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IAC–17–D2.7.12
Conceptual Design Analysis for a Two-Stage-to-OrbitSemi-Reusable Launch System for Small Satellites
Christie Alisa Maddocka, Federico Tosoa, Michael Westb, Joanne Westb, Konstantinos Kontisc, SriramRengarajanc, David Evansd, Andy Milned, and Stuart McIntyree
aAerospace Centre of Excellence, University of Strathclyde, Glasgow, Scotland, United Kingdom, email:[email protected] Systems Regional Aircraft, Prestwick, Scotland, United Kingdom, email: [email protected] Sciences, University of Glasgow, Scotland, United Kingdom, email: [email protected] Gravity Engineering, Hants, England, United Kingdom, email: [email protected] Access, Prestwick, Scotland, United Kingdom, email: [email protected]
Abstract
This paper presents the conceptual design and performance analysis of a partially reusable space launch vehiclefor small payloads. The system uses a multi-stage vehicle with rocket engines, with a reusable first stage capable ofglided or powered flight, and expendable upper stage(s) to inject 500 kg payload in different low Earth orbits. Thespace access vehicle is designed to be air-launched from a modified aircraft carrier. The aim of the system design isto develop a commercially viable launch system for near-term operation, thus emphasis is placed on the efficient useof high TRL technologies. The vehicle design are analysed using a multi-disciplinary design optimisation approachto evaluate the performance, operational capabilities and design trade-offs. Results from two trade-off studies areshown, evaluating the choice wing area and thus aerodynamic characteristics, and the choice of stage masses andengines selection on the mission performance.Keywords: space access, trajectory optimisation, space transportation
1. IntroductionThe space market is shifting to include smaller sa-
tellites with a focus on expanding commercial ap-plications. Since 2012, 71% of satellites launchedhave a spacecraft mass less than 600 kg, with 34% ofthose being cubesats [1]. The growing market for do-wnsteam applications from single consumers to largebusinesses, and the planned development of mega-constellations has translated into a predicted demandfor small satellite launchers, from a current launchrate of 400 satellites in 2016, to a forecasted marketof 600 by 2020, and over 2000 satellites by 2030 [1].
Along with this predicted growth, is a predictedbottleneck due to low-cost launch options. A fo-recast by SpaceWorks overestimated the numberof nano/microsatellites launched in 2016 by nearly100%, predicting 210 satellites launched comparedto an actual figure of only 101. Their forecast for2017 predicts a continuing high backlog of nano- andmicrosats due to “technical challenges and limitedlaunch vehicle availability.” [2]
These commercial drivers within the new space [3]market have also driven a number of government ini-tiatives, in particular in the domain of space access.The UK National Space Policy (2016) states “access
to safe and cost-effective launchers is clearly funda-mental to any countrys long term capacity to parti-cipate in space-based activities.” There have been anumber of programmes to establish a UK-based ope-rational spaceport, and to promote the UK commer-cial space sector within the global market.
Orbital Access formed to lead the development ofUK small payload launch systems and provide launchservices from the UK and globally. The goal is todevelop commercially viable launch systems tailoredto meet the needs of UK payload manufacturers andsecure the IPR and industrial value in the UK ma-nufacturing base. In 2015, Orbital Access formed aconsortium with several aerospace companies, rese-arch centres and universities to further advance theUK space access sector, in particular to develop na-tional technology roadmaps, market forecast studies[1], technical studies and R&D ventures under theFuture UK Small Payload Launcher (FSPLUK) pro-gramme.
Several industrial research projects have been car-ried out towards the conceptual design of a of a two-stage to orbit, semi-reusable launch system for smallsatellites. The aim of the system design is to developa commercially viable launch system for near-term
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operation, thus emphasis is placed on the efficient useof high TRL technologies. The commercial viabilityis the underlying driver for all the mission and systemrequirements during the initial stages of design.
The following details the progress made on the con-ceptual design and analysis focusing on concept fea-sibility. A multidisciplinary design optimisation wasundertaken to assess key design parameters withinthe vehicle design. The vehicle sizing and perfor-mance was optimised against a set of mission requi-rements stemming from the commercial drivers.
The system is a multi-stage vehicle using rocketpropulsion that will be air-launched from a carrier ai-rcraft. The main vehicle is a reusable spaceplane de-sign allowing for unpowered, glided re-entry/returnflights. The second stage(s) are stored within themain body of the spaceplane, among other benefitsthis allows for better control of the moments indu-ced by the movement of the centre of gravity thoughintroduces complexity and release issues. The mainoperational spaceport is located at Prestwick on thewestern coast of Scotland, with alternate landing si-tes identified in Northern Europe and Scandinavia.The air-launch increases the range of orbits that canbe reached, and improves the flexibility of the systemby allowing the transport and recovery of the firststage.
In particular, the paper describes the overall appro-ach with design objectives and mission requirements,then details the subsystem models developed for usewithin a specialised integrated design platform forspace access vehicles. The optimisation used withinthe system performance analysis is described, withresults presented examining the trade-off in perfor-mance of altering key design variables in the configu-ration, specifically the engine and wing sizing (aero-dynamic efficiency). The nominal mission is to deploy500 kg payload into 650 km altitude circular orbit atan inclination of 88.2 deg, targeting the OneWeb con-stellation. An extended mission would deploy 150 kgpayload, equivalent to a single OneWeb satellite, toa 1200 km altitude, circular polar low earth orbit inthe same inclination plane.
2. Approach
The design approach for the concept feasibilityphase is to assess the design drivers linking thecommercially-driven mission and system require-ments to technical design parameters.
A previous study [1, 4] looked at a market fore-cast and demand study and developed a cost mo-del relating the technology readiness level (TRL) of
critical technologies to the development cost againstthe predicted market demands. The output drove tothe design decisions, mapped into requirements, fora reusable first stage based on COTS (TRL 8-9) roc-ket engines. The decision to air-launch the vehiclefrom modified commercial carrier aircraft will allowthe system to operate globally and increases the flexi-bility of the system to reach different orbits, and havedifferent take-off and landing sites. Based on an eva-luation of the TRL, and impact on cost, of certaintechnologies, a number of additional constraints weredetermined, for example the acceleration limits andheating loads.
The launch vehicle is modelled in a modular formatto be run within a multi-disciplinary design optimi-sation (MDO) environment. The MDO software canoptimise the performance of the system by adjustinga number of optimisation control parameters. Com-putationally fast engineering models were developedfor the different subsystems of the vehicle, and theoperational environment.
Different design criteria were selected as inputswith the models relating the impact of changes onthose variables on the system. In this study, threedesign variables are analysed to size the wing areaand engine sizing of the first and second stage. Theaerodynamic wing reference area affects the aerody-namic performance, generating necessary lift for theglide re-entry while minimising drag on the ascent,and the vehicle dry mass. The performance of theengines affect the maximum level of thrust produced,the vehicle dry mass and impacts the fuel mass re-quired. The trajectory for both ascent and descentis simultaneously optimised to minimise the mass ofthe required on-board propellant and oxidiser.
The mission is analysed in a single optimisation,starting just after the spaceplane is released from car-rier aircraft and includes the Stage 1 ascent and des-cent to an airport approach, and the Stage 2 ascentand injection into orbit.
3. System modelsIn this section, mathematical models are presen-
ted for the vehicle design and operation. The modelsare divided by discipline: vehicle mass and configura-tion, aerodynamics, propulsion, environment modelsfor Earth including geometry, gravitational field andatmospheric model, and the flight dynamics and con-trol.
3.1 Vehicle configurationThe fundamental systems concept consists of a win-
ged recoverable booster vehicle which is air laun-
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ched from a converted large commercial aircraft. Thebooster carries one or multiple disposable upper sta-ges, each with their own individual payload. Thevehicle configuration is driven by the constraints in-herent in an air launched system and the desire toprovide as much flexibility as possible in the payloadcarriage.
An earlier study [5] describes the evolution of theconcept from a winged rocket to an integrated spa-ceplane with a central payload cartridge. This con-cept allows for rapid integration of payloads and as-sociated upper stages into the booster, the payloadcartridges themselves being loaded and integrationtested remotely. This allows each booster to attainthe high launch rates required for an economically at-tractive business case. The following analysis is for aventral launch system, wherein the booster is moun-ted under a converted large commercial aircraft. Forthe purposes of the study in question, this was takento be a McDonnell Douglas DC-10 / MD-11 seriesaircraft, which has significant advantages in terms ofunder-fuselage space volume over other types. Theprimary design constraints driven by this concept arethe maximum height of the booster due to ground cle-arance and the maximum launch mass. In addition,the wing span of the booster is limited by clearancefrom the carrier aircraft wing-mounted engines andthe length is fixed by the carrier aircraft nose gearand the tail strike angle.
A parametric mass estimation tool was developedbased on a number of published methods for bothreusable launch vehicles and high performance air-craft Maddock et al. [5], Rohrschneider [6], MacCo-nochie and Lepsch Jr [7]. Using this tool, full compo-nent mass breakdowns and scaling laws were determi-ned and supplied to the trajectory analysis and sizingmodels. Mass estimating relationships were develo-ped for the major structural components (e.g., wing,fins, fuselage structure, propellant tanks) and majorsystems (e.g., propulsion, avionics, landing gear) todetermine the gross and dry masses of the stages asa function of the optimisable design inputs.
Knowing the mass breakdown and component la-youts, the vehicle centre of gravity and its variationwith fuel burn and payload deployment was determi-ned and assessments made of the ability to trim i.e.,reduce the pitching moment to zero during ascent andre-entry. Following this the propellant tanks were re-distributed to give an acceptable centre of gravityrange during flight. The internal layout of the confi-guration is shown in Fig. 1. Note that the propulsionsystem shown is indicative of the size and location
but does not include any engineering details of theinstallation.
3.2 Aerodynamics
The aerodynamic force coefficients for the vehicleconfiguration were estimated for Mach numbers ran-ging from 0.2 to 30, angles of attack of −5◦ to 40◦ andfor altitudes up to 100 km. The drag coefficient atzero incidence CD0
and the normal force coefficientCN at different angles of attack α for each compo-nent of the vehicle (fuselage, fairing, wings and tail)are estimated separately. The approach for the esti-mation is based on different theories for each Machnumber range, from subsonic to hypersonic, detailedby Mason et al. [8] and Fleeman [9].
The lift and drag force coefficients of each compo-nent at different Mach numbers and angles of attackare modelled by,
CL = CN cosα− CD0sinα (1a)
CD = CN sinα+ CD0cosα (1b)
Eqs. 1 are applicable for small angles of attack atwhich the axial force is approximately equal to drag.Although large angles of attack are considered themethod is expected over predict the lift at such an-gles. This is further complicated by the stall effects athigher angles, which are not accounted in the method.Through validation with experimental data [10, 11],the extent of deviation of the predictions from theexperiments was assessed. However, the method con-siders the effect of flow separation at the base of thefuselage. The fuselage cross section is approximatedto be elliptic (with same area of cross section andmajor axis equal to half of the maximum width ofthe fuselage) in order to enable the application oftheories. The lift and drag coefficients, after nor-malization using the wing surface area, are then ad-ded up to give the total lift and drag coefficient ofthe entire configuration. Linear theory and modi-fied Newtonian theory are used to deduce the wavedrag coefficient at zero incidence over slender circu-lar/elliptic nose Cd0,wave,b, wave drag coefficient atzero incidence over the delta wing (as well as tail,which has similar form) Cd0,wave,w, and the normalforce coefficient as a function of angle of attack forthe cone-cylinder CN,b as well as wings CN,w, givenby the following equations.
Cd0,wave,b =
{0 for M < 1
3.6dN`N (M−1)+3 for M ≥ 1
(2)
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Fig. 1: General configuration and internal layout
Cd0,wave,w =
{0 for M < 1
f (MλLE , γ, δLE , tb/Sw) for M ≥ 1
(3)
|CN,b| =aNbN
sin(2α) cos(α/2) + 2`CdC
(4)
|CN,w| =
πA2 |sinα cosα|+2 sin2 α for M2 < 1 + (8/πA)2
4|sinα cosα|√M2−1
+2 sin2 α for M2 ≥ 1 + (8/πA)2
(5)where `N is the length of the cone nose, dN is theequivalent diameter with major axis aN and minoraxis bN , `C is the length of the cylindrical body, A isthe aspect ratio of the wing, t is the wing thickness,b is the wing width, Sw wing reference area, δLE isthe wing thickness angle, γ is the specific heat ratio,α is the angle of attack, and M is the freestreamMach number with MλLE the Mach number resolvedin the direction normal to the wing leading edge witha sweep angle λLE .
The complex algebraic functional form f of thebase wave drag on the wing Cd0,wave,w is given byFleeman [9]. The above coefficients are all norma-lised by their respective reference areas (and not acommon reference area).
The coast drag of the cone-cylinder body Cd0,c isgiven by the following engineering correlation [9].
Cd0,c =
{0.12 + 0.13M2 for M < 1
0.25/M for M ≥ 1(6)
The inviscid drag at zero incidence also includes dragdue to nose and leading edge bluntness, which arealso estimated using the semi-empirical expressionsgiven by Fleeman [9].
While the inviscid coefficients are only dependenton Mach number and angle of attack and independent
of altitude, the contribution of skin friction- whichis dependent of Reynolds number- leads to altitudedependence of the force coefficients. The skin frictiondrag coefficient at zero incidence for the cone-cylinderbody CD0,f,b and for the wing CD0,f,w (tail too hassimilar functional form) are given by the followingengineering correlations.
Cd0,f,b = 0.053`
d
(M
q`
)0.2
(7a)
Cd0,f,w =0.0266
(qcmax)0.2(7b)
In the above equations q is the dynamic pressure andcmax is the length of mean wing chord. The skinfriction drag coefficient is added to the inviscid dragcoefficients at zero incidence (for each component).The lift and drag coefficients due to each componentare then calculated using Eq. 1 from the estimatedtotal drag coefficient at zero incidence and the normalforce coefficient of the component.
The method is validated using wind tunnel data atMach 2, 3 and 4 [10] and using gun tunnel data atMach 8.2 for a simple cone-cylinder configuration aswell as a cone-cylinder with a pair of delta wings usinggun-tunnel data [11]. In general the comparison bet-ween the predictions and experiments were good upto an angle of attack of 10◦ after which the methodstarts to over-predict the lift, sometime by over 35%.This is because the wing stall is not presently conside-red. The drag for the wing configuration is also gene-rally over-predicted, therefore giving a conservativeestimate. Details of the validation, the comparisonwith the wind/gun tunnel data, and some illustrativeresults (predicted lift and drag coefficients) for thepresent aerodynamic configuration are presented inMaddock et al. [5]. The lift and drag coefficients foreach individual components as well as for the wholevehicle configuration are thus estimated as a functionof Mach number, angle of attack and altitude; thus
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the aerodynamic data of force coefficients is genera-ted as three-dimensional arrays which, along with theaero-thermal models, is used in the subsequent ana-lysis of flight trajectory and optimisation.
3.3 PropulsionThe rocket engines are modelled using standard
Tsiolkovsky rocket equations, with configurable in-puts specifying the specific impulse Isp and thrustFTvac
in a vacuum. A throttle control τ ∈ [0, 1] isadded that dictates the fraction of maximum availa-ble thrust applied and fuel mass flow (and thereforefuel consumption). A simplifying assumption is madethat the mass flow varies linearly with thrust. Theapplied thrust and mass flow rate per engine are thencalculated as,
dmp
dt= mp = τnengnnozz
FTvac
g0Isp(8a)
FT (h) = τnengnnozz (FTvac − patmAe) (8b)
where nnozz are the number of nozzles per engine,and neng number of engines on the vehicle. A penaltyproportional to atmospheric pressure patm and nozzleexit areaAe is introduced to account for the differencein nozzle expansion under pressure compared to in avacuum.
The two main stage engines uses a LOX/Kerosenepropellant with an Isp between 300-400 s, based onthe Yuzhnoye RD-8 series of rocket engines. Thenumber and rating of engines are determined throughthe design trade-off studies accounting for engine de-signs currently at TRL 7-9 (i.e., that are either cur-rently available, or predicted to be available in thenext 5 years).
3.4 EnvironmentThe Earth is modelled as an oblate spheroid ba-
sed on the WSG-84 model. The gravitational fieldwas modelled using 4th order spherical harmonics (ac-counting for J2, J3 and J4 terms) for accelerations inthe radial gr and transverse gφ directions [12].
The atmospheric conditions – temperature Tatm,pressure patm, density ρatm and speed of sound –are modelled using the Standard US-76 global sta-tic atmospheric model extended up to an altitude of1000 km above the Earth surface [13].
3.5 Flight dynamics and controlA 3-DOF variable point mass dynamic model is
used where the spaceplane is a time-varying masslocated at the centre-of-gravity of the vehicle. Thestate vector for the flight dynamics xdyn = [r, r] isthe spherical coordinates for the position r = [r, λ, θ]
and the velocity r = [v, γ, χ] where r is the radialdistance, (λ, θ) are the latitude and longitude, v isthe magnitude of the relative velocity vector directedby the flight path angle γ and the flight heading an-gle χ. The equations of motion are expressed in theEarth-Centred-Earth-Fixed rotating reference frame[12, 14].
h =r = v sin γ (9a)
λ =v cos γ sinχ
r(9b)
θ =v cos γ cosχ
r cosλ(9c)
v =FT cos(α+ ε)−D
m− gr sin γ + gφ cos γ cosχ
+ ω2er cosλ (sin γ cosλ− cos γ sinχ sinλ) (9d)
γ =FT sin(α+ ε) cosµ+ L
mv− gr
vcos γ − gφ
vsin γ cosχ
+v
rcos γ + 2ωe cosχ cosλ (9e)
+ ω2e
( rv
)cosλ (sinχ sin γ sinλ+ cos γ cosλ)
χ =L sinµ
mv cos γ− gφ sinχ−
(vr
)cos γ cosχ tanλ
+ 2ωe (sinχ cosλ tan γ − sinλ) (9f)
− ω2e
(r
v cos γ
)cosλ sin γ cosχ
where m is the time-varying mass of the vehicle, ε isthe pitch offset angle between the direction of thrustFT and the longitudinal plane of the vehicle, [gr, gφ]are the gravitational accelerations in the radial andtransverse directions, and L and D are the aerodyn-amic lift and drag forces, respectively.
The trajectory dynamics are controlled by adjus-ting the thrust vector. The magnitude of the thrustand mass flow applied is controlled by τ(t), and thedirection through the angle of attack α(t), thrust off-set angle ε and the bank angle µ(t). The engines areassumed fixed with no gimbled thrust at this stage,thus the control law also dictates the partial attitudeof the vehicle.
4. OptimisationIn this section, the general formulation is presen-
ted for trajectory and design optimisation of the con-ceptual design. The optimisation seeks to find a mis-sion flight profile that minimises the propellant usage,subject to a number of vehicle loading and thermalconstraints, and a set of design parameters that bothminimise the required gross vehicle mass and maxi-mise the downrange distance while being able to meetthe target mission.
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The first step was to formulate the problem as anoptimal control problem: given the system dynamicsfor the chosen vehicle configuration, full or partialboundary conditions for the initial and final statesof the vehicle and any path constraints, the aim isto find a optimal control law that minimises a givenperformance index.
The mission is decomposed into a number of user-defined phases, with different system models, objecti-ves and constraints used within each phase (see Fig.2. The phase decomposition is also used to accom-modate discontinuities within the system and perfor-mance models, such as separating the sub-, trans- andsuper/hypersonic aerodynamic models, or for vehiclestaging.
A direct multi-shooting transcription method isthen employed to transform the continuous optimalcontrol problem into a non-linear programming pro-blem (NLP). The NLP is then solved with a localgradient based optimisation algorithm using a multi-start approach to generate first-guess solutions.
4.1 Optimal control problem formulationOptimal control problems are generally formulated
as:minu∈U
J(x,u, t)
s.t. x = F(x,u, t)g(x,u, t) ≥ 0ψ(x0,xf , t0, tf ) ≥ 0t ∈ [t0, tf ]
(10)
where J is the objective function of the state vectorx : [t0, tf ]→ Rn, control vector u ∈ L∞ and time t, Fis a set of differential equations describing the dyna-mics of the system, g is a set of algebraic inequalitiesdescribing path constraints and ψ is a set of algebraicinequalities describing boundary constraints.
The optimal control problem is transcribed into anonlinear programming problem by using a multi-phase, multiple-shooting approach. The mission isinitially divided into np user-defined phases. Withineach phase, the time interval is further divided intone multiple shooting element.
∪np
k=1 ∪n−1i=0 [ti,k, ti+1,k] (11)
The trajectory is numerically integrated for interval[ti,k, ti+1,k] with initial conditions xi,k. Within eachinterval [ti,k, ti+1,k], the control is further discretised
into nc control nodes {ui,k0 , ..., ui,knc} and collocated on
Tchebycheff points in time.Continuity constraints on the control and states are
imposed between each shooting element, and betweenphases, matching the state and control vectors at the
end of one element, with those at the start of thenext.
The trajectory optimisation vector is thereforecomposed of:
• control nodes within each shooting segment{ui,k0 , ...,ui,knc
} for i = 1, ..., n and k = 1, ..., np,
• time of flight for each shooting segment ∆tk fork = 1, ..., np,
• initial state and control variables of each shoot-ing segment within every phase that should bematched with the previous segment or phase x1,k
and u1,k0 for k = 2, ..., np.
In addition, the initial states of the problem can befixed by the user or left as optimisable parameters.For the latter case, any initial state variable that isleft free is added to the optimisation vector.
The desired final states are added as boundary con-straints to the problem, along with any path con-straints evaluated at every integration time step. Theconstraint can either be equality (ceq = 0) or inequa-lity (cineq ≤ 0).
4.2 Single objective optimisation algorithm
Problem (10) was solved with the Matlab optimiserfmincon, a gradient based local solver for the solutionof single objective NLP with nonlinear constraints,using either the interior point or sequential quadra-tic programming (sqp) algorithms. The optimisationvector was scaled before the optimisation algorithmsuch that u ∈ [0, 1]; the constraints and objectivefunction were also normalised.
A multi-start strategy was used to generate a po-pulation of first guess solution vectors within the defi-ned search space. A combination of problem-specificrules, e.g., holding the trajectory controls constantwithin each element, and assuring an ascending tra-jectory for the starting state vector of each element)and random sampling through Latin Hypercube Sam-pling was used to generate the first guesses. This al-lowed a better exploration of the search space andreduces the sensitivity of system to the first guess va-lues while generally allowing for a faster ad higherrate of converge over some stochastic global optimi-sers. Integration of the dynamic equations of motionin Eqs. (9) was performed with a fixed step 3rd orderBogacki-Shampine Runge-Kutta method within theoptimisatiaon, and refined, as a post-process, witha variable step Dormand Prince Runge Kutta (4,5)scheme.
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Fig. 2: Mission phase decomposition
4.3 Multidisciplinary design optimisation
A multidisciplinary design optimisation (MDO)approach was used to study the optimality of keydesign parameters of the vehicle. These design opti-misation parameters were added to the optimisationvector along with the trajectory control parametersgiven in Section 4.1.
The mission flight path starts just after the sepa-ration of the launch vehicle from the carrier aircraft,therefore the initial state vector of the spaceplane isdependant on the state of the carrier aircraft. The al-titude and velocity are fixed at a nominal state thatcould be achieved by the carrier aircraft at separa-tion. A geographic point (latitude and longitude) wasselected accounting for range of the carrier aircraft,and safety/regulatory criteria. The flight path andheading angle were left as optimisation design vari-ables, with upper and lower bounds set to allow forthe limitations due to the separation manoeuvre.
Static design parameters were added to size theengines for each stage, and the wing area for the re-turnable, reusable first stage. The overall objectivewas the minimisation of the gross vehicle mass sub-ject to the nominal design mission which included atarget orbit and payload mass, and an unpowereddownrange return. This choice of objective requiredthat each of the design choices directly or indirectly
affect the mass of the vehicle. The system of parame-tric mass estimating relationships in Section 3.1 weredefined relative to these design variables. For thisstudy, the mass and sizing of the thermal protectionsystem (TPS) was not included directly in the designoptimisation loop, though later studies will examinethe requirements for limits on heat load and tempe-ratures based on different TPS.
The propulsion system were sized based on optimi-sing the total mass of propellants for each stage andscaling factors on the maximum vacuum thrust ratingfor the engines. The mass of the propellant was usedto determine the volume and mass of the tanks, whilethe vacuum rating was used to scale the mass of theengine and engine structure. The engines were scaledrelative to two nominal LOX-Kerosene rocket engi-nes manufactured by Yuzhnoye Design Office: thefirst stage has a main engine with a vacuum thrustof 88.4 tf, vacuum Isp of 332 s and a mass of 1280kg. The second stage uses the RD-809K engine, witha vacuum thrust of 10 tf, vacuum Isp of 352 s, and amass of 330 kg.
The sizing of the aerodynamic surfaces is anotherkey design parameter for the vehicle, here throughthe wing area. As the ascent is rocket-based, with arelatively high thrust force compared to the lift, theascent drives the design to small wing areas to re-
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duce drag (not accounting for any stability or controlsurface requirements). The requirement for a glidedreturn to some coastal site relatively in-plane to thetrajectory, drives up the wing area to improve thedown or cross ranges achievable. The aerodynamiccoefficients for the components are assumed constantfor all design options, with the wing reference areaSwing scaled relative to the total reference area Sref .The lift force L is calculated based on,
CL,mdoSref = CL,wingSwing + CL,iSi (12)
L =1
2ρv2∞CL,mdoSref (13)
where CL,i, Si are the coefficients of lift and corre-sponding reference area for the unchanged compo-nents of the fuselage, fairing and tail. The wing re-ference area Swing is scaled relative to the nominaldesign value. Drag is calculated in the same manner.
In this study, the downrange distance is maximi-sed assuming no cross-range (i.e., the trajectory isentirely in-plane). This is used as a figure of meritfor the capabilities of the system assuming no specificlanding sites are given, and assuming no requirementsfor a return to landing site. This is consistent withthe commercial drivers for the system that prioritisedglobal operation and flexibility.
5. Analysis and resultsTwo analysis were conducted: the first examines
the effect of altering the wing aerodynamics by chan-ging the wing surface area on the vehicle masses anddescent performance. The second uses a constantwing surface area and examine the trade-off betweenmass and engine design with downrange capabilities.
In the following, three different scaling factors forthe wing reference area are analysed: 60%, 100% and120% of Swing. The release point was chosen off thewest coast of the UK to minimise (or eliminate) thetime the atmospheric trajectory was over any popu-lated land. The drop point is determine assumingnorth-west flight of the carrier aircraft departing fromPrestwick airport in Scotland. The initial state vec-tor x(t0) = [r,v] is:
r(t0) = [12 km, 58.8058◦N, 12.7471◦E]
v(t0) = [200 m/s, γ ≤ 15◦, 0 ≤ χ ≤ 90◦]
The final state vector for Stage 2 ascent to orbitwas constrained by the Keplerian orbital parameters:semi-major axis a = RE + 650 km (where RE(λ) isthe radius of Earth), eccentricity e = 0, inclinationi = 88.2◦. The final state vector for Stage 1 descent
was constrained by: altitude h ≤ 1 km, velocity v ≤200 m/s, and flight path angle ‖γ‖ ≤ 20◦.
Path constraints are added on the normal and axialaccelerations such that |ax(t)| , |az(t)| ≤ 4g0.
The ascent was optimised based on the objectivefunction,
minu∈D
(mgross) (14)
where the gross vehicle mass is the sum of the dryand fuel masses of Stage 1 and Stage 2, plus the pay-load mass. The optimisation vector u contains: the4 vehicle design variables (vacuum thrust scaling fac-tors for Stage 1 and 2, total fuel mass for Stage 1 and2), the initial flight path γ0 and heading angle χ0 justafter carrier separation, and the trajectory optimisa-tion vector listed in Section 4.1. The user-definedphases of the mission, and the relation to vehicle sta-ging, are shown in Fig. 2.
The atmospheric descent was optimised based onthe objective function maximising the central angleof the descent range dgnd based on the start and endpoints of the atmospheric re-entry phase (Phase 4)and calculated using the Haversine formula.
maxu∈D
(dgnd
re(λ = 0)
)(15)
The re-entry trajectory was broken into 2 phases.The first phase (Phase 3) is the trajectory arc bet-ween the separation point of the two stages and theatmospheric re-entry, here defined to start at an al-titude of 80 km. In that high altitude phase, thetrajectory is ballistic due to the absence of signifi-cant atmospheric density and thrust. As such thereis no need to derive an optimal control law based onvehicle attitude; this phase was excluded from theoptimisation and simply propagated forward in timeuntil the descent altitude reached the set limit. Thesecond phase, Phase 4, is controllable with aerodyn-amic surfaces, and was thus optimised.
The optimised vehicle design parameters are givenin Table 1 based on estimates for a composite mate-rial structure. Table 2 gives the optimal initial con-ditions for the ascent trajectory, and Table 3 reportsthe optimised values for the approach to landing ofStage 1, including the maximised downrange distan-ces.
As expected, higher wing areas generally resultedin higher dry masses, propellent masses and enginesizes for each stage. An exception is the second stagefor the nominal wing area (1.0Swing) departing fromPrestwick. While the gross vehicle mass for this caseis between the gross masses for the smaller and larger
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wing areas, as expected, the sizings for each stagediffers. The optimiser found a solution with a largerfirst stage, very similar to that of the 1.2Swing casefor both engine sizing and mass, and a lighter secondstage with a smaller engine. This combination gavethe longest downrange distance as a larger first stagemeans a higher velocity at stage separation, longerballistic phase and hence better downrange distance.This is also evident from Fig. 5(e) that shows thiscase has the highest T/W ratio.
Figures 3 and 4 show the optimal trajectories forthe nominal wing area for the two different releasepoints. The trajectories are shown for all 4 phases (asillustrated conceptually in Fig. 2). While the trendof the two trajectories are the same, and both fulfilthe mission requirements, the absolute values for thedescent are different. This highlights the competingobjectives finding the minimal gross vehicle mass inorder to inject 500 kg into the target orbit, and themaximal downrange distance.
Figure 5 shows the trajectories for the Stage 1+2combined ascent (Phase 1), followed by the Stage 1ballistic coast after stage separation (Phase 3), andthe Stage 1 atmospheric re-entry (Phase 4) for the 3different wing areas studied. This shows the trade-offof increasing wing area, where increasing the aero-dynamic contribution of wing can increase the glideperformance of the vehicle, it is at the expense of in-creased dry mass. The net effect shows an optimalconfiguration somewhere near the nominal wing refe-rence area, looking only at the descent performance.
6. Conclusion
This paper presented a conceptual design andperformance analysis of a partially re-usable spacelaunch vehicle for small payloads. The system wasdesigned for a nominal mission of delivering a 500kg payload to a circular 600 km, 88.2◦ polar orbit.The aim of the system design was to develop a com-mercially viable launch system for near-term opera-tion, thus emphasis is placed on the efficient use ofhigh TRL technologies. The final design employeda multi-stage, rocket-based spaceplane air-launchedfrom a carrier aircraft. The first stage is fully reco-verable through an unpowered glided descent to a se-condary landing site. Stage separation occurs around70 km, with the second expendable stage reaching thenominal mission orbit.
A multidisciplinary design optimisation on the sy-stem configuration was run to size the engines of bothstages and the Stage 1 wing area. The system hadto meet two objectives: to minimise the gross vehicle
mass, and to maximise the downrange. Test caseswere run for two different geographic release pointsoff the UK west coast, and for 3 different wing areasrelative to the nominal aerodynamic Swing. All 6 testcases are capable of meeting all the mission require-ments. The gross masses range between 65–72 ton-nes, and the downrange between 716–1343 km. Thebest downrange was achieved with the nominal wingreference area departing off the coast of Prestwick,with a gross vehicle mass of 70.87 tonnes and a do-wnrange of 1343 km. This configuration had a com-paratively larger first stage with an engine vacuumthrust rating of 1164 kN and dry mass of 11343 kg,and a second stage with an engine vacuum thrust ra-ting of 10.6 kN and dry mass of 1852.6 kg.
AcknowledgementsThis work was partially funded by the UK Space
Agency through the National Space Technology Pro-gramme (NSTP-2) Sub-Orbital and Small LauncherResearch Projects Call, and the European SpaceAgency through General Support Technology Pro-gramme (GSTP).
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Fig. 3: Trajectory results for reference case, 1.0Swing departing from Prestwick (blue/green solid lines) andFaroe (red/orange dotted lines). Start/end of phases are indicated by crosses.
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Fig. 4: Control laws, forces and accelerations for reference case, 1.0Swing departing from Prestwick(blue/green solid lines) and Faroe (red/orange dotted lines). Start/end of phases are indicated by crosses.
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Fig. 5: Comparison of trajectory and design parameters for different wing surface areas: blue 0.6Swing (blue),1.0Swing (green), and 1.2Swing (red). All trajectories leave from Prestwick, dashed lines indicate ballisticspaceflight segments.
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Table 1: Optimal vehicle design parameters (for a fixed payload mass of 500 kg)
Prestwick FaroeWing area: 0.6Swing Swing 1.2Swing 0.6Swing Swing 1.2Swing
Stage 1: Vacuum thrust (kN) 1112.6 1164.3 1170.6 1050.1 1097.1 1123.9Propellant mass (tonne) 43.628 45.87 45.957 39.276 41.094 43.814Dry mass (tonne) 10.665 11.343 11.635 10.638 11.304 11.535Residual mass (kg) 0.13458 0.12949 0.13277 0.036833 0.036644 0.14578
Stage 2: Vacuum thrust (kN) 139.17 129.61 140.28 139.03 143.31 151.87Propellant mass (tonne) 10.96 10.643 11.258 12.089 12.505 12.778Dry mass (tonne) 1.8863 1.8526 1.898 1.931 1.9572 1.9706Residual mass (kg) 0.016405 0.016636 0.016187 0.0044781 0.0013427 0.017646
Vehicle gross mass (tonne) 68.307 70.872 71.914 64.98 67.899 71.279
Table 2: Optimal initial conditions just after release point from carrier aircraft
Prestwick FaroeWing area: 0.6Swing Swing 1.2Swing 0.6Swing Swing 1.2Swing
Flight path angle γ(t0) (deg) 9.47 10.81 7.06 12.44 9.18 7.17Flight heading angle χ(t0) (deg) 0.15 0.12 0.09 0.90 0.80 0.73
Table 3: Final spaceport approach conditions
Prestwick FaroeWing area: 0.6Swing Swing 1.2Swing 0.6Swing Swing 1.2Swing
Altitude h (m) 928 442 503 261 648 861Velocity v (m/s) 265 294 328 303 297 405
Mach 0.788 0.87 0.97 0.89 0.88 1.20Flight path angle γ (deg) -14.00 -19.95 -18.19 -17.79 -19.04 -19.71Downrange distance (km) 1332 1343 961 1079 1167 716
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