QUANTIFYING OPERATING COST REDUCTION FROM AIRCRAFT PERFORMANCE OPTIMIZATION

David Lax, Mark Darnell, Owen O’Keefe, Brandon Rhone, Nick Visser, GE Aviation Systems, Grand Rapids, MI

Reza Ghaemi, Eric R. Westervelt, GE Global Research, Niskayuna, NY

AbstractThe advent of high-bandwidth data link radios,

airborne broadband internet service, and Electronic Flight Bags (EFB) has enabled the development of low-cost decision support tools that improve operating efficiency. Government laboratories, private companies, and academia are developing these tools as software applications installed on EFBs and computing resources in airline dispatch centers. While these tools achieve small improvements in efficiency on a per flight basis, the cost savings is significant over the service life of an airplane and substantial for a fleet of airplanes.

Considering the many unpredictable and uncontrolled variables that affect fuel burn and operating cost, the problem of quantifying the benefit over a specified service interval becomes a fundamental challenge. The basis of comparison that determines the value of a technology in today’s market is very subjective. A consensus-based industry standard for measuring the monetary benefit of optimal guidance and control has not been established. GE has developed new methods for computing cost-optimal control and state trajectories for air transports and an approach to quantify the monetary benefit an operator can expect relative to a baseline control system. This method yields a fair comparison given the nature of uncontrolled variables that affect fuel burn and non-deterministic control constraints due to air traffic and weather which limit the crew’s discretionary control of the airplane.

This paper describes one of GE’s flight path optimization applications that eliminates the simplifying assumptions applied to legacy path

construction methods to improve operational efficiency. The benefits of this new approach have been assessed using a high-fidelity, physics-based computer simulation of various aircraft types. A novel approach to quantify the benefit compares the cost of GE’s state-of-the-art Flight Management System (FMS) augmented by GE’s decision support tool with the cost realized by GE’s FMS operating without the benefit of decision support. Weather data from NOAA’s Rapid Refresh (RAP) system are used to simulate flights on different calendar days. Comparing two simulated flights removes uncertainties due to aircraft modelling, weather, and ATM routing. The results of the Monte Carlo study are characterized statistically to quantify the cost savings.

Performance OptimizationThe goal of GE’s performance optimization

initiative is to determine cost-optimal control that eliminates the simplifying assumptions of legacy methods to improve operational efficiency while complying with the Instrument Flight Rules (IFR). The pursuit of this goal has led to the development of a flight path optimization tool that can be hosted on an EFB to provide cost-optimal guidance of an air transport. Conceptually, the flight path generation procedure finds the minimum point of a cost function subject to control constraints. Minimization of direct operating cost (DOC) is a complex problem with many contributing factors, including altitude, airspeed, engine throttle, winds and temperatures aloft, and time and fuel burn climbing and descending. Each factor can shift the minimum of the cost function, and thus change the resulting optimal

control. This concept is depicted in Figure 1, which shows the case where different weather patterns change the optimal control.

Figure 1. Flight Path Optimization s.t. Constraints

The problem of minimizing Direct Operating Cost (DOC) is briefly formulated here. In commercial aviation DOC is defined as:

D OC [ $ ]=Fuel Cost [ $ ]+Time Cost [ $ ]

To define DOC as a function of service time, it is expressed in integral form:

DOC=∫t 0

t f

(c t+ c f ) dt

where ct is the time-related cost rate to operate the airplane, ċf is the cost rate of fuel, to is the departure time from the origin, and tf is the arrival time at the destination. The cost rate of fuel, ċf, in units of dollars per hour may be expressed as the product of fuel flow rate, wf, and the cost of fuel, cf, expressed in dollars per pound. Substituting gives:

DOC=∫t 0

t f

(c t+w f c f ) dt

Historically, airspeed (Mach number) and altitude are fundamental pilot controls for longitudinal motion of the airplane. To formulate the problem using these control variables, the

independent variable is changed from time to distance:

DOC=∫R0

R f

( c t+w f c f

V g )dr

where r is along-track position, Ro is the position at to, Rf is the position at tf, and vg is ground speed.

On most commercial transports today, the operator specifies the cost of time and the cost of fuel as a single parameter called the Cost Index, CI, which is defined as:

CI [ 100lbhr ]=TimeCost [ $

hr ]Fuel Cost [ ₵

lb ],

100∗CI=Ct

C f

Re-arranging and substituting gives:

DOC=∫R0

R f 100 ∙CI ∙ c f +W f ∙c f

V gdr

Dividing both sides by constant cf and defining a new cost function, ψc, gives

ψc=DOC

cf=∫

R 0

R f 100 ∙CI+W f

V gdr

Thus, the problem is to find the speed and altitude that minimizes ψc. Note that the cost of fuel burned to traverse from Ro to Rf depends on weight, altitude, Mach number, engine deterioration, atmospheric conditions (weather patterns), and aircraft trim (control surface deflections).

GE has chosen several technological pursuits that are believed to be the primary contributors driving operational costs. Initial work performed by GE for the Federal Aviation Administration (FAA) Continuous Lower Energy, Emissions, and Noise (CLEEN) program [1] produced a method based on an Energy State Approximation to determine cost-optimal control for the climb phase. For the CLEEN II program, GE is extending this method to the cruise

and descent phases of flight. GE is applying a phased development process that continuously builds upon previous work. The improvements implemented by each generation of the design are described below.

Generation A: CLEEN II technologies began by refining the cruise profile prediction algorithms to consider mass as a state variable, allowing a more optimal constant altitude selection for cruises of varying distances. With an optimal climb and cruise profile established independently, the next step was to unify each of the optimized phases and ensure that their independent optimization does not compromise overall savings. Intuitively, it can be reasoned that the cruise altitude selection affects the cost of the climb and descent flight phases. Climbing to a higher altitude inevitably includes a longer climb phase, which takes place at a higher thrust setting than that of cruise and demands more fuel. A similar effect occurs for descent due to the longer duration required to descend from a higher altitude. This tradeoff between the cost of the cruise and ascending/descending phases demands consideration of the cost to climb and descent in the calculation of the cruise altitude. The optimizer was improved to balance these costs and generate an optimal profile to smoothly transition between phases of flight.

Generation B: Successful completion of Generation A resulted in significant fuel savings for standard day operations. Further work was conducted to account for non-standard day wind and temperature in the generation of the optimal flight profile using a high-fidelity weather data. GE’s EFB-hosted technology has access to a weather server that can provide the optimizer with 4D weather data. The result is an optimizer that can produce a flight profile that tracks favorable weather (such as tailwinds or colder air) to extract further savings, especially when compared to legacy low-fidelity weather data. Figure2 shows a continental map with wind data, along with an overlaid representative lateral flight path (shown in yellow). Weather data is extracted from the 4D grid along the flight trajectory.

Wind Speed (kt)

20

40

60

80

100

120

140

Temperature (K)

226

228

230

232

234

236

238

240

242

244

Figure 2: Wind Data with Overlaid Lateral Flight

Generation C: The next improvement was to improve the constant-altitude cruise phase developed in Generation A with a phase that included altitude and speed changes. Legacy methods for computing these “cruise steps” either do not exist for some aircraft, or are overly simplistic by not fully utilizing available weather data for others. Generation C implemented an exhaustive graph search algorithm to compute multiple optimal climb and descent steps of varying magnitude. These multiple steps track both aircraft performance changes with weight and favorable weather patterns, such as tailwinds at different cruise altitudes, as shown in Figure 3. Similar work was performed by MIT Lincoln Laboratories in their CASO study, which confirmed the benefits of tracking weather patterns during the cruise phase [2].

Figure 3. Altitude Profile Tracking Temperature

Detailed Problem StatementA fundamental chicken or the egg problem

arises when considering benefit assessment for performance optimization technologies. The benefit of these technologies must be proven before expending significant effort to produce a flight-

worthy certified system, and the most accurate way to assess the benefit is to collect data from a fielded fleet of aircraft.

Direct Comparison in Flight Test Experiments A solution to the problem of demonstrating

benefit would be to perform a small number of controlled flight tests comparing outputs of pre-production versions of the new technology against the legacy production system. In these tests, the aircraft is equipped with an advanced sensor package and all variables are held at prescribed values during the test interval (on the order of minutes). In engine testing for fuel efficiency, even the physical position of crew members aboard the aircraft is fixed to ensure the aircraft center of gravity doesn’t shift during the test. Despite efforts to control the aircraft environment, small variations arise due to factors outside of crew control (wind gusts, turbulence, etc.). The uncertainty in test results caused by these effects is further compounded by sensor measurement errors, making it very difficult to measure a benefit smaller than 1% with statistical significance.

The aircraft trajectory optimization benefit assessment cannot be performed over a short, highly controlled experiment. To measure the benefits of this technology, one must look at an entire flight, end-to-end. The experiment must be statistically significant over conditions relevant to a fleet of aircraft for their service life.

The total fuel burn and time of arrival (the primary operating cost drivers described in the preceding section) are dependent on environmental conditions and aircraft performance. In this type of experiment, issues arise when attempting to duplicate flight conditions between two flights.

In an experiment, one could fly the same aircraft with the same weight and balance, flying the same filed flight plan between the same two cities within a window of several hours. Even in this scenario, weather patterns vary, in addition to discrepancies due to the timing of air traffic control clearances.

Another option would be to fly two aircraft (one with new technology and one with old) simultaneously along the same route. In this hypothetical experiment, slight differences between engine performance and aerodynamics would introduce fuel and time differences between the flights.

Comparison to Fleet Metrics using Flight Test Experiments

Statistical hypothesis testing may be used to estimate the number of flight trials (observations) required to demonstrate fuel savings. The concept is to use an estimator for fuel burn and pose the detection of fuel burn improvement as a statistical hypothesis testing problem. If there is fuel burn reduction with the improved FMS technology (relative to the legacy), the estimator applied to a set of flight trials with the improved FMS will have a different mean error than the estimator applied to a set of flight trials with the legacy FMS. The problem may be formulated as follows:

Let μ0 be the mean of the estimator error when applied to trials with the legacy FMS and μ1be the mean of the estimator error when applied to trials with the GE FMS. Then, to show at least QUOTE δ δbenefit, the following null and alternate hypothesizes may be formulated:

• H 0 : μ1<μ0+δ

• H 1: μ1≥ μ0+δ

In words, the null hypothesis is that at least δ amount of cost isn’t saved and the alternate hypothesis is that at least δ amount of cost is saved. Several assumptions are made:

A1. The estimator error is normally distributed

A2. The standard deviation of the estimator, σ e, is known and is the same when the estimator is applied to either set of trials

A3. The observed difference between the means is:

D :=μ1−μ0>δ

Note that the D must always be strictly greater thanδ ; that is, it can never be shown that more cost is saved than was observed. Moreover, the closer δ is to D, the more trials that will be required.

Currently, the estimation methods are accurate within 0.4% - 1.0% standard deviation, including modelling and sensor measurement errors. We optimistically assume the σ e≔0.4% standard deviation case for the remainder of this analysis.

Preliminary computer simulations of the trajectory optimization benefits result a mean of 0.5% cost savings over the legacy system with a standard deviation of 0.15% for a single aircraft model. Estimation methods suggest errors in estimation of tail-specific performance variation of 0.3%. Statistically combining error sources results and reframing into the hypothesis testing framework resulting in a population mean of D ( μD )≔0.5 %, and standard deviation of the experimental results σ D≔0.34 %.

The experimental benefit observations are taken as random draws from the distribution described above. As such, there will be flights that exceed the mean savings, and some that do not. There may even be observations where the new technology is costlier than the legacy system. Figure 4 shows that the probability that the experiment is successful (defined as showing a 0.5% benefit with statistical significance) will require hundreds or potentially thousands of flight trials, which is an economically infeasible proposition. To perform a flight trial of this scale, the trials would need to be performed as part of normal commercial revenue flight, which leads back to the original problem of incurring cost to produce a certified system without proof of benefit.

Figure 4. Likelihood of statistical significance

Assessment through SimulationWhere flight test approaches fall short, a

properly structured experiment using computer simulation can provide an economically feasible way to show realistic fleet-wide benefits. This method must ensure an “apples-to-apples” comparison, that eliminates differences due to environmental conditions and tail specific performance.

Another consideration when assessing the benefit of any new technology is the baseline to which it is compared. It is reasonable to expect comparisons to a few different baseline profiles. One possible comparison is to the best profile a comparable legacy solution can provide. A second option is to compare to flight profiles as flown, using along-track and other recorded data as the baseline. It is important to note this difference, as reports from competing entities may not use the same baseline, and thus a direct comparison between each entity’s report may inaccurately represent the relative benefit. The methods presented within this report provide a more conservative estimate of the fleetwide operating cost reduction obtained through comparison to the optimal legacy solution.

The remainder of this paper discusses one simulation approach, and the results of this assessment for an early version of GE’s trajectory optimization decision support tool, including technologies through Generation B (unified climb,

cruise, descent and high-fidelity weather – no cruise steps).

Benefit AssessmentGE has developed an approach to accurately

assess the benefit gained from cost optimal trajectories. This approach compares the cost of an optimal trajectory generated by GE’s flight path optimization application to profiles generated by baseline, or legacy, FMS technologies. These baseline and optimized trajectories are simulated by a 3DOF simulator which calculates the time and fuel used in each flight profile. The same weather day and time is used for compared profiles.

To ensure a fair comparison, a few assumptions are necessary:

Generated flight profiles are flown as is. That is, there is no rerouting or commanded altitude changes

Altitudes for each profile must adhere to flight levels (increments of 1000 ft. or 2000 ft.)

The aircraft model is perfect

These assumptions are enforceable on the generated profiles in simulation, but impractical in ordinary real-world flight. It is for this reason that comparing between simulation and real-world trajectories (such as radar tracks) is not used to judge the benefit of the flight path optimization application generated profile. Comparing the optimal profiles to radar tracks, or similar, would inflate the claimed savings due to errors introduced by an imperfect aircraft model, rerouting, or other uncontrollable sources of error. Flight path optimization benefits in the presence of air traffic management intervention (real-world conditions) will be very close to these results; we assume both the optimal and legacy profiles would be managed similarly and the benefit impact would cancel over many flights.

In this experiment, flight profiles are generated for many cases whose inputs are determined via a Monte Carlo method. The inputs for each case are

aircraft type, route, weight, and weather date and time. Each case is run using a specified vertical separation minimum of 1000 ft. and 2000 ft. (impacting the available cruise altitude selections) as well as a cost index of 0 and 25. Each case is simulated using a profile created using GE’s flight path optimization application and a legacy profile generated from baseline FMS technologies. Profiles generated by the flight path optimization application are then compared to the legacy profile.

Advanced Technology TestbedThe Advanced Technology Testbed (ATT) is a

simulation environment developed to serve as the simulation platform for quantifying the cost benefit of using a path provided by GE’s decision support tool. The ATT houses a three degree of freedom dynamics model and contains all the logic necessary to track a reference trajectory. The simulation avoids the need to model almost all inner-loop controllers by modeling closed-loop transient performance with filters.

The ATT contains three main models necessary for accurate simulations of flight profiles:

1. FMS Model: Contains the model of the FMS, the main purpose of which is generating target commands for the aircraft model. It is a general representation of the real FMS and contains the logic necessary for parsing FMS generated prediction blocks.

2. Environment Model: Contains the model of the environment, including wind and temperature. This system is capable of modeling various weather days.

3. Aircraft Model: Contains the model of the aircraft and engines including drag, thrust, and fuel flow. Additionally, this model contains the logic that moves the aircraft through space. To do this, the model contains kinetics, to describe steady state aircraft motion, and kinematics, to describe the transient performance of an aircraft.

These two solutions combine to create a representation of real aircraft dynamics.

After completing a simulation, the ATT outputs the time and fuel required for the specified flight profile. This simulation enables the study of many flights combining multiple input parameters such as aircraft type, weight, route length, weather day, etc.

Monte Carlo SetupTo prove the viability of this technology over a

wide application range, a large test set of flights is simulated for comparison against the baseline technology. Flights are generated with varying combinations of aircraft type, takeoff gross weight, lateral routes, and other typical operational demands (for instance, flight level must be at 2000 ft. intervals to meet the vertical separation minimums).

A Monte Carlo method is employed to generate scenarios for the individual test flights. This random sampling of probabilistic distributions allows for a relatively small number of test flights to be representative of the target fleet, as opposed to an exhaustive set of all combinations of variability. The following sections describe the distributions driving the selection of simulation inputs.

AircraftThe trajectory optimization technology can be

employed on any airframe model. Five different aircraft are chosen for this assessment to be characteristic of the commercial airline fleet in service today. Table 1 contains an estimated fleet breakdown for the top eight largest passenger airlines of North America in terms of enplaned passengers, fleet size and number of destinations. These fleet estimates classify over 70% as narrow-body, 14% as wide-body, and 13% as regional carriers [3].

The Boeing 737-800 and Airbus A320-200 are chosen in the narrow body category, the Boeing 777-300 and Airbus A330-200 as wide bodies, and the Embraer 175 AR as a regional jet. The aircraft chosen for a test case is randomly selected based off

the percentages in Table 1, with a slight preference given to the 737 for narrow-body flights based on distribution of these aircraft in service.

Airline Narrow Wide RegionalAmerican 76% 15% 8%Delta 49% 18% 33%Southwest 100% 0% 0%United 76% 24% 0%Air Canada 43% 42% 15%Alaska 76% 0% 24%JetBlue 61% 0% 39%WestJet 97% 3% 0%Totals 73% 14% 13%

Table 1. Fleet Aircraft Classification

Performance and physical characteristics for each aircraft are obtained using an aircraft analysis tool called Project Interactive Analysis and Optimization (PIANO) [4]. These data are then used to derive additional data required to execute the FMS.

RoutesAn analysis of the daily flights by each chosen

airframe is conducted to determine what distances are representative of in-service operation. Table 2 contains a summary of this data. Note that the minimum and maximum distances are not absolute, but rather represent the observed extrema found in the selected date range.

Airframe Min [NM]

Median [NM]

Max [NM]

Boeing 737-800 25 1125 3325Airbus A320-200 25 975 2775Boeing 777-300 100 3500 10900Airbus A330-200 50 1750 6650Embraer 170 AR 25 600 2075

Table 2. Flight Distance Statistics

The final route length distribution in the Monte Carlo analysis is generated to match those observed in the historical data. The test set is discretized into twenty routes, with distances varying from 200 to

7000 nautical miles. Each route is created by selecting origin and destination airports whose separating distances fall within the ranges of Table 2. Jeppesen-documented airways and navigable waypoints are then chosen between airports to elongate paths and create realistic lateral tracks for simulation; several routes also included standard instrument departures and standard terminal arrival

routes. Figure 5 depicts the lateral path of several planned routes.

Limited weather data availability demands that all routes be constructed within the United States. To prevent the effective cancellation or stabilization of weather, longer routes are constructed to traverse large latitude and longitude spans. Traveling around large portions of the contiguous US increases the technologies exposure to varying weather types and severity.

Route distances for each test flight are chosen via random sampling of a probability distribution function that is constructed to fit the historical data. Route direction was randomly selected to provide more variance in weather effects.

Figure 5. Benefit Assessment Route Mapping

An additional consideration when choosing airport pairs is frequency of use. Preference is given to airports that are considered “hubs.” Runways are selected for each airport to ensure takeoff and landing into the wind. Where appropriate, each runway also has an associated standard instrument departure, possibly with an enroute transition, and a standard terminal arrival with relevant approach and transition.

WeightsA weight range for each aircraft is chosen to

represent the in-service operational range and an estimate of the rate of occurrence of each weight. This is accomplished by assuming

W Gross=W operatingempty +¿W fuel+¿ PAX∗Seats∗W passenger¿¿

subject to the limitation of maximum takeoff weight.

A survey of publicly available data was conducted to determine each airframe’s number of available seats. PIANO source data provided operational empty weight and maximum takeoff weight. FAA advisory circular AC120-27E [5] provides for estimation of the average passenger weight to be approximately 200 lbs. The passenger load factor (PAX) is the independent variable used to create a gross weight range representative of in-service operation. A random passenger weight between 0% PAX and 100% PAX, as shown in Figure6, is selected from a truncated normal distribution centered at 80% [N(80,20)] to determine the passenger weight for each case. Final weight for each airframe, route, and weather day combination is determined to be the summation of operating empty weight, passenger weight, and the weight of fuel required to reach the destination with the addition of reserve fuel.

0 20 40 60 80 100PAX Percentage

0

0.005

0.01

0.015

0.02

0.025

Pro

babi

lity

Den

sity

Fun

ctio

n

Possible PAX Distributions

Figure 6. Truncated Normal Distribution for PAX

Weather ConditionsSeveral representative days, containing nominal

days and “inclement” days where major weather events occurred, are chosen to be used in the benefit assessment. RAP data for these days exists as actual observed data (recorded every hour) and as forecasted data (as predicted at each hour, for the next 18 hours). Predicted profiles utilize the freshest forecast data relative to the takeoff time and date. Random takeoff times are chosen using a uniform distribution. The simulation of each of the flights utilize only the observed weather data.

A subset of seven “normal” and three “inclement” weather days were used for random selection, with approximately 87% of the days being “normal” and 13% being “inclement.” The effects of weather events are regional and therefore do not affect all chosen routes on a specific weather day.

Additional ParametersSeveral other parameters are varied as part of the

GE decision support tool benefit assessment. Altitude separation is used to assess the impact of complying with FAR 14 CFR 91.159 and 91.179, which requires cruise at flight levels that are multiplicative by 1000 feet. To assess the full range of impact, separation is selected from 1000 and 2000 feet to represent one-way and two-way airways in both the East and West primary directions.

Carriers use cost indices to account for the cost of the aircraft operating crew by specifying the relation between the cost of time and fuel. Every generated case is conducted with cost indices of both 0 (fuel cost only) and 25 (typical fuel and time blend for commercial revenue service flight) to assess direct operating cost.

ResultsThe following sections discuss the benefit

assessment results of the Generation B technology.

The assessment of Generation C and Generation D are in progress.

Cost Savings (Cost Index 0)A total of 4000 cases were simulated in the ATT

to determine the benefit of GE’s flight path optimization application. Cumulative fuel savings of 0.53% are observed over the legacy method. This metric represents the total fuel savings from all flights as a percentage of the total fuel burn for all flights. The fleetwide mean savings over legacy 99% confidence interval is 0.49% - 0.57%. In other words, if the legacy FMS is operated in a manner consistent with the Monte Carlo set up for 2000 flights; there is a 99% certainty that the average, aggregate benefit observed in that sample will be between 0.49% and 0.57%.1 Operating cost reduction for any single flight varies between -0.7% and 4.3% [0.5 th - 99.5th

percentile]. A histogram for the dataset is shown in Figure 7. Note that outliers have been removed from the data set.

-1 0 1 2 3 4 5Percent Savings

0

50

100

150

200

250

300Legacy Direct Operating Cost Savings (CI 0) - Mean = 0.53%

Losing cases (red)mitigated byproductionized sytem

Figure 7. Histogram of Cost Savings (CI = 0)

In a productized version of this technology, operational mechanisms will be enforced to analyze the predicted cost savings to reduce the likelihood of making a flight plan change to a costlier trajectory.

Cost Savings (Cost Index 25)Cumulative Direct Operating Cost savings of

0.44% are observed over Legacy. This metric 1 As described in previous sections, this experiment is designed carefully to mimic real-world conditions, however, there may be other conditions encountered in real flights that are not accounted for in this study that may vary results.

represents the total direct operating cost savings from all flights as a percentage of the total direct operating cost. The fleetwide mean savings over Legacy 99% confidence interval is 0.41% - 0.48%. Operating cost reduction for any single flight varies between -0.8% and 2.5% [0.5th - 99.5th percentile]. A histogram for the data set is shown in Figure 8. Note that outliers have been removed from the data set.

-1 -0.5 0 0.5 1 1.5 2 2.5 3Percent Savings

0

50

100

150

200

250

300

350Legacy Direct Operating Cost Savings (CI 25) - Mean = 0.53%

Losing cases (red)mitigated byproductionized system

Figure 8. Histogram of Cost Savings (CI = 25)

Example ProfileFigure 9 depicts an altitude profile of a flight

and the resulting cumulative fuel savings as a function of distance. This specific case is a typical example of how a profile generated by GE’s flight path optimization application saves fuel.

0 100 200 300 400 500 600 700 800Distance (nm)

0

2

4

6

Alti

tude

(ft)

104 Altitude Profile

LegacyGE

0 100 200 300 400 500 600 700 800Distance (nm)

0

100

200

Cos

t Sav

ed (l

bs) Fuel Savings (Positive means GE saved)

GE Savings over legacy

Figure 9. Example Flight Profile Saves Fuel

To understand how savings are generated, it is important to look at each phase of flight individually as well as the combined effect of all flight phases. In this case, it is shown that the optimal path saves fuel throughout the climb phase. The reason for this is twofold. First, variable control profiles allow for more efficient climbing flight compared to a constant control profile. Second, in this case, the optimal profile selects a lower cruise altitude. When only considering the cruise phase of flight, the legacy altitude is more optimal, causing fuel savings to decrease during cruise; however, when combining climb, cruise, and descent, an overall more optimal flight profile is generated from the lower cruise altitude. The generated optimal profile has sections of optimality and suboptimality during different phases of flight showcasing how the optimal profile is generated by assessing tradeoffs between climb, cruise, and descent.

Aircraft TypeFive aircraft models are assessed to determine

the benefit of GE’s flight path optimization application. Generally, the savings remain similar between aircraft models, but the Embraer 175 and A320 have the lowest amount of savings among all aircraft tested. The A330, B737, and B777 follow in their respective order. The specific percent savings is shown in Table 3.

E175

B737

A320

A330

B777

Mean Savings (%)

0.10 0.41 0.17 0.31 1.08

Table 3. Percent savings for CI = 0

Splitting this data into aircraft class, as shown in Figure 10, shows that narrow body aircraft, the most common aircraft type, has the highest median savings driven from the flight path optimization application.

Regional Narrow WideAircraft

-0.5

0

0.5

1

1.5G

ross

Sav

ings

(lbs

)DOC Savings Over Legacy

Figure 10. Percent Savings by Aircraft Type

It was found that the E175, the only analyzed regional aircraft, performs the worst due to low savings in climb. Some investigation revealed that the optimal climb profile for many E175 flights tends to resemble the legacy constant control profile. This results in lower savings at the end of climb and therefore, lower savings for the overall flight.

Route LengthTwenty routes are chosen to represent route

distances flown commonly in industry today. The number of flights along each route is specific to each airframe, based on available historical data. By sorting the savings by aircraft type and route, as is done in Figure 11, the effect of route length on the generated savings varies; the dark lines are placed at the mean savings. Note that what is considered a long flight is relative to aircraft size; the larger the aircraft, the longer flights that exist for that aircraft.

Short Medium LongRoute

-4

-3

-2

-1

0

1

2

3

4

Per

cent

Sav

ings

DOC Savings Over Legacy Sorted by Route Sorted by Aircraft Type

RegionalNarrowWide

Figure 11. Results Sorted by Aircraft and Route

For short flights, narrow body aircraft benefit the most from GE’s flight path optimization technology. This can be attributed to the lower cruise altitudes selected for shorter cruise distances – a direct result of the unification of climb, cruise and descent. In long flights, the savings increase with the increase in aircraft size. Wide body aircraft save the most while regional aircraft save the least. The length distribution of wide body flights causes this trend, which includes routes up to 7000nm in length. The long distance allows for significant savings to accumulate throughout cruise when different altitudes are selected as compared to those of the legacy method, leading to a slightly lower fuel burn rate. Generally, the percent savings are directly correlated to the difference in selected cruise altitude, shown in Figure 12. A positive altitude difference represents a higher optimal altitude than legacy.

-10000 -5000 0 5000Cruise Altitude Difference [ft]

-6

-4

-2

0

2

4

6P

erce

nt S

avin

gsImpact of Route Length on Savings

Figure 12. Impact of Different Cruise Altitude

The percentage of fuel saved scales directly with the magnitude of difference in altitude selection.

Next StepsBy duplicating the operating conditions and

procedural constraints in both trials of a comparative assessment, the benefit of an improved control relative to a legacy control can be quantified for a single flight cycle. By varying the vehicle weight and the state of the atmosphere probabilistically and flying many routes of different range and using different procedures, a Monte Carlo simulation yields the benefit an operator can expect for a fleet of airplanes—again relative to the performance of the legacy design that is the basis of comparison. Thus, with this type of assessment, an operator can judge how well the improved system performs relative to the legacy design.

To decide if the new system is worth the cost to replace the legacy design, the operator must know the monetary benefit of using the new system in place of the current design in actual service, which includes additional effects beyond those considered in this assessment.

Clearly, to minimize cost, a crew must have the authority to fly the airplane in the most efficient manner. When discretionary control is constrained—to comply with instrument procedures and airspace

restrictions or to avoid convective weather and air traffic—then the opportunity to minimize cost is likewise constrained. Therefore, to quantify the actual benefit of an improved control, all constraints must be identified and applied equally to both the new control and the baseline method. Both systems will perform the same during those times where the controls are constrained the same. This method is a conservative quantification of the benefits compared to other baselines, but is most likely to be aligned with true operational savings in revenue service flight.

Considering the current assessment and the need to quantify the benefit in revenue service, two questions must be addressed:

1. Are all constraints that affect operating cost properly accounted for in GE’s benefit assessment?

2. How well does GE’s optimal control perform compared to competing designs—that is, when a competing design is not the basis of comparison for judging relative performance.Regarding the first question, GE’s Monte Carlo

study accounts for random weather, but not control constraints due to random weather and air traffic that must be avoided. Therefore, the simulation must be extended as follows to better estimate the benefit in revenue service:

The optimizer must search the model of the atmosphere for convective and turbulent weather and constrain the admissible control to avoid operating in this airspace.

The conditional probability of ATC ordering a deviation from the flight plan (due to weather or traffic) as a function of the airspace, the season, and time of day must be derived. As well, the trajectory of the deviation must be characterized probabilistically to account for the increased cost due to the resulting increase in time and or distance of the flight.Recall, also, that GEN C of GE’s optimal

control includes altitude changes during the cruise phase. To ensure an accurate comparison for

measuring the benefit, the legacy cruise altitude is updated using the most common methods that dispatchers and Flight Management Systems use today to determine a step climb during cruise.

Note, however, a pre-planned variable cruise altitude cannot be filed as the flight plan. Step changes in altitude during cruise are opportunistic. Clearance for a change is unlikely in crowded airspace, but probable for long-range and transoceanic routes. Accordingly, the conditional probability of a clearance as a function of the operating region and time of day must be established to determine the benefit an operator can expect. Moreover, in the event a request is not approved, the optimum cruise control must be recomputed while a flight is underway to determine the next opportunity for a favorable maneuver.

Regarding the second question above, the only practical way to judge the value of competing designs—without directly comparing the performance of each design—is to establish a standard benchmark for measuring relative performance. This benchmark must be a consensus-based industry standard that accounts for all random and uncontrolled variables that effect the cost of operations and is statistically representative of how air transports are flown today.

This means all factors that affect operating cost must be accounted for, including control constraints imposed by convective and turbulent weather and air traffic. Indeed, if the system finds a control that avoids poor weather and traffic, it does not increase the burden on crews, dispatchers, and controllers to verify the control is safe, and thus it is more likely to be used in practice.

Other factors must also be considered for acceptance by the aviation community. For example, the variable climb control generally yields a greater time and distance to cruise and, potentially, a different ride quality.2 This means the airplane may enter enroute airspace at a different time and position

—even a different sector—relative to standard operations today.3 For controllers to be receptive of this change, their workload to manage the traffic cannot increase.

Conversely, if the operational constraints imposed by the present Instrument Flight Rules can be relaxed, a greater benefit may be realized by cost-optimal control. Arguably, the central pillar of the Next-Generation Air Transportation System (NextGen ATS) is performance-based air traffic management to improve operational efficiency. By characterizing performance relative to a standard baseline, using tools such as GE’s Advanced Technology Testbed, new figures-of-merit may be developed for judging the quality of an FMS or EFB application. To be sure, these metrics are also needed for measuring the value of the candidate policies proposed for managing traffic in the NextGen ATS.

References

[1] FAA, 2018, Continuous Lower Energy, Emissions, and Noise Program, Washington, DC. https://www.faa.gov/about/office_org/headquarters_offices/apl/research/aircraft_technology/cleen/ .

[2] Jensen, Luke, R. John Hansman, Tom G. Reynolds, Joseph Venuti, 2014, Cruise Altitude & Speed Optimization (CASO) Research Overview, Massachusetts Institute of Technology Lincoln Laboratory

[3] Planespotters, 2017, Planespotters Airline Index, Berlin, Germany https://www.planespotters.net/.

[4] Simos, Dr. Dimitri / Lissys Limited, 1990-2017, Piano v5.3 [Computer Software], Woodhouse Eaves, LE, UK.

[5] FAA. (2005). Advisory Circular - Aircraft Weight and Balance Control. Washington, DC: Flight Standards Service.

2 The admissible control in GE’s method is constrained to ensure a specified ride quality.3 GE has studied the effect of the variable control climb on the air traffic control environment and determined the state trajectory is not substantially different from that of a heavier aircraft.

AcknowledgementsThe authors wish to thank the Federal Aviation

Administration for their generous support of this work under programs Continuous Lower Energy, Emissions, and Noise (CLEEN) and CLEEN II, contract numbers DTFAWA-10-C-00046 and DTFAWA-15-A-80013.

Thanks to Ben Bennink, Perry Bonanni, Mack Cumings, and Max Ellison for their work in developing the trajectory optimization software.

DisclaimerThe results and opinions expressed within do not

necessarily reflect the view of the FAA.

Email AddressesFor more information on this technology or

assessment method, please contact:

Dave Lax: david.lax@ge.com

2018 Integrated Communications Navigation and Surveillance (ICNS) Conference

April 10-12, 2018