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10.2514/6.2017-5127
AIAA SPACE Forum
12 - 14 Sep 2017, Orlando, FL
AIAA SPACE and Astronautics Forum and Exposition
Conceptual Design Synthesis of Orbital Lifting Reentry
Vehicles based on Generic Wing-Body Configuration
Loveneesh Rana∗, Thomas McCall†, James Haley‡, and Bernd Chudoba§
Downloaded by 80.82.77.83 on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2017-5127
AVD Laboratory, UT Arlington, Arlington, TX, 76019, U.S.A
The conceptual design phase is the first stage of product design where a tangible physical
product is conceptually defined in response to non-tangible requirements. In the case
of space access vehicles, the conceptual design phase represents the point where critical
decisions are made specifying the geometric configuration, sub-system technologies, and
operational requirements. An important aspect while considering the conceptual design
assessment for a complicated system like a space access vehicles, is the multi-disciplinary
effects and interactions among involved subsystems represented by the classical disciplines
of aerodynamics, propulsion, performance, and weights. The current research develops a
conceptual design synthesis system for a wing-body lifting reentry vehicle. The synthesis
approach is based on the constant mission sizing logic of Hypersonic Convergence by Paul
Czysz. It is a first order sizing application, where the most critical design parameters are
recognized and employed to find a solution design space of converged design points. The
wing-body configuration specifies the gross geometry configuration of the vehicle. Based
on this specification, a series of geometry and propulsion trades are applied. The geometry
is defined through analytic relationships of the fuselage, wings, and control surfaces. This
generic geometry configuration is assigned specific attributes to develop unique geometry
profiles. The on-board propulsion system is similarly executed, with the consideration of
pre-selected off-the-shelf upper stage rocket engines as the controlling factor. The synthesis
analysis sizes the vehicle based on a weight and volume convergence logic. The results are
analyzed and presented with the objective to demonstrate the influence and importance of
primary design drivers—geometry configuration and propulsion—on the complete vehicle
system.
Nomenclature
γ
flight path angle
1.5
τ
vehicle slenderness parameter, τ = Vtotal /Spln
D
drag
g
acceleration due to gravity
h
altitue
Isp
specific impulse
L
lift
OW EV operating weight empty based on volume relations, volume budget
OW EW operating weight empty based on weight relations, weight budget
Spln
planform area
T
thrust available
T OGW take-off gross weight
V
velocity
Ve
velocity at atmospheric reentry, initial glide velocity
∗ PhD
Canidate, AVD Laboratory, UT Arlington, Arlington, TX, 76019, U.S.A, and Student AIAA Member.
Canidate, AVD Laboratory, UT Arlington, Arlington, TX, 76019, U.S.A, and Student AIAA Member.
‡ PhD Canidate, AVD Laboratory, UT Arlington, Arlington, TX, 76019, U.S.A, and Student AIAA Member.
§ Associate Professor, Director AVD Laboratory, UT Arlington, Arlington, TX, 76019 and AIAA Member.
† PhD
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American
Institute of Aeronautics and Astronautics
Copyright © 2017 by Loveneesh Rana, Thomas McCall, James Haley, Bernd
Chudoba.
Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
W
Wstr
DBMS
LRV
weight
weight of the structural material
database management system
Lifting Reentry Vehicle
I.
Introduction
Downloaded by 80.82.77.83 on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2017-5127
he lifting reentry vehicles (LRVs) represent a convenient horizontal landing mode of space access transT
portation that impose operational and technological challenges. A number of private companies and
major space agencies initiated programs to develop commercial and fully reusable spaceplanes but no such
vehicle has reached the operational status. The LRV is representative of primarily three major vehicle classes,
namely: wing-body, lifting-body or blended-body configurations. Among these three class of vehicles, wingbody was the first configuration to be studied as a space access vehicle, mimicking an aircraft’s operational
effectiveness. Eugene Sänger1 in 1933 started working on a wing-body shape rocket-powered vehicle concept,
Silbervogel as shown in Figure 1. Although the design overlooked critical thermal constraints, the vehicle
concept defined the feasibility of a wing-body vehicle as a space access vehicle. Since then, numerous studies
and programs have been initiated but failed to develop a commercially successful wing-body aerospaceplane.
The conceptual design phase is identified as the primary gestation phase, the decisions locked in this phase
essentially define the success or failure of the program. A quick overview of the past wing-body programs
shows that almost no conceptual design report is found in public domain and thus the critical reasoning
behind the technology-mission-operation related decision is hidden. Following this reasoning, the current
research study aims to address the wing-body configuration in a multi-disciplinary framework and assess the
conceptual design feasibility for this configuration for a Low Earth Orbit (LEO) reentry mission profile.
II.
Wing-Body Configuration
This section provides an overview summary of the wing-body configuration as addressed in the past LRV programs. The typical lifting reentry
mission profile is then addressed to select a specific LEO trajectory that is
used as imposing primary mission requirements for the conceptual design
assessment for this study.
A.
Legacy Programs
Wing-body configuration is a well-researched design for orbital reentry
programs. Unfortunately, the majority of these programs were terminated or canceled intermittently, with only three exceptions being the
STS, BURAN, and X-37. Despite such a widespread and well-funded
research domain, numerous multi-billion dollar programs have failed to
develop a commercially successful operational vehicle.2 In-light-of these
facts, it is necessary to consider why. A attempt to answer this complex question, a literature survey was conducted for the legacy programs
from a disciplinary and synthesis point-of-view. The survey was part of
a comprehensive review of the legacy LRV programs by Rana2 addressing 60 LRV programs measuring individual disciplinary contribution of
each program for the primary design disciplines of aerothermodynamics,
propulsion, stability, structures and thermal management. This review
covers an exhaustive body of existing literature covering 172 literature Figure 1: Eugene Sänger’s wingbody concept Silbervogel, cicra
sources to provide a quantified account of contribution of each LRV program. The review finds that the majority of the information in these 1933.
legacy programs sits in the detailed design phase while the primary design understanding and decisionmaking done during the conceptual design phase is either completely neglected or is obscure and unclear at
best. Most of the reviewed programs provide detailed information on the classical aerospace disciplines but
very few documented reports are found where the design synthesis process is addressed. Thus, a disciplinestrong, synthesis-weak trend is observed.
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To add to the literature focused in the synthesis and sizing realm of LRVs, this study conducts a conceptual design assessment to understand the fundamental design effects observed for a wing-body LRV vehicle
conducting a LEO mission.
B.
Mission Specification
The mission selected for sizing the wing body vehicles is a nominal ISS resupply mission. A standard orbital
operations and equilibrium gliding reentry mission profile is assumed. The wing body case-study executes a
deorbit burn from the orbital altitude of the ISS (400 km) and enters the Earth’s atmosphere at an specified
altitude (entry altitude is a trade study investigation for this study). The entry flight path angle at this
point is assumed to be -1.5 degrees. The mission objective is to carry a payload of 450 kg ( 1000 lb) and 1
crew member. The selected mission profile and mission path values are shown in Figure 2.
International Space Station
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Propulsive
Deorbit Burn
bit
LTOr
00
=4
km
A
m
= 120 k
o
.5
= -1
ry
ALT Reentry
γ Reent
Landing
Site
Figure 2: A Simplified LEO reentry mission profile is selected for sizing the wing body case-study.
III.
Design Synthesis Specifications
An aerospace vehicle design synthesis process is a systematic way to conceptually design the complex
vehicle system by considering the interdisciplinary effects among primary design disciplines. Generally, a
synthesis approach includes a set of analysis methods for main design disciplines and a synthesis process
logic to integrate the methods in a cohesive simulated environment, thus providing a conceptual design of a
flight vehicle system. This section describes an overview of the fundamental design logic applied to obtain
the first conceptual sizing estimates of a wing-body LRV configuration.
A.
Synthesis Methodology
“Parametric Sizing is the first step of the design process after the mission has been defined. This step serves
to establish the 1st order solution space for the mission and gives the designer an idea related to the gross
geometry, weight and cost of performing the mission. In this step the designer begins with the (1) fixed
mission, (2) gross configurations concepts and (3) disciplinary technology assumptions. Sizing allows for
1st order trading of these concepts and technologies.” 3 A multi-disciplinary analysis process consisting of
primary design disciplines (Aerodynamics, Propulsion, Trajectory etc) is used for feasibility implementation
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Downloaded by 80.82.77.83 on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2017-5127
Figure 3: Multidisciplinary analysis approach applied
and sizing the vehicle to provide the first physical characteristic estimates (Weight, Volume, dimensions etc).
Traditionally, sizing has been executed using, 1) Legacy by-hand textbook based synthesis methodologies
(eg. Wood,4 Corning,5 Nicolai,6 Loftin7 ) or 2) Modern computerized synthesis systems (ACSYNT,8 ASAP,9
FLOPS,10 PrADO11 )
The synthesis methodology used here for the wing-body orbital reentry vehicle is based on the constant
mission sizing logic of Hypersonic Convergence by Paul Czysz.12 The process is representative of the the
fundamental synthesis logic which has been adopted, applied and modified by Chudoba,13 Coleman3 and
Gonzalez.14 It is a first order sizing application, where the most critical disciplinary parameters are combined
in an integrated multi-disciplinary synthesis analysis to find a solution space of feasible design points. This
method of sizing the vehicle concept is used to measure the design with current day available technology and
identify if any specific technology requirement can cause the program to fail in later development stages. The
methodology implemented to execute the sizing study consists of a a modular process structure, composed
of individual disciplinary analysis methods and the computational integration process.
B.
Sizing and Convergence Logic
The sizing process begins with specified mission requirements. For this study, a standard reentry from
low earth orbit is the primary mission requirement with specified cross-range and payload capacity as discussed in Section B. In the next step, the wing-body shape and rocket propulsion are selected as primary
configuration-defining aspects. The generic wing-body geometry is then traded for primary geometry variables to develop a series of unique wing-body profiles. Similarly, the rocket propulsion mode is implemented
by selecting and trading the on-board rocket propulsion engines. The top-level sub-system trade options for
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geometry and propulsion combinations are shown in Figure 3. Once the geometry and propulsion decisions
are made, each case is then a starting point for executing follow-on primary disciplinary analysis in sequence;
aerodynamics, propulsion, performance matching, and weights and volumes. The weight and volume budget
estimates are obtained following the trajectory analysis which estimates the required fuel. The performance
matching step implements the trajectory analysis by matching the required mission performance constraints
to provide the fuel fraction, and weight ratio values required to perform the mission. The weight and volume
budgets, performance matching, and constraint analysis implements modules representing structures, stability and control, and aero-thermodynamics heating limitations. Following the disciplinary analysis execution,
a convergence logic is implemented to ensure the design feasibility. This convergence logic is the heart of
the sizing process that solves for wing loading and planform area simultaneously by converging weight and
volume for a given set of design variables. The convergence logic is defined in terms of two primary objective
functions shown in Figure 4.
The first objective function for the sizing process centers around the vehicle’s weight and
volume budget estimates. The results from the geometry, aerodynamics, propulsion, and performance matching modules are provided to assess the total weight and volume required vs available.
Given a unique value of a vehicle’s slenderness parameter (τ = Vtotal /(Splan )1.5 ), the planform
area and wing loading are iterated through the total design process until weight and volume
available equal weight and volume required. In order to do this the weight and volume of the
vehicle are transformed into two equations that can be simultaneously solved for Operational
Weight Empty (OWE). The initial planform and wing loading provides the analysis process an
estimate for TOGW. The second objective function is a check to see if the initial guess for wing
loading matches the wing loading output of the system.
1.
System Execution
The multi disciplinary process and methods used are implemented into a functioning sizing architecture by means of a
data base management system that provides the unique capability of developing and delivering custom-tailored sizing codes
specific to the user’s requirements. The system was developed
at the Aerospace Vehicle Design Laboratory at The University
of Texas at Arlington.14–16 The data base management system
(DBMS) is not a design synthesis program. It is a software
that outputs unique multi-disciplinary analysis (MDA) sizing
codes. The DBMS is a warehouse of the essential primary components of a synthesis system where a sizing code can be created in piece-wise integration of those components. The user
selects problem specific components from this warehouse–type
setting and combines them together by following a systematic
step by step process to create unique synthesis MDA based on
problem specific demands. A user defined general vehicle shell
and MDA process are two components housed in this system
and are key to the sizing code generation process. Based on
the vehicle and process provided, suitable methods are identi- Figure 4: The essential objective function
fied and subsequently processed into a functioning sizing code must be satisfied for executing the fundaas described above. The result is a problem specific unique mental convergence logic.
sizing code embodying a total system convergence logic. Additionally, the DBMS is executed in Microsoft ACCESS. The same platform manages integrated libraries of
references, methods, vehicle definitions, processes, and sizing architectures. The MDA methodology for the
present study is created using this generic synthesis system and platform.
IV.
Disciplinary Analysis Methods
This section describes the individual disciplinary methods executed in the AVDWB synthesis system.
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MACH
L(induced)
0.009384 0.717261
0.317811
0.613777
0.872743
1.020713
1.304371
1.563389
1.809997
2.019606
2.192114
2.438645
2.623409
2.808275
2.980706
3.264107
3.547561
3.769374
3.978778
4.163619
4.3731
4.730448
5.026183
5.395916
5.654626
5.975052
6.246172
6.615956
Equations for CL_alpha for transonic region
0.692473
0.698864
0.705235
0.711549
0.711697
0.715
0.718196
0.730779
0.768291
0.799604
0.855833
0.887114
0.943337
1.005855
1.055898
1.099672
1.162151
1.199669
1.243437
1.318467
1.380991
1.443553
1.512295
1.568594
1.618631
1.668719
0.0220
0.0218
0.0216
0.0214
0.0212
0.0210
0.0208
0.0206
y0.0204
= -0.0049x 2 + 0.0138x +
0.0202 0.012
0.0200
0.0000 1.0000 2.0000 3.0000
0.0218
0.0216
0.0212
Series1
0.0210
Poly. (Series1)
0.0208
Series1
Linear (Series1)
0.0206
0.0204
0.0202
0.0200
0.0000
0.0250
0.0200
0.0150
Series1
0.0100
2 per. Mov.
Avg. (Series1)
0.0050
y = 0.0038x + 0.017
0.0214
0.0000
0.0000 5.0000 10.0000 15.0000
0.5000
1.0000
0.0220
0.0218
0.0216
0.0214
0.0212
0.0210
0.0208
0.0206
0.0204
y = -0.0042x 2 + 0.0116x +
0.0202
0.0136
0.0200
0.0000 1.0000 2.0000 3.0000
1.5000
Series1
Poly. (Series1)
Downloaded by 80.82.77.83 on October 27, 2017 | http://arc.aiaa.org | DOI: 10.2514/6.2017-5127
Figure 6: Creation of MATLAB lookup tables using aerodynamic data graphs for aerodynamic methods.
A.
Wing-Body Geometry Configuration Specification
To define the generic wing-body configuration the vehicle is parameterized by considering the major design
features. The nose of the craft is defined by the radius, the fuselage by the cross-sectional shape and length,
the wings by the leading edge sweep and planform shape etc. Modeling the vehicle in this generic piecewise parametric manner allows for flexibility in the geometry function which provides a greater range of
trade options. The generic geometry breakdown is applied to develop specific geometry profiles by assigning
attributes to the geometry design parameters. Figure 5 shows a generic wing body buildup and description
of the major parameters that define the configuration. NASA’s open source geometry modeling software,
OpenVSP,17 is utilized as the primary geometry generation tool as it provides a flexible platform to build
parametric geometries. The process of building a geometry configuration begins with selecting the desired
configuration. The wing body is the selected primary configuration chosen for the present study. Then a
cross section shape is chosen and a fixed model is generated.
Once the VSP file is prepared, an in-house analysis script utilizes the calculation tools in VSP to
generate a data table. The analysis script generates
values of tau, volume, wetted area, frontal area etc.
and makes a feasible geometry map. The geometry
map also shows the sensitivity of the geometry to
the changing parameters. This allows the configuration behind the lookup table to be tuned for the
related disciplinary parameters.
B.
Aerodynamics
The aerodynamic discipline calculates the primary
aerodynamic characteristics of the vehicle as func- Figure 5: Geometric break-down of a wing-body vehition of the geometric parameters for the different cle into key geometric components
flight regimes the vehicle is operating in. The methods used here range from subsonic to hypersonic
Mach number, and they are derived from empirical
correlations for maximum trimmed L/D for a specific τ and induced drag coefficient (L‘). The data for the
method was generated initially at the McDonnel Douglas Company during the HyFAC studies18 and the data
are provided in the form of charts showing empirical relationships between various geometric parameters.
This is expensive and accurate data that was produced from extensive wind tunnel experimental tests on
trimmed vehicle geometry shapes and has been proven reliable in multiple sizing executions by Chudoba,13
Coleman,3 and Gonzalez.14 The data is converted to lookup tables for application in the MATLAB analysis
file. Figure 8 shows this process, while Table 1 shows the parametric relationships, primary aerodynamic
equations and geometric and aerodynamic parameters.
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American Institute of Aeronautics and Astronautics
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Table 1: Aerodynamic methods primary parametric relationships.
C.
Propulsion
A simple liquid rocket engine analysis is applied based on the standard textbook method by Sutton.19 Rocket
performance analysis relationships for the on and off design point determine the Isp and thrust available
T . An engine deck of 14 existing upper-stage rocket engines has been created where physical characteristics
of each rocket engine is stored. Then any of the engines can be selected by using a switch variable that
enables the analysis method to calculate the fractional thrust (as specified by the user) that is provided by
the selected engine. With this implementation, the need to size the engine (rubber engine) is eliminated and
existing off-the-shelf technology engines can be quickly selected. The engine dry weight and volume are also
used in the weights and volume estimation method which allows the sizing code to accommodate for the size
and weight of the engine inside a vehicle’s geometry mold. Table 2 shows the upper-stage engines used for
this analysis.
D.
Trajectory/Performance Matching
During atmospheric flight, the vehicle is a glider. For all phases after the deorbit, weight is constant and
thrust is equal to zero. The general equations of motion for gliding flight, as given by Miele,20 therefore are
Ẋ − V cos γ = 0
(1)
ḣ − V sin γ = 0
(2)
D+W
L−W
V̇
sin γ +
g
!
V γ̇
cos γ +
g
=0
(3)
=0
(4)
where X is the horizontal distance, h, is altitude, V is velocity, γ is flight path angle, g is the gravitational
constant, W is weight, and D and L are drag and lift respectively. The dot character denotes a derivative
with respect to time.
E.
Weight and Volume
This is the last discipline which calculates the total weight and volume for the vehicle based on the above
outputs stemming from all other disciplines. The method used here is a modified version of the parametric
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ENGINE_NAME
ENGSELECT
Status
Origin
Propellant
Oxidiser
Oxidiser density
Fuel
Fuel Density
PERFORMANCE
ALT_REF(km)
AISP_REF(s)
THRUST_REF (N)
AEXIT (m^2)
AE_AT
PC_RKT(atm)
PC_RKT(N/m^2)
PE_RKT (atm)
GAMMA_RKT
OF_RKT
GEOMTERY
WENG(N)
WENG(kg)
LENGTH (m)
DIAMETER (m)
EFFICIENCY
THRUST/WENG
LENGTH/DIA
HM7B
1
France
LO2/LH2'
'LO2'
1141
'LH2'
66
VINCI
2
RL10A-1
3
In Production
France
USA
LO2/LH2'
LO2/LH2'
'LO2'
'LO2'
1141
1141
'LH2'
'LH2'
66
66
RL10A-4
4
RL10C-1
5
RL60
6
LE-5B2
7
CE-7.5
8
CE-20
9
YF-75
10
YF-75D
11
USA
LO2/LH2'
'LO2'
1141
'LH2'
66
USA
LO2/LH2'
'LO2'
1141
'LH2'
66
USA
LO2/LH2'
'LO2'
1141
'LH2'
66
Japan
LO2/LH2'
'LO2'
1141
'LH2'
66
India
LO2/LH2'
'LO2'
1141
'LH2'
66
India
LO2/LH2'
'LO2'
1141
'LH2'
66
China
LO2/LH2'
'LO2'
1141
'LH2'
66
China
LO2/LH2'
'LO2'
1141
'LH2'
66
RD-0146
12
S5.92
13
In Production
S5.80
14
In Production
Russia
LO2/LH2' N2O4 / UDMH'
'LO2'
'N2O4'
1141
1442
'LH2'
'UDMH'
66
791
N2O4 / UDMH'
'N2O4'
1442
'UDMH'
791
100
445
62000
0.77
83.1
35.5
3599996
0.01
1.25
5.14
100
465
180000
3.63
240
59.2
6000000
0.01
1.25
5.8
100
410
68000
0.64
40
23.7
2400004
0.01
1.25
5
100
451
99000
1.84
84
38.5
3899999
0.01
1.25
5.5
100
450
101000
1.63
130
43.0
4356975
0.01
1.25
5.5
100
465
250000
3.80
80
81.5
8257988
0.01
1.25
6
100
447
150000
12.56
110
37.2
3769290
0.01
1.25
5
100
454
73500
1.91
80
59.1
5990334
0.01
1.25
5.05
100
443
200000
1.77
100
5.2
526890
0.01
1.25
5
100
438
785000
1.77
80
36.3
3678098
0.01
1.25
5.2
100
442
88000
1.77
80
40.5
4099610
0.01
1.25
6
100
451
98000
1.22
210
78.0
7899297
0.01
1.25
6
100
327
19610
0.55
153
95.7
9700004
0.01
1.25
2
100
302
2950
3.46
153
8.7
880000
0.01
1.25
1.8
1618.7
165
2.1
0.99
5395.5
550
4.2
2.15
1285.1
131
1.73
0.9
1648.1
168
2.3
1.53
1863.9
190
2.22
1.44
4885.4
498
2.25
2.2
2844.9
290
2.8
4
4267.4
435
2.14
1.56
5768.3
588
2.2
1.5
5395.5
550
2.8
1.5
5395.5
550
2.8
1.5
2383.8
243
2.2
1.2
735.8
75
1.03
0.84
3041.1
310
1.2
2.1
38.30
2.12
33.36
1.95
52.91
1.92
60.07
1.50
54.19
1.54
51.17
1.02
52.73
0.70
17.22
1.37
34.67
1.47
145.49
1.87
16.31
1.87
41.11
1.83
26.65
1.23
0.97
0.57
Table 2: Deck of liquid rocket engines created to be used as a quick switch method with standard textbook
propulsion analysis.
relations given by Czysz21 for the second stage of a TSTO vehicle. The method calculates the vehicle’s weight
and volume budgets considering the technology level by the use of empirical coefficients which account for
the thermal protection system in the total structure of the vehicle and other fixed systems to calculate the
empty weight of the vehicle. Additionally the volume estimate is used to account for the volumes of the
subsystems, which is used to calculate a second estimate of vehicle’s empty weight. Through these two
independent calculations of the total empty weight of the system, the weight and volume method provides
a way to implement a unique convergence criteria on the system which is explained in next section. The
primary equations and coefficient’s values are shown in the Figure 7.
V.
Results
At this point the design synthesis MDA is setup and ready to execute the sizing code. First, a single-point
convergence design study is executed which is iterated on planform and wing-loading until the objective function is satisfied. A single point design solution calculates 27 primary disciplinary outputs which are passed
among disciplines through the interdisciplinary process. The overall total number of variables calculated
when internal disciplinary variables are considered as well is 201. Once a single point design convergence is
achieved, an additional iteration is implemented on the overall sizing code for iterating on the slenderness
parameter, τ and other technology and mission parameters. These iterations form a trade matrix which is
described in the following section.
A.
Design S
Investigation of geometry and technology is the primary objective of the current study. The geometry trades
conducted are for vehicle configuration profile and leading edge angle (LEA). A technology trade is performed
through the variation of fuel and oxidizer type. This is achieved by selecting an off-the-shelf engine from the
engine deck as explained in the propulsion discipline description. Each trade study and the corresponding
details are summarized in Table 3. Note that the range of τ and leading edge angles are dependent on the
constraints implemented by the geometry profile shape and OpenVSP model. The variation of the ranges
is primarily due to the numerical limitation of the geometric solver in VSP analysis script. Although the
maxima and minima of the τ and LEA are different, the number of steps for both in all geometric iterations
are the same. The total number of design points sized for this study are 540 as shown in the Table 3. Each
of these points is a converged design solution which is executed by a iteration of planform and wing laoding
area as explained above. Thus a huge amount of data was generated for primarily three geometry profiles.
This is addressed in the next section.
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Table 3: Different trade studies investigated
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WEIGHTS
ESTIMATE
VOLUME
ESTIMATE
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EMPIRICAL COEFFICIENTS
The engine coefficients are not used as engine weight and
volume is taken from selected rocket engine.
Figure 7: Primary Weight and Volume budget equations as given by VDK and Czysz.21 The engine parameters and equations are not used here and taken from Table 2 for selected rocket engines.
B.
Solution Space Definition
Following the sizing of all 540 single point design solution a design solution continuum is prepared that
addresses the overall bigger picture configuration level solution space. This is different from the individual
design-points solution space obtained by trading tau and planform since here several inherently different
design options are considered. Figure 8 shows example of a design solution continuum for geometry profile
2 with all trades of engines and reentry altitudes.
C.
Sizing Results
The overall solution space continuum as shown in the Figure 9 the effect of certain trades on the three
performance metrics. The relationship between wing loading and structural weight is positive and increasing
with a distinct difference between two sets of data which correspond to different engines using different fuel
types. Rotation of the solution space to show the performance index reveals that not all points along those
lines are equal and there is a wide spread of performance related to engine ISP, L/D and reentry velocity.
The range of values for each vehicle shape are also different (denoted by color) which is attributed to a
difference in feasible tau ranges for each shape. This is a feature of a geometry type and cannot be greatly
influenced by modifying the geometry i.e. a cylinder has higher volumetric efficiency than a half cylinder.
Examining the specific wing body geometry solution space there exist an optimal solution at the minimum
wing loading, structural weight and highest performance index. This area is denoted by the red circle and is
populated by both 78 degree and 75 degree leading edge angle vehicles. The highest performance is associated
with the 78 degree leading edge although this solution space shows that the 75 degree vehicles are not much
further away and could be an alternative if further studies show an advantage to lower angles. There are
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WB GEOMETRY 2
DESIGN SOLUTION SPACE
# DESIGN POINTS = 180
1.6
Leading Edge Angle variation
for same outer mold shell
GEO = 2, ALLE = 72
WB02
GEO = 2, ALLE = 75
1.4
72
WB02 75
WB02 78
GEO = 2, ALLE = 78
Performance Index, I
per f
1.2
1
0.8
0.6
Optimum Desogn Solution Space:
• Maximum Performance Index
• Minimum wing Loading
• Minimum WSTR
0.4
0.2
1600
1800
2000
2200
2400
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2600
2800
Wing Loading, W/S (N/m
2
2.35
2.4
2.45
)
2.5
2.6
2.55
Weight Structure, W
2.65
# 10
s tr
2.75
2.7
2.8
4
(N)
Figure 8: Creation of overall solution space for a geometry profile. Similar design solution continuum is
generated for all three geometry profiles.
No. of Design Point # 540
No. of Design Point # 540
• Trends Observed on 2-D plot.
• Well behaved Data along
Wing laoding & Wstr
• Data-spread along Performance index.
• Based on trades on Eng (Isp), L/D and VE
Figure 9: Creation of overall solution space for a geometry profile. Similar design solution continuum is
generated for all three geometry profiles.
higher performance index vehicles but at the cost of much higher wing loading and structural weight seen in
the middle of the solution space. Determining if the extra performance is worth the extra weight and wing
loading depends on the decision drivers and required margins.
VI.
Conclusion
This study has demonstrated the use of a state of the art synthesis system which is capable of rapidly
developing unique system architectures for studying a variety of vehicle concepts. The unique geometry
configurations were defined using the numerical analysis capability of OpenVSP which allowed for greater
flexibility and complexity in the geometry. Analytic and empiric methods were behind the aerodynamic,
structural and performance disciplines and allowed the system to converge multiple points for each configuration by running them through said analyses. On top of the geometry trades a level of technology trade was
also performed by considering different off the shelf rocket engine systems. The geometric trades coupled
with the engine trades leads to a staggering amount of vehicles to be analyzed which is why the scope of
geometries was limited in this study by fixing the attachment points of the wing and the height of vertical
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surfaces. Even with the restrictions the solution spaces showed a great variety in available wing loading,
structural weight and performance index for converged solutions. Ultimately the choice of which vehicle
moves into more detailed analysis is up to the project manager however his /or her decision is made easier
by the study of these spaces.
References
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2 Rana,
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