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AIAA 2000-1045 

A Multidisciplinary Performance 
Analysis of a Lifting-Body 
Single-Stage-to-Orbit Vehicle 

Paul V. Tartabini 

Roger A. Lepsch 

J. J. Korte 

Kathryn E. Wurster 

NASA Langley Research Center 

Hampton, VA 23681-2199 


38th Aerospace Sciences 
Meeting & Exhibit 

1 0-1 3 January 2000 / Reno, NV 


For permission to copy or republish, contact the American Institue of Aeronautics and Astronautics 
1801 Alexander Bell Drive, Suite 500, Reston, VA 20191 



AIAA-2000-1045 


A MULTIDISCIPLINARY PERFORMANCE ANALYSIS OF A LIFTING-BODY 
SINGLE-STAGE-TO-ORBIT VEHICLE 

Paul V. Tartabini*, Roger A. Lepsch', J. J. Korte* and Kathryn E. Wurster* 

NASA Langley Research Center 
Hampton, Virginia 23681 


ABSTRACT 

Lockheed Martin Skunk Works (LMSW) is currently 
developing a single-stage-to-orbit reusable launch vehi- 
cle called VentureStar™. A team at NASA Langley Re- 
search Center participated with LMSW in the screening 
and evaluation of a number of early VentureStar™ con- 
figurations. The performance analyses that supported 
these initial studies were conducted to assess the effect 
of a lifting body shape, linear aerospike engine and me- 
tallic thermal protection system (TPS) on the weight and 
performance of the vehicle. These performance studies 
were performed in a multidisciplinary fashion that indi- 
rectly linked the trajectory optimization with weight es- 
timation and aerothermal analysis tools. This approach 
was necessary to develop optimized ascent and entry tra- 
jectories that met all vehicle design constraints. 

Significant improvements in ascent performance 
were achieved when the vehicle flew a lifting trajectory 
and varied the engine mixture ratio during flight. Also, a 
considerable reduction in empty weight was possible by 
adjusting the total oxidizer-to-fuel and liftoff thrust-lo- 
weight ratios. However, the optimal ascent flight profile 
had to be altered to ensure that the vehicle could be 
trimmed in pitch using only the flow diverting capability 
of the aerospike engine. Likewise, the optimal entry tra- 
jectory had to be tailored to meet TPS heating rate and 
transition constraints while satisfying a crossrange re- 
quirement. 

NOMENCLATURE 

eg Center-of-gravity 

Cj Lift coefficient 


GLOW 

Gross Lift-off Weight, klbs 

^SP 

Specific Impulse, sec 

LaRC 

NASA Langley Research Center 

LH, 

Liquid Hydrogen 

LMSW 

Lockheed Martin Skunk Works 

LOX 

Liquid Oxygen 

MECO 

Main Engine Cut Off 

M e 

Edge Mach Number 


Freestream Mach Number 

O/F 

Total oxidizer-to-fuel ratio 

q 

Dynamic pressure, psf 

q-a 

Dynamic pressure times angle-of-attack, 


psf-deg 

Re e 

Momentum Thickness Reynolds Number 

RLV 

Reusable Launch Vehicle 

S ■ 

Aerodynamic reference area, ft 2 

TAV 

Thrust-to- weight ratio 

(T/W) 

Engine thrust-to-weight ratio 

TVC 

Thrust Vector Control 

w 

Entry weight, lbs 

^empiy 

Empty weight, lbs 

w 

ins 

Inserted weight, lbs 

X/L 

Body position over vehicle length 

a 

Angle-of-attack, deg 

A payload 

Change in payload from baseline 


INTRODUCTION 


Many papers have been written describing the diffi- 
culty of designing a fully reusable single-stage-to-orbit 
launch vehicle. 1 1 1 The physical difficulty of this prob- 
lem is further exacerbated by the large degree of cou- 
pling between the various design disciplines. Nearly ev- 
ery subsystem design decision has far reaching 
consequences that must be evaluated in a multidisci- 


* Research Engineer, Mail Stop 365, Vehicle Analysis Branch. 

f Senior Research Engineer , Mail Stop 365, Vehicle Analysis Branch , Member A1AA. 

^Senior Research Engineer, Mail Stop 159 , Multidisciplinary Optimization Branch, Senior Member AIAA. 
s Senior Research Engineer, Mail Stop 365, Vehicle Analysis Branch, Associate Fellow AIAA . 

The use of trademarks or names of manufacturers in this report is for accurate reporting and does not constitute an official 
endorsement, either expressed or implied, of such products or manufacturers by the National Aeronautics and Space Administration. 

Copyright © 2000 American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 
17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for 
Governmental purposes. All other rights are reserved by the copyright owner. 


1 

American Institute of Aeronautics and Astronautics 


pli nary fashion in order to assess the impact on the weight 
and performance of the entire vehicle. This paper dis- 
cusses this process as it relates to the conceptual design 
and analysis of Lockheed Martin Skunk Works' (LMSW) 
proposed single-stage-to-orbft commercial reusable 
launch vehicle (RLV), VentureStar™. 

LMSW is currently studying the VentureStar'' 1 RLV 
which has a number of unique features that differentiate 
it from other SSTO concepts evaluated in the past. Chief 
among these differences is the lifting body shape of the 
vehicle and the utilization of the linear aerospikc engine. 
These design features and others, such as the use of a 
metallic thermal protection system (TPS), provide nu- 
merous benefits that may ultimately contribute to a ful- 
ly capable vehicle that approaches NASA's goal of en- 
abling commercial access to space at an order of 
magnitude less than today’s cost. 4 A representative Ven- 
tureStar''' configuration is shown in Fig. 1 . 



Figure /. A representative VentureStar™ 
Configuration. 

The decision to proceed w ith the full-scale devel- 
opment of VentureStar'” will be made upon the conclu- 
sion of the X-33 program. This program is a joint ven- 
ture between NASA and LMSW and includes the design, 
construction, and flight testing of the X-33 in order to 
demonstrate technologies critical to the development of 
VentureStar™. In 1997, after a year of dedicated effort 
in the design of the X-33, LMSW began to use the les- 
sons learned to improve the conceptual design of the full- 
scale VentureStar™. During this phase of the program, 
NASA Langley Research Center (LaRC) participated in 
the design, analysis and screening of a number of differ- 
ent vehicle concepts and configurations/ 


Throughout the duration of the LaRC study, the fea- 
sibility of numerous configurations was evaluated in 
terms of vehicle mass and payload capability. These mass 
properties are directly related to the overall performance 
of the vehicle. Since many design parameters affect both 
weight and performance, accurate determination of ve- 
hicle sizing information requires a multidisciplinary ap- 
proach to performance analysis. The approach utilized 
in this study indirectly coupled trajectory optimization, 
weight estimation, and heating analysis tools to ascer- 
tain the impact of various design options on the payload 
capability of each configuration. Using this approach, 
trade studies were conducted to maximize vehicle per- 
formance and cost effectiveness. The primary objective 
of these studies was to address design issues that pre- 
sented opportunities and challenges that were unique to 
VentureStar™. Specifically, this paper addresses issues 
that pertain to 1) the effect of the lifting body shape and 
aerospike engine on ascent performance, 2) the ability 
to influence vehicle sizing by varying the engine size 
and mixture ratio, and 3) the ramifications of the metal- 
lic thermal protection system on the entry trajectory de- 
sign. A multidisciplinary approach was the only way to 
ensure that the system fully exploited the performance 
benefits offered by the unique VentureStar™ design while 
staying within the operational limits imposed by its cost- 
saving elements. 

APPROACH 

Many of the trades discussed in this paper required 
the calculation of various physical characteristics of the 
vehicle including payload capability, empty weight and 
gross lift-off weight (GLOW). These quantities were pre- 
dicted using a multi-disciplinary analysis that included 
trajectory optimization, weights and sizing estimation 
and engine performance prediction. 

Trajectory optimization, which formed the core of 
this analysis method, was performed using the three-de- 
gree-of-freedom version of the Program to Optimize 
Simulated Trajectories (POST). 6 This program has been 
developed as a joint govemment/contractor effort, and 
it is available and widely used within the aerospace com- 
munity. Inputs to this code include Earth atmospheric 
and gravitational models, system mass properties, en- 
gine performance, and vehicle aerodynamics. 

Mass property estimation was conducted using the 
Configuration Sizing program (CONSIZ). 7 CONSIZ uti- 
lizes parametric mass-estimating relationships based on 
historical regression, finite element analysis and tech- 
nology readiness level. With knowledge of the vehicle 
layout, CONSIZ can also be used to estimate the loca- 


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American Institute of Aeronautics and Astronautics 


tion of the vehicle center-of-gravity For trim calculations. 
In this paper, mass property data was generated by LaRC 
using CONSIZ and was calibrated to weight statements 
released by LMSW. Another required input to POST was 
a propulsion data model that was computed using a suite 
of computer codes that simulated linear aerospike en- 
gine performance. These codes were able to generate an 
aerospike engine database as a function of altitude, mix- 
ture ratio, power level and thrust vectoring for use with- 
in the POST trajectory code. The capabilities and devel- 
opment of these tools are discussed in Reference 8. A 
final input to the trajectory optimization was an aerody- 
namic database that included coefficients for lift, drag 
and pitching moment as a function of Mach number, 
angle-of-attack and control surface deflection. This da- 
tabase was obtained through the blending of solutions 
from computational methods and wind tunnel data. Up- 
dates to the aerodynamic coefficients were made peri- 
odically during the conceptual design phase to reflect 
configuration shape changes. 

All of the entry performance trades discussed in this 
paper were performed using POST and MINIVER. 9 
POST was the ideal tool to perform entry trajectory op- 
timization, but was limited in its ability to provide heat- 
ing environments. An aerothermal analysis tool, MINI- 
VER, was chosen to complement POST and to provide 
a reliable measure of the healing levels during trajecto- 
ry development. MINIVER is an engineering code that 
uses approximate heating methods with simple flowfield 
and geometric shapes to model healing on critical re- 
gions of the vehicle. MINIVER has been used exten- 
sively as a preliminary design tool and has demonstrat- 
ed excellent agreement with more detailed heating 
solutions for stagnation and windward acreage areas on 
a wide variety of vehicle configurations. In ' 12 In addition 
to providing sufficiently accurate heating levels, it can 
be used to predict the onset of transition to turbulent flow. 

RESULTS AND DISCUSSION 
Ascent Performance 

The figure of merit used for the ascent trade studies 
was payload capability. This parameter was determined 
for each vehicle assuming a constant propellant volume, 
which ensured that the vehicles being compared were 
similar in size (dry weight), thus minimizing errors due 
to scaling. The design reference mission for the Ventur- 
cStar™ RLV was delivery of a 25-kIb payload to the In- 
ternational Space Station (ISS). The nominal ascent tra- 
jectory began with launch at Kennedy Space Center and 
ended with the insertion of the payload into a 50 x 248 
nmi orbit inclined 51.6°. At this point the RLV coasted 


to apogee where the Orbital Maneuvering System (OMS) 
engines were used to circularize at the ISS altitude. 

The aerospike engine performance reflected the 
baseline propulsion system at the conclusion of this study 
with 8 engines operating at a chamber pressure of 2,500 
psia and an area ratio of 1 96. A LaRC version of this 
database was created that provided realistic engine per- 
formance across the mixture ratio/power level envelope, 
thereby minimizing the amount of interpolation error. 

The nominal VentureStar™ ascent trajectory was 
determined by maximizing the weight inserted into the 
target orbit. The trajectory was optimized by adjusting 
the pitch attitude, engine power level and engine mix- 
ture ratio flight profiles. These control variables were 
constrained by angle-of-attack and engine operating lim- 
its. An additional constraint was imposed on the mix- 
ture ratio profile which had to be varied such that the 
ratio of oxidizer to fuel was consistent with the vehicle 
tank design value of 6.0. The optimized trajectory had 
to meet a number of inflight constraints including limits 
on axial acceleration, dynamic pressure, q-a, and angle 
of attack. The parameter q-a is proportional to the struc- 
tural loading of the vehicle during flight and is the prod- 
uct of dynamic pressure and angle-of-attack. The nomi- 
nal trajectory was untrimmed. A subsequent section will 
discuss the trim capability of the aerospike thrust vector 
control (TVC) system and the effect of a trim constraint 
on vehicle performance. The values of all flight con- 
straints and control limits are listed in Table 1, 

The significant flight parameter profiles for the nom- 
inal VentureStar™ ascent trajectory are shown in Figs. 
2a and 2b, Main engine cut off (MECO) took place near 
perigee of the transfer orbit, at an altitude of 57 nmi and 
a flight path angle near 0. 1 °. The peak dynamic pressure 

Table T Constraints imposed upon nominal 
ascent trajectory 


Constraint Name 

Constraint Value 

Final Orbit 

50 x 248 nmi 

Final Inclination 

5 1.6 deg 

Axial Acceleration Limit 

a x < 3 g’s 

Dynamic Pressure Limit 

q < 600 psf 

q-a Limits 

lq-al < 1 500 psf 

Angle-of-attack Limits 

-2 deg < a < 1 2 deg 

Lift-off Thrust to Weight Ratio 1 .35 

Overall Tank Ratio 

6.0 

Engine Power Level 

0.2 < power level < 1 .0 

Engine Mixture Ratio 

5.5 < mixture ratio < 7.0 


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American Institute of Aeronautics and Astronautics 


400 


Structural Constraint 


350 - 
300 - 
250 - 

£ 

J 200 - 

150 - 
100 - 
50 - 

0 - 



a. Altitude, Mach , and angle -of -attack profiles , 


8 . 

£ 360 


§ 



One feature of the VentureStar™ design that could 
be exploited during ascent was its lifting body shape. 
By flying a lifting trajectory, it was possible to signifi- 
cantly decrease the amount of gravity losses, thereby 
improving vehicle performance and payload capability. 
Yet increasing the amount of lift during ascent general- 
ly required flight at higher angles-of-attack and resulted 
in greater stress on the vehicle structure. Accordingly, 
the nominal trajectory was constrained to keep the pa- 
rameter q-a below a 1500 psf-deg structural design lim- 
it to ensure that the aerodynamic loads did not exceed 
the structural capability of the vehicle. The effect of this 
trajectory constraint on vehicle performance is shown 
in Fig. 3. There was a substantial benefit associated with 
using lift during ascent since flying a non-lifting trajec- 
tory resulted in a payload penalty of over 1000 lbs com- 
pared to the nominal case. As the q-a limit was raised 
the payload increased because the vehicle could use more 
lift to further reduce gravity losses. Eventually, the ad- 
ditional payload capability flattened out at a q-a limit 
near 5000 psf-deg because higher drag losses, which arc 
also incurred by flying a lifting trajectory, began to over- 
come the corresponding decrease in gravity losses. The 
results shown in Fig. 3 only reflected the effect of chang- 
ing the structural limit on vehicle performance and did 
not account for the impact of structural w eight increases 
that would be required to design a vehicle that could 
endure higher aerodynamic loading. 


b . Acceleration , dynamic pressure, and q-a profiles. 

Figure 2. Important flight parameter profiles for the 
nominal ascent trajectory. 

of 540 psf occurred at a Mach number of I . I and the q- 
a limit of 1 500 psf-deg was held for roughly 25 sec. from 
Mach 0.4 to 0.6. Although these two structural parame- 
ters were kept within their required limits throughout the 
trajectory, the peak normal force w'as nearly 2.3 times 
the empty weight of the vehicle and may present struc- 
tural problems since it is near the normal load factor limit 
of 2.5 used by the Space Shuttle. The engine was flown 
at 1009? power level from liftoff until the 3-g axial ac- 
celeration limit was reached at approximately 125 sec into 
night (h= 1 12 kft, M = 4.2). At this point the engine w ? as 
gradually throttled down to nearly 209? at MECO to 
maintain the 3-g limit. The engine mixture ratio w'as 
varied continuously throughout ascent. The manner in 
which this parameter is varied during flight has a signif- 
icant effect and will be discussed in more detail later. 



0 1000 2000 3000 4000 5000 

Peak q-a, psf-deg 

Figure 3 . Effect of the q-a structural design constraint 
on vehicle payload capability . 

Axial Acceleration Limit 

A series of ascent trajectories was optimized at a 
range of axial acceleration constraints from 3 to 5-g’s. 
Changing this constraint had a small effect on the vehi- 


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American Institute of Aeronautics and Astronautics 



cle payload capability (see Fig. 4). Increasing the accel- 
eration limit from 3.0 to 3.3-g’s resulted in slightly low- 
er gravity losses, which led to an additional 300 lbs of 
payload capability. As the limit was increased beyond 
3.3-g’s, the lower gravity losses were eradicated by an 
increase in thrust vectoring losses (the AV required to 
turn the velocity vector). To insert into a 50 x 248 nmi- 
orbit, the vehicle must perform much of its pitch-over at 
altitudes high enough to avoid accumulating excessive 
drag losses. As the g-limit was increased, the velocity at 
which this pitch-over occurred became higher and more 
energy had to be expended to turn the velocity vector. 
Although changing the acceleration limit had a small 
effect on payload capability increasing the limit may be 
beneficial to the engine development since a higher lim- 
it enables higher power levels at MECO and shorter burn 
times (see Fig. 4). The former could facilitate the design 
of the engine control system while the latter may increase 
the overall engine life. 


included TVC data was used to assess the impact of a 
trim constraint on the nominal ascent trajectory. The 
trimmed trajectory Was designed such that no more than 
509? of the control authority was used throughout the 
ascent. The vehicle eg was varied linearly with weight 
from the lift-off position of 39.9% of the reference length 
(nose to cowl) to the MECO value of 77.6% . In order to 
keep the amount of TVC used below 50% , the angle-of- 
attack had to be kept within the envelope shown in Fig. 
5. Also shown in Fig. 5 are the angle-of-attack profiles 
for the trimmed and untrimmed nominal ascent trajecto- 
ries. At altitudes below 40-kft, the angle-of-attack had 
to be kept lower than optimal in order to meet the trim 
constraint. This loss of optimality led to an I 1 00-lb pen- 
alty in vehicle payload capability. Note that the TVC 
effectiveness varied with altitude and was lowest at 35- 
kft where the angle-of-attack had to be kept within a 
t .3° window. 



30 3.5 40 4.5 5.0 

Axial acceleration limit, g's 


Figure 4. Effect of the axial acceleration limit on 
vehicle payload capability. 


The VentureStar™ is intended to be trimmed during 
ascent using only thrust vector control (TVC) supplied 
by the linear aerospike engine. The aerospike could pro- 
duce a thrust moment to counteract the aerodynamic 
pitching moment of the vehicle by diverting up to 15% 
of the outflow from the top engine banks to the bottom 
engine banks, or vice-versa. Diverting the flow created 
a couple from the difference in axial force between the 
top and bottom of the engine (although the net axial force 
remained unchanged). This couple was the largest con- 
tributor to the total thrust moment (there was an addi- 
tional smaller contributor due to differences in the nor- 
mal force acting on the top and bottom engine ramps). 
An engine performance database created by LaRC that 



0 50 100 150 200 250 300 350 

Altitude, kft 


Figure 5. Effect of trim constraint on angle-of-attack 
profile for nominal ascent trajectory . 

The baseline configuration discussed in this paper 
had the LOX tank positioned in the nose of the vehicle. 
One trade that was considered by the LaRC team was 
moving the LOX tank to the aft end of the vehicle which 
could potentially decrease the weight of the LH, lank 
and the intertank structure significantly. One concern 
with moving the LOX tank aft, however, was the effect 
of the resulting rearward shift in eg location on the abil- 
ity of the vehicle to trim during ascent. The effect of 
pitch trim was computed for two LOX aft vehicles that 
were modeled as having a constant eg position during 
ascent at locations of 78% and 82% of the reference body 
length (nose to cowl), respectively. Figure 6 compares 
the trim capability of these LOX aft configurations with 
the baseline LOX forward configuration. These results 
show that the TVC requirements actually decreased the 


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American Institute of Aeronautics and Astronautics 



Figure 6. Comparison of the thrust vector control 
profile required for pitch trim for the baseline and two 
LOX-aft configurations. 

more the longitudinal eg was moved aft. This behavior 
occurred because most of the thrust moment was due to 
the couple created by the difference in axial force be- 
tween the top and bottom engine banks. Since this cou- 
ple was independent of longitudinal eg position, the 
maximum attainable thrust moment did not change much 
as the eg was moved. The effect of the eg location was 
much stronger on the aerodynamic moment, and a rear- 
ward shift in eg generally resulted in smaller aerody- 
namic moments for the low angles-of-attack seen dur- 
ing ascent. Therefore, the net effect of moving the LOX 
tank aft was to increase the pitch trim control margin. 
Although moving the LOX tank aft may ease pitch trim 
concerns during ascent, more work must be done to ful- 
ly understand the effect of such a move on pitch trim 
during entry. 


With the aerospike engine it was possible lb vary 
the mixture ratio between values of 5.5 and 7.0 during 
flight. In general, as the engine mixture ratio was in- 
creased, total thrust increased and the specific impulse 
(I S|J ) decreased. Ideally the mixture ratio should be set 
high early in flight, where high thrust levels are required 
to accelerate the fuel-heavy vehicle, and later transitioned 
to the lowest allowable value to maximize vacuum I S|> . 
Generally engine development becomes more compli- 
cated and expensive as the flexibility of the engine to 
vary mixture ratio is increased. 

A performance assessment was made for three dif- 
ferent modes of mixture ratio adjustment during flight 
(constant, step, and continuously varying). In cases w here 
the mixture ratio w^as varied, the total O/F ratio (the ra- 


tio of total LOX weight to total LH, weight) had to be 
kept consistent with the vehicle propellant tank design 
(baseline O/F was 6.0). The mixture ratio profiles for 
each case are shown in Fig. 7 along with the correspond- 
ing effect that each had on the I profile. By continu- 
ously varying the mixture ratio, the inserted weight could 
be increased by 1 900 lbs over the constant case and 200 
lbs over the step case. In the step and variable cases the 
mixture ratio was initially set to 6.5 because the slight 
increase in thrust that could be gained by increasing the 
mixture ratio to 7.0 was overpowered by a greater loss 
in I s|> . The variable case differed from the step case at 
low altitudes because the mixture ratio profile could be 
tailored to take advantage of a lower I SJ) caused by shock 
interference with the nozzle wall (see Reference 8). The 
profile differed at higher altitudes because it was more 
efficient to lower the thrust to meet the g-limit by de- 
creasing mixture ratio (variable case) rather than power 
level (step case). The added design complexity of a con- 
tinuously varying engine over one that performs a step 
change may not be worth the small accompanying per- 
formance increase. 



0 SO 100 150 200 250 300 350 

Altitude, kft 


Figure 7. Engine mixture ratio profiles and 
corresponding effect on l Sj> during flight. 



The liftoff T/W and total O/F ratios were critical 
parameters that influenced the weight and performance 
of the vehicle. Since both of these parameters affected 
weight and performance in opposite ways, it was impor- 
tant to link the weight estimation and trajectory optimi- 
zation in order to capture the combined effect. An itera- 
tive process was undertaken that coupled the results of 
POST and CONSIZ. This process began with an initial 
guess of the mass ratio (GLOW/W ) which is a mea- 
sure of vehicle performance. Next, values for the liftoff 
T/W and O/F ratio were selected. All three of these pa- 


6 

American Institute of Aeronautics and Astronautics 



rameters were input into CONSIZ to determine their ef- 
fect on the weight of the VentureStar™ vehicle. The mass 
ratio essentially determined the total propellant load of 
the vehicle. The liftoff TAV was directly proportional to 
the size of the engine and impacted the weight of the 
propulsion system (engines, feed system, etc) and thrust 
structure. The total O/F ratio determined the propellant 
bulk density and consequently affected the weight of the 
tanks and propellants. 

In this analysis, CONSIZ was used to size the vehi- 
cle to deliver a 25,000-lb payload to the ISS. That is, as 
changes were made to mass ratio, liftoff TAV and the 
total O/F, the vehicle was photographically scaled to 
maintain a fixed 25,000-lb payload. Favorable changes 
to these three parameters resulted in a vehicle that was 
smaller than the baseline (in physical dimensions and 
empty weight) and could still deliver the required pay- 
load. The vehicle was scaled under the assumption that 
the volumetric efficiency (ratio of tank volume to total 
volume) remained constant. The impact of this assump- 
tion was not significant since vehicles were not scaled 
by huge amounts (less than 15% throughout the study) 
and the results were concerned primarily with changes 
in empty weight rather than absolute values. Using this 
technique the effect of the liftoff T/W and total O/F on 
the empty weight was determined with the assumption 
that a vehicle with a lower empty weight would ulti- 
mately have lower development costs. 

The other key component of this iterative sizing pro- 
cess was the optimization of the ascent trajectory using 
the weights calculated with CONSIZ. The same mission 
and constraints listed in Table I were used in the trajec- 
tory calculations. For each optimized trajectory the en- 
gine performance model was scaled to meet the required 
liftoff T/W and the engine mixture ratio was varied such 
that the total O/F was consistent with what was used in 
the weight calculation. Trajectories were determined that 
maximized the weight inserted into orbit, (which was 
equivalent to the lowest possible mass ratio). Once the 
minimum mass ratio was determined from the trajecto- 
ry optimization, it was fed back into CONSIZ and this 
whole process was repeated until convergence. This en- 
tire multidisciplinary analysis was performed for enough 
values of T/W and O/F to demonstrate how the empty 
weight changed with respect to the baseline vehicle. 


1.20 r- 

1 15 - 
1.10 - 
1.05 - 

Normalized 
empty 1.00 - 
weight 

.95 - 
.90 - 


O Performance only - Isp effect 
□ Weights only - bulk density effect 
A Weights and performance 



.85 \~ 


.80 I i 1 i 1 i I i l i -l -j 1 1 1 

5.6 5.8 6.0 6.2 64 66 6.8 7.0 

Total O/F 


Figure 8 . Variation of vehicle empty weight with total 
O/F ratio (normalized with baseline). 

liftoff T/W of 1 .35 was approximately 6.5 and was char- 
acterized by a reduction in empty weight of over 2.5% 
from the baseline. Two additional curves are shown in 
Fig. 8 to demonstrate the importance of coupling the per- 
formance and sizing analyses. When only performance 
changes due to varying the total O/F were considered 
(i.e., weight changes due to varying the propellant bulk 
density were neglected) the empty weight increased rap- 
idly as the total O/F was raised. This increase occurred 
because the engine had to operate at high mixture ratios 
for a longer duration during the trajectory in order to raise 
the total O/F, thus decreasing the average I SJ> and increas- 
ing the mass ratio. On the other hand, if the mass ratio 
was assumed to remain constant as the total O/F ratio 
was changed (i.e., the effect of total O/F on performance 
was neglected) then the empty weight went down as the 
total O/F was increased. This improvement in empty 
weight occurred because of the increase in propellant 
bulk density resulting from the higher ratio of liquid 
oxygen to liquid hydrogen. With a larger bulk density, 
more propellant could be held in a given volume, so that, 
with no penalty in performance, a smaller vehicle could 
carry the same amount of propellant and consequently 
deliver the same payload to the target orbit. In reality, 
both effects work against each other, resulting in the 
actual curve that was minimized around 6.5. This trend 
was nearly independent of the liftoff T/W, with the opti- 
mal ratio of LOX to LH, weight being around 6.5 for 
values ofliftoff T/W between 1.15 and 1 .35 (see Fig. 9). 


The effect of the total O/F ratio on the empty weight 
is shown in Fig. 8. All values have been normalized with 
respect to the baseline vehicle (T/W = 1 .35, O/F = 6.0). 
Changing the O/F ratio had a notable effect on empty 
weight and led to differences of more than 5% between 
the best and worst values. The optimal O/F value for a 


A similar trade was conducted to determine the sen- 
sitivity of empty weight to liftoff T/W. The results of 
this trade assuming a total O/F ratio of 6.0 are presented 
in Figure 10. Each point on the curve was determined 
using the same iterative process that was used in the O/F 
trade. The empty weight was minimized when the lift- 


7 

American Institute of Aeronautics and Astronautics 


Normalized 

empty 

weight 



Totai O/F 


I 

7.00 


Figure 9 . Effect of liftoff T/W on optimal O/F ratio. 

off T/W was approximately 1 .23. Changing the TAV from 
1 .35 (baseline) to 1 .23 resulted in a 2% decrease in empty 
weight. If gross lift-off weight was minimized instead 
of empty weight (also shown in Fig. 10), the optimal 
TAV was somewhat higher (between 1 .30 and 1 .35). The 
optimal TAV differed between the two curves because 
the increase in engine weight that would accompany a 
higher liftoff TAV was a much larger percentage of empty 
weight than GLOW. Therefore the performance benefit 
from a higher TAV was overcome by the added engine 
weight sooner when empty weight was minimized. Since 
cost is more closely related to the empty weight rather 
than GLOW, the lower T/W of 1 .23 would likely lead to 
the lower cost configuration. However, the benefit in 
empty weight resulting from a lower T/W would have 
to be weighed against the affect such a change might 
have on the engine-out abort capability of the vehicle. 
For VentureSlar' M in particular, a single engine-out is 


actually two engines-out (an additional engine must be 
powered down to eliminate thrust imbalances between 
each side of the linear aerospike). This would limit the 
lower T/W bound to about 1 .25 assuming a 10% throttle 
up of the remaining engines. 

The trend of empty weight with liftoff T/W was in- 
dependent of the total ratio of LOX to LH2, with the 
optimal T/W being about 1.23 for O/F ratios between 
6.0 and 6.5 (sec Fig. 1 1). As shown in the figure, a 5% 
decrease in empty weight is possible by changing the 
baseline values of liftoff TAV from 1.35 to 1.23 and to- 
tal O/F from 6.0 to 6.5, abort concerns notwithstanding. 
Also shown in Fig. i l is the influence of the weight of 
the engine per pound of thrust (engine T/W) on the opti- 
mal value of liftoff T/W. The engine T/W is a key input 
to the weights model and directly influences the weight 
of a number of propulsion system elements. For a de- 
crease in engine T/W of 10%, the trend of empty weight 
with respect to lift-off T/W was unchanged, although 
the empty weight increased uniformly by over 6%. 




Figure 10. Variation of gross liftoff weight and 
vehicle empty weight with liftoff TAV ratio 
(normalized with baseline). 


Figure 1 1. Effect of O/F ratio and engine T/W on 
optimal liftoff TAV. 

Entry Trajectory Performance 

An aerospace vehicle that operates in the hyperson- 
ic flight regime must be protected from the aerodynam- 
ic heating environment. The use of a relatively low-tem- 
perature (~ 1 800°F max) metallic thermal protection 
system has been proposed to meet this need for the Ven- 
tures tar™ RLV. In contrast, the current Shuttle orbiter 
employs relatively high-temperature ceramic tiles 
(~2600°F max). Although the metallic system may of- 
fer some benefit in reduced maintenance requirements, 
its lower temperature capability necessarily constrains 
the vehicle flight envelope so that excessive heating lev- 
els are avoided. The lowest achievable peak laminar 


8 

American Institute of Aeronautics and Astronautics 


heating rate is a function of the vehicle configuration, 
hypersonic aerodynamics, and weight (W/C | S). 13 Based 
on the preliminary assessment shown in Fig. 12, it ap- 
peared possible, in theory, to maintain the VentureStar™ 
laminar heating levels to within the limits required for 
the metallic TPS. However, turbulent heating levels can 
easily double the laminar values. Reference 14 illustrates 
the dramatic impact transition can have on TPS require- 
ments, particularly in the case of a metallic system. 



Hypersonic W/ClS, lb/ft 2 


Figure 12. Variation of peak reference heating rate 
with W/C L -S. 

The objective of the entry trajectory development 
was to limit the laminar heating to levels within the ca- 
pability of the proposed TPS and to delay the onset of 
transition such that turbulent heating levels did not ex- 
ceed those experienced in the earlier laminar phase of 
the entry. A coupled approach that used POST and MIN- 
IVER together was employed to achieve these heating 
objectives and to satisfy other flight constraints such as 
the minimum crossrange requirement (750 nmi). Initial- 
ly, a two-phased approach was used to develop an entry 
trajectory that met the thermal constraints. In the first 
phase, aerothermal constraints were imposed on the en- 
try through the use of a reference heating indicator based 
on the work of Chapman.' 5 This correlation, as applied 
in POST, is roughly proportional to p ! 2 v\ Although it is 
only an indicator of stagnation heating rates and loads, 
windward areas of the vehicle (where laminar continu- 
um flow predominates) typically tend to track this indi- 
cator. Thus, it can be used directly in the optimization 
process if the appropriate target value can be determined. 
For this investigation it was assumed that keeping the 
chine and nosccap regions below radiation equilibrium 
temperatures of 2000°F, was sufficient to limit most of 
the acreage to temperatures below the 1 800°F allowable 
for the metallic TPS. Heat transfer distributions for the 
similarly shaped X-33 vehicle supported this assump- 
tion. 16 Transforming the temperature limit (2000°F) to 
a heating rate, adjusting for the vehicle scale and apply- 
ing a hot-wall correction resulted in the desired refer- 


ence heating rate for the trajectory optimization process. 
This value (~45 Btu/ff-sec) was very close to the theo- 
retical minimum noted in Fig. 12. 

Once a trajectory that met the laminar heating con- 
straint was computed, the trajectory was post-processed 
using MINIVER to determine the occurrence of transi- 
tion and the expected laminar and turbulent healing lev- 
els at the vehicle surface. The thermal model used in 
MINIVER was the same as that used in Reference 1 1 
which was shown to yield excellent agreement with de- 
tailed CFD predictionsoblained for a similar lifting body 
configuration. The parameter used to predict transition 
onset in this study, Re e /M c , is one which has been exten- 
sively validated in the Shuttle program. 17 Unlike a sim- 
ple length-based Reynolds number, this local parameter 
takes into account angle-of-attack effects, known to have 
a strong influence on the occurrence of transition. The 
transition work of Thompson, et al presented in Refer- 
ence 1 8, led to selection of a value of 250 for this study. 
In Thompson’s paper, this parameter was predicted us- 
ing the in viscid/boundary- layer code LATCH |l> and com- 
pared to experimental observations of transition on the 
X-33 forebody. A value of 300 was found to accurately 
predict smooth-body transition results. Potential rough- 
ness elements on the metallic TPS led to the selection of 
the more conservative value of 250 for the work pre- 
sented here. 

An evaluation of the initial entry trajectory that was 
post-processed using MINIVER indicated acceptable 
laminar but excessive turbulent heating rates. The high 
turbulent heating rates occurred because the optimized 
trajectory required flight at altitudes low enough to in- 
duce transition between 10 and 15 kft/sec, where lami- 
nar heating rates were still fairly high. The flight profile 
was optimized at these lower altitudes because the den- 
sity was higher and more lift could be generated to help 
meet the 750 nmi minimum crossrange requirement. This 
two-phase approach, in which a trajectory was first de- 
veloped based on laminar heating constraints and then 
post-processed to evaluate for transitional heating lev- 
els, was found to be cumbersome and failed to take ad- 
vantage of the optimization capability within POST. An 
alternative approach was taken that indirectly coupled 
POST and MINIVER so that the transition parameter 
Re e /M c could be used to influence the trajectory design. 
A series of MINIVER solutions were generated at a ref- 
erence point immediately ahead of the expansion on the 
windward surface (90$ of the vehicle length) fora range 
of velocities from 5 to 17 kft/sec and angles of attack 
from 20° to 50°. For each angle of attack and velocity, 
the altitude at which the transition parameter (Re 0 /M, ) 
reached a pre-selected value was determined. Tables rep- 


9 

American Institute of Aeronautics and Astronautics 



Figure 13. Optimized entry trajectory and transition 
constraint surface. 

resenting a series of “transition surfaces” similar to the 
one shown in Fig. 13 were generated for transition pa- 
rameter values ranging from 200 to 350. These tables 
were used to place additional constraints on the trajec- 
tory optimization in order to delay transition to as low a 
Mach number as possible. 

The success of this approach depended on the abil- 
ity of MINIVER to accurately predict the transition pa- 
rameter Re 0 /M c . This capability is demonstrated in Fig. 
14 where LATCH-based predictions were compared to 
predictions made using MINIVER, This comparison is 
illustrative of the level of agreement between MINIVER 
and LATCH windward centerline predictions for Ven- 
lureStar™ and the subscale X-33 demonstrator. Similar 
agreement was obtained for five other representative 
flight conditions ranging from Mach 10 to 20 and five 
angles of attack from 25° to 45°. 


Using the existing reference heating calculation to- 
gether with the new' transition tables, an optimized entry 
trajectory w'hich targeted the desired heating rates and 
loads was generated for the VentureStar™. Simultaneous- 


ly the onset of transition to turbulent flow was delayed. 
This optimized entry trajectory is presented in Fig. 15. 
The trajectory began with a deorbit maneuver from the 
ISS orbit that put the vehicle at atmospheric interface 
(altitude of 400 kft ) with a flight path angle of-1 . 1°. At 
this point the angle-of-attaek and bank angle profiles 
were tailored to minimize the reference heating rate and 
to meet the 750 nmi minimum crossrange requirement. 
In addition, the effect of trimming the vehicle in pilch 
using body flap and elevon deflections was modeled, 
and constraints were placed on the trajectory to ensure 
that the control surface deflections required for trim re- 
mained below 20°. Also, for this trajectory transition was 
delayed to approximately Mach 9.3. To delay transition 
for as long as possible, the vehicle flew near the transi- 
tion surface (see Fig. 13) beginning at a velocity of ap- 
proximately 12 kft/sec until transition finally occurred 
near 10 kft/sec. Subsequent heating predictions based 
both on MINIVER and more detailed solutions using 



Figure 75. Altitude , reference heating rate and 
crossrange profiles for optimized nominal entry 
trajectory. 


W/C L S = 53 lb/ft 2 



Reference 

peak 

healing 50 


45 h 



40 i - l- --4- . - J i i i 1 .i. I 

500 600 700 800 000 1000 

Crossrange, nmi 


Figure 14. M1NIVER/LATCH Re /A/ centerline 
comparison. 


Figure 16. Effect of minimum crossrange requirement 
on reference peak heating rate . 


10 

American Institute of Aeronautics and Astronautics 


LATCH, indicated that peak laminar and turbulent heat- 
ing levels were indeed within the capability of the me- 
tallic TPS. Figure 16 shows the effect of the crossrangc 
requirement on the minimum peak heating rate for a typ- 
ical lifting body configuration. As shown, lowering the 
750 nmi requirement would not enable significantly low- 
er peak heating rates. 

The transition surfaces generated for this study can- 
not be applied directly to other configurations. Howev- 
er, the procedure to develop similar transition surfaces 
is straightforward. MINIVER has been successfully used 
to predict the windward centerline healing environments 
for a wide variety of configurations. Assuming that a 
reasonable assumption can be made for the transition 
value ofRe/M c , surfaces similar to those developed here 
can be generated rapidly to aid in the trajectory devel- 
opment process for other vehicles. The integration of 
the aerothermal/TPS considerations directly within the 
trajectory optimization as developed here can potential- 
ly reduce the number of design cycles required to achie ve 
the optimal trajectory /TPS balance for hypersonic flight 
vehicles. 

SUMMARY 

Lockheed Martin Skunk Works is currently devel- 
oping a single-stage-to-orbit reusable launch vehicle 
called VentureStar™. As part of the X-33 program, 
NASA Langley Research Center participated in concep- 
tual studies that focused on the design, analysis and 
screening of a number of early VentureStar™ concepts 
and configurations. This investigation presents the re- 
sults of various performance trade studies that were per- 
formed in support of this effort. These trade studies were 
conducted using a multidisciplinary performance analy- 
sis approach that indirectly coupled trajectory optimiza- 
tion, weight estimation and heating analysis tools. 

The sensitivity of vehicle performance to a number 
of ascent trajectory constraints was determined. Results 
were presented that quantified the benefit of utilizing the 
VentureStar™ shape to fly a lifting trajectory. Although 
the flight profile had to he limited so that structural de- 
sign limits were not exceeded, using lift during ascent 
still resulted in additional payload capability of over 1 000 
lbs. In addition it was found that the axial acceleration 
limit did not have a significant effect on payload capa- 
bility, although altering it may ease engine-operating 
requirements. Finally, requiring the vehicle to be trimmed 
in pitch during ascent limited the range of angles-of-at- 
tack that could be flown and resulted in a payload penal- 
ty of more than 1 000 lbs compared to an untrimmed case 
where this requirement was ignored. Also, the pilch trim 


control authority of the linear aerospike thrust vector con- 
trol system was relatively independent of longitudinal 
eg location. This insensitivity to eg location may be ad- 
vantageous for a configuration with the liquid oxygen 
tank located in the aft end of the vehicle. 

The linear aerospike engine had the ability to vary 
the mixture ratio during flight. Varying the mixture ra- 
tio in a step-like or continuous manner throughout the 
ascent increased the vehicle payload capability by near- 
ly 2000 lbs compared to the case in which it was held 
constant. Also, by varying the mixture ratio profile, the 
total oxidizer to fuel ratio of the vehicle could be affect- 
ed. Since this ratio influenced the weight and perfor- 
mance of the vehicle, its true effect could only be deter- 
mined through an approach that coupled the vehicle siz- 
ing with the trajectory optimization. This approach was 
also used to determine the optimal liftoff thrust-to-weight 
ratio which was directly related to the size of the engine. 
By changing the oxidizer-to-fuel ratio to 6.5 and the lift- 
off thrust-to-weight ratio to 1.23, the vehicle empty 
weight could be reduced by 5 % compared to the base- 
line case. 

In addition to the ascent trajectory trades, coupled 
trajectory /thermal analyses were conducted to optimize 
the VentureStar™ entry flight profile to the requirements 
of its proposed metallic thermal protection system. The 
objective of these analyses was to limit the laminar heal- 
ing to levels within the capability of the proposed TPS 
and to delay the onset of transition such that turbulent 
heating levels did not exceed those experienced in the 
earlier laminar phase of the entry. Using an aerothermal 
analysis tool, transition surfaces were generated that 
could be used to predict transition onset as a function of 
altitude, velocity and angle-of-attack. These surfaces 
were used directly by the trajectory optimization tool to 
achieve the heating objectives while meeting the mini- 
mum crossrange requirement of 750 nmi. Reducing the 
crossrange requirement did not result in significantly 
lower peak heating rates. 

This study provided a broad view of a number of 
issues and concerns that should be considered in the per- 
formance analysis of a lifting body single-slage-lo-orbit 
RLV. Emphasis was placed on the multidisciplinary na- 
ture of the analyses that were performed. It was neces- 
sary to couple the trajectory optimization with other dis- 
cipline tools since changes in vehicle performance often 
affected the weight and design of many different systems. 
Capturing the effect of various design changes on both 
weight and performance is vital if the physical difficulty 
and small margins that characterize the design of a fully 
reusable single-stage launch vehicle are to be overcome. 


11 

American Institute of Aeronautics and Astronautics 


ACKNOWLEDGEMENTS 

The authors would like to acknowledge Lockheed 
Martin Skunk Works for the opportunity to work with 
them on Venture Star™ and for the various data models 
that were provided by them during the course of this 
analysis. In addition, the authors would like to thank 
Anne Costa who was instrumental in the preparation of 
this paper for publication. 

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American Institute of Aeronautics and Astronautics