cruise

Descent

Landing

HoldLoiter



Comparison


Wiring

Other Components

Component Placement

Implementation

Limitations

Results

Reference Aircraft

Hybrid Aircraft

Inputs


Operating Modes

Optimal Power Split


Range


Final Design


Conclusion

Recommendations


Bibliography

PREFACE




iii

SUMMARY







v

vi PREFACE




CONTENTS

List of Figures ix

List of Tables xiii

1 Introduction 1

















332 Fuel 25


341 Take-off 32

342 Climb 36

343 Cruise 39

344 Descent 42

345 Landing 44

346 HoldLoiter 46



352 Comparison 51


37 Wiring 53




311 Limitations 56

vii

viii CONTENTS




44 Final Design 79



Bibliography 87

LIST OF FIGURES



34 Slope of PP0














ix

x LIST OF FIGURES


















LIST OF FIGURES xi


LIST OF TABLES








craft 80

xiii

NOMENCLATURE

Acronyms



FF Fuel fraction








SOC State of charge



Subscripts

bat Battery


em Electric motor


avg Average

cable Cable


cryo Cryocooler

disk Propeller disk


gasturb Gas turbine


xv

xvi LIST OF TABLES

prop Propeller


tot total

Symbols

∆ Change in [-]


η Efficiency [-]



ρ Density [ kgm3 ]

A Area [m2]






b Wing span [m]

D Drag [N]

d Diameter [m]

E Energy [Wh]

f Frequency [Hz]



h Altitude [m]

L Lift [N]

l Length [m]

m Mass [kg]

N number

P Power [W]

Q Heat energy [J]

LIST OF TABLES xvii

R Range [km]

S Power split [-]

T Thrust [N]

t time [sec]

U Voltage [V]

V Speed [ms]

1INTRODUCTION






1










3





bull Range 1528 km

















LITHIUM ION





LITHIUM SULPHUR










LITHIUM AIR








Ah



W h(21)

























9






















Power converter

Electric motor


Generator







Power converter

Electric motor

Gas turbine








ηbat ηEM

ηgasturb


Gas turbine

Pbat

PbatOffTake

Pem

Pgasturb

Pshaft

ηprop

Pfuel

ηelec







Si =Pemi

Psha f ti

(22)









HP = Pemmax

Psha f tmax

(23)

and

HE = Ebat

Etot(24)


Φ= Eemtot

Esha f ttot

(25)


3METHODOLOGY







15

16 3 METHODOLOGY

Class 1

Weight

Estimation

Wing- and

power

loading

Geometry

design

modules

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis

Performance

Estimation

Modules

Design

converged

Reference

aircraft

database

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis


Converged

No

Yes

No

Design

Yes


All modules
















Pg astur b

1000

)012

(31)


Pg astur b

1000

)0373

(32)


Pg astur b

1000

)0803

(33)


dpr op =radic

a2



18 3 METHODOLOGY


ηpr opi deal =2

1+(


2+1

)12(35)







P

P0=

(ρ

ρ0

)n

(36)





20 3 METHODOLOGY



0 01 02 03 04 05 06 07 08 09 1middot104

04

06

08

1

12

14

16

18middot106

Altitude [m]

Max

co

nti

no

us

pow

er[W

]



0 01 02 03 04 05 06 07 08 09 1middot104

04

05

06

07

08

09

1

11

Altitude [m]

( ρ ρ0

) n [-]

PP0(ρρ0

)n n=075





0 01 02 03 04 05 06 07 08 09 1middot104

60

80

100

120

140

Altitude [m]

Fuel

flow

[gs



0 01 02 03 04 05 06 07 08 09 1middot104

260

280

300

320

340

Altitude [m]

SFC

[g

kW

h]



22 3 METHODOLOGY

02 03 04 05 06 07 08 09 1280

300

320

340

360

Power setting [-]

SFC

[g

kW

h]







331 BATTERY SIZING








SFC(38)





24 3 METHODOLOGY



2(310)




ηpr op(311)


Pbat =Pem










Pt akeo f f(313)













LIMITATIONS




332 FUEL



26 3 METHODOLOGY




1000

1000(318)




SFC

L

Dln

(mpr ecr ui se

mendcr ui se

)(319)


R = 1Sηel





mempt y

)(320)







x = Ebat

Etot= S



CD Using



ebat(324)


e f uel(325)






bull ηel = 095 [-]


bull CLCD

= 20 [-]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

Power Split [-]

Mas

s[k

g]




28 3 METHODOLOGY


1 Standard Mission

bull Take off

bull Climb 1

bull Cruise 1

bull Descent 1

bull Landing 1

2 Extended Mission

bull Climb 2

bull Cruise 2

bull Descent 2

bull HoldLoiter

bull Descent 3

bull Landing 2

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 24000

02

04

06

08

1

12

14middot104

Clim

b1

Cruise 1

Des

cen

t1

Clim

b2

Cru

ise

2

Des

cen

t2

Loit

erD

esce

nt3

range (m)

alti

tud

e(m

)









sec




in the missionkg


kg


kg



30 3 METHODOLOGY




Start

Set initial

conditions of state

matrix S

Take-off

Climb 1

Cruise 1


Extended

cruise time

Extended

mission

Landing 1Landing 2


burn and battery

weight

Descent 3

Loiter

Descent 2

Cruise 2

Climb 2

Calculate diversion

Rrest Wfbrest

Calculate Rrest

Wfbrest

Fuel weight

converged

End

No

No

Yes

Yes

No

Yes


32 3 METHODOLOGY

341 TAKE-OFF







(Dpr op

2

)2)13

(326)














dEbat

d t= Pbat

3600(328)

dmbat

d t=

dEbatd t

ebat(329)

dm f uel










d t ispositive




V(332)


34 3 METHODOLOGY

0 01 02 03 04 05 06 07 08 09 10

5

10

15

alti

tud

e(m

)

0 01 02 03 04 05 06 07 08 09 10

20

40

60

spee

d(m

s)

0 01 02 03 04 05 06 07 08 09 102468

10

range (km)

γ(d

eg)



Aircraft on

ground

Determine

take-off

power

Initial aircraft

state

Relevant

settings

Select power

setting (1)

Calculate

static thrust

Calculate

propeller

efficiency

Calculate lift

and drag

Calculate

ground

friction drag

Yes

Determine

derivatives

No

Calculate

SFC

Constant power

operating mode

Calculate Pem Pbat

Pgasturb based on

the power split

No

Determine change

in battery and fuel

energy and weight

Calculate Pem Pbat

based on selected

Pgasturb

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Screen height

reached

Calculate

new thrust

No

End Yes


36 3 METHODOLOGY

342 CLIMB










0 20 40 60 80 100 120 140 1601

15

2

25

3

35

4middot106

Range [km]

Pow

er[W

]



0 20 40 60 80 100 120 140 1600

02040608

1middot104

alti

tud

e(m

)

0 20 40 60 80 100 120 140 1606080

100120140

spee

d(m

s)

0 20 40 60 80 100 120 140 1600

5

10

15

20

range (km)

γ(d

eg)


38 3 METHODOLOGY

Determine

maximum

power (take-

off power)

Aircraft state

at end take-off

Relevant

settings

Select

iteration

time step

Determine

drag polar

Calculate

propeller

efficiency

Calculate

thrust

Constant power

operating mode

Determine Pgasturb

based on power

splitNo

Scale max gas

turbine power

based on altitude

and speed

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

End

Calculate lift

and drag

Determine

derivatives

Pgasturb is maximum

gas turbine power

Pgasturb

more than max

turboprop

power

Yes

No

Determine power

setting

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight


Scale max gas

turbine power

based on altitude

and speed


Determine Pem and

Pbat

Cruise altitude

and speed

reachedYes

No



343 CRUISE







Psha f t =T lowastV

ηpr op(333)






40 3 METHODOLOGY


0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 14007500

7600

7700

7800

alti

tud

e(m

)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400139

1392139413961398

140

spee

d(m

s)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400minus05

0

05

1middot10minus2

range (km)

γ(d

eg)



Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

lift drag and

thrust

Calculate

propeller

efficiency

Constant power

operating mode

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Determine

derivatives

No

No

Determine

power

setting for

minimal SFC

Yes

Determine

Pshaft

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Scale max gas

turbine power

based on altitude

and speed

Determine Pgasturb

Battery not

charging and

battery energy

depleted

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Range reached

Yes

End Yes


42 3 METHODOLOGY

344 DESCENT









1360 1380 1400 1420 1440 1460 1480 1500 1520 15400

02040608

1middot104

alti

tud

e(m

)

1360 1380 1400 1420 1440 1460 1480 1500 1520 15406080

100120140

spee

d(m

s)

1360 1380 1400 1420 1440 1460 1480 1500 1520 1540minus15

minus10

minus5

0

range (km)

γ(d

eg)



Aircraft state

at end cruise

Relevant

settings


step

Scale maximum

Pgasturb based on

altitude and speed


Determine change

in aircraft weight


matrix

End

Calculate propeller

efficiency

Determine

derivatives

Descent altitude

reached

Yes

No

Calculate lift and

dragCalculate SFC

Determine Pem and

Pbat (= 0)

Determine Pgasturb

(= Pidle)

Determine change

in fuel weight (no

change in battery

weight)


44 3 METHODOLOGY

345 LANDING





15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

5

10

15

alti

tud

e(m

)

15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

20

40

60

spee

d(m

s)

15272 15273 15274 15275 15276 15277 15278 15279 1528 15281minus3

minus2

minus1

0

range (km)

γ(d

eg)




Determine

landing drag

polar

Aircraft state

at end take-off

Relevant

settings

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Calculate lift

and drag

No

Determine

Pshaft and

thrust

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Pgasturb = Pshaft

Scale max gas

turbine power

based on altitude

and speed

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Speed and

altitude = 0

Yes

End Yes

Aircraft on

ground

Determine

derivatives

Calculate ground

friction drag and

reverse thrust if

applicable

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Calculate SFC

Yes

No

Yes


46 3 METHODOLOGY

346 HOLDLOITER





L CD







Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Determine

CLCD for

max LD

No

Determine

max Pgasturb

and Pidle

Determine Pshaft

based on target

velocity

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Loiter time

reached

Yes

End Yes

Determine Pgasturb

Determine power

setting


48 3 METHODOLOGY









0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2middot104

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

alti

tud

e(m

)

0 200 400 600 800 1000 1200 1400 1600 1800 20000

50

100

150

spee

d(m

s)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus20

minus10

0

10

range (km)

γ(d

eg)


50 3 METHODOLOGY

0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2

25

3

35

4

45

5

middot106

Cli

mb

1Cruise

Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1000

2000

3000

4000

5000

Clim

b1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

range [km]

Mas

s[k

g]

Battery Fuel



352 COMPARISON





S = 100mfuel[kg] 0 0 00 mbat[kg] 5317 5635 + 60



S = 000mfuel[kg] 1735 1804 + 40 mbat[kg] 0 0 00





52 3 METHODOLOGY












37 WIRING 53

0 05 1 15 2 25 3middot106

0

50

100

150

200

250


Ele

ctri

cm

oto

r+

cryo

coo

ler

wei

ght[

kg]


37 WIRING




54 3 METHODOLOGY

100 150 200 250 300 350 400 4501

2

3

4

5

6

7

8


Cable current [A]

Cab

lew

eigh

t[kg

m]

















56 3 METHODOLOGY







1419000 pounds

311 LIMITATIONS 57





58 3 METHODOLOGY




-




kgWh


-


pack-


-



-





-


-



W

4RESULTS




68 -




59

60 4 RESULTS








62 4 RESULTS



22800 22340 - 20


393 392 - 03



421 INPUTS















64 4 RESULTS





0 01 02 03 04 05 06 07 08 09 10

05

1

middot104



Bat

tery

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

500

1000

1500

2000

2500



Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

1

2

3

4middot104



MT

OM

[kg]



66 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

2

4

6middot106


Max

imu

mP

em



0 01 02 03 04 05 06 07 080

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000


Gas

Turb

ine

Mas

s[k

g]



68 4 RESULTS

423 OPERATING MODES


0 01 02 03 04 05 06 07 08 09 10

05

1

15

2

25

3middot106


Max

imu

mC

on

tin

uo

us

Gas

Turb

ine

Pow

er[W

]






0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



70 4 RESULTS






0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

2000


Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

02

04

06

08

1

12middot104


Bat

tery

Mas

s[k

g]



72 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1

2

3

4

5

6middot106


Max

imu

mP

em[W



0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000


Gas

Turb

ine

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34

36

38

4middot104


MT

OM

[kg]



74 4 RESULTS







0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]


0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]







76 4 RESULTS


0 01 02 03 04 05 06 07 08 09 10

2000

4000

6000

8000


Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34middot104


MT

OM

[kg]



431 RANGE


78 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1000

2000

3000

4000

5000

6000


Fuel

wei

ght[

kg]



0 01 02 03 04 05 06 07 08 09 12

25

3

35

4middot104


MT

OW

[kg]



44 FINAL DESIGN 79



700 800 900 1000 1100 1200 1300 1400 1500800

1000

1200

1400

1600

1800

2000


Φ= 01

Φ= 02

Φ= 03

Φ= 04

Φ= 05

Φ= 06

Φ= 00

ebat [ W hkg ]

Fuel

Mas

s[k

g]




80 4 RESULTS






Difference


22340 25470 + 14


103 72 ndash 29


2619 2173 ndash 17





Difference


44 FINAL DESIGN 81

510

1520

25

minus10minus5

05

10

2

4

6

8




82 4 RESULTS







83












EQUATION


t1

V d t (A1)

usingdE


Equation A1 becomes

R =int E f i nal

Est ar t

minus V

Pbat +P f ueldE

=int Est ar t

E f i nal

V

Pbat +P f ueldE

(A3)

Using



And


ηel(A5)


R =int Est ar t

E f i nal

V(Sηel


)lowastPsha f t

dE (A6)


Psha f t =D lowastV

ηpr op(A7)

And

D = C D

C LlowastW (A8)

85


So VPsha f t

becomes

V

Psha f t= C L

C Dlowast ηpr op

W(A9)


R = 1Sηel



int Est ar t

E f i nal

1

WdE (A10)



=Wempt y + Ebat

ebat+ E f uel

e f uel


e f uel lowastebat

(A11)



x = Ebat

Etot

= Ebat

Ebat +E f uel

=Eemηel

Eemηel


(A12)




= S


(A13)

With x = EbatEtot







R = 1Sηel



int Est ar t

E f i nal

1



R = 1Sηel





Wempt y

)(A16)

BIBLIOGRAPHY















87

88 BIBLIOGRAPHY



















BIBLIOGRAPHY 89



















List of Figures

List of Tables

Introduction

Project Description


Technology Overview

Battery Technology





Control Strategies


Methodology

Initiator




Other Modifications


Battery Sizing

Fuel


Take-off

Climb

Cruise

Descent

Landing

HoldLoiter



Comparison


Wiring

Other Components

Component Placement

Implementation

Limitations

Results

Reference Aircraft

Hybrid Aircraft

Inputs


Operating Modes

Optimal Power Split


Range


Final Design


Conclusion

Recommendations


Bibliography

SUMMARY







v

vi PREFACE




CONTENTS

List of Figures ix

List of Tables xiii

1 Introduction 1

















332 Fuel 25


341 Take-off 32

342 Climb 36

343 Cruise 39

344 Descent 42

345 Landing 44

346 HoldLoiter 46



352 Comparison 51


37 Wiring 53




311 Limitations 56

vii

viii CONTENTS




44 Final Design 79



Bibliography 87

LIST OF FIGURES



34 Slope of PP0














ix

x LIST OF FIGURES


















LIST OF FIGURES xi


LIST OF TABLES








craft 80

xiii

NOMENCLATURE

Acronyms



FF Fuel fraction








SOC State of charge



Subscripts

bat Battery


em Electric motor


avg Average

cable Cable


cryo Cryocooler

disk Propeller disk


gasturb Gas turbine


xv

xvi LIST OF TABLES

prop Propeller


tot total

Symbols

∆ Change in [-]


η Efficiency [-]



ρ Density [ kgm3 ]

A Area [m2]






b Wing span [m]

D Drag [N]

d Diameter [m]

E Energy [Wh]

f Frequency [Hz]



h Altitude [m]

L Lift [N]

l Length [m]

m Mass [kg]

N number

P Power [W]

Q Heat energy [J]

LIST OF TABLES xvii

R Range [km]

S Power split [-]

T Thrust [N]

t time [sec]

U Voltage [V]

V Speed [ms]

1INTRODUCTION






1










3





bull Range 1528 km

















LITHIUM ION





LITHIUM SULPHUR










LITHIUM AIR








Ah



W h(21)

























9






















Power converter

Electric motor


Generator







Power converter

Electric motor

Gas turbine








ηbat ηEM

ηgasturb


Gas turbine

Pbat

PbatOffTake

Pem

Pgasturb

Pshaft

ηprop

Pfuel

ηelec







Si =Pemi

Psha f ti

(22)









HP = Pemmax

Psha f tmax

(23)

and

HE = Ebat

Etot(24)


Φ= Eemtot

Esha f ttot

(25)


3METHODOLOGY







15

16 3 METHODOLOGY

Class 1

Weight

Estimation

Wing- and

power

loading

Geometry

design

modules

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis

Performance

Estimation

Modules

Design

converged

Reference

aircraft

database

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis


Converged

No

Yes

No

Design

Yes


All modules
















Pg astur b

1000

)012

(31)


Pg astur b

1000

)0373

(32)


Pg astur b

1000

)0803

(33)


dpr op =radic

a2



18 3 METHODOLOGY


ηpr opi deal =2

1+(


2+1

)12(35)







P

P0=

(ρ

ρ0

)n

(36)





20 3 METHODOLOGY



0 01 02 03 04 05 06 07 08 09 1middot104

04

06

08

1

12

14

16

18middot106

Altitude [m]

Max

co

nti

no

us

pow

er[W

]



0 01 02 03 04 05 06 07 08 09 1middot104

04

05

06

07

08

09

1

11

Altitude [m]

( ρ ρ0

) n [-]

PP0(ρρ0

)n n=075





0 01 02 03 04 05 06 07 08 09 1middot104

60

80

100

120

140

Altitude [m]

Fuel

flow

[gs



0 01 02 03 04 05 06 07 08 09 1middot104

260

280

300

320

340

Altitude [m]

SFC

[g

kW

h]



22 3 METHODOLOGY

02 03 04 05 06 07 08 09 1280

300

320

340

360

Power setting [-]

SFC

[g

kW

h]







331 BATTERY SIZING








SFC(38)





24 3 METHODOLOGY



2(310)




ηpr op(311)


Pbat =Pem










Pt akeo f f(313)













LIMITATIONS




332 FUEL



26 3 METHODOLOGY




1000

1000(318)




SFC

L

Dln

(mpr ecr ui se

mendcr ui se

)(319)


R = 1Sηel





mempt y

)(320)







x = Ebat

Etot= S



CD Using



ebat(324)


e f uel(325)






bull ηel = 095 [-]


bull CLCD

= 20 [-]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

Power Split [-]

Mas

s[k

g]




28 3 METHODOLOGY


1 Standard Mission

bull Take off

bull Climb 1

bull Cruise 1

bull Descent 1

bull Landing 1

2 Extended Mission

bull Climb 2

bull Cruise 2

bull Descent 2

bull HoldLoiter

bull Descent 3

bull Landing 2

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 24000

02

04

06

08

1

12

14middot104

Clim

b1

Cruise 1

Des

cen

t1

Clim

b2

Cru

ise

2

Des

cen

t2

Loit

erD

esce

nt3

range (m)

alti

tud

e(m

)









sec




in the missionkg


kg


kg



30 3 METHODOLOGY




Start

Set initial

conditions of state

matrix S

Take-off

Climb 1

Cruise 1


Extended

cruise time

Extended

mission

Landing 1Landing 2


burn and battery

weight

Descent 3

Loiter

Descent 2

Cruise 2

Climb 2

Calculate diversion

Rrest Wfbrest

Calculate Rrest

Wfbrest

Fuel weight

converged

End

No

No

Yes

Yes

No

Yes


32 3 METHODOLOGY

341 TAKE-OFF







(Dpr op

2

)2)13

(326)














dEbat

d t= Pbat

3600(328)

dmbat

d t=

dEbatd t

ebat(329)

dm f uel










d t ispositive




V(332)


34 3 METHODOLOGY

0 01 02 03 04 05 06 07 08 09 10

5

10

15

alti

tud

e(m

)

0 01 02 03 04 05 06 07 08 09 10

20

40

60

spee

d(m

s)

0 01 02 03 04 05 06 07 08 09 102468

10

range (km)

γ(d

eg)



Aircraft on

ground

Determine

take-off

power

Initial aircraft

state

Relevant

settings

Select power

setting (1)

Calculate

static thrust

Calculate

propeller

efficiency

Calculate lift

and drag

Calculate

ground

friction drag

Yes

Determine

derivatives

No

Calculate

SFC

Constant power

operating mode

Calculate Pem Pbat

Pgasturb based on

the power split

No

Determine change

in battery and fuel

energy and weight

Calculate Pem Pbat

based on selected

Pgasturb

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Screen height

reached

Calculate

new thrust

No

End Yes


36 3 METHODOLOGY

342 CLIMB










0 20 40 60 80 100 120 140 1601

15

2

25

3

35

4middot106

Range [km]

Pow

er[W

]



0 20 40 60 80 100 120 140 1600

02040608

1middot104

alti

tud

e(m

)

0 20 40 60 80 100 120 140 1606080

100120140

spee

d(m

s)

0 20 40 60 80 100 120 140 1600

5

10

15

20

range (km)

γ(d

eg)


38 3 METHODOLOGY

Determine

maximum

power (take-

off power)

Aircraft state

at end take-off

Relevant

settings

Select

iteration

time step

Determine

drag polar

Calculate

propeller

efficiency

Calculate

thrust

Constant power

operating mode

Determine Pgasturb

based on power

splitNo

Scale max gas

turbine power

based on altitude

and speed

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

End

Calculate lift

and drag

Determine

derivatives

Pgasturb is maximum

gas turbine power

Pgasturb

more than max

turboprop

power

Yes

No

Determine power

setting

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight


Scale max gas

turbine power

based on altitude

and speed


Determine Pem and

Pbat

Cruise altitude

and speed

reachedYes

No



343 CRUISE







Psha f t =T lowastV

ηpr op(333)






40 3 METHODOLOGY


0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 14007500

7600

7700

7800

alti

tud

e(m

)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400139

1392139413961398

140

spee

d(m

s)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400minus05

0

05

1middot10minus2

range (km)

γ(d

eg)



Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

lift drag and

thrust

Calculate

propeller

efficiency

Constant power

operating mode

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Determine

derivatives

No

No

Determine

power

setting for

minimal SFC

Yes

Determine

Pshaft

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Scale max gas

turbine power

based on altitude

and speed

Determine Pgasturb

Battery not

charging and

battery energy

depleted

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Range reached

Yes

End Yes


42 3 METHODOLOGY

344 DESCENT









1360 1380 1400 1420 1440 1460 1480 1500 1520 15400

02040608

1middot104

alti

tud

e(m

)

1360 1380 1400 1420 1440 1460 1480 1500 1520 15406080

100120140

spee

d(m

s)

1360 1380 1400 1420 1440 1460 1480 1500 1520 1540minus15

minus10

minus5

0

range (km)

γ(d

eg)



Aircraft state

at end cruise

Relevant

settings


step

Scale maximum

Pgasturb based on

altitude and speed


Determine change

in aircraft weight


matrix

End

Calculate propeller

efficiency

Determine

derivatives

Descent altitude

reached

Yes

No

Calculate lift and

dragCalculate SFC

Determine Pem and

Pbat (= 0)

Determine Pgasturb

(= Pidle)

Determine change

in fuel weight (no

change in battery

weight)


44 3 METHODOLOGY

345 LANDING





15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

5

10

15

alti

tud

e(m

)

15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

20

40

60

spee

d(m

s)

15272 15273 15274 15275 15276 15277 15278 15279 1528 15281minus3

minus2

minus1

0

range (km)

γ(d

eg)




Determine

landing drag

polar

Aircraft state

at end take-off

Relevant

settings

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Calculate lift

and drag

No

Determine

Pshaft and

thrust

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Pgasturb = Pshaft

Scale max gas

turbine power

based on altitude

and speed

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Speed and

altitude = 0

Yes

End Yes

Aircraft on

ground

Determine

derivatives

Calculate ground

friction drag and

reverse thrust if

applicable

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Calculate SFC

Yes

No

Yes


46 3 METHODOLOGY

346 HOLDLOITER





L CD







Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Determine

CLCD for

max LD

No

Determine

max Pgasturb

and Pidle

Determine Pshaft

based on target

velocity

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Loiter time

reached

Yes

End Yes

Determine Pgasturb

Determine power

setting


48 3 METHODOLOGY









0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2middot104

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

alti

tud

e(m

)

0 200 400 600 800 1000 1200 1400 1600 1800 20000

50

100

150

spee

d(m

s)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus20

minus10

0

10

range (km)

γ(d

eg)


50 3 METHODOLOGY

0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2

25

3

35

4

45

5

middot106

Cli

mb

1Cruise

Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1000

2000

3000

4000

5000

Clim

b1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

range [km]

Mas

s[k

g]

Battery Fuel



352 COMPARISON





S = 100mfuel[kg] 0 0 00 mbat[kg] 5317 5635 + 60



S = 000mfuel[kg] 1735 1804 + 40 mbat[kg] 0 0 00





52 3 METHODOLOGY












37 WIRING 53

0 05 1 15 2 25 3middot106

0

50

100

150

200

250


Ele

ctri

cm

oto

r+

cryo

coo

ler

wei

ght[

kg]


37 WIRING




54 3 METHODOLOGY

100 150 200 250 300 350 400 4501

2

3

4

5

6

7

8


Cable current [A]

Cab

lew

eigh

t[kg

m]

















56 3 METHODOLOGY







1419000 pounds

311 LIMITATIONS 57





58 3 METHODOLOGY




-




kgWh


-


pack-


-



-





-


-



W

4RESULTS




68 -




59

60 4 RESULTS








62 4 RESULTS



22800 22340 - 20


393 392 - 03



421 INPUTS















64 4 RESULTS





0 01 02 03 04 05 06 07 08 09 10

05

1

middot104



Bat

tery

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

500

1000

1500

2000

2500



Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

1

2

3

4middot104



MT

OM

[kg]



66 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

2

4

6middot106


Max

imu

mP

em



0 01 02 03 04 05 06 07 080

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000


Gas

Turb

ine

Mas

s[k

g]



68 4 RESULTS

423 OPERATING MODES


0 01 02 03 04 05 06 07 08 09 10

05

1

15

2

25

3middot106


Max

imu

mC

on

tin

uo

us

Gas

Turb

ine

Pow

er[W

]






0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



70 4 RESULTS






0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

2000


Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

02

04

06

08

1

12middot104


Bat

tery

Mas

s[k

g]



72 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1

2

3

4

5

6middot106


Max

imu

mP

em[W



0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000


Gas

Turb

ine

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34

36

38

4middot104


MT

OM

[kg]



74 4 RESULTS







0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]


0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]







76 4 RESULTS


0 01 02 03 04 05 06 07 08 09 10

2000

4000

6000

8000


Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34middot104


MT

OM

[kg]



431 RANGE


78 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1000

2000

3000

4000

5000

6000


Fuel

wei

ght[

kg]



0 01 02 03 04 05 06 07 08 09 12

25

3

35

4middot104


MT

OW

[kg]



44 FINAL DESIGN 79



700 800 900 1000 1100 1200 1300 1400 1500800

1000

1200

1400

1600

1800

2000


Φ= 01

Φ= 02

Φ= 03

Φ= 04

Φ= 05

Φ= 06

Φ= 00

ebat [ W hkg ]

Fuel

Mas

s[k

g]




80 4 RESULTS






Difference


22340 25470 + 14


103 72 ndash 29


2619 2173 ndash 17





Difference


44 FINAL DESIGN 81

510

1520

25

minus10minus5

05

10

2

4

6

8




82 4 RESULTS







83












EQUATION


t1

V d t (A1)

usingdE


Equation A1 becomes

R =int E f i nal

Est ar t

minus V

Pbat +P f ueldE

=int Est ar t

E f i nal

V

Pbat +P f ueldE

(A3)

Using



And


ηel(A5)


R =int Est ar t

E f i nal

V(Sηel


)lowastPsha f t

dE (A6)


Psha f t =D lowastV

ηpr op(A7)

And

D = C D

C LlowastW (A8)

85


So VPsha f t

becomes

V

Psha f t= C L

C Dlowast ηpr op

W(A9)


R = 1Sηel



int Est ar t

E f i nal

1

WdE (A10)



=Wempt y + Ebat

ebat+ E f uel

e f uel


e f uel lowastebat

(A11)



x = Ebat

Etot

= Ebat

Ebat +E f uel

=Eemηel

Eemηel


(A12)




= S


(A13)

With x = EbatEtot







R = 1Sηel



int Est ar t

E f i nal

1



R = 1Sηel





Wempt y

)(A16)

BIBLIOGRAPHY















87

88 BIBLIOGRAPHY



















BIBLIOGRAPHY 89



















List of Figures

List of Tables

Introduction

Project Description


Technology Overview

Battery Technology





Control Strategies


Methodology

Initiator




Other Modifications


Battery Sizing

Fuel


Take-off

Climb

Cruise

Descent

Landing

HoldLoiter



Comparison


Wiring

Other Components

Component Placement

Implementation

Limitations

Results

Reference Aircraft

Hybrid Aircraft

Inputs


Operating Modes

Optimal Power Split


Range


Final Design


Conclusion

Recommendations


Bibliography

vi PREFACE




CONTENTS

List of Figures ix

List of Tables xiii

1 Introduction 1

















332 Fuel 25


341 Take-off 32

342 Climb 36

343 Cruise 39

344 Descent 42

345 Landing 44

346 HoldLoiter 46



352 Comparison 51


37 Wiring 53




311 Limitations 56

vii

viii CONTENTS




44 Final Design 79



Bibliography 87

LIST OF FIGURES



34 Slope of PP0














ix

x LIST OF FIGURES


















LIST OF FIGURES xi


LIST OF TABLES








craft 80

xiii

NOMENCLATURE

Acronyms



FF Fuel fraction








SOC State of charge



Subscripts

bat Battery


em Electric motor


avg Average

cable Cable


cryo Cryocooler

disk Propeller disk


gasturb Gas turbine


xv

xvi LIST OF TABLES

prop Propeller


tot total

Symbols

∆ Change in [-]


η Efficiency [-]



ρ Density [ kgm3 ]

A Area [m2]






b Wing span [m]

D Drag [N]

d Diameter [m]

E Energy [Wh]

f Frequency [Hz]



h Altitude [m]

L Lift [N]

l Length [m]

m Mass [kg]

N number

P Power [W]

Q Heat energy [J]

LIST OF TABLES xvii

R Range [km]

S Power split [-]

T Thrust [N]

t time [sec]

U Voltage [V]

V Speed [ms]

1INTRODUCTION






1










3





bull Range 1528 km

















LITHIUM ION





LITHIUM SULPHUR










LITHIUM AIR








Ah



W h(21)

























9






















Power converter

Electric motor


Generator







Power converter

Electric motor

Gas turbine








ηbat ηEM

ηgasturb


Gas turbine

Pbat

PbatOffTake

Pem

Pgasturb

Pshaft

ηprop

Pfuel

ηelec







Si =Pemi

Psha f ti

(22)









HP = Pemmax

Psha f tmax

(23)

and

HE = Ebat

Etot(24)


Φ= Eemtot

Esha f ttot

(25)


3METHODOLOGY







15

16 3 METHODOLOGY

Class 1

Weight

Estimation

Wing- and

power

loading

Geometry

design

modules

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis

Performance

Estimation

Modules

Design

converged

Reference

aircraft

database

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis


Converged

No

Yes

No

Design

Yes


All modules
















Pg astur b

1000

)012

(31)


Pg astur b

1000

)0373

(32)


Pg astur b

1000

)0803

(33)


dpr op =radic

a2



18 3 METHODOLOGY


ηpr opi deal =2

1+(


2+1

)12(35)







P

P0=

(ρ

ρ0

)n

(36)





20 3 METHODOLOGY



0 01 02 03 04 05 06 07 08 09 1middot104

04

06

08

1

12

14

16

18middot106

Altitude [m]

Max

co

nti

no

us

pow

er[W

]



0 01 02 03 04 05 06 07 08 09 1middot104

04

05

06

07

08

09

1

11

Altitude [m]

( ρ ρ0

) n [-]

PP0(ρρ0

)n n=075





0 01 02 03 04 05 06 07 08 09 1middot104

60

80

100

120

140

Altitude [m]

Fuel

flow

[gs



0 01 02 03 04 05 06 07 08 09 1middot104

260

280

300

320

340

Altitude [m]

SFC

[g

kW

h]



22 3 METHODOLOGY

02 03 04 05 06 07 08 09 1280

300

320

340

360

Power setting [-]

SFC

[g

kW

h]







331 BATTERY SIZING








SFC(38)





24 3 METHODOLOGY



2(310)




ηpr op(311)


Pbat =Pem










Pt akeo f f(313)













LIMITATIONS




332 FUEL



26 3 METHODOLOGY




1000

1000(318)




SFC

L

Dln

(mpr ecr ui se

mendcr ui se

)(319)


R = 1Sηel





mempt y

)(320)







x = Ebat

Etot= S



CD Using



ebat(324)


e f uel(325)






bull ηel = 095 [-]


bull CLCD

= 20 [-]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

Power Split [-]

Mas

s[k

g]




28 3 METHODOLOGY


1 Standard Mission

bull Take off

bull Climb 1

bull Cruise 1

bull Descent 1

bull Landing 1

2 Extended Mission

bull Climb 2

bull Cruise 2

bull Descent 2

bull HoldLoiter

bull Descent 3

bull Landing 2

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 24000

02

04

06

08

1

12

14middot104

Clim

b1

Cruise 1

Des

cen

t1

Clim

b2

Cru

ise

2

Des

cen

t2

Loit

erD

esce

nt3

range (m)

alti

tud

e(m

)









sec




in the missionkg


kg


kg



30 3 METHODOLOGY




Start

Set initial

conditions of state

matrix S

Take-off

Climb 1

Cruise 1


Extended

cruise time

Extended

mission

Landing 1Landing 2


burn and battery

weight

Descent 3

Loiter

Descent 2

Cruise 2

Climb 2

Calculate diversion

Rrest Wfbrest

Calculate Rrest

Wfbrest

Fuel weight

converged

End

No

No

Yes

Yes

No

Yes


32 3 METHODOLOGY

341 TAKE-OFF







(Dpr op

2

)2)13

(326)














dEbat

d t= Pbat

3600(328)

dmbat

d t=

dEbatd t

ebat(329)

dm f uel










d t ispositive




V(332)


34 3 METHODOLOGY

0 01 02 03 04 05 06 07 08 09 10

5

10

15

alti

tud

e(m

)

0 01 02 03 04 05 06 07 08 09 10

20

40

60

spee

d(m

s)

0 01 02 03 04 05 06 07 08 09 102468

10

range (km)

γ(d

eg)



Aircraft on

ground

Determine

take-off

power

Initial aircraft

state

Relevant

settings

Select power

setting (1)

Calculate

static thrust

Calculate

propeller

efficiency

Calculate lift

and drag

Calculate

ground

friction drag

Yes

Determine

derivatives

No

Calculate

SFC

Constant power

operating mode

Calculate Pem Pbat

Pgasturb based on

the power split

No

Determine change

in battery and fuel

energy and weight

Calculate Pem Pbat

based on selected

Pgasturb

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Screen height

reached

Calculate

new thrust

No

End Yes


36 3 METHODOLOGY

342 CLIMB










0 20 40 60 80 100 120 140 1601

15

2

25

3

35

4middot106

Range [km]

Pow

er[W

]



0 20 40 60 80 100 120 140 1600

02040608

1middot104

alti

tud

e(m

)

0 20 40 60 80 100 120 140 1606080

100120140

spee

d(m

s)

0 20 40 60 80 100 120 140 1600

5

10

15

20

range (km)

γ(d

eg)


38 3 METHODOLOGY

Determine

maximum

power (take-

off power)

Aircraft state

at end take-off

Relevant

settings

Select

iteration

time step

Determine

drag polar

Calculate

propeller

efficiency

Calculate

thrust

Constant power

operating mode

Determine Pgasturb

based on power

splitNo

Scale max gas

turbine power

based on altitude

and speed

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

End

Calculate lift

and drag

Determine

derivatives

Pgasturb is maximum

gas turbine power

Pgasturb

more than max

turboprop

power

Yes

No

Determine power

setting

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight


Scale max gas

turbine power

based on altitude

and speed


Determine Pem and

Pbat

Cruise altitude

and speed

reachedYes

No



343 CRUISE







Psha f t =T lowastV

ηpr op(333)






40 3 METHODOLOGY


0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 14007500

7600

7700

7800

alti

tud

e(m

)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400139

1392139413961398

140

spee

d(m

s)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400minus05

0

05

1middot10minus2

range (km)

γ(d

eg)



Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

lift drag and

thrust

Calculate

propeller

efficiency

Constant power

operating mode

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Determine

derivatives

No

No

Determine

power

setting for

minimal SFC

Yes

Determine

Pshaft

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Scale max gas

turbine power

based on altitude

and speed

Determine Pgasturb

Battery not

charging and

battery energy

depleted

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Range reached

Yes

End Yes


42 3 METHODOLOGY

344 DESCENT









1360 1380 1400 1420 1440 1460 1480 1500 1520 15400

02040608

1middot104

alti

tud

e(m

)

1360 1380 1400 1420 1440 1460 1480 1500 1520 15406080

100120140

spee

d(m

s)

1360 1380 1400 1420 1440 1460 1480 1500 1520 1540minus15

minus10

minus5

0

range (km)

γ(d

eg)



Aircraft state

at end cruise

Relevant

settings


step

Scale maximum

Pgasturb based on

altitude and speed


Determine change

in aircraft weight


matrix

End

Calculate propeller

efficiency

Determine

derivatives

Descent altitude

reached

Yes

No

Calculate lift and

dragCalculate SFC

Determine Pem and

Pbat (= 0)

Determine Pgasturb

(= Pidle)

Determine change

in fuel weight (no

change in battery

weight)


44 3 METHODOLOGY

345 LANDING





15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

5

10

15

alti

tud

e(m

)

15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

20

40

60

spee

d(m

s)

15272 15273 15274 15275 15276 15277 15278 15279 1528 15281minus3

minus2

minus1

0

range (km)

γ(d

eg)




Determine

landing drag

polar

Aircraft state

at end take-off

Relevant

settings

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Calculate lift

and drag

No

Determine

Pshaft and

thrust

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Pgasturb = Pshaft

Scale max gas

turbine power

based on altitude

and speed

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Speed and

altitude = 0

Yes

End Yes

Aircraft on

ground

Determine

derivatives

Calculate ground

friction drag and

reverse thrust if

applicable

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Calculate SFC

Yes

No

Yes


46 3 METHODOLOGY

346 HOLDLOITER





L CD







Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Determine

CLCD for

max LD

No

Determine

max Pgasturb

and Pidle

Determine Pshaft

based on target

velocity

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Loiter time

reached

Yes

End Yes

Determine Pgasturb

Determine power

setting


48 3 METHODOLOGY









0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2middot104

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

alti

tud

e(m

)

0 200 400 600 800 1000 1200 1400 1600 1800 20000

50

100

150

spee

d(m

s)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus20

minus10

0

10

range (km)

γ(d

eg)


50 3 METHODOLOGY

0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2

25

3

35

4

45

5

middot106

Cli

mb

1Cruise

Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1000

2000

3000

4000

5000

Clim

b1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

range [km]

Mas

s[k

g]

Battery Fuel



352 COMPARISON





S = 100mfuel[kg] 0 0 00 mbat[kg] 5317 5635 + 60



S = 000mfuel[kg] 1735 1804 + 40 mbat[kg] 0 0 00





52 3 METHODOLOGY












37 WIRING 53

0 05 1 15 2 25 3middot106

0

50

100

150

200

250


Ele

ctri

cm

oto

r+

cryo

coo

ler

wei

ght[

kg]


37 WIRING




54 3 METHODOLOGY

100 150 200 250 300 350 400 4501

2

3

4

5

6

7

8


Cable current [A]

Cab

lew

eigh

t[kg

m]

















56 3 METHODOLOGY







1419000 pounds

311 LIMITATIONS 57





58 3 METHODOLOGY




-




kgWh


-


pack-


-



-





-


-



W

4RESULTS




68 -




59

60 4 RESULTS








62 4 RESULTS



22800 22340 - 20


393 392 - 03



421 INPUTS















64 4 RESULTS





0 01 02 03 04 05 06 07 08 09 10

05

1

middot104



Bat

tery

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

500

1000

1500

2000

2500



Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

1

2

3

4middot104



MT

OM

[kg]



66 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

2

4

6middot106


Max

imu

mP

em



0 01 02 03 04 05 06 07 080

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000


Gas

Turb

ine

Mas

s[k

g]



68 4 RESULTS

423 OPERATING MODES


0 01 02 03 04 05 06 07 08 09 10

05

1

15

2

25

3middot106


Max

imu

mC

on

tin

uo

us

Gas

Turb

ine

Pow

er[W

]






0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



70 4 RESULTS






0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

2000


Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

02

04

06

08

1

12middot104


Bat

tery

Mas

s[k

g]



72 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1

2

3

4

5

6middot106


Max

imu

mP

em[W



0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000


Gas

Turb

ine

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34

36

38

4middot104


MT

OM

[kg]



74 4 RESULTS







0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]


0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]







76 4 RESULTS


0 01 02 03 04 05 06 07 08 09 10

2000

4000

6000

8000


Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34middot104


MT

OM

[kg]



431 RANGE


78 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1000

2000

3000

4000

5000

6000


Fuel

wei

ght[

kg]



0 01 02 03 04 05 06 07 08 09 12

25

3

35

4middot104


MT

OW

[kg]



44 FINAL DESIGN 79



700 800 900 1000 1100 1200 1300 1400 1500800

1000

1200

1400

1600

1800

2000


Φ= 01

Φ= 02

Φ= 03

Φ= 04

Φ= 05

Φ= 06

Φ= 00

ebat [ W hkg ]

Fuel

Mas

s[k

g]




80 4 RESULTS






Difference


22340 25470 + 14


103 72 ndash 29


2619 2173 ndash 17





Difference


44 FINAL DESIGN 81

510

1520

25

minus10minus5

05

10

2

4

6

8




82 4 RESULTS







83












EQUATION


t1

V d t (A1)

usingdE


Equation A1 becomes

R =int E f i nal

Est ar t

minus V

Pbat +P f ueldE

=int Est ar t

E f i nal

V

Pbat +P f ueldE

(A3)

Using



And


ηel(A5)


R =int Est ar t

E f i nal

V(Sηel


)lowastPsha f t

dE (A6)


Psha f t =D lowastV

ηpr op(A7)

And

D = C D

C LlowastW (A8)

85


So VPsha f t

becomes

V

Psha f t= C L

C Dlowast ηpr op

W(A9)


R = 1Sηel



int Est ar t

E f i nal

1

WdE (A10)



=Wempt y + Ebat

ebat+ E f uel

e f uel


e f uel lowastebat

(A11)



x = Ebat

Etot

= Ebat

Ebat +E f uel

=Eemηel

Eemηel


(A12)




= S


(A13)

With x = EbatEtot







R = 1Sηel



int Est ar t

E f i nal

1



R = 1Sηel





Wempt y

)(A16)

BIBLIOGRAPHY















87

88 BIBLIOGRAPHY



















BIBLIOGRAPHY 89



















List of Figures

List of Tables

Introduction

Project Description


Technology Overview

Battery Technology





Control Strategies


Methodology

Initiator




Other Modifications


Battery Sizing

Fuel


Take-off

Climb

Cruise

Descent

Landing

HoldLoiter



Comparison


Wiring

Other Components

Component Placement

Implementation

Limitations

Results

Reference Aircraft

Hybrid Aircraft

Inputs


Operating Modes

Optimal Power Split


Range


Final Design


Conclusion

Recommendations


Bibliography

CONTENTS

List of Figures ix

List of Tables xiii

1 Introduction 1

















332 Fuel 25


341 Take-off 32

342 Climb 36

343 Cruise 39

344 Descent 42

345 Landing 44

346 HoldLoiter 46



352 Comparison 51


37 Wiring 53




311 Limitations 56

vii

viii CONTENTS




44 Final Design 79



Bibliography 87

LIST OF FIGURES



34 Slope of PP0














ix

x LIST OF FIGURES


















LIST OF FIGURES xi


LIST OF TABLES








craft 80

xiii

NOMENCLATURE

Acronyms



FF Fuel fraction








SOC State of charge



Subscripts

bat Battery


em Electric motor


avg Average

cable Cable


cryo Cryocooler

disk Propeller disk


gasturb Gas turbine


xv

xvi LIST OF TABLES

prop Propeller


tot total

Symbols

∆ Change in [-]


η Efficiency [-]



ρ Density [ kgm3 ]

A Area [m2]






b Wing span [m]

D Drag [N]

d Diameter [m]

E Energy [Wh]

f Frequency [Hz]



h Altitude [m]

L Lift [N]

l Length [m]

m Mass [kg]

N number

P Power [W]

Q Heat energy [J]

LIST OF TABLES xvii

R Range [km]

S Power split [-]

T Thrust [N]

t time [sec]

U Voltage [V]

V Speed [ms]

1INTRODUCTION






1










3





bull Range 1528 km

















LITHIUM ION





LITHIUM SULPHUR










LITHIUM AIR








Ah



W h(21)

























9






















Power converter

Electric motor


Generator







Power converter

Electric motor

Gas turbine








ηbat ηEM

ηgasturb


Gas turbine

Pbat

PbatOffTake

Pem

Pgasturb

Pshaft

ηprop

Pfuel

ηelec







Si =Pemi

Psha f ti

(22)









HP = Pemmax

Psha f tmax

(23)

and

HE = Ebat

Etot(24)


Φ= Eemtot

Esha f ttot

(25)


3METHODOLOGY







15

16 3 METHODOLOGY

Class 1

Weight

Estimation

Wing- and

power

loading

Geometry

design

modules

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis

Performance

Estimation

Modules

Design

converged

Reference

aircraft

database

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis


Converged

No

Yes

No

Design

Yes


All modules
















Pg astur b

1000

)012

(31)


Pg astur b

1000

)0373

(32)


Pg astur b

1000

)0803

(33)


dpr op =radic

a2



18 3 METHODOLOGY


ηpr opi deal =2

1+(


2+1

)12(35)







P

P0=

(ρ

ρ0

)n

(36)





20 3 METHODOLOGY



0 01 02 03 04 05 06 07 08 09 1middot104

04

06

08

1

12

14

16

18middot106

Altitude [m]

Max

co

nti

no

us

pow

er[W

]



0 01 02 03 04 05 06 07 08 09 1middot104

04

05

06

07

08

09

1

11

Altitude [m]

( ρ ρ0

) n [-]

PP0(ρρ0

)n n=075





0 01 02 03 04 05 06 07 08 09 1middot104

60

80

100

120

140

Altitude [m]

Fuel

flow

[gs



0 01 02 03 04 05 06 07 08 09 1middot104

260

280

300

320

340

Altitude [m]

SFC

[g

kW

h]



22 3 METHODOLOGY

02 03 04 05 06 07 08 09 1280

300

320

340

360

Power setting [-]

SFC

[g

kW

h]







331 BATTERY SIZING








SFC(38)





24 3 METHODOLOGY



2(310)




ηpr op(311)


Pbat =Pem










Pt akeo f f(313)













LIMITATIONS




332 FUEL



26 3 METHODOLOGY




1000

1000(318)




SFC

L

Dln

(mpr ecr ui se

mendcr ui se

)(319)


R = 1Sηel





mempt y

)(320)







x = Ebat

Etot= S



CD Using



ebat(324)


e f uel(325)






bull ηel = 095 [-]


bull CLCD

= 20 [-]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

Power Split [-]

Mas

s[k

g]




28 3 METHODOLOGY


1 Standard Mission

bull Take off

bull Climb 1

bull Cruise 1

bull Descent 1

bull Landing 1

2 Extended Mission

bull Climb 2

bull Cruise 2

bull Descent 2

bull HoldLoiter

bull Descent 3

bull Landing 2

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 24000

02

04

06

08

1

12

14middot104

Clim

b1

Cruise 1

Des

cen

t1

Clim

b2

Cru

ise

2

Des

cen

t2

Loit

erD

esce

nt3

range (m)

alti

tud

e(m

)









sec




in the missionkg


kg


kg



30 3 METHODOLOGY




Start

Set initial

conditions of state

matrix S

Take-off

Climb 1

Cruise 1


Extended

cruise time

Extended

mission

Landing 1Landing 2


burn and battery

weight

Descent 3

Loiter

Descent 2

Cruise 2

Climb 2

Calculate diversion

Rrest Wfbrest

Calculate Rrest

Wfbrest

Fuel weight

converged

End

No

No

Yes

Yes

No

Yes


32 3 METHODOLOGY

341 TAKE-OFF







(Dpr op

2

)2)13

(326)














dEbat

d t= Pbat

3600(328)

dmbat

d t=

dEbatd t

ebat(329)

dm f uel










d t ispositive




V(332)


34 3 METHODOLOGY

0 01 02 03 04 05 06 07 08 09 10

5

10

15

alti

tud

e(m

)

0 01 02 03 04 05 06 07 08 09 10

20

40

60

spee

d(m

s)

0 01 02 03 04 05 06 07 08 09 102468

10

range (km)

γ(d

eg)



Aircraft on

ground

Determine

take-off

power

Initial aircraft

state

Relevant

settings

Select power

setting (1)

Calculate

static thrust

Calculate

propeller

efficiency

Calculate lift

and drag

Calculate

ground

friction drag

Yes

Determine

derivatives

No

Calculate

SFC

Constant power

operating mode

Calculate Pem Pbat

Pgasturb based on

the power split

No

Determine change

in battery and fuel

energy and weight

Calculate Pem Pbat

based on selected

Pgasturb

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Screen height

reached

Calculate

new thrust

No

End Yes


36 3 METHODOLOGY

342 CLIMB










0 20 40 60 80 100 120 140 1601

15

2

25

3

35

4middot106

Range [km]

Pow

er[W

]



0 20 40 60 80 100 120 140 1600

02040608

1middot104

alti

tud

e(m

)

0 20 40 60 80 100 120 140 1606080

100120140

spee

d(m

s)

0 20 40 60 80 100 120 140 1600

5

10

15

20

range (km)

γ(d

eg)


38 3 METHODOLOGY

Determine

maximum

power (take-

off power)

Aircraft state

at end take-off

Relevant

settings

Select

iteration

time step

Determine

drag polar

Calculate

propeller

efficiency

Calculate

thrust

Constant power

operating mode

Determine Pgasturb

based on power

splitNo

Scale max gas

turbine power

based on altitude

and speed

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

End

Calculate lift

and drag

Determine

derivatives

Pgasturb is maximum

gas turbine power

Pgasturb

more than max

turboprop

power

Yes

No

Determine power

setting

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight


Scale max gas

turbine power

based on altitude

and speed


Determine Pem and

Pbat

Cruise altitude

and speed

reachedYes

No



343 CRUISE







Psha f t =T lowastV

ηpr op(333)






40 3 METHODOLOGY


0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 14007500

7600

7700

7800

alti

tud

e(m

)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400139

1392139413961398

140

spee

d(m

s)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400minus05

0

05

1middot10minus2

range (km)

γ(d

eg)



Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

lift drag and

thrust

Calculate

propeller

efficiency

Constant power

operating mode

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Determine

derivatives

No

No

Determine

power

setting for

minimal SFC

Yes

Determine

Pshaft

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Scale max gas

turbine power

based on altitude

and speed

Determine Pgasturb

Battery not

charging and

battery energy

depleted

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Range reached

Yes

End Yes


42 3 METHODOLOGY

344 DESCENT









1360 1380 1400 1420 1440 1460 1480 1500 1520 15400

02040608

1middot104

alti

tud

e(m

)

1360 1380 1400 1420 1440 1460 1480 1500 1520 15406080

100120140

spee

d(m

s)

1360 1380 1400 1420 1440 1460 1480 1500 1520 1540minus15

minus10

minus5

0

range (km)

γ(d

eg)



Aircraft state

at end cruise

Relevant

settings


step

Scale maximum

Pgasturb based on

altitude and speed


Determine change

in aircraft weight


matrix

End

Calculate propeller

efficiency

Determine

derivatives

Descent altitude

reached

Yes

No

Calculate lift and

dragCalculate SFC

Determine Pem and

Pbat (= 0)

Determine Pgasturb

(= Pidle)

Determine change

in fuel weight (no

change in battery

weight)


44 3 METHODOLOGY

345 LANDING





15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

5

10

15

alti

tud

e(m

)

15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

20

40

60

spee

d(m

s)

15272 15273 15274 15275 15276 15277 15278 15279 1528 15281minus3

minus2

minus1

0

range (km)

γ(d

eg)




Determine

landing drag

polar

Aircraft state

at end take-off

Relevant

settings

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Calculate lift

and drag

No

Determine

Pshaft and

thrust

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Pgasturb = Pshaft

Scale max gas

turbine power

based on altitude

and speed

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Speed and

altitude = 0

Yes

End Yes

Aircraft on

ground

Determine

derivatives

Calculate ground

friction drag and

reverse thrust if

applicable

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Calculate SFC

Yes

No

Yes


46 3 METHODOLOGY

346 HOLDLOITER





L CD







Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Determine

CLCD for

max LD

No

Determine

max Pgasturb

and Pidle

Determine Pshaft

based on target

velocity

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Loiter time

reached

Yes

End Yes

Determine Pgasturb

Determine power

setting


48 3 METHODOLOGY









0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2middot104

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

alti

tud

e(m

)

0 200 400 600 800 1000 1200 1400 1600 1800 20000

50

100

150

spee

d(m

s)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus20

minus10

0

10

range (km)

γ(d

eg)


50 3 METHODOLOGY

0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2

25

3

35

4

45

5

middot106

Cli

mb

1Cruise

Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1000

2000

3000

4000

5000

Clim

b1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

range [km]

Mas

s[k

g]

Battery Fuel



352 COMPARISON





S = 100mfuel[kg] 0 0 00 mbat[kg] 5317 5635 + 60



S = 000mfuel[kg] 1735 1804 + 40 mbat[kg] 0 0 00





52 3 METHODOLOGY












37 WIRING 53

0 05 1 15 2 25 3middot106

0

50

100

150

200

250


Ele

ctri

cm

oto

r+

cryo

coo

ler

wei

ght[

kg]


37 WIRING




54 3 METHODOLOGY

100 150 200 250 300 350 400 4501

2

3

4

5

6

7

8


Cable current [A]

Cab

lew

eigh

t[kg

m]

















56 3 METHODOLOGY







1419000 pounds

311 LIMITATIONS 57





58 3 METHODOLOGY




-




kgWh


-


pack-


-



-





-


-



W

4RESULTS




68 -




59

60 4 RESULTS








62 4 RESULTS



22800 22340 - 20


393 392 - 03



421 INPUTS















64 4 RESULTS





0 01 02 03 04 05 06 07 08 09 10

05

1

middot104



Bat

tery

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

500

1000

1500

2000

2500



Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

1

2

3

4middot104



MT

OM

[kg]



66 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

2

4

6middot106


Max

imu

mP

em



0 01 02 03 04 05 06 07 080

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000


Gas

Turb

ine

Mas

s[k

g]



68 4 RESULTS

423 OPERATING MODES


0 01 02 03 04 05 06 07 08 09 10

05

1

15

2

25

3middot106


Max

imu

mC

on

tin

uo

us

Gas

Turb

ine

Pow

er[W

]






0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



70 4 RESULTS






0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

2000


Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

02

04

06

08

1

12middot104


Bat

tery

Mas

s[k

g]



72 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1

2

3

4

5

6middot106


Max

imu

mP

em[W



0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000


Gas

Turb

ine

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34

36

38

4middot104


MT

OM

[kg]



74 4 RESULTS







0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]


0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]







76 4 RESULTS


0 01 02 03 04 05 06 07 08 09 10

2000

4000

6000

8000


Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34middot104


MT

OM

[kg]



431 RANGE


78 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1000

2000

3000

4000

5000

6000


Fuel

wei

ght[

kg]



0 01 02 03 04 05 06 07 08 09 12

25

3

35

4middot104


MT

OW

[kg]



44 FINAL DESIGN 79



700 800 900 1000 1100 1200 1300 1400 1500800

1000

1200

1400

1600

1800

2000


Φ= 01

Φ= 02

Φ= 03

Φ= 04

Φ= 05

Φ= 06

Φ= 00

ebat [ W hkg ]

Fuel

Mas

s[k

g]




80 4 RESULTS






Difference


22340 25470 + 14


103 72 ndash 29


2619 2173 ndash 17





Difference


44 FINAL DESIGN 81

510

1520

25

minus10minus5

05

10

2

4

6

8




82 4 RESULTS







83












EQUATION


t1

V d t (A1)

usingdE


Equation A1 becomes

R =int E f i nal

Est ar t

minus V

Pbat +P f ueldE

=int Est ar t

E f i nal

V

Pbat +P f ueldE

(A3)

Using



And


ηel(A5)


R =int Est ar t

E f i nal

V(Sηel


)lowastPsha f t

dE (A6)


Psha f t =D lowastV

ηpr op(A7)

And

D = C D

C LlowastW (A8)

85


So VPsha f t

becomes

V

Psha f t= C L

C Dlowast ηpr op

W(A9)


R = 1Sηel



int Est ar t

E f i nal

1

WdE (A10)



=Wempt y + Ebat

ebat+ E f uel

e f uel


e f uel lowastebat

(A11)



x = Ebat

Etot

= Ebat

Ebat +E f uel

=Eemηel

Eemηel


(A12)




= S


(A13)

With x = EbatEtot







R = 1Sηel



int Est ar t

E f i nal

1



R = 1Sηel





Wempt y

)(A16)

BIBLIOGRAPHY















87

88 BIBLIOGRAPHY



















BIBLIOGRAPHY 89



















List of Figures

List of Tables

Introduction

Project Description


Technology Overview

Battery Technology





Control Strategies


Methodology

Initiator




Other Modifications


Battery Sizing

Fuel


Take-off

Climb

Cruise

Descent

Landing

HoldLoiter



Comparison


Wiring

Other Components

Component Placement

Implementation

Limitations

Results

Reference Aircraft

Hybrid Aircraft

Inputs


Operating Modes

Optimal Power Split


Range


Final Design


Conclusion

Recommendations


Bibliography

viii CONTENTS




44 Final Design 79



Bibliography 87

LIST OF FIGURES



34 Slope of PP0














ix

x LIST OF FIGURES


















LIST OF FIGURES xi


LIST OF TABLES








craft 80

xiii

NOMENCLATURE

Acronyms



FF Fuel fraction








SOC State of charge



Subscripts

bat Battery


em Electric motor


avg Average

cable Cable


cryo Cryocooler

disk Propeller disk


gasturb Gas turbine


xv

xvi LIST OF TABLES

prop Propeller


tot total

Symbols

∆ Change in [-]


η Efficiency [-]



ρ Density [ kgm3 ]

A Area [m2]






b Wing span [m]

D Drag [N]

d Diameter [m]

E Energy [Wh]

f Frequency [Hz]



h Altitude [m]

L Lift [N]

l Length [m]

m Mass [kg]

N number

P Power [W]

Q Heat energy [J]

LIST OF TABLES xvii

R Range [km]

S Power split [-]

T Thrust [N]

t time [sec]

U Voltage [V]

V Speed [ms]

1INTRODUCTION






1










3





bull Range 1528 km

















LITHIUM ION





LITHIUM SULPHUR










LITHIUM AIR








Ah



W h(21)

























9






















Power converter

Electric motor


Generator







Power converter

Electric motor

Gas turbine








ηbat ηEM

ηgasturb


Gas turbine

Pbat

PbatOffTake

Pem

Pgasturb

Pshaft

ηprop

Pfuel

ηelec







Si =Pemi

Psha f ti

(22)









HP = Pemmax

Psha f tmax

(23)

and

HE = Ebat

Etot(24)


Φ= Eemtot

Esha f ttot

(25)


3METHODOLOGY







15

16 3 METHODOLOGY

Class 1

Weight

Estimation

Wing- and

power

loading

Geometry

design

modules

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis

Performance

Estimation

Modules

Design

converged

Reference

aircraft

database

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis


Converged

No

Yes

No

Design

Yes


All modules
















Pg astur b

1000

)012

(31)


Pg astur b

1000

)0373

(32)


Pg astur b

1000

)0803

(33)


dpr op =radic

a2



18 3 METHODOLOGY


ηpr opi deal =2

1+(


2+1

)12(35)







P

P0=

(ρ

ρ0

)n

(36)





20 3 METHODOLOGY



0 01 02 03 04 05 06 07 08 09 1middot104

04

06

08

1

12

14

16

18middot106

Altitude [m]

Max

co

nti

no

us

pow

er[W

]



0 01 02 03 04 05 06 07 08 09 1middot104

04

05

06

07

08

09

1

11

Altitude [m]

( ρ ρ0

) n [-]

PP0(ρρ0

)n n=075





0 01 02 03 04 05 06 07 08 09 1middot104

60

80

100

120

140

Altitude [m]

Fuel

flow

[gs



0 01 02 03 04 05 06 07 08 09 1middot104

260

280

300

320

340

Altitude [m]

SFC

[g

kW

h]



22 3 METHODOLOGY

02 03 04 05 06 07 08 09 1280

300

320

340

360

Power setting [-]

SFC

[g

kW

h]







331 BATTERY SIZING








SFC(38)





24 3 METHODOLOGY



2(310)




ηpr op(311)


Pbat =Pem










Pt akeo f f(313)













LIMITATIONS




332 FUEL



26 3 METHODOLOGY




1000

1000(318)




SFC

L

Dln

(mpr ecr ui se

mendcr ui se

)(319)


R = 1Sηel





mempt y

)(320)







x = Ebat

Etot= S



CD Using



ebat(324)


e f uel(325)






bull ηel = 095 [-]


bull CLCD

= 20 [-]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

Power Split [-]

Mas

s[k

g]




28 3 METHODOLOGY


1 Standard Mission

bull Take off

bull Climb 1

bull Cruise 1

bull Descent 1

bull Landing 1

2 Extended Mission

bull Climb 2

bull Cruise 2

bull Descent 2

bull HoldLoiter

bull Descent 3

bull Landing 2

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 24000

02

04

06

08

1

12

14middot104

Clim

b1

Cruise 1

Des

cen

t1

Clim

b2

Cru

ise

2

Des

cen

t2

Loit

erD

esce

nt3

range (m)

alti

tud

e(m

)









sec




in the missionkg


kg


kg



30 3 METHODOLOGY




Start

Set initial

conditions of state

matrix S

Take-off

Climb 1

Cruise 1


Extended

cruise time

Extended

mission

Landing 1Landing 2


burn and battery

weight

Descent 3

Loiter

Descent 2

Cruise 2

Climb 2

Calculate diversion

Rrest Wfbrest

Calculate Rrest

Wfbrest

Fuel weight

converged

End

No

No

Yes

Yes

No

Yes


32 3 METHODOLOGY

341 TAKE-OFF







(Dpr op

2

)2)13

(326)














dEbat

d t= Pbat

3600(328)

dmbat

d t=

dEbatd t

ebat(329)

dm f uel










d t ispositive




V(332)


34 3 METHODOLOGY

0 01 02 03 04 05 06 07 08 09 10

5

10

15

alti

tud

e(m

)

0 01 02 03 04 05 06 07 08 09 10

20

40

60

spee

d(m

s)

0 01 02 03 04 05 06 07 08 09 102468

10

range (km)

γ(d

eg)



Aircraft on

ground

Determine

take-off

power

Initial aircraft

state

Relevant

settings

Select power

setting (1)

Calculate

static thrust

Calculate

propeller

efficiency

Calculate lift

and drag

Calculate

ground

friction drag

Yes

Determine

derivatives

No

Calculate

SFC

Constant power

operating mode

Calculate Pem Pbat

Pgasturb based on

the power split

No

Determine change

in battery and fuel

energy and weight

Calculate Pem Pbat

based on selected

Pgasturb

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Screen height

reached

Calculate

new thrust

No

End Yes


36 3 METHODOLOGY

342 CLIMB










0 20 40 60 80 100 120 140 1601

15

2

25

3

35

4middot106

Range [km]

Pow

er[W

]



0 20 40 60 80 100 120 140 1600

02040608

1middot104

alti

tud

e(m

)

0 20 40 60 80 100 120 140 1606080

100120140

spee

d(m

s)

0 20 40 60 80 100 120 140 1600

5

10

15

20

range (km)

γ(d

eg)


38 3 METHODOLOGY

Determine

maximum

power (take-

off power)

Aircraft state

at end take-off

Relevant

settings

Select

iteration

time step

Determine

drag polar

Calculate

propeller

efficiency

Calculate

thrust

Constant power

operating mode

Determine Pgasturb

based on power

splitNo

Scale max gas

turbine power

based on altitude

and speed

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

End

Calculate lift

and drag

Determine

derivatives

Pgasturb is maximum

gas turbine power

Pgasturb

more than max

turboprop

power

Yes

No

Determine power

setting

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight


Scale max gas

turbine power

based on altitude

and speed


Determine Pem and

Pbat

Cruise altitude

and speed

reachedYes

No



343 CRUISE







Psha f t =T lowastV

ηpr op(333)






40 3 METHODOLOGY


0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 14007500

7600

7700

7800

alti

tud

e(m

)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400139

1392139413961398

140

spee

d(m

s)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400minus05

0

05

1middot10minus2

range (km)

γ(d

eg)



Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

lift drag and

thrust

Calculate

propeller

efficiency

Constant power

operating mode

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Determine

derivatives

No

No

Determine

power

setting for

minimal SFC

Yes

Determine

Pshaft

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Scale max gas

turbine power

based on altitude

and speed

Determine Pgasturb

Battery not

charging and

battery energy

depleted

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Range reached

Yes

End Yes


42 3 METHODOLOGY

344 DESCENT









1360 1380 1400 1420 1440 1460 1480 1500 1520 15400

02040608

1middot104

alti

tud

e(m

)

1360 1380 1400 1420 1440 1460 1480 1500 1520 15406080

100120140

spee

d(m

s)

1360 1380 1400 1420 1440 1460 1480 1500 1520 1540minus15

minus10

minus5

0

range (km)

γ(d

eg)



Aircraft state

at end cruise

Relevant

settings


step

Scale maximum

Pgasturb based on

altitude and speed


Determine change

in aircraft weight


matrix

End

Calculate propeller

efficiency

Determine

derivatives

Descent altitude

reached

Yes

No

Calculate lift and

dragCalculate SFC

Determine Pem and

Pbat (= 0)

Determine Pgasturb

(= Pidle)

Determine change

in fuel weight (no

change in battery

weight)


44 3 METHODOLOGY

345 LANDING





15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

5

10

15

alti

tud

e(m

)

15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

20

40

60

spee

d(m

s)

15272 15273 15274 15275 15276 15277 15278 15279 1528 15281minus3

minus2

minus1

0

range (km)

γ(d

eg)




Determine

landing drag

polar

Aircraft state

at end take-off

Relevant

settings

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Calculate lift

and drag

No

Determine

Pshaft and

thrust

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Pgasturb = Pshaft

Scale max gas

turbine power

based on altitude

and speed

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Speed and

altitude = 0

Yes

End Yes

Aircraft on

ground

Determine

derivatives

Calculate ground

friction drag and

reverse thrust if

applicable

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Calculate SFC

Yes

No

Yes


46 3 METHODOLOGY

346 HOLDLOITER





L CD







Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Determine

CLCD for

max LD

No

Determine

max Pgasturb

and Pidle

Determine Pshaft

based on target

velocity

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Loiter time

reached

Yes

End Yes

Determine Pgasturb

Determine power

setting


48 3 METHODOLOGY









0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2middot104

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

alti

tud

e(m

)

0 200 400 600 800 1000 1200 1400 1600 1800 20000

50

100

150

spee

d(m

s)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus20

minus10

0

10

range (km)

γ(d

eg)


50 3 METHODOLOGY

0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2

25

3

35

4

45

5

middot106

Cli

mb

1Cruise

Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1000

2000

3000

4000

5000

Clim

b1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

range [km]

Mas

s[k

g]

Battery Fuel



352 COMPARISON





S = 100mfuel[kg] 0 0 00 mbat[kg] 5317 5635 + 60



S = 000mfuel[kg] 1735 1804 + 40 mbat[kg] 0 0 00





52 3 METHODOLOGY












37 WIRING 53

0 05 1 15 2 25 3middot106

0

50

100

150

200

250


Ele

ctri

cm

oto

r+

cryo

coo

ler

wei

ght[

kg]


37 WIRING




54 3 METHODOLOGY

100 150 200 250 300 350 400 4501

2

3

4

5

6

7

8


Cable current [A]

Cab

lew

eigh

t[kg

m]

















56 3 METHODOLOGY







1419000 pounds

311 LIMITATIONS 57





58 3 METHODOLOGY




-




kgWh


-


pack-


-



-





-


-



W

4RESULTS




68 -




59

60 4 RESULTS








62 4 RESULTS



22800 22340 - 20


393 392 - 03



421 INPUTS















64 4 RESULTS





0 01 02 03 04 05 06 07 08 09 10

05

1

middot104



Bat

tery

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

500

1000

1500

2000

2500



Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

1

2

3

4middot104



MT

OM

[kg]



66 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

2

4

6middot106


Max

imu

mP

em



0 01 02 03 04 05 06 07 080

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000


Gas

Turb

ine

Mas

s[k

g]



68 4 RESULTS

423 OPERATING MODES


0 01 02 03 04 05 06 07 08 09 10

05

1

15

2

25

3middot106


Max

imu

mC

on

tin

uo

us

Gas

Turb

ine

Pow

er[W

]






0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



70 4 RESULTS






0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

2000


Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

02

04

06

08

1

12middot104


Bat

tery

Mas

s[k

g]



72 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1

2

3

4

5

6middot106


Max

imu

mP

em[W



0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000


Gas

Turb

ine

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34

36

38

4middot104


MT

OM

[kg]



74 4 RESULTS







0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]


0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]







76 4 RESULTS


0 01 02 03 04 05 06 07 08 09 10

2000

4000

6000

8000


Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34middot104


MT

OM

[kg]



431 RANGE


78 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1000

2000

3000

4000

5000

6000


Fuel

wei

ght[

kg]



0 01 02 03 04 05 06 07 08 09 12

25

3

35

4middot104


MT

OW

[kg]



44 FINAL DESIGN 79



700 800 900 1000 1100 1200 1300 1400 1500800

1000

1200

1400

1600

1800

2000


Φ= 01

Φ= 02

Φ= 03

Φ= 04

Φ= 05

Φ= 06

Φ= 00

ebat [ W hkg ]

Fuel

Mas

s[k

g]




80 4 RESULTS






Difference


22340 25470 + 14


103 72 ndash 29


2619 2173 ndash 17





Difference


44 FINAL DESIGN 81

510

1520

25

minus10minus5

05

10

2

4

6

8




82 4 RESULTS







83












EQUATION


t1

V d t (A1)

usingdE


Equation A1 becomes

R =int E f i nal

Est ar t

minus V

Pbat +P f ueldE

=int Est ar t

E f i nal

V

Pbat +P f ueldE

(A3)

Using



And


ηel(A5)


R =int Est ar t

E f i nal

V(Sηel


)lowastPsha f t

dE (A6)


Psha f t =D lowastV

ηpr op(A7)

And

D = C D

C LlowastW (A8)

85


So VPsha f t

becomes

V

Psha f t= C L

C Dlowast ηpr op

W(A9)


R = 1Sηel



int Est ar t

E f i nal

1

WdE (A10)



=Wempt y + Ebat

ebat+ E f uel

e f uel


e f uel lowastebat

(A11)



x = Ebat

Etot

= Ebat

Ebat +E f uel

=Eemηel

Eemηel


(A12)




= S


(A13)

With x = EbatEtot







R = 1Sηel



int Est ar t

E f i nal

1



R = 1Sηel





Wempt y

)(A16)

BIBLIOGRAPHY















87

88 BIBLIOGRAPHY



















BIBLIOGRAPHY 89



















List of Figures

List of Tables

Introduction

Project Description


Technology Overview

Battery Technology





Control Strategies


Methodology

Initiator




Other Modifications


Battery Sizing

Fuel


Take-off

Climb

Cruise

Descent

Landing

HoldLoiter



Comparison


Wiring

Other Components

Component Placement

Implementation

Limitations

Results

Reference Aircraft

Hybrid Aircraft

Inputs


Operating Modes

Optimal Power Split


Range


Final Design


Conclusion

Recommendations


Bibliography

LIST OF FIGURES



34 Slope of PP0














ix

x LIST OF FIGURES


















LIST OF FIGURES xi


LIST OF TABLES








craft 80

xiii

NOMENCLATURE

Acronyms



FF Fuel fraction








SOC State of charge



Subscripts

bat Battery


em Electric motor


avg Average

cable Cable


cryo Cryocooler

disk Propeller disk


gasturb Gas turbine


xv

xvi LIST OF TABLES

prop Propeller


tot total

Symbols

∆ Change in [-]


η Efficiency [-]



ρ Density [ kgm3 ]

A Area [m2]






b Wing span [m]

D Drag [N]

d Diameter [m]

E Energy [Wh]

f Frequency [Hz]



h Altitude [m]

L Lift [N]

l Length [m]

m Mass [kg]

N number

P Power [W]

Q Heat energy [J]

LIST OF TABLES xvii

R Range [km]

S Power split [-]

T Thrust [N]

t time [sec]

U Voltage [V]

V Speed [ms]

1INTRODUCTION






1










3





bull Range 1528 km

















LITHIUM ION





LITHIUM SULPHUR










LITHIUM AIR








Ah



W h(21)

























9






















Power converter

Electric motor


Generator







Power converter

Electric motor

Gas turbine








ηbat ηEM

ηgasturb


Gas turbine

Pbat

PbatOffTake

Pem

Pgasturb

Pshaft

ηprop

Pfuel

ηelec







Si =Pemi

Psha f ti

(22)









HP = Pemmax

Psha f tmax

(23)

and

HE = Ebat

Etot(24)


Φ= Eemtot

Esha f ttot

(25)


3METHODOLOGY







15

16 3 METHODOLOGY

Class 1

Weight

Estimation

Wing- and

power

loading

Geometry

design

modules

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis

Performance

Estimation

Modules

Design

converged

Reference

aircraft

database

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis


Converged

No

Yes

No

Design

Yes


All modules
















Pg astur b

1000

)012

(31)


Pg astur b

1000

)0373

(32)


Pg astur b

1000

)0803

(33)


dpr op =radic

a2



18 3 METHODOLOGY


ηpr opi deal =2

1+(


2+1

)12(35)







P

P0=

(ρ

ρ0

)n

(36)





20 3 METHODOLOGY



0 01 02 03 04 05 06 07 08 09 1middot104

04

06

08

1

12

14

16

18middot106

Altitude [m]

Max

co

nti

no

us

pow

er[W

]



0 01 02 03 04 05 06 07 08 09 1middot104

04

05

06

07

08

09

1

11

Altitude [m]

( ρ ρ0

) n [-]

PP0(ρρ0

)n n=075





0 01 02 03 04 05 06 07 08 09 1middot104

60

80

100

120

140

Altitude [m]

Fuel

flow

[gs



0 01 02 03 04 05 06 07 08 09 1middot104

260

280

300

320

340

Altitude [m]

SFC

[g

kW

h]



22 3 METHODOLOGY

02 03 04 05 06 07 08 09 1280

300

320

340

360

Power setting [-]

SFC

[g

kW

h]







331 BATTERY SIZING








SFC(38)





24 3 METHODOLOGY



2(310)




ηpr op(311)


Pbat =Pem










Pt akeo f f(313)













LIMITATIONS




332 FUEL



26 3 METHODOLOGY




1000

1000(318)




SFC

L

Dln

(mpr ecr ui se

mendcr ui se

)(319)


R = 1Sηel





mempt y

)(320)







x = Ebat

Etot= S



CD Using



ebat(324)


e f uel(325)






bull ηel = 095 [-]


bull CLCD

= 20 [-]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

Power Split [-]

Mas

s[k

g]




28 3 METHODOLOGY


1 Standard Mission

bull Take off

bull Climb 1

bull Cruise 1

bull Descent 1

bull Landing 1

2 Extended Mission

bull Climb 2

bull Cruise 2

bull Descent 2

bull HoldLoiter

bull Descent 3

bull Landing 2

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 24000

02

04

06

08

1

12

14middot104

Clim

b1

Cruise 1

Des

cen

t1

Clim

b2

Cru

ise

2

Des

cen

t2

Loit

erD

esce

nt3

range (m)

alti

tud

e(m

)









sec




in the missionkg


kg


kg



30 3 METHODOLOGY




Start

Set initial

conditions of state

matrix S

Take-off

Climb 1

Cruise 1


Extended

cruise time

Extended

mission

Landing 1Landing 2


burn and battery

weight

Descent 3

Loiter

Descent 2

Cruise 2

Climb 2

Calculate diversion

Rrest Wfbrest

Calculate Rrest

Wfbrest

Fuel weight

converged

End

No

No

Yes

Yes

No

Yes


32 3 METHODOLOGY

341 TAKE-OFF







(Dpr op

2

)2)13

(326)














dEbat

d t= Pbat

3600(328)

dmbat

d t=

dEbatd t

ebat(329)

dm f uel










d t ispositive




V(332)


34 3 METHODOLOGY

0 01 02 03 04 05 06 07 08 09 10

5

10

15

alti

tud

e(m

)

0 01 02 03 04 05 06 07 08 09 10

20

40

60

spee

d(m

s)

0 01 02 03 04 05 06 07 08 09 102468

10

range (km)

γ(d

eg)



Aircraft on

ground

Determine

take-off

power

Initial aircraft

state

Relevant

settings

Select power

setting (1)

Calculate

static thrust

Calculate

propeller

efficiency

Calculate lift

and drag

Calculate

ground

friction drag

Yes

Determine

derivatives

No

Calculate

SFC

Constant power

operating mode

Calculate Pem Pbat

Pgasturb based on

the power split

No

Determine change

in battery and fuel

energy and weight

Calculate Pem Pbat

based on selected

Pgasturb

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Screen height

reached

Calculate

new thrust

No

End Yes


36 3 METHODOLOGY

342 CLIMB










0 20 40 60 80 100 120 140 1601

15

2

25

3

35

4middot106

Range [km]

Pow

er[W

]



0 20 40 60 80 100 120 140 1600

02040608

1middot104

alti

tud

e(m

)

0 20 40 60 80 100 120 140 1606080

100120140

spee

d(m

s)

0 20 40 60 80 100 120 140 1600

5

10

15

20

range (km)

γ(d

eg)


38 3 METHODOLOGY

Determine

maximum

power (take-

off power)

Aircraft state

at end take-off

Relevant

settings

Select

iteration

time step

Determine

drag polar

Calculate

propeller

efficiency

Calculate

thrust

Constant power

operating mode

Determine Pgasturb

based on power

splitNo

Scale max gas

turbine power

based on altitude

and speed

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

End

Calculate lift

and drag

Determine

derivatives

Pgasturb is maximum

gas turbine power

Pgasturb

more than max

turboprop

power

Yes

No

Determine power

setting

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight


Scale max gas

turbine power

based on altitude

and speed


Determine Pem and

Pbat

Cruise altitude

and speed

reachedYes

No



343 CRUISE







Psha f t =T lowastV

ηpr op(333)






40 3 METHODOLOGY


0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 14007500

7600

7700

7800

alti

tud

e(m

)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400139

1392139413961398

140

spee

d(m

s)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400minus05

0

05

1middot10minus2

range (km)

γ(d

eg)



Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

lift drag and

thrust

Calculate

propeller

efficiency

Constant power

operating mode

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Determine

derivatives

No

No

Determine

power

setting for

minimal SFC

Yes

Determine

Pshaft

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Scale max gas

turbine power

based on altitude

and speed

Determine Pgasturb

Battery not

charging and

battery energy

depleted

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Range reached

Yes

End Yes


42 3 METHODOLOGY

344 DESCENT









1360 1380 1400 1420 1440 1460 1480 1500 1520 15400

02040608

1middot104

alti

tud

e(m

)

1360 1380 1400 1420 1440 1460 1480 1500 1520 15406080

100120140

spee

d(m

s)

1360 1380 1400 1420 1440 1460 1480 1500 1520 1540minus15

minus10

minus5

0

range (km)

γ(d

eg)



Aircraft state

at end cruise

Relevant

settings


step

Scale maximum

Pgasturb based on

altitude and speed


Determine change

in aircraft weight


matrix

End

Calculate propeller

efficiency

Determine

derivatives

Descent altitude

reached

Yes

No

Calculate lift and

dragCalculate SFC

Determine Pem and

Pbat (= 0)

Determine Pgasturb

(= Pidle)

Determine change

in fuel weight (no

change in battery

weight)


44 3 METHODOLOGY

345 LANDING





15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

5

10

15

alti

tud

e(m

)

15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

20

40

60

spee

d(m

s)

15272 15273 15274 15275 15276 15277 15278 15279 1528 15281minus3

minus2

minus1

0

range (km)

γ(d

eg)




Determine

landing drag

polar

Aircraft state

at end take-off

Relevant

settings

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Calculate lift

and drag

No

Determine

Pshaft and

thrust

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Pgasturb = Pshaft

Scale max gas

turbine power

based on altitude

and speed

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Speed and

altitude = 0

Yes

End Yes

Aircraft on

ground

Determine

derivatives

Calculate ground

friction drag and

reverse thrust if

applicable

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Calculate SFC

Yes

No

Yes


46 3 METHODOLOGY

346 HOLDLOITER





L CD







Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Determine

CLCD for

max LD

No

Determine

max Pgasturb

and Pidle

Determine Pshaft

based on target

velocity

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Loiter time

reached

Yes

End Yes

Determine Pgasturb

Determine power

setting


48 3 METHODOLOGY









0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2middot104

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

alti

tud

e(m

)

0 200 400 600 800 1000 1200 1400 1600 1800 20000

50

100

150

spee

d(m

s)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus20

minus10

0

10

range (km)

γ(d

eg)


50 3 METHODOLOGY

0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2

25

3

35

4

45

5

middot106

Cli

mb

1Cruise

Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1000

2000

3000

4000

5000

Clim

b1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

range [km]

Mas

s[k

g]

Battery Fuel



352 COMPARISON





S = 100mfuel[kg] 0 0 00 mbat[kg] 5317 5635 + 60



S = 000mfuel[kg] 1735 1804 + 40 mbat[kg] 0 0 00





52 3 METHODOLOGY












37 WIRING 53

0 05 1 15 2 25 3middot106

0

50

100

150

200

250


Ele

ctri

cm

oto

r+

cryo

coo

ler

wei

ght[

kg]


37 WIRING




54 3 METHODOLOGY

100 150 200 250 300 350 400 4501

2

3

4

5

6

7

8


Cable current [A]

Cab

lew

eigh

t[kg

m]

















56 3 METHODOLOGY







1419000 pounds

311 LIMITATIONS 57





58 3 METHODOLOGY




-




kgWh


-


pack-


-



-





-


-



W

4RESULTS




68 -




59

60 4 RESULTS








62 4 RESULTS



22800 22340 - 20


393 392 - 03



421 INPUTS















64 4 RESULTS





0 01 02 03 04 05 06 07 08 09 10

05

1

middot104



Bat

tery

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

500

1000

1500

2000

2500



Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

1

2

3

4middot104



MT

OM

[kg]



66 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

2

4

6middot106


Max

imu

mP

em



0 01 02 03 04 05 06 07 080

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000


Gas

Turb

ine

Mas

s[k

g]



68 4 RESULTS

423 OPERATING MODES


0 01 02 03 04 05 06 07 08 09 10

05

1

15

2

25

3middot106


Max

imu

mC

on

tin

uo

us

Gas

Turb

ine

Pow

er[W

]






0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



70 4 RESULTS






0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

2000


Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

02

04

06

08

1

12middot104


Bat

tery

Mas

s[k

g]



72 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1

2

3

4

5

6middot106


Max

imu

mP

em[W



0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000


Gas

Turb

ine

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34

36

38

4middot104


MT

OM

[kg]



74 4 RESULTS







0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]


0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]







76 4 RESULTS


0 01 02 03 04 05 06 07 08 09 10

2000

4000

6000

8000


Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34middot104


MT

OM

[kg]



431 RANGE


78 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1000

2000

3000

4000

5000

6000


Fuel

wei

ght[

kg]



0 01 02 03 04 05 06 07 08 09 12

25

3

35

4middot104


MT

OW

[kg]



44 FINAL DESIGN 79



700 800 900 1000 1100 1200 1300 1400 1500800

1000

1200

1400

1600

1800

2000


Φ= 01

Φ= 02

Φ= 03

Φ= 04

Φ= 05

Φ= 06

Φ= 00

ebat [ W hkg ]

Fuel

Mas

s[k

g]




80 4 RESULTS






Difference


22340 25470 + 14


103 72 ndash 29


2619 2173 ndash 17





Difference


44 FINAL DESIGN 81

510

1520

25

minus10minus5

05

10

2

4

6

8




82 4 RESULTS







83












EQUATION


t1

V d t (A1)

usingdE


Equation A1 becomes

R =int E f i nal

Est ar t

minus V

Pbat +P f ueldE

=int Est ar t

E f i nal

V

Pbat +P f ueldE

(A3)

Using



And


ηel(A5)


R =int Est ar t

E f i nal

V(Sηel


)lowastPsha f t

dE (A6)


Psha f t =D lowastV

ηpr op(A7)

And

D = C D

C LlowastW (A8)

85


So VPsha f t

becomes

V

Psha f t= C L

C Dlowast ηpr op

W(A9)


R = 1Sηel



int Est ar t

E f i nal

1

WdE (A10)



=Wempt y + Ebat

ebat+ E f uel

e f uel


e f uel lowastebat

(A11)



x = Ebat

Etot

= Ebat

Ebat +E f uel

=Eemηel

Eemηel


(A12)




= S


(A13)

With x = EbatEtot







R = 1Sηel



int Est ar t

E f i nal

1



R = 1Sηel





Wempt y

)(A16)

BIBLIOGRAPHY















87

88 BIBLIOGRAPHY



















BIBLIOGRAPHY 89



















List of Figures

List of Tables

Introduction

Project Description


Technology Overview

Battery Technology





Control Strategies


Methodology

Initiator




Other Modifications


Battery Sizing

Fuel


Take-off

Climb

Cruise

Descent

Landing

HoldLoiter



Comparison


Wiring

Other Components

Component Placement

Implementation

Limitations

Results

Reference Aircraft

Hybrid Aircraft

Inputs


Operating Modes

Optimal Power Split


Range


Final Design


Conclusion

Recommendations


Bibliography

x LIST OF FIGURES


















LIST OF FIGURES xi


LIST OF TABLES








craft 80

xiii

NOMENCLATURE

Acronyms



FF Fuel fraction








SOC State of charge



Subscripts

bat Battery


em Electric motor


avg Average

cable Cable


cryo Cryocooler

disk Propeller disk


gasturb Gas turbine


xv

xvi LIST OF TABLES

prop Propeller


tot total

Symbols

∆ Change in [-]


η Efficiency [-]



ρ Density [ kgm3 ]

A Area [m2]






b Wing span [m]

D Drag [N]

d Diameter [m]

E Energy [Wh]

f Frequency [Hz]



h Altitude [m]

L Lift [N]

l Length [m]

m Mass [kg]

N number

P Power [W]

Q Heat energy [J]

LIST OF TABLES xvii

R Range [km]

S Power split [-]

T Thrust [N]

t time [sec]

U Voltage [V]

V Speed [ms]

1INTRODUCTION






1










3





bull Range 1528 km

















LITHIUM ION





LITHIUM SULPHUR










LITHIUM AIR








Ah



W h(21)

























9






















Power converter

Electric motor


Generator







Power converter

Electric motor

Gas turbine








ηbat ηEM

ηgasturb


Gas turbine

Pbat

PbatOffTake

Pem

Pgasturb

Pshaft

ηprop

Pfuel

ηelec







Si =Pemi

Psha f ti

(22)









HP = Pemmax

Psha f tmax

(23)

and

HE = Ebat

Etot(24)


Φ= Eemtot

Esha f ttot

(25)


3METHODOLOGY







15

16 3 METHODOLOGY

Class 1

Weight

Estimation

Wing- and

power

loading

Geometry

design

modules

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis

Performance

Estimation

Modules

Design

converged

Reference

aircraft

database

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis


Converged

No

Yes

No

Design

Yes


All modules
















Pg astur b

1000

)012

(31)


Pg astur b

1000

)0373

(32)


Pg astur b

1000

)0803

(33)


dpr op =radic

a2



18 3 METHODOLOGY


ηpr opi deal =2

1+(


2+1

)12(35)







P

P0=

(ρ

ρ0

)n

(36)





20 3 METHODOLOGY



0 01 02 03 04 05 06 07 08 09 1middot104

04

06

08

1

12

14

16

18middot106

Altitude [m]

Max

co

nti

no

us

pow

er[W

]



0 01 02 03 04 05 06 07 08 09 1middot104

04

05

06

07

08

09

1

11

Altitude [m]

( ρ ρ0

) n [-]

PP0(ρρ0

)n n=075





0 01 02 03 04 05 06 07 08 09 1middot104

60

80

100

120

140

Altitude [m]

Fuel

flow

[gs



0 01 02 03 04 05 06 07 08 09 1middot104

260

280

300

320

340

Altitude [m]

SFC

[g

kW

h]



22 3 METHODOLOGY

02 03 04 05 06 07 08 09 1280

300

320

340

360

Power setting [-]

SFC

[g

kW

h]







331 BATTERY SIZING








SFC(38)





24 3 METHODOLOGY



2(310)




ηpr op(311)


Pbat =Pem










Pt akeo f f(313)













LIMITATIONS




332 FUEL



26 3 METHODOLOGY




1000

1000(318)




SFC

L

Dln

(mpr ecr ui se

mendcr ui se

)(319)


R = 1Sηel





mempt y

)(320)







x = Ebat

Etot= S



CD Using



ebat(324)


e f uel(325)






bull ηel = 095 [-]


bull CLCD

= 20 [-]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

Power Split [-]

Mas

s[k

g]




28 3 METHODOLOGY


1 Standard Mission

bull Take off

bull Climb 1

bull Cruise 1

bull Descent 1

bull Landing 1

2 Extended Mission

bull Climb 2

bull Cruise 2

bull Descent 2

bull HoldLoiter

bull Descent 3

bull Landing 2

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 24000

02

04

06

08

1

12

14middot104

Clim

b1

Cruise 1

Des

cen

t1

Clim

b2

Cru

ise

2

Des

cen

t2

Loit

erD

esce

nt3

range (m)

alti

tud

e(m

)









sec




in the missionkg


kg


kg



30 3 METHODOLOGY




Start

Set initial

conditions of state

matrix S

Take-off

Climb 1

Cruise 1


Extended

cruise time

Extended

mission

Landing 1Landing 2


burn and battery

weight

Descent 3

Loiter

Descent 2

Cruise 2

Climb 2

Calculate diversion

Rrest Wfbrest

Calculate Rrest

Wfbrest

Fuel weight

converged

End

No

No

Yes

Yes

No

Yes


32 3 METHODOLOGY

341 TAKE-OFF







(Dpr op

2

)2)13

(326)














dEbat

d t= Pbat

3600(328)

dmbat

d t=

dEbatd t

ebat(329)

dm f uel










d t ispositive




V(332)


34 3 METHODOLOGY

0 01 02 03 04 05 06 07 08 09 10

5

10

15

alti

tud

e(m

)

0 01 02 03 04 05 06 07 08 09 10

20

40

60

spee

d(m

s)

0 01 02 03 04 05 06 07 08 09 102468

10

range (km)

γ(d

eg)



Aircraft on

ground

Determine

take-off

power

Initial aircraft

state

Relevant

settings

Select power

setting (1)

Calculate

static thrust

Calculate

propeller

efficiency

Calculate lift

and drag

Calculate

ground

friction drag

Yes

Determine

derivatives

No

Calculate

SFC

Constant power

operating mode

Calculate Pem Pbat

Pgasturb based on

the power split

No

Determine change

in battery and fuel

energy and weight

Calculate Pem Pbat

based on selected

Pgasturb

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Screen height

reached

Calculate

new thrust

No

End Yes


36 3 METHODOLOGY

342 CLIMB










0 20 40 60 80 100 120 140 1601

15

2

25

3

35

4middot106

Range [km]

Pow

er[W

]



0 20 40 60 80 100 120 140 1600

02040608

1middot104

alti

tud

e(m

)

0 20 40 60 80 100 120 140 1606080

100120140

spee

d(m

s)

0 20 40 60 80 100 120 140 1600

5

10

15

20

range (km)

γ(d

eg)


38 3 METHODOLOGY

Determine

maximum

power (take-

off power)

Aircraft state

at end take-off

Relevant

settings

Select

iteration

time step

Determine

drag polar

Calculate

propeller

efficiency

Calculate

thrust

Constant power

operating mode

Determine Pgasturb

based on power

splitNo

Scale max gas

turbine power

based on altitude

and speed

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

End

Calculate lift

and drag

Determine

derivatives

Pgasturb is maximum

gas turbine power

Pgasturb

more than max

turboprop

power

Yes

No

Determine power

setting

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight


Scale max gas

turbine power

based on altitude

and speed


Determine Pem and

Pbat

Cruise altitude

and speed

reachedYes

No



343 CRUISE







Psha f t =T lowastV

ηpr op(333)






40 3 METHODOLOGY


0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 14007500

7600

7700

7800

alti

tud

e(m

)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400139

1392139413961398

140

spee

d(m

s)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400minus05

0

05

1middot10minus2

range (km)

γ(d

eg)



Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

lift drag and

thrust

Calculate

propeller

efficiency

Constant power

operating mode

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Determine

derivatives

No

No

Determine

power

setting for

minimal SFC

Yes

Determine

Pshaft

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Scale max gas

turbine power

based on altitude

and speed

Determine Pgasturb

Battery not

charging and

battery energy

depleted

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Range reached

Yes

End Yes


42 3 METHODOLOGY

344 DESCENT









1360 1380 1400 1420 1440 1460 1480 1500 1520 15400

02040608

1middot104

alti

tud

e(m

)

1360 1380 1400 1420 1440 1460 1480 1500 1520 15406080

100120140

spee

d(m

s)

1360 1380 1400 1420 1440 1460 1480 1500 1520 1540minus15

minus10

minus5

0

range (km)

γ(d

eg)



Aircraft state

at end cruise

Relevant

settings


step

Scale maximum

Pgasturb based on

altitude and speed


Determine change

in aircraft weight


matrix

End

Calculate propeller

efficiency

Determine

derivatives

Descent altitude

reached

Yes

No

Calculate lift and

dragCalculate SFC

Determine Pem and

Pbat (= 0)

Determine Pgasturb

(= Pidle)

Determine change

in fuel weight (no

change in battery

weight)


44 3 METHODOLOGY

345 LANDING





15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

5

10

15

alti

tud

e(m

)

15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

20

40

60

spee

d(m

s)

15272 15273 15274 15275 15276 15277 15278 15279 1528 15281minus3

minus2

minus1

0

range (km)

γ(d

eg)




Determine

landing drag

polar

Aircraft state

at end take-off

Relevant

settings

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Calculate lift

and drag

No

Determine

Pshaft and

thrust

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Pgasturb = Pshaft

Scale max gas

turbine power

based on altitude

and speed

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Speed and

altitude = 0

Yes

End Yes

Aircraft on

ground

Determine

derivatives

Calculate ground

friction drag and

reverse thrust if

applicable

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Calculate SFC

Yes

No

Yes


46 3 METHODOLOGY

346 HOLDLOITER





L CD







Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Determine

CLCD for

max LD

No

Determine

max Pgasturb

and Pidle

Determine Pshaft

based on target

velocity

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Loiter time

reached

Yes

End Yes

Determine Pgasturb

Determine power

setting


48 3 METHODOLOGY









0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2middot104

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

alti

tud

e(m

)

0 200 400 600 800 1000 1200 1400 1600 1800 20000

50

100

150

spee

d(m

s)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus20

minus10

0

10

range (km)

γ(d

eg)


50 3 METHODOLOGY

0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2

25

3

35

4

45

5

middot106

Cli

mb

1Cruise

Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1000

2000

3000

4000

5000

Clim

b1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

range [km]

Mas

s[k

g]

Battery Fuel



352 COMPARISON





S = 100mfuel[kg] 0 0 00 mbat[kg] 5317 5635 + 60



S = 000mfuel[kg] 1735 1804 + 40 mbat[kg] 0 0 00





52 3 METHODOLOGY












37 WIRING 53

0 05 1 15 2 25 3middot106

0

50

100

150

200

250


Ele

ctri

cm

oto

r+

cryo

coo

ler

wei

ght[

kg]


37 WIRING




54 3 METHODOLOGY

100 150 200 250 300 350 400 4501

2

3

4

5

6

7

8


Cable current [A]

Cab

lew

eigh

t[kg

m]

















56 3 METHODOLOGY







1419000 pounds

311 LIMITATIONS 57





58 3 METHODOLOGY




-




kgWh


-


pack-


-



-





-


-



W

4RESULTS




68 -




59

60 4 RESULTS








62 4 RESULTS



22800 22340 - 20


393 392 - 03



421 INPUTS















64 4 RESULTS





0 01 02 03 04 05 06 07 08 09 10

05

1

middot104



Bat

tery

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

500

1000

1500

2000

2500



Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

1

2

3

4middot104



MT

OM

[kg]



66 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

2

4

6middot106


Max

imu

mP

em



0 01 02 03 04 05 06 07 080

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000


Gas

Turb

ine

Mas

s[k

g]



68 4 RESULTS

423 OPERATING MODES


0 01 02 03 04 05 06 07 08 09 10

05

1

15

2

25

3middot106


Max

imu

mC

on

tin

uo

us

Gas

Turb

ine

Pow

er[W

]






0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



70 4 RESULTS






0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

2000


Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

02

04

06

08

1

12middot104


Bat

tery

Mas

s[k

g]



72 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1

2

3

4

5

6middot106


Max

imu

mP

em[W



0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000


Gas

Turb

ine

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34

36

38

4middot104


MT

OM

[kg]



74 4 RESULTS







0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]


0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]







76 4 RESULTS


0 01 02 03 04 05 06 07 08 09 10

2000

4000

6000

8000


Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34middot104


MT

OM

[kg]



431 RANGE


78 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1000

2000

3000

4000

5000

6000


Fuel

wei

ght[

kg]



0 01 02 03 04 05 06 07 08 09 12

25

3

35

4middot104


MT

OW

[kg]



44 FINAL DESIGN 79



700 800 900 1000 1100 1200 1300 1400 1500800

1000

1200

1400

1600

1800

2000


Φ= 01

Φ= 02

Φ= 03

Φ= 04

Φ= 05

Φ= 06

Φ= 00

ebat [ W hkg ]

Fuel

Mas

s[k

g]




80 4 RESULTS






Difference


22340 25470 + 14


103 72 ndash 29


2619 2173 ndash 17





Difference


44 FINAL DESIGN 81

510

1520

25

minus10minus5

05

10

2

4

6

8




82 4 RESULTS







83












EQUATION


t1

V d t (A1)

usingdE


Equation A1 becomes

R =int E f i nal

Est ar t

minus V

Pbat +P f ueldE

=int Est ar t

E f i nal

V

Pbat +P f ueldE

(A3)

Using



And


ηel(A5)


R =int Est ar t

E f i nal

V(Sηel


)lowastPsha f t

dE (A6)


Psha f t =D lowastV

ηpr op(A7)

And

D = C D

C LlowastW (A8)

85


So VPsha f t

becomes

V

Psha f t= C L

C Dlowast ηpr op

W(A9)


R = 1Sηel



int Est ar t

E f i nal

1

WdE (A10)



=Wempt y + Ebat

ebat+ E f uel

e f uel


e f uel lowastebat

(A11)



x = Ebat

Etot

= Ebat

Ebat +E f uel

=Eemηel

Eemηel


(A12)




= S


(A13)

With x = EbatEtot







R = 1Sηel



int Est ar t

E f i nal

1



R = 1Sηel





Wempt y

)(A16)

BIBLIOGRAPHY















87

88 BIBLIOGRAPHY



















BIBLIOGRAPHY 89



















List of Figures

List of Tables

Introduction

Project Description


Technology Overview

Battery Technology





Control Strategies


Methodology

Initiator




Other Modifications


Battery Sizing

Fuel


Take-off

Climb

Cruise

Descent

Landing

HoldLoiter



Comparison


Wiring

Other Components

Component Placement

Implementation

Limitations

Results

Reference Aircraft

Hybrid Aircraft

Inputs


Operating Modes

Optimal Power Split


Range


Final Design


Conclusion

Recommendations


Bibliography

LIST OF FIGURES xi


LIST OF TABLES








craft 80

xiii

NOMENCLATURE

Acronyms



FF Fuel fraction








SOC State of charge



Subscripts

bat Battery


em Electric motor


avg Average

cable Cable


cryo Cryocooler

disk Propeller disk


gasturb Gas turbine


xv

xvi LIST OF TABLES

prop Propeller


tot total

Symbols

∆ Change in [-]


η Efficiency [-]



ρ Density [ kgm3 ]

A Area [m2]






b Wing span [m]

D Drag [N]

d Diameter [m]

E Energy [Wh]

f Frequency [Hz]



h Altitude [m]

L Lift [N]

l Length [m]

m Mass [kg]

N number

P Power [W]

Q Heat energy [J]

LIST OF TABLES xvii

R Range [km]

S Power split [-]

T Thrust [N]

t time [sec]

U Voltage [V]

V Speed [ms]

1INTRODUCTION






1










3





bull Range 1528 km

















LITHIUM ION





LITHIUM SULPHUR










LITHIUM AIR








Ah



W h(21)

























9






















Power converter

Electric motor


Generator







Power converter

Electric motor

Gas turbine








ηbat ηEM

ηgasturb


Gas turbine

Pbat

PbatOffTake

Pem

Pgasturb

Pshaft

ηprop

Pfuel

ηelec







Si =Pemi

Psha f ti

(22)









HP = Pemmax

Psha f tmax

(23)

and

HE = Ebat

Etot(24)


Φ= Eemtot

Esha f ttot

(25)


3METHODOLOGY







15

16 3 METHODOLOGY

Class 1

Weight

Estimation

Wing- and

power

loading

Geometry

design

modules

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis

Performance

Estimation

Modules

Design

converged

Reference

aircraft

database

Class 2

Weight

Estimation

Aerodynamic

analysis

modules

Mission

Analysis


Converged

No

Yes

No

Design

Yes


All modules
















Pg astur b

1000

)012

(31)


Pg astur b

1000

)0373

(32)


Pg astur b

1000

)0803

(33)


dpr op =radic

a2



18 3 METHODOLOGY


ηpr opi deal =2

1+(


2+1

)12(35)







P

P0=

(ρ

ρ0

)n

(36)





20 3 METHODOLOGY



0 01 02 03 04 05 06 07 08 09 1middot104

04

06

08

1

12

14

16

18middot106

Altitude [m]

Max

co

nti

no

us

pow

er[W

]



0 01 02 03 04 05 06 07 08 09 1middot104

04

05

06

07

08

09

1

11

Altitude [m]

( ρ ρ0

) n [-]

PP0(ρρ0

)n n=075





0 01 02 03 04 05 06 07 08 09 1middot104

60

80

100

120

140

Altitude [m]

Fuel

flow

[gs



0 01 02 03 04 05 06 07 08 09 1middot104

260

280

300

320

340

Altitude [m]

SFC

[g

kW

h]



22 3 METHODOLOGY

02 03 04 05 06 07 08 09 1280

300

320

340

360

Power setting [-]

SFC

[g

kW

h]







331 BATTERY SIZING








SFC(38)





24 3 METHODOLOGY



2(310)




ηpr op(311)


Pbat =Pem










Pt akeo f f(313)













LIMITATIONS




332 FUEL



26 3 METHODOLOGY




1000

1000(318)




SFC

L

Dln

(mpr ecr ui se

mendcr ui se

)(319)


R = 1Sηel





mempt y

)(320)







x = Ebat

Etot= S



CD Using



ebat(324)


e f uel(325)






bull ηel = 095 [-]


bull CLCD

= 20 [-]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

Power Split [-]

Mas

s[k

g]




28 3 METHODOLOGY


1 Standard Mission

bull Take off

bull Climb 1

bull Cruise 1

bull Descent 1

bull Landing 1

2 Extended Mission

bull Climb 2

bull Cruise 2

bull Descent 2

bull HoldLoiter

bull Descent 3

bull Landing 2

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 24000

02

04

06

08

1

12

14middot104

Clim

b1

Cruise 1

Des

cen

t1

Clim

b2

Cru

ise

2

Des

cen

t2

Loit

erD

esce

nt3

range (m)

alti

tud

e(m

)









sec




in the missionkg


kg


kg



30 3 METHODOLOGY




Start

Set initial

conditions of state

matrix S

Take-off

Climb 1

Cruise 1


Extended

cruise time

Extended

mission

Landing 1Landing 2


burn and battery

weight

Descent 3

Loiter

Descent 2

Cruise 2

Climb 2

Calculate diversion

Rrest Wfbrest

Calculate Rrest

Wfbrest

Fuel weight

converged

End

No

No

Yes

Yes

No

Yes


32 3 METHODOLOGY

341 TAKE-OFF







(Dpr op

2

)2)13

(326)














dEbat

d t= Pbat

3600(328)

dmbat

d t=

dEbatd t

ebat(329)

dm f uel










d t ispositive




V(332)


34 3 METHODOLOGY

0 01 02 03 04 05 06 07 08 09 10

5

10

15

alti

tud

e(m

)

0 01 02 03 04 05 06 07 08 09 10

20

40

60

spee

d(m

s)

0 01 02 03 04 05 06 07 08 09 102468

10

range (km)

γ(d

eg)



Aircraft on

ground

Determine

take-off

power

Initial aircraft

state

Relevant

settings

Select power

setting (1)

Calculate

static thrust

Calculate

propeller

efficiency

Calculate lift

and drag

Calculate

ground

friction drag

Yes

Determine

derivatives

No

Calculate

SFC

Constant power

operating mode

Calculate Pem Pbat

Pgasturb based on

the power split

No

Determine change

in battery and fuel

energy and weight

Calculate Pem Pbat

based on selected

Pgasturb

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Screen height

reached

Calculate

new thrust

No

End Yes


36 3 METHODOLOGY

342 CLIMB










0 20 40 60 80 100 120 140 1601

15

2

25

3

35

4middot106

Range [km]

Pow

er[W

]



0 20 40 60 80 100 120 140 1600

02040608

1middot104

alti

tud

e(m

)

0 20 40 60 80 100 120 140 1606080

100120140

spee

d(m

s)

0 20 40 60 80 100 120 140 1600

5

10

15

20

range (km)

γ(d

eg)


38 3 METHODOLOGY

Determine

maximum

power (take-

off power)

Aircraft state

at end take-off

Relevant

settings

Select

iteration

time step

Determine

drag polar

Calculate

propeller

efficiency

Calculate

thrust

Constant power

operating mode

Determine Pgasturb

based on power

splitNo

Scale max gas

turbine power

based on altitude

and speed

Battery not

charging and

battery energy

depleted

Yes

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine change

in fuel weight

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

End

Calculate lift

and drag

Determine

derivatives

Pgasturb is maximum

gas turbine power

Pgasturb

more than max

turboprop

power

Yes

No

Determine power

setting

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight


Scale max gas

turbine power

based on altitude

and speed


Determine Pem and

Pbat

Cruise altitude

and speed

reachedYes

No



343 CRUISE







Psha f t =T lowastV

ηpr op(333)






40 3 METHODOLOGY


0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 14007500

7600

7700

7800

alti

tud

e(m

)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400139

1392139413961398

140

spee

d(m

s)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400minus05

0

05

1middot10minus2

range (km)

γ(d

eg)



Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

lift drag and

thrust

Calculate

propeller

efficiency

Constant power

operating mode

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Determine

derivatives

No

No

Determine

power

setting for

minimal SFC

Yes

Determine

Pshaft

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Scale max gas

turbine power

based on altitude

and speed

Determine Pgasturb

Battery not

charging and

battery energy

depleted

Determine change

in battery energy

no change in

battery mass

No

Yes

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Range reached

Yes

End Yes


42 3 METHODOLOGY

344 DESCENT









1360 1380 1400 1420 1440 1460 1480 1500 1520 15400

02040608

1middot104

alti

tud

e(m

)

1360 1380 1400 1420 1440 1460 1480 1500 1520 15406080

100120140

spee

d(m

s)

1360 1380 1400 1420 1440 1460 1480 1500 1520 1540minus15

minus10

minus5

0

range (km)

γ(d

eg)



Aircraft state

at end cruise

Relevant

settings


step

Scale maximum

Pgasturb based on

altitude and speed


Determine change

in aircraft weight


matrix

End

Calculate propeller

efficiency

Determine

derivatives

Descent altitude

reached

Yes

No

Calculate lift and

dragCalculate SFC

Determine Pem and

Pbat (= 0)

Determine Pgasturb

(= Pidle)

Determine change

in fuel weight (no

change in battery

weight)


44 3 METHODOLOGY

345 LANDING





15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

5

10

15

alti

tud

e(m

)

15272 15273 15274 15275 15276 15277 15278 15279 1528 152810

20

40

60

spee

d(m

s)

15272 15273 15274 15275 15276 15277 15278 15279 1528 15281minus3

minus2

minus1

0

range (km)

γ(d

eg)




Determine

landing drag

polar

Aircraft state

at end take-off

Relevant

settings

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Scale max gas

turbine power

based on altitude

and speed

Calculate lift

and drag

No

Determine

Pshaft and

thrust

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Pgasturb = Pshaft

Scale max gas

turbine power

based on altitude

and speed

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Speed and

altitude = 0

Yes

End Yes

Aircraft on

ground

Determine

derivatives

Calculate ground

friction drag and

reverse thrust if

applicable

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Calculate SFC

Yes

No

Yes


46 3 METHODOLOGY

346 HOLDLOITER





L CD







Determine

drag polar

Aircraft state

at end take-off

Relevant

settings

Retrim drag

polar

Calculate

propeller

efficiency

Determine Pgasturb

based on power

split

Determine

CLCD for

max LD

No

Determine

max Pgasturb

and Pidle

Determine Pshaft

based on target

velocity

Constant power

operating mode

Pgasturb is max gas

turbine power

Pgasturb

more than max

turboprop

power

No

Determine power

setting

Yes

No

Determine change

in fuel weight

Calculate SFC

Determine Pem and

Pbat

Determine change

in battery energy

and weight

Determine

derivative of power

split

Calculate SFC

Determine change

in battery energy

and mass

Determine Pem and

Pbat

Determine

change in

aircraft

weight

Calculate

emissions

Calculate

new state

matrix

Loiter time

reached

Yes

End Yes

Determine Pgasturb

Determine power

setting


48 3 METHODOLOGY









0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2middot104

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

alti

tud

e(m

)

0 200 400 600 800 1000 1200 1400 1600 1800 20000

50

100

150

spee

d(m

s)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus20

minus10

0

10

range (km)

γ(d

eg)


50 3 METHODOLOGY

0 200 400 600 800 1000 1200 1400 1600 1800 20000

05

1

15

2

25

3

35

4

45

5

middot106

Cli

mb

1Cruise

Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1000

2000

3000

4000

5000

Clim

b1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

range [km]

Mas

s[k

g]

Battery Fuel



352 COMPARISON





S = 100mfuel[kg] 0 0 00 mbat[kg] 5317 5635 + 60



S = 000mfuel[kg] 1735 1804 + 40 mbat[kg] 0 0 00





52 3 METHODOLOGY












37 WIRING 53

0 05 1 15 2 25 3middot106

0

50

100

150

200

250


Ele

ctri

cm

oto

r+

cryo

coo

ler

wei

ght[

kg]


37 WIRING




54 3 METHODOLOGY

100 150 200 250 300 350 400 4501

2

3

4

5

6

7

8


Cable current [A]

Cab

lew

eigh

t[kg

m]

















56 3 METHODOLOGY







1419000 pounds

311 LIMITATIONS 57





58 3 METHODOLOGY




-




kgWh


-


pack-


-



-





-


-



W

4RESULTS




68 -




59

60 4 RESULTS








62 4 RESULTS



22800 22340 - 20


393 392 - 03



421 INPUTS















64 4 RESULTS





0 01 02 03 04 05 06 07 08 09 10

05

1

middot104



Bat

tery

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

500

1000

1500

2000

2500



Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

1

2

3

4middot104



MT

OM

[kg]



66 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

2

4

6middot106


Max

imu

mP

em



0 01 02 03 04 05 06 07 080

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000


Gas

Turb

ine

Mas

s[k

g]



68 4 RESULTS

423 OPERATING MODES


0 01 02 03 04 05 06 07 08 09 10

05

1

15

2

25

3middot106


Max

imu

mC

on

tin

uo

us

Gas

Turb

ine

Pow

er[W

]






0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Cli

mb

2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W



0 200 400 600 800 1000 1200 1400 1600 1800 20000

1

2

3

4

5

middot106

Cli

mb

1

Cruise Des

cen

t1

Clim

b2

Des

cen

t2

Loit

er

Des

cen

t3

Range [km]

Pow

er[W

]



70 4 RESULTS






0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400

1600

1800

2000


Fuel

Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

02

04

06

08

1

12middot104


Bat

tery

Mas

s[k

g]



72 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1

2

3

4

5

6middot106


Max

imu

mP

em[W



0 01 02 03 04 05 06 07 08 09 10

100

200

300

400

500

600

700

800

900

1000


Gas

Turb

ine

Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34

36

38

4middot104


MT

OM

[kg]



74 4 RESULTS







0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]


0 200 400 600 800 1000 1200 1400 1600 1800 20000

02

04

06

08

1

Range [km]

1-

S[-

]







76 4 RESULTS


0 01 02 03 04 05 06 07 08 09 10

2000

4000

6000

8000


Mas

s[k

g]



0 01 02 03 04 05 06 07 08 09 10

200

400

600

800

1000

1200

1400


Mas

s[k

g]




0 01 02 03 04 05 06 07 08 09 12

22

24

26

28

3

32

34middot104


MT

OM

[kg]



431 RANGE


78 4 RESULTS

0 01 02 03 04 05 06 07 08 09 10

1000

2000

3000

4000

5000

6000


Fuel

wei

ght[

kg]



0 01 02 03 04 05 06 07 08 09 12

25

3

35

4middot104


MT

OW

[kg]



44 FINAL DESIGN 79



700 800 900 1000 1100 1200 1300 1400 1500800

1000

1200

1400

1600

1800

2000


Φ= 01

Φ= 02

Φ= 03

Φ= 04

Φ= 05

Φ= 06

Φ= 00

ebat [ W hkg ]

Fuel

Mas

s[k

g]




80 4 RESULTS






Difference


22340 25470 + 14


103 72 ndash 29


2619 2173 ndash 17





Difference


44 FINAL DESIGN 81

510

1520

25

minus10minus5

05

10

2

4

6

8




82 4 RESULTS







83












EQUATION


t1

V d t (A1)

usingdE


Equation A1 becomes

R =int E f i nal

Est ar t

minus V

Pbat +P f ueldE

=int Est ar t

E f i nal

V

Pbat +P f ueldE

(A3)

Using



And


ηel(A5)


R =int Est ar t

E f i nal

V(Sηel


)lowastPsha f t

dE (A6)


Psha f t =D lowastV

ηpr op(A7)

And

D = C D

C LlowastW (A8)

85


So VPsha f t

becomes

V

Psha f t= C L

C Dlowast ηpr op

W(A9)


R = 1Sηel



int Est ar t

E f i nal

1

WdE (A10)



=Wempt y + Ebat

ebat+ E f uel

e f uel


e f uel lowastebat

(A11)



x = Ebat

Etot

= Ebat

Ebat +E f uel

=Eemηel

Eemηel


(A12)




= S


(A13)

With x = EbatEtot







R = 1Sηel



int Est ar t

E f i nal

1



R = 1Sηel





Wempt y

)(A16)

BIBLIOGRAPHY















87

88 BIBLIOGRAPHY



















BIBLIOGRAPHY 89



















List of Figures

List of Tables

Introduction

Project Description


Technology Overview

Battery Technology





Control Strategies


Methodology

Initiator




Other Modifications


Battery Sizing

Fuel


Take-off

Climb

Cruise

Descent

Landing

HoldLoiter



Comparison


Wiring

Other Components

Component Placement

Implementation

Limitations

Results

Reference Aircraft

Hybrid Aircraft

Inputs


Operating Modes

Optimal Power Split


Range


Final Design


Conclusion

Recommendations


Bibliography

assessment of potential fuel saving benefits of hybrid

Documents