Development of a Mass Estimating Relationship Database for ...

Development of a Mass Estimating 

Relationship Database for Launch Vehicle 

Conceptual Design 

Reuben R. Rohrschneider 

Georgia Institute of Technology 

Under the Academic Supervision of Dr. John R. Olds 

AE 8900 

April 26, 2002

Table of Contents 

Abstract........................................................................................................................4 

Acronyms & Notation.................................................................................................. 5 

I Introduction .............................................................................................................. 6 

II Background ............................................................................................................. 6 

III Approach................................................................................................................ 7 

IV Description of Sources........................................................................................... 9 

V Future Work .......................................................................................................... 13 

VI Acknowledgements.............................................................................................. 13 

References.................................................................................................................. 14 

1.0 Wing.................................................................................................................1.0-1 

2.0 Tail...................................................................................................................2.0-1 

3.0 Body.................................................................................................................3.0-1 

4.0 TPS ..................................................................................................................4.0-1 

5.0 Landing Gear ...................................................................................................5.0-1 

6.0 Main Propulsion...............................................................................................6.0-1 

7.0 RCS..................................................................................................................7.0-1 

8.0 OMS.................................................................................................................8.0-1 

9.0 Primary Power .................................................................................................9.0-1 

10.0 Electrical Conversion & Distribution ..........................................................10.0-1 

11.0 Hydraulics....................................................................................................11.0-1 

12.0 Surface Control & Actuators .......................................................................12.0-1 

13.0 Avionics.......................................................................................................13.0-1 

14.0 Environmental Control & Life Support Systems.........................................14.0-1 

15.0 Personnel Equipment ...................................................................................15.0-1 

16.0 Dry Weight Margin......................................................................................16.0-1 

17.0 Crew & Gear................................................................................................17.0-1 

18.0 Payload Provisions.......................................................................................18.0-1 

19.0 Cargo (up and down) ...................................................................................19.0-1 


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20.0 Residual Propellants ....................................................................................20.0-1 

21.0 OMS/RCS Reserve Propellants ...................................................................21.0-1 

22.0 RCS Entry Propellants.................................................................................22.0-1 

23.0 OMS/RCS On-Orbit Propellants .................................................................23.0-1 

24.0 Cargo Discharged ........................................................................................24.0-1 

25.0 Ascent Reserve Propellants .........................................................................25.0-1 

26.0 Inflight Losses & Vents ...............................................................................26.0-1 

27.0 Ascent Propellants .......................................................................................27.0-1 

28.0 Startup Losses..............................................................................................28.0-1 

Technology Reduction Factors ..........................TRF-Error! Bookmark not defined. 


TRF-3

Abstract 

This report attempts to bring mass estimating relations (MERs) for the conceptual design 

of launch vehicles into the open, and establish a baseline for their comparison. Data was 

taken from multiple design organizations from around the country and compiled into a 

database that is freely available for use. To validate the equations, Space Shuttle 

component masses were predicted. A percentage error was reported, with the sign 

indicating the direction of the error. No single set of MERs is uniformly more accurate 

than another. To improve the utility of the equations, modifications can be made to the 

equations to model improved technologies, such as those used in advanced launch 

vehicles. Technology reduction factors are also compiled from multiple sources. No 

proof of their accuracy is available at this time. The greatest accuracy in predicting the 

mass of a future launch vehicle would be attained by using the most accurate equation for 

each component, and an appropriate technology reduction factor. 


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Acronyms & Notation 

AMLS 

AVID 

EMA 

ET 

IHOT 

LaRC 

LOX 

LH2 

MBS 

MER 

MSFC 

NASA 

NASP 

OMS 

RBCC 

RCC 

RCS 

SRB 

SSTO 

TRF 

TSTO 

Advanced Manned Launch System 

Aerospace Vehicle Interactive Design system 

Electro-Mechanical Actuator 

External Tank from Space Shuttle System 

Integrated Hydrogen Oxygen Technology 

Langley Research Center 

Liquid Oxygen 

Liquid Hydrogen 

Mass Breakdown Structure 

Mass Estimating Relation 

Marshall Space Flight Center 

National Aeronautics and Space Administration 

National Aero Space Plane 

Orbital Maneuvering System 

Rocket Based Combined Cycle 

Reinforced Carbon-Carbon TPS 

Reaction Control System 

Solid Rocket Booster from Space Shuttle System 

Single Stage To Orbit 

Technology Reduction Factor 

Two Stage To Orbit 


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I Introduction 

Estimating the mass of future launch vehicles is typically done using parametric 

equations for each component of the vehicle. While effective, and fast, this method is not 

perfect. Many design organizations have their own equations, and do not trust equations 

from other sources. This paper attempts to solve this problem by making mass estimating 

relations freely available to the design community. Further, the Space Shuttle system is 

used as a reference point to validate the equations. It turns out there is no single set of 

mass estimating relations (MER) that is most accurate. The highest accuracy would be 

gained by taking the best MER for each component, from multiple sources. Additionally, 

technology reduction factors are supplied to enable designers to model future vehicles 

using equations derived from current and past technology. 

II Background 

Mass estimation of future air and space vehicles is typically done using parameterized 

equations for each component of a vehicle. These equations are then summed to find the 

total mass of the vehicle. For example, the mass of the anti-vortex baffles in a propellant 

tank, according to Brothers, is given by: 

M 

antivortex 

mF & 

= 

ρ 

prop 

( 0 .64 + 0.0184ρ) 

Here the mass of the baffles is a function of propellant density, and mass flow rate from 

the tank. There is not a unique set of parameters to base the mass of the anti-vortex 

baffles on, and different equations use different parameters. Often a minor component, 

such as the anti-vortex baffles, may be included in another equation for a larger 

component, such as the tank mass. Due to the many ways to parameterize a vehicle 

component, and the available levels of detail that the vehicle can be broken into, different 

design organizations often have different equations to model launch vehicles. This 

process works, but contains flaws. 

The largest problem with the currently used system is the lack of data available on space 

vehicles. In particular, there is only one data point for reusable launch vehicles, and none 


TRF-6

for air-breathing launch vehicles. This problem is often remedied by fitting curves to 

aircraft components and then shifting the intercept such that data from the Space Shuttle 

lies on the curve, as is done by Brothers, and MacConochie. Brothers also fits curves to a 

combination of expendable launch vehicles and the Space Shuttle. This ensures that all 

data is for space hardware, but the durability, and hence weight of components is lower 

for expendable vehicles. The lack of data is exacerbated by the fact that all data is not 

available to all design organizations. Hence each organization’s in-house MERs are 

based on different data points. All of these methods work, but for different vehicle 

configurations, and over different parameter ranges. More often that not, the valid range 

of the parameters is unpublished and often unknown since no data points exist for 

comparison beyond values of current space vehicles or aircraft. 

A further flaw with this approach is the consistency between the mass predictions of 

different organization’s MERs. If one design organization uses their in-house equations 

for a new vehicle, and a second organization uses their in-house equations for the same 

vehicle, will they get the same answer? This flaw is inspired by the difficulty in 

comparing ideas generated at different design organizations. If two different ideas for a 

launch vehicle are posed and one is lighter, it is typically labeled as the better design. 

This could actually be the case, or one of the design organizations may be using mass 

estimating relationships that are heavier (or lighter) than the other organization, 

producing an invalid comparison of the vehicle concepts. 

III Approach 

This paper attempts to solve the problem of comparing vehicles through a two pronged 

approach. First a database of MERs was created to make a large number of equations 

available, and second a baseline was used to compare the predicted mass of the equations 

to a flight vehicle. 

By providing a database of equations to the conceptual design community a common set 

of equations will be available to all design organizations. If the same equations are used 

for vehicle design at different organizations, then the results should be easy to compare. 


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Even if different equations are used from the database, they can be referenced, and the 

difference between the equations used can be found. 

By comparing the compiled mass estimating equations to a baseline vehicle the validity 

of the equation is verified against an actual flight vehicle. The chosen reference is the 

Space Shuttle, specifically orbital vehicle 103 circa 1983, and external tank 7 on a due 

East mission [i]. Many equations in the database are not intended to model Space Shuttle 

technology, and are not compared. 

Several organizations have provided equations for this database, and in the future users 

should be encouraged to submit their equations with applicable parameter ranges for 

inclusion in the database. The database is presented in subsequent sections of this paper. 

The equations were compiled from multiple sources of data, many of which are 

unpublished. A description of each primary source (and a sub source if cited) is provided 

below. On a macro level the data is organized in the order of a typical mass breakdown 

structure. Within each group in the MBS there are two columns, and a page for each 

source. The first page of each component group contains the variables used to predict the 

mass of components in that group, and any supporting illustrations. On each subsequent 

page, the reference is listed along with a brief description of the data source. The first 

column under each reference contains the equations and applicable parameters and 

known limitations. The second column is a percentage error from the Space Shuttle. In 

the following equation E is the percent error from the Space Shuttle, M i is the mass 

predicted by the MER, and M shuttle is the corresponding Space Shuttle component mass. 

M 

i 

− M 

E = 

M 

A positive error percentage indicates that the equation produces a mass higher than that 

of the Space Shuttle, and a negative error shows an equation that predicts lighter than the 

Space Shuttle. All equations in the database are set up for use in the English unit system. 

Standard measures for this database are feet, pounds, and seconds, with pressure in psi, 

and power in kilowatts, unless otherwise noted. 

shuttle 

shuttle 


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Equations that predict this vehicle accurately are likely only good for near term 

technology without adjustment. This adjustment is provided in the form of a technology 

reduction factor. Provided the trend of the equation is correct, the mass can be reduced 

by a percentage to represent an improvement in material technology. The mass of a 

component using improved technology can be found by the following equation: 

M improved = M original (1-TRF) 

Here M improved is the mass of the component being modeled using improved technology, 

M original is the mass of that component predicted by an MER for current technology, and 

TRF is the appropriate technology reduction factor from the last section of this paper 

(starting on page TRF-1). This technique allows the use of MERs created using current 

technology to approximate what can be done in the future. In essence, this extends the 

useful life of an MER. 

IV Description of Sources 

Each source of MERs is intended to model a different type of vehicle, or has been 

derived from a particular configuration. This helps decipher the applicable range of the 

equations, and the vehicle configuration that they will model best. This description 

attempts to make available to the database user some of this knowledge so that the 

equations provided can be used in their proper context, and with confidence. 

1. I.O. MacConochie and P.J. Klich [ii] 

MacConochie worked in the Vehicle Analysis Branch at the Langley Research 

Center in Hampton Virginia. These equations are from NASA Technical 

Memorandum 78661, published in 1978. This predates the Space Shuttle first 

flight, but makes use of known shuttle subsystem masses. Equations are based on 

commercial and fighter aircraft data. 

2. Dr. John R. Olds [iii] 

Dr. Olds published these equations in his PhD dissertation in 1993. They are 

primarily a collection of equations from sources at NASA Langley Research 

Center, with a few that he created himself. The equations were used for design of 


TRF-9

a vertical take off horizontal landing RBCC SSTO vehicle, shown in Figure 1. 

Projects and authors of the original source are listed in the database where 

available. 

Figure 1: RBCC SSTO vehicle. [ref. 2] 

3. Dr. Ted Talay 

Dr. Talay worked in the Vehicle Analysis Branch at NASA Langley Research 

Center. These equations were handed out as class notes for ME250, Launch 

Vehicle Design, at George Washington University in 1992, which he taught. 

Their emphasis is on rocket powered vehicles. Many of the equations provided 

are based on the Space Shuttle. 

4. Marquardt report NAS7-377 [iv] 

a. These equations are from a report by The Marquardt Corporation in 1966. 

They are published in NAS7-377, a study of composite propulsion systems on 

launch vehicle mass. The study vehicle is TSTO, and takes off horizontally. 

The first stage uses the composite propulsion system on multiple body 

configurations. The lifting body version of the first stage can be seen in Figure 

2 with the second stage attached. Conical and cylindrical body versions were 

also modeled with these equations. 


TRF-10

. The second stage is a rocket powered lifting body, based on a previously 

designed second stage by General Dynamics and Convair. These equations 

originate from report GD/C-DCB-65-018 [v]. 

Figure 2: TSTO composite propulsion first stage with rocket powered lifting body 

second stage nestled on top. [ref. 4] 

5. Aircraft Design: A Conceptual Approach, Daniel P. Raymer [vi] 

As the title implies, equations from Raymer are intended for use on aircraft. Only 

his equations for fighter/attack aircraft are provided in this database since they are 

subject to high speeds and similar redundancy requirements as space vehicles. 

6. Bobby Brothers 

Brothers’ equations are derived primarily from expendable vehicles and the Space 

Shuttle. He provides the most extensive set of equations, including multiple 

equations for many components, and careful delineation of parts based on their 

function and load in a vehicle. Some equations are taken from AVID, a sizing 


TRF-11

code developed by A. W. Wilhite at NASA Langley Research Center. When 

applicable, he also uses aircraft derived equations. 

7. Airplane Design, Dr. Jan Roskam [vii] 

Roskam’s focus is on aircraft, including everything from single propeller planes 

to fighter jets. For this database, only jet vehicles were considered, and almost 

exclusively fighter aircraft. 

8. Forbis and Kotker, The Boeing Company [viii] 

This paper is aimed at the design of hypersonic aerospace vehicles. The only 

portion of this paper used is for landing gear weight. 

9. Forbis and Woodhead, The Boeing Company [ix] 

This paper is also aimed at hypersonic aerospace vehicle analysis, and it appears 

to be an extension of the work done in the other listed paper by Forbis. Only the 

landing gear weight is used from this source. 

10. AC-Sizer, NASA MSFC 

This data was taken from a spreadsheet sizing program written by D. R. Komar 

and company at NASA Marshall Spaceflight Center. Both rocket and airbreathing 

vehicles are provided. The primary use is for modeling future 

technology vehicles with wings, both air-breathing and rocket powered. 

a. Many of the equations provided are from Alpha Technologies’ MER database. 

Alpha Technologies is run by Bobby Brothers, so many equations are derived 

from those in source 6, above. 

b. Wing MERs are from Boeing report AFWAL-TR-87-3056 on hypersonic 

aerospace vehicles. 

c. Landing gear is from report GDA-DCB-64-073. 


TRF-12

11. Hawkins [x] 

This source is focused purely on weight growth through the design cycle. The 

data presented is taken from a paper presented at a Society of Allied Weight 

Engineers Conference in Detroit Michigan, 23-25 May, 1988. 

12. Dr. Ted Talay, NASA LaRC 

This is from a presentation from the Space Systems Division at NASA Langley 

Research Center to Dave Pine, Code B at NASA Headquarters on June 10, 1993. 

It is titled “Effect of Concept Maturity on Weight Growth and Cost Estimation.” 

Of primary interest is a chart showing dry weight growth on NASA space vehicle 

projects through the development cycle. 

V Future Work 

This database is only a start towards improving mass estimation for launch vehicles. In 

the future more equations need to be added as they become available. A second baseline 

point would also be very useful, especially a vehicle that uses current technologies, and 

has a different configuration than the Space Shuttle. This would allow verification of 

nearly all the equations provided in the database, and would lend some merit to the 

design of future vehicles. Further if an equation could predict the mass of both vehicles 

well, there would be improved confidence in the accuracy of the trend. 

VI Acknowledgements 

Due to the nature of the work, much of the data collected would not be available without 

the help of others. Mr. Bobby Brothers has been very helpful in providing data and 

information on the topic, and answering questions. D.R. Komar also has been generous 

in his contributions of equations to the database. Finally, Dr. John Olds has been 

instrumental in helping find data sources. 


TRF-13

References 

i 

ii 

iii 

iv 

v 

vi 

vii 

viii 

ix 

x 

MacConochie, I.O., “Shuttle Design Data and Mass Properties,” prepared under 

contract NAS1-19000, Lockheed Engineering and Sciences Company, April 

1992. 

MacConochie, I.O., Klich, P.J., “Techniques for the Determination of Mass 

Properties of Earth – To – Orbit Transportation Systems,” NASA Technical 

Memorandum 78661, June 1978. 

Olds, J. R., "Multidisciplinary Design Techniques Applied to Conceptual 

Aerospace Vehicle Design," Ph.D. Dissertation, North Carolina State University, 

Raleigh, NC, June 1993. 

Escher, W.J.D., Flornes, B.J., “A Study of Composite Propulsion Systems for 

Advanced Launch Vehicle Applications,” final report under NASA Contract 

NAS7-377, the Marquardt Corporation Report No. 25,294, September 1966 (7 

volumes). [NASA Scientific and Technical Information Facility no. X67- 

19028/19034] 

Brady, J.F., Lynch, R.A., “Reusable Orbital Transport Second Summary 

Technical Report,” GD/C-DCB-65-018, Volume I, Contract NAS8-11463, April 

1965. [NASA Scientific and Technical Information Facility no. 65X-17521] 

Raymer, Daniel P. Aircraft Design: A Conceptual Approach. Washington D.C., 

American Institute of Aeronautics and Astronautics, 1999. 

Roskam, Dr. Jan. Airplane Design, Part V: Component Weight Estimation. 

Ottawa, Kansas, 1989. 

Forbis, J.C., Kotker, D.J., “Conceptual Design and Analysis of Hypervelocity 

Aerospace Vehicles, Volume 1 – Mass Properties,” final report for period June 

1986 – March 1987, prepared under contract AFWAL-TR-87-3056 by the Boeing 

Aerospace Company of Seattle Washington, February 1988. 

Forbis, J.C., Woodhead, G.E., “Conceptual Design and Analysis of Hypervelocity 

Aerospace Vehicles, Volume 1 – Mass Properties, Section 2 – Aerospace – 

Vehicle Mass Properties System,” final report for the period July 1988 – October 

1990, prepared by Boeing Military Airplanes, Seattle Washington, October 1990. 

Hawkins, K., “Space vehicle and Associated Subsystem Weight Growth,” SAWE 

paper 1816, May, 1988. 


TRF-14

1.0 Wing 

1.0 Wing 

AR – Aspect ratio (b 

2 /S ref ) 

AR 

exp – Exposed aspect ratio (b 2 exp /S exp ) 

b – Wing span 

b 

body – Maximum width of the body 

b 

exp – Span of exposed wing (b-b body at wing root) 

b 

cthru – Width of wing carry through 

b 

str – Wing structural span along the half chord line (picture) 

c 

xx – Wing chord at xx location 

F 

safety – Safety factor 

M 

wing – Mass of all components in wing group 

M 

wing_exp – Mass of exposed wing 

M 

cthru – Mass of wing carry thru structure 

M 

elevons – Mass of elevons and attach structure 

M 

land – Landed mass of vehicle 

M 

entry – Entry mass of vehicle 

M 

glow – Gross liftoff mass of vehicle 

M 

gross – Gross vehicle mass on the pad or runway 

N 

z – Ultimate load factor = 1.5*2.5 (factor of safety * limit load) 

P 

exp – Exposed wing planform loading (lb/ft 2 ) 

q 

max – Maximum dynamic pressure (lb/ft 2 ) 

R 

t – Taper ratio ( c tip /c root ) 

S 

body – Planform area of the body 

S 

csw – Planform of wing mounted control surfaces 

S 

exp – Exposed wing planform area 

S 

fairing – Surface area of wing fairing 

S 

ref – Theoretical wing planform area 

S 

strakes – Planform area of wing strakes 

S ref (Shaded) 

b cthru 

S csw 

b 

S exp (Shaded) 

C root 

C exp_root 

C tip 

Georgia Institute of Technology 1-1

1.0 Wing 

S 

TEextensions – Planform area of trailing edge extensions 

t 

xx – Wing max thickness at xx location 

TRF – Technology reduction factor 

Λ – Wing sweep at 25% MAC 

θ le – Sweep angle of leading edge 

b str 

Sbody 

b body 

θ le 

L 


1.0 Wing 

Reference: 1 

Derived from: Aircraft and Space Shuttle. 

Options: Materials, and wing tanks. 

0.386 

⎡ 

⎤ 

⎢ 

⎥ 

0.572 

⎢ 

1 ⎥ ⎛ Sexp 

⎞ 

M 

wing 

= ⎢N 

zM 

land 

⎥ 

wing str 

+ 

S 

⎜ 

t 

⎟ 

⎢ 

⎛ 

body 

⎞ ⎝ root ⎠ 

1+ 

η⎜ 

⎟⎥ 

⎢ 

S 

⎥ 

⎣ 

⎝ exp ⎠⎦ 

0.572 

0.572 

[ K b K b ] 

ct 

body 

Space Shuttle 

Comparison 

2% 

Exposed wing material/configuration constants 

K wing = 0.286 – Aluminum skin/stringer, dry wing, no TPS 

= 0.343 – same as above but wet wing for storable propellants 

= 0.229 – metallic composite (Boron Aluminum) honeycomb dry wing, no TPS 

= 0.263 – same as above but wet wing for storable propellant such as RP 

= 0.214 – Organic composite honeycomb, no TPS 

= 0.453 – Honeycomb dry wing super alloy hot structure, no TPS required 

Wing carry-thru constants 

K ct = 0.0267 – dry carry-thru (integral) 

= 0.0347 – wet carry-thru (integral) 

= 0.100 – dry carry-thru (conventional) 

= 0.120 – wet carry-thru (conventional) 

Wing/body efficiency factor 

η = 0.20 – for conventional vehicle to 

= 0.15 – for control configured vehicle. 


1.0 Wing 

b body – Maximum width of the body 

b str – Wing structural span along the half chord line 

M land – Landed mass of vehicle 

N z – Ultimate load factor = 1.5*2.5 (factor of safety * limit load) 

S body – Planform area of the body 

S exp – Exposed wing planform area 

t root – Wing thickness at root 


1.0 Wing 

Reference: 2 

Derived for: Airbreathing horizontal takeoff vehicle. 

Options: Wing material technology. 

M 

wing 

0.4 

⎡ 1+ 

Rt 

⎤ ⎡ N 

zM 

land ⎤ 0.67 0.67 

−exp 

= 0.82954⎢ 

Sexp 

AR 

t ⎥ ⎢ ⎥ 

exp 

1 

⎣ c ⎦ ⎣ 1000 ⎦ 

0.48 

( − TRF ) 

Space Shuttle 

Comparison 

-13% 

M 

cthru 

b b 

= 0.00636 

t exp ⎢ ⎥⎢ 

⎥ 1 

⎣ 1000 ⎦⎣ 

troot 

⎦ 

0.5 ⎡M 

land 

N 

z ⎤⎡ 

str body ⎤ 

[( 1− 

R ) AR ] ( − TRF ) 

TRF 

= 1.0 – for aluminum skin stringer construction 

= 0.4 – for Ti3Al Beta 21S w/SiC 

AR exp – Exposed aspect ratio (b exp 2 /S exp ) 





R t – Taper ratio ( c tip /c root ) 



(t/c) – Thickness to chord ratio on the wing 


1.0 Wing 

Reference: 3 

Derived from: Dr. Talay, LaRC. 

Options: None. 

M 

wing 

2375 ⎡M 

⎢ 

9 

10 

⎥ ⎤ 

entry 

N 

zbstr 

Sref 

= 

⎣ troot 

× ⎦ 

0.584 

Space Shuttle 

Comparison 

43% 


M entry – Entry mass of vehicle 


S ref – Theoretical wing planform area 



1.0 Wing 

Reference: 4a 

Derived from: Airbreathing booster. 

Options: Maximum airbreathing Mach number. 

M 

wing _ exp 

= K 

wing 

S exp 

Includes exposed wing and carry through 

Space Shuttle 

Comparison 

N/A 

elevons 

K wing = 9.847 – for max airbreathing Mach number of 8? 


M = K S Mass of elevons using columbium, including hardware 

elevons 

csw 

K elevons = 11.51 – max airbreathing Mach number of 8 

= 13.70 – max airbreathing Mach number of 12 

S csw – Planform of wing mounted control surfaces 


1.0 Wing 

Reference: 4b 

Derived from: Lifting body rocket. 


elevons 

( 0.14Sbody 

) 0. Sbody 

M = 9 .4 + 07 

Elevons and attachment for lifting body second stage. 


Space Shuttle 

Comparison 

N/A 


1.0 Wing 

Reference: 5 

Derived from: Aircraft. 

Options: Varying wing shapes. 

M 

wing 

0.5 0.622 0.785 

( ) ( t −0.4 

0.05 

−1 

0. 04 

M N S AR ) ( 1+ 

R ) ( cos Λ) S 

= 0.0103K 

K 

c 

t 

csw 

dw 

vs 

gross 

z 

ref 

root 

Space Shuttle 

Comparison 

-54% 

Wing configuration factors 

K dw = 0.768 – for delta wing 

= 1.0 – otherwise 

K vs = 1.19 – for variable sweep 


N z here is the ultimate load factor = 1.5*limit load factor 

1.5 is the typical factor of safety and the limit load factor is typically 2.5 

AR – Aspect ratio (b 2 /S ref ) 

M gross – Gross vehicle mass on the pad or runway 


R t – Taper ratio ( c tip /c root ) 



(t/c) root – Thickness to chord ratio at the wing root 

Λ – Wing sweep at 25% MAC 


1.0 Wing 

Reference: 6 

Derived from: AVID equations from LaRC adjusted to Space Shuttle, includes aircraft for curve fit. 

Options: Two equations with different parameters. 

0.67 

⎡M 

land 

3.75bSexp 

⎤ 

1575⎢ 

9 ⎥ 

c ( 

t 

root c) 

× 10 ⎦ 

M 

wing−exp 

= 

Primary wing equation 

⎣ 

Space Shuttle 

Comparison 

1% 

M 

wing−carrythru 

wing − fairing 

⎡1.06c 

= ⎢ 

⎢⎣ 

S 

fairing 

root 

ref 

( b 

cthru 

) ⎤ ⎡M 

⎥1575⎢ 

⎥⎦ 

⎣ c 

land 

root 

3.75bS 

( 

t 

) 

c 

× 10 

[ 0002499q 

+ 1.7008 + (.00003695q 

− . ) b ] 

M = S 

003252 

exp 

9 

⎤ 

⎥ 

⎦ 

0.67 

. 

max 

max 


b body – maximum width of the body 

c root – Wing chord at exposed root 


q max – maximum dynamic pressure (psf) 


S fairing – Surface area of wing fairing 

S ref – theoretical wing planform area 

(t/c) – Thickness to chord ratio on the wing 

body 

1.176 

M 

wing− exp 

= 1. 

498S 

ref 

Includes carry through, and is considered a secondary equation. 

2% 



1.0 Wing 

Reference: 7 

Derived from: Aircraft 

Options: fixed or variable sweep wings. 

( K N M ) 

0.593 

2 

⎡⎧ 

w z glow ⎫ 

1 R 

⎤ 

t 

6 

3.08⎢ 

⎪ 

⎧⎛ 

− ⎞ ⎪ 

⎫ 

− 

⎨ 

⎬⎨ 

tan( 

le 

) 2 

+ 1.0⎬10 

⎥ 

t ref 

( 

t 

⎢ c) ⎜ θ − 

max 

AR( 1 Rt 

) 

⎟ 

+ 

⎥ 

M 

wing 

= 

+ 

⎣⎩ 

⎭⎪⎩ 

⎝ 

⎠ ⎪⎭ ⎦ 

0.89 0. 741 

{ AR( 1 R )} S 

Space Shuttle 

Comparison 

-35% 

K w 

= 1.0 – for fixed wing airplanes 

= 1.175 – for variable sweep wing airplanes 

AR – aspect ratio (b 2 /S ref ) 

M glow – Gross liftoff mass of vehicle 

N z – ultimate load factor = 1.5*2.5 (factor of safety * limit load) 

R t – taper ratio ( c tip /c root ) 


(t/c) max – Maximum thickness to chord ratio on the wing 

θ le – sweep angle of leading edge 


1.0 Wing 

Reference: 10b 

Derived from: Hypervelocity Aircraft 

Options: Continuous our discontinuous carry thru, landing gear location, strakes, trailing edge extension, and more. 

M = K K K K K K K K K K K K + K 

wing _ box 

wing 

lcf 

trc 

arc 

tac 

swc 

bwc 

gear 

dwr 

tm 

ps 

dc 

dw 

Space Shuttle 

Comparison 

-34% 

Elastic Axis Sweep =30deg ? 

bexp=baero ? 

1.334 

K wing = .7072S 

- for continuous wing/carry-thru structures 

0 

ref 

1.334 

= 0.7072S 

- for discontinuous wing/carry-thru structures (mid mount wings) 

exp 



K lfc – loading correction factor 

= 

0.581 

0.5585 

0.00286N z 

Pexp 

+ 0.1624N 

z 


P exp – Exposed wing planform loading (lb/ft 2 ) 

−1.385 

⎛ t ⎞ 

K trc – taper ratio correction factor = 0.0141⎜ 

⎟ + 0. 758 

⎝ c ⎠ struct 

(t/c) struct – Thickness to chord ratio of the wing structure 

K arc – aspect ratio correction factor 

1.148 

= 0.0588AR exp 

+ 0.28 

AR exp – Aspect ratio of the exposed wing (b 2 exp/S exp ) 

K tac – taper ratio correction factor 0 .47R 

+ 0. 833 

= 

t 


1.0 Wing 

Rt – Wing taper ratio = tip chord over centerline root chord 

K swc – sweepback correction factor 

θ elastic_axis – unknown number?? 

−1.282 

= 0.9031cos( θ elastic _ axis 

) 

K bwc – body width correction factor 

b 

= 1.011− 

0.07 

b 

body 

b body – maximum width of vehicle body 

b exp – Exposed wing span = wing span less b body 

exp 

⎛ b 

− 0.5⎜ 

⎝ b 

body 

exp 

⎞ 

⎟ 

⎠ 

2 

K gear – landing gear support penalty = 1.1 – for wing mounted gear, 1.0 – otherwise 

K dwr – dead weight relief factor 

= 1.0 – for wing without fuel or vertical tail 

⎛ M 

f _ wing 

D 

f _ wing 

+ M 

vert _ wing 

Dvert 

⎞ 

= −1.2⎜ 

⎟ − for wings with fuel and vertical tails attached. 

⎝ 0.5M 

wing 

Dcp 

⎠ 

D vert – distance from vehicle centerline to CG of wing mounted vertical tail 

D f_wing – distance from vehicle centerline to CG of wing stored fuel 

D cp – distance from vehicle centerline to wing center of pressure 

M f_wing – mass of fuel in the wing 

M vert_wing – mass of vertical control surfaces attached to the wing 

M wing – mass of the wing 

K tm – temperature and materials factor 

= 1.0 – for aluminum 

= 1.15 – for titanium 

= 2.8 – for nickel based superalloy 


1.0 Wing 

= 0.88 – for cold composite 

= 0.92 – for titanium composite 

K ps – panel stiffness factor = 1.92 – for ceramic TPS, 1.0 – otherwise 

K dc – design concept factor = 0.97 – for thick truss structure design, 1.0 – otherwise 

K dw – discontinuous wing structural penalty = 0.0 – for continuous wing/carry-thru structures 

1 

= ( M 

wing _ box 

− M 

) 

continuous wing _ box 

3 

discontinuous 

− for discontinuous wing/carry-thru structures 

M 

1.275 

wing _ misc 

= 0.1716Sexp 

0. 564 

−0.2098 

⎛ bbody 

⎞ 

⎜ ⎟ 

⎝ bexp 

⎠ 

b body – maximum width of vehicle body 

b exp – Exposed wing span = wing span less b body 

M = 6 + 

wing _ extensions 

( S S ) 

strakes 

TEextensions 

S strakes – planform area of wing strakes 

S TEextensions – planform area of trailing edge extensions 


2.0 Tail 

2.0 Tail 

AR vert – Aspect ratio of vertical tail or tip fins 


b vert – Span of tail or tip fins 

c tip – Tip chord of vertical tail or wingtip fins 

M – Maximum flight Mach number 



R vert – Taper ratio of vertical tail or tip fins ( c tip /c root ) 

S rud – Planform area of rudder 

S vert – Total planform area of vertical tail or wingtip fins 

(t/c)vert – Thickness to chord ratio of the vertical tail or wingtip fins 

TRF – Technology reduction factor 

Λ vert – Sweep angle at 25% MAC 

b vert 

C root 

C tip 

S rud 

S vert 

S body 

b body 

L 


2.0 Tail 

Reference: 1 


Options: Materials. 

M = K 

tail 

t 

( S ) 1. 24 

vert 

Space Shuttle 

Comparison 

23% 

K t 

=1.872 – aluminum skin/stringer, no TPS 

=1.108 – metallic composite structure, no TPS 

=1.000 − graphite epoxy composite structure, no TPS 



2.0 Tail 

Reference: 2 


Options: Wing material technology. 

M 

tail 

= 5.0S 

1.09 

vert 

(1 − TRF ) 

Space Shuttle 

Comparison 

36% 

TRF 

=1.0 – aluminum skin/stringer structure 

=0.2 – Ti3Al Beta 21s 



2.0 Tail 

Reference: 3 

Derived from: Dr. Talay, LaRC. 


M = 

tail 

1.24 

1.678Svert 

Space Shuttle 

Comparison 

13% 



2.0 Tail 

Reference: 4a 



M = K 

tail 

vert 

S 

vert 

K vert = 7.68 – for max airbreathing Mach number of 8 

= 9.20 – for max airbreathing Mach number of 12 

Space Shuttle 

Comparison 

22% 

using 

K vert =7.68 



2.0 Tail 

Reference: 4b 



tail 

( 0.2Sbody 

) 0. Sbody 

M = 6 .8 + 15 Vertical tail mass for a lifting body upper stage. 

Space Shuttle 

Comparison 

89% 



2.0 Tail 

Reference: 5 


Options: Varying tail shapes. 

M 

tail 

0.348 

0.488 0.718 0.341 −1 

0.25 

0. 323 

( ) 

⎛ S 

− 

M N S M b 1 + 

rud ⎞ 

AR ( 1+ 

R ) ( cos( Λ )) = 0.452 

glow z vert 

vert ⎜ ⎟ vert vert 

vert 

⎝ S 

vert ⎠ 

Assumes no T-tail and no rolling tail. 

Space Shuttle 

Comparison 

28% 

N z = 3.75 

0% 

N z = 2.25 

AR vert – Aspect ratio of vertical tail or tip fins 


M – Maximum flight Mach number 



R vert – Taper ratio of vertical tail or tip fins 

S rud – Planform area of rudder 


Λ vert – Sweep angle at 25% MAC 


2.0 Tail 

Reference: 6 

Derived from: Boeing aircraft tail equations adjusted for Space Shuttle. 

Options: Component inclusion. 

The following three equations must be summed to find the total tail mass. 

Space Shuttle 

Comparison 

-8% 

0.244 0.0364 

( S ( ) ) t 

0. 8674 

c b 

M = 26.06 

vert 

M 

tail 

vert _ spar 

= 

fairing 

c 

tip 

2S 

vert 

b 

fairing 

vert 

vert 

M 

vert 

tail 

( .02499q 

+ 1.7008 + ( 0.003695q 

− 0. ) b ) 

M = S 

3252 

0 

max 

max 

body 



c tip – Tip chord of vertical tail or wingtip fins 

q max – Maximum dynamic pressure during flight 

S fairing – Surface area of tail fairing 


(t/c) vert – Thickness to chord ratio of the vertical tail or wingtip fins 


2.0 Tail 

Reference: 10 

Derived from: NASA MSFC 3rd generation launch vehicle office (mostly airbreathing). 


0.901 0.244 0.0364 

[( S ) R b ] 0. 8674 

M 

tail 

= 28.1 

vert vert vert 

Space Shuttle 

Comparison 

9% 


R vert – Taper ratio of vertical tail or tip fins 



3.0 Body 

3.0 Body 

A as – surface area of aft structure 

A body – surface area of vehicle body 

A body-tank – exposed area of body minus exposed area of integral tanks 

A exit – Total exit area of main engines 

A inlet – cross sectional area of inlet 

A tank – Surface area of tank 


D eng – Diameter of a main engine 

D nose – Diameter of the nosecone base 

F ullage – Ullage fraction (typically ~4 to 5%) 

F prop – Propellant fraction of either oxidizer or fuel 

H body – height of body 

H inlet – Height of engine inlet 

Isp – Specific impulse of engines 

L – Length of vehicle 

L inlet – Length of engine inlet 

L s – Length of single duct (for Y inlet ducts) 

m& − Total propellant mass flow rate (lbm/s) 

M body – Total mass of body group 

M eng – Mass of a single main engine 

M glow – Gross liftoff mass 

M gross – Gross vehicle mass on the pad or runway prior to liftoff 

M insert – Insertion mass, sometimes called burnout mass 


M pl – Mass of payload 

M strapon – Mass of strap on boosters 

M tot_fuel – Mass of all fuel on stage 

M tot_ox – Mass of all oxidizer on stage 

S body 

L 

b body 


3.0 Body 

N crew – Number of crew 

N days – Number of days spent on orbit 

N eng – Number of main engines on stage 

N inlet – Number of inlets 

N struts – Number of struts in engine inlet 

N t – Number of fuel tanks 


P 2 – Pressure in inlet 

P f – Pressure of fuel tank 

P ox – Pressure of oxidizer tank 

q max – Maximum dynamic pressure during flight (lb/ft 2 ) 

S as – Surface area of aft skirt 

S base – Surface area of base closeout 

S body – Planform area of vehicle body 

S bf – Planform area of body flap 

S ec – Surface area of engine compartment 

S f – Surface area of fuel tanks 

S fwds – Surface area of forward skirt 

S inlet – Surface area of inlet and cowl ring 

S is – Surface area of interstage structure 

S it – Surface area of intertank structure 

S nose – Surface area of nosecone 

S ns_cowl – Non-inlet surface area of cowl 

S ox – Surface area of oxidizer tanks 

S pl – Surface area of payload bay, not including doors 

S pldoors – Surface area of payload bay doors 

S tc – Surface area of tail cone 

SFC – Specific fuel consumption 

T sls – Total stage thrust at sea level static conditions 

T vac – Vacuum thrust per main engine 

V crew – Volume of crew cabin 


3.0 Body 

V f – Total fuel volume 

V i – Fuel volume in integral tanks 

V ox – Total oxidizer volume 

ρ f – Density of fuel 

ρ ox – Density of oxidizer 

θ nose – Nose cone angle 


3.0 Body 

Reference: 1 


Options: Materials, windshield, and tanks.. 

body 

c 

0.5 

crew 

b 

body 

1/ 3 

z 

f 

f 

ox 

1.1 

ox 

t 

1. 15 

( N T ) K S 

M = K N + K A N + K V + K V + K + 

Crew cabin constants 

K c = 2043 – full windshield aluminum construction 

= 1293 – aluminum construction with no windshield 

= 1740 – full windshield composite construction 

= 1140 – composite construction with no windshield 

eng 

vac 

bf 

bf 

Space Shuttle 

Comparison 

-7% 

Assumes no 

ascent 

propellant in 

orbiter. 

Body construction constants 

K b = 2.72 – composite structure, no TPS 

= 3.20 – aluminum structure, no composites, no TPS 

= 3.40 – hot metallic Ti/Rene HC, no TPS required 

= 4.43 – moldline tankage; tank, body structure, cryogenic insulation integrated 

Tank geometry/propellant constants 

K f , and K ox – see table below. 


3.0 Body 

Table showing tank constants from [ref. 1]. 

* EN designates in-house LARC study vehicles. 


3.0 Body 

K t 

= 0.0030 – aluminum thrust structure 

= 0.0024 – composite thrust structure 

Body flap construction constants 

K bf = 1.59 – hot structure 

= 1.38 – aluminum skin/stringer, no TPS 


M body – Total mass of body group 









3.0 Body 

Reference: 2 


Options: Material technology. 

M = K 

no sec one 

nc 

S 

nose 

Space Shuttle 

Comparison 

-42% 

M = 

N 

0.5 

crew _ cabin 

1455 crew 

M 15M 

pl _ bay 

= K 

pl 

S 

pl 

+ K 

pldoors 

S 

pldoors 

+ 0. 

pl 

M 

fuel _ tan k 

K 

f 

V 

f 

+ 

= K S includes insulation 

f _ ins 

f 

M 

ox _ tan k 

K 

oxVox 

+ 

= K S includes insulation 

ox _ ins 

ox 

M = K S + K 

aft _ body 

tc 

tc 

base 

S 

base 

M = K 

2 + 

cowl 

ns _ cowl 

S 

ns _ cowl 

+ K 

inlet 

Sinlet 

K 

struts 

Linlet 

H 

inlet 

N 

struts 

airbreather only 

K nc 

K pl 

= 2.21 – Ti3Al Beta 21S 

= 2.21 – Ti3Al Beta 21S 

K pldoors = 3.5 – 20% less than STS honeycomb doors (incl. fittings & mechanisms) 

K f = 0.255 – Hydrogen, wound integral Gr/PEEK 

K f_ins = 0.26 – Based on rohacell insulation 

K ox = 0.33 – LOX, aluminum lithium, non-integral 

K ox_ins = 0.20 – Based on rohacell insulation 

K tc = 2.21 – Ti3Al Beta 21S 

= 1.99 – Secondary structure (10% lower than baseline?) 

K base 


3.0 Body 

K ns_cowl =2.21 – Ti3Al Beta21S 

K inlet = 2.75 – Advanced materials, 150psi, top & bottom required 

K struts = 2.21 – Baseline structural unit weight 

S nose – Surface area of nosecone 






S tc – Surface area of tail cone 


S ns_cowl – Non-inlet surface area of cowl 



H inlet – Height of engine inlet 


N struts – Number of struts in engine inlet 




3.0 Body 

Reference: 3 

Derived from: Dr. Talay, LaRC, rocket based. 


M 

fuse 

3.4A body −tan 

ks 

= Includes fore, aft, mid fuselage, and payload bay doors 

( S S ) 

M + 

sec ondary 

= 2. 0 

base pl 

Add any other secondary structures’ areas specific to vehicle 

Space Shuttle 

Comparison 

-3% 

M = 

N 

0.5 

crew _ cabin 

2347 crew 

M = 3. 135 

bf 

S bf 

M 0. 0023T 

thrust _ struct 

= 

vac 

N 

eng 

M 

fuel _ tan k 

= 

K 

f 

V 

(1 − F 

f 

ullage 

) 

M 

ox _ tan k 

K 

oxV 

= 

(1 − F 

ox 

ullage 

) 

K f 

K ox 

= 0.5595 – Shuttle technology 

= 0.8086 – Shuttle technology 

A body-tank – Exposed area of body minus exposed area of integral tanks 





3.0 Body 








3.0 Body 

Reference: 4a 


Options: Maximum airbreathing Mach number, engine type, and body type. 

M = 

aft _ struct 

K 

as 

Aas 

Inconel 718 aft structure mass 

K as = 2.86 – Max airbreathing Mach number of 8 

= 3.10 – Max airbreathing Mach number of 12 

A as – surface area of aft structure 

Space Shuttle 

Comparison 

N/A 

Air-breathing 

vehicles only 

M = K T Thrust structure mass for aibreathing booster vehicle 

thrust 

thrust 

sls 

M 

K thrust = 0.01025 – Thrust acting below body (ie. Ramjet) 

= 0.0070 – Thrust acting on aft expansion surface (ie. Scramjet) 


fuel _ tan ks 

= 

K 

fuel 

M 

tot _ fuel 

Mass of liquid hydrogen tanks for an airbreathing booster vehicle. This tank is integral with the forebody of 

the vehicle and includes structure. 

K fuel 

= 0.259 – Augmented rocket 

= 0.409 – Ejector ramjet, or supercharged ejector ramjet 

= 0.416 – Ejector scramjet, or supercharged ejector scramjet 

= 0.341 – RL, or RRL, or SRL, or RSRL 

= 0.339 – SL, or RSL, or SSL, or RSSL 



3.0 Body 

M 

ox _ tan ks 

0. 0255 

= M Mass of liquid oxygen tanks for an airbreathing booster vehicle 

tot _ ox 

cowl 

M tot_oxl – Mass of all oxidizer on stage 

M = K A Mass of inlets 

cowl 

inlet 

K cowl 

= 175 – Cylindrical body with wing configuration, 120 psia inlet pressure 

= 154 – Lifting body configuration, subsonic combustion, 120 psia inlet pressure 

= 125 – Lifting body configuration, supersonic combustion, 120 psia inlet pressure 

= See chart for different inlet pressures. 

A inlet – cross sectional area of inlet 

M = 1400 860 Fixed mass for crew cabin structure, and personnel compartment. 

crew _ cabin 

+ 

M = 0. 0133 

separation 

M insert 

Separation system on booster stage, piggy-back configuration. Includes separation rockets, mounting system, 

and controls. 

M insert – Orbital insertion mass of vehicle, sometimes called burnout mass. 


3.0 Body 

Chart showing inlet weight per square foot of inlet area as a function of inlet pressure for three different vehicle 

configurations. Source [ref. 4]. 


3.0 Body 

Reference: 4b 



M = 3 .0724A 

+ 0. 0008T 

body 

body 

vac 

N 

eng 

Body mass including fuselage, thrust structure, and miscellaneous, for a lifting body upper stage. 

Space Shuttle 

Comparison 

N/A 

Lifting body 

design 

M 

crew 

_ cabin 

= 1801 + 1.15V 

crew 

+ 180 

Mass of crew cabin and windscreen/canopy. This reference recommends that the volume for the crew be 

calculated as: V crew = 60N crew +255 

M 0. 224S 

M 

M 

aft _ skirt 

= 

body 

Mass of aft skirt, aerodynamic fairing over engines. 


ox _ tan k 

= 0. 0181 

M 

tot _ ox 

Mass of liquid oxygen tank for lifting body second stage 


f _ tan k 

= 0. 1188 

M 

tot _ fuel 

Mass of liquid hydrogen tank for lifting body second stage, including mounting. 


M 

_ 

= 555 

f 

ins 

0.666 

1. 

V 

f 

Mass of insulation for liquid hydrogen tank on lifting body second stage. 



3.0 Body 

M = 1. 4 

plbay 

V plbay 

Mass of payload bay, including doors. 

Recommended cargo volume is: V plbay = 0.111M pl 

V plbay – Volume of payload bay 

M 

sep _ syst 

= 220 

Mass of separation system on second stage lifting body, piggy-back config. 


3.0 Body 

Reference: 5 


Options: Different inlet geometry including variable shape, and wing shape. 

M = 

fuse 

0.35 0.25 0.5 0.849 0.685 

0.499K 

dwf 

M 

gross 

N 

z 

L H 

body 

bbody 

Space Shuttle 

Comparison 

-26% 

M 

thrust 

_ 

= 0 .013N 

T N + 0. 01M 

struct 

0.795 

eng 

0.579 

vac 

z 

0.717 

eng 

N 

eng 

N 

z 

M 

cowl 

⎛ 

⎜ 

⎝ 

L 

⎞ 

⎟ 

⎠ 

−.0373 

0.643 0.182 1.498 s 

= 13.29K 

vg 

Linlet 

K 

duct 

N 

eng ⎜ 

Deng 

L ⎟ 

based on fighter aircraft inlet ducts 

inlet 

M 

−0.095 

0.249 

⎛ ⎞ 

0.47 

0.066 0.052 

_ tan 

7.45 

⎜ 

V 

⎛ ⎞ 

= 1 + 

i 

⎟ 

TvacSFC 

fuel ks 

V 

f 

N N 

t eng ⎜ ⎟ JP fuel tanks only 

⎝ V 

f ⎠ 

⎝ 1000 ⎠ 

K dwf = 0.774 – for delta wing 

K vg 

K duct 


= 1.62 – for variable geometry inlet 

= 1.0 – fixed geometry inlet 

= 1.0 – circular inlet 

= 1.31 – half circle inlet 

= 2.2 – square and circle combination inlet (stretched D) 

= 2.75 – square inlet 

= 1.68 – ellipsoid, height to width ratio of 1.5:1 

= 2.6 – ellipsoid, height to width ratio of 2:1 

= 3.43 – smile shape (ie. F-16), height to width ratio of 1:3.2 


3.0 Body 

Inlet duct geometry coefficients [ref. 5]. 


D eng – Diameter of a main engine 


L – Vehicle length 

L s – Length of single duct (for Y inlet ducts) 




N t – Number of fuel tanks 


SFC – Specific fuel consumption 



V i – Fuel volume in integral tanks 


3.0 Body 

Reference: 6 

Derived from: Fuselage from aircraft & Space Shuttle, others from Space Shuttle and expendable vehicles. 

Options: Stage number, attachment configuration. 

Shuttle comparison includes fuselage, nosecap, thrust structure, payload bay and doors, crew cabin, and stage to stage 

attachment structure. 

Space Shuttle 

Comparison 

2% 

M = Mass of vehicle body, including base 

fuse 

1.075 

2.167Abody 

M 

M 

nose 

nose 

= S 

nose 

nose 

( ) ( 0.0001034q 

) 

max −0.5878 

14.31− 

0.003462qmax 

θ 

nose 

+ 

−9 

−5 

−3 

( 0.0006864 − 6.1e 

q ) θ + ( 4.385e 

q − 3.252e 

) 

⎡ 

{ }⎥ ⎥ ⎤ 

⎢ 

⎢⎣ 

max nose 

max 

Dnose 

⎦ 

−4 

−5 

−3 

[ 2.499e 

q + 1.7008 + ( 3.695e 

q − 3.252e 

) D ] 

= S 

ellipsoid 

max 

max 

nose 

right cone 

( 0.8548+ 

0.0003189ρox 

) 

( 2.44 − 0. ρ ) 

M ox 

= V 

P

3.0 Body 

M 

slosh _ 

2 

−7 

ρ 

baffles 

= 6.77e 

bbodyV 

adapt for propellant type 

1.01 

For M antivortex and M slosh_baffles the volume, density and F prop need to have the correct subscript for the fluid in the 

tank. For example for a LOX tank F prop would be the oxidizer fraction, V would be the oxidizer tank volume, 

and ρ would be the density of LOX. 

k it 2 

M = S K b Structure between tanks for inline configuration 

int er tan k 

it 

it 

body 

K it = 26.36 – stage 1 of 1 

= 27.04 – stage 1 of 2 


K it2 = 0.5169 – stage 1 of 1 or stage 1 of 2 


K is 2 

M = S K b Structure connecting two stages of an inline vehicle 

int erstage 

is 

is 

body 

K is = 17.92 – stage 1 of 1 



K is2 = 0.4856 – stage 1 of 1 or stage 1 of 2 


fwd _ skirt 

fwds 

fwds 

K fwds 2 

body 

M = S K b Mass of structure between forward tank and payload or next stage 

K fwds = 37.35 – stage 1 of 1 



K fwds2 = 0.6722 – stage 1 of 1 or stage 1 of 2 


M = K T 

Thrust structure mass 

thrust 

thrust 

1.0687 

vac 


3.0 Body 

K thrust = 1.949e-3 – inline launch vehicle 

= 7.995e-4 – side mount propulsion module (orbiter type) 

K ec 2 

M = S K b structure from aft tank to interstage or pad tie-down 

M 

eng _ comp 

aft 

ec 

ec 

body 

K ec = 31.66 – stage 1 of 1 



K ec2 = 0.5498 – stage 1 of 1 or stage 1 of 2 


skirt 

as 

−4 

−5 

−3 

[ 2.499e 

q + 1.7008 + ( 3.695e 

q − 3. e ) b ] 

_ 

= S 

max 

max 

252 aerodynamic fairing 

stg _ attach 

( M M ) 

M = 0. 0148 + 

gross 

pl 

Orbiter type vehicle to ET or booster stage where attach structure stays with ET or booster stage. 

body 

M 0. 00148M 

stg _ attach 

= 

strapon 

SRB to ET or core stage where attach structure stays with ET or booster stage 

M 000314 

stg _ attach 

= 0. M 

strapon 

SRB attach structure stays with SRB 

M 

crew _ cabin 

= .3139. 66 

1.002 

[ ( N N ) ] 0. 6916 

28 

crew days 

Abody 

M 

pldoors 

= 0.257 Payload bay doors including hardware 

2 

Abody 

M 

plbay 

= 0.4808Abody 

+ 0.2336 Internal cargo bay mass, including support structure (ie.STS) 

2 


3.0 Body 

A body – Surface area of the vehicle body 


D nose – Diameter of the nosecone base 

F prop – Propellant fraction of either oxidizer or fuel 




M strapon – Mass of strap on boosters 



P f – Pressure of fuel tank 

P ox – Pressure of oxidizer tank 


S as – Surface area of aft skirt 

S ec – Surface area of engine compartment 

S fwds – Surface area of forward skirt 

S is – Surface area of interstage structure 

S it – Surface area of intertank structure 

S nose – Surface area of the nosecone 




ρ f – Density of fuel 

ρ ox – Density of oxidizer 

θ nose – Nose cone angle 


3.0 Body 

Reference: 7 


Options: Inlet geometry and pressure. 

M 

fuse 

0.95 

0.283 

1.42 ⎛ qmax 

⎞ ⎛ M 

glow ⎞ ⎛ ⎞ 

20.86 

⎜ 

L 

= K ⎜ ⎟ 

⎟ 

100 

⎜ 

1000 

⎟ 

inl 

⎝ ⎠ 

⎝ ⎠ ⎝ H 

body ⎠ 

Fuselage mass based on fighter planes using the General Dynamics method. 

0.71 

Space Shuttle 

Comparison 

3% 

M 

cowl 

= 

0.5 

( S L P ) 0. 731 

K 

inlet 

N 

inlet inlet inlet 2 

Cowl mass based on aircraft inlets 

K inlet = 3.0 – turbojet 

= 7.435 – turbofan 





N inlet – Number of inlets 


P 2 – Pressure in inlet 



3.0 Body 

Reference: 10 


Options: Integral or non-integral tanks. 

Shuttle comparison includes the rocket fuselage, body flap, payload bay and doors, crew cabin, stage to stage 

attachment, and separation system. 

Space Shuttle 

Comparison 

-9% 

2 

( + 0.272ρ veh 

/ 9.55 + 0.046( veh 

/ 9.55) 

) body 

M fuse 

= 2.8279 0.682 

ρ A Airbreather smeared fuse 

M 

fuse 

( T N b ) 

0.9846 

⎡ 

( ) 

( ) ⎥ ⎥ ⎤ 

1.075 

0.000011689 

sls eng body 

= 2.0833Abody 

+ ⎢ 

Rocket smeared fuse 

⎢⎣ 

+ 5.02 Sbase 

− Aexit 

⎦ 

Integral tanks are included in the body area for these equations. 

⎧ 

⎫ 

⎪ 

( 0.8548+ 

0.0003189ρ 

) 

[( 2.44 − 0.007702ρ 

) V 

] + ⎪ 

⎪ 

⎪ 

⎪⎡Tsls 

( 1− 

R) ( ) 

⎤ ⎪ 

M 

non −int 

egral−tan 

ks 

= 1.68⎨⎢ 

0.64 + 0.0184ρ 

⎥ + ⎬ (source 10a) 

⎪⎣ 

Isp ρ 

⎦ 

⎪ 

V 

⎪ 

⎪ ⎪⎪ 2 

0.000000677bbody 

ρ 

⎩ 

1.01 

⎭ 

Valid for all propellant types, includes slosh baffles, anti-vortex baffles, and are intended for use with pump fed 

engines in the horizontal mounting position. 

M 

insulation _ non int egral _ tan k 

0. 2 

= A For non-integral tanks only 

tan k 

M = 3. 421 Body flap mass 

bf 

S bf 

M = 0. 5108 Payload bay mass 

plbay 

S pl 


3.0 Body 

M = 0. 5623 Payload bay doors mass 

pldoors 

S pldoors 

M 

_ 

= 31 Crew cabin mass 

crew 

cabin 

0.6916 

28. 

Vcrew 

M = 0. 00155 State to stage attachment structure, for either booster or orbiter 

attach 

M land 

M = Booster side of separation system 

sep 

0.7728 

0.0404M 

insert 

M = Orbiter side of separation system 

sep 

0.9182 

0.00989M 

gross 


A exit – Total exit area of main engines 

A tank – Surface area of tank 







R – fraction of total ascent propellant that is the propellant used in this tank 






V – volume of propellant stored in tank 


ρ – density of propellant stored in tank 


3.0 Body 

ρ veh – Vehicle bulk density 


4.0 TPS 

4.0 TPS 

A acc – Area of advanced carbon-carbon TPS 


A body_tps – Wetted area of TPS on vehicle body 

A exit – Exit area of main engines 

A ins – Wetted area of vehicle covered by insulation 

A ref – reference aerodynamic area (front projected shadow area) 

A sa_standoff – Area of superalloy standoff TPS 

A sb – exposed surface area of speed brakes 

A ti_standoff – Area of titanium standoff TPS 

A tps – Wetted area of vehicle covered by TPS 

C L – Average coefficient of lift from orbit to Mach 10 

D nose – Diameter of base of nosecone 

H le – Height of leading edge 

L cowl_le – Length of cowl leading edge 

L le – Length of leading edges (wing and nose if applicable) 

L wing_le – Length of wing leading edge 







S exp – Planform area of exposed wing 


S mono_tank – Surface area of monopropellant tank 


S tps – Planform area covered by TPS 


S body 

L 


b body 


4.0 TPS 



ψ le – Leading edge angle (? Sweep or angle of airfoil nose) 

C tip 

S vert 

b vert 

C root 


4.0 TPS 

Reference: 1 


Options: Materials. 

Shuttle comparison uses C l = 0.65 and K flow = 0.556. 

Space Shuttle 

Comparison 

0% 

M 

tps 

0.302 

K 

flow 

⎛ 1 ⎞ ⎛ M 

entry 

⎞ 

= K ⎜ 

⎟ 

r 

⎜ 

( ) 

( Abody 

+ 2S 

exp 

) 

K 

⎟ 

Rocket vehicle, lifting re-entry. 

t 

Sbody 

S 

exp 

C 

⎝ ⎠ ⎝ + 

L ⎠ 

K r 

= 0.140 – RSI (shuttle technology) – material/config. constant 

= 0.110 – RSI Advanced 

= 0.145 – metallic 

K t = 0.100 – aluminum skin/stringer – equivalent thermal thickness of backup structure (in.) 

= 0.085 – titanium 

= 0.115 – graphite epoxy 

K flow – Flow constant in the range below. 

= 0.5 – Pure laminar flow 

= 0.8 – Pure turbulent flow 


C L – Average coefficient of lift from orbit to Mach 10 





4.0 TPS 

Reference: 2 


Options: Material technology. 

M 3. 50A 

active _ cooling 

= 150 + 2.70Lcowl 

_ le 

+ 2.70Lwing 

_ le 

+ 

exit 

Based on 5deg. Cone for heat rates (Wilhite) 

Includes nosecap (150 lbs.), wing leading edges, cowl leading edges, and cooled engine exit are. Primarily 

intended for airbreather. 

Space Shuttle 

Comparison 

N/A 

Different 

technology 

M 

acc 

= 2. 0A acc 

Advanced carbon/carbon, based on advanced NASP TPS, Shideler. For T>1800F 

Typically used on wing, body, and cowl windward sides. 

M 

M 

= 

sa _ s tan doff 

1. 06 

A 

sa _ s tan doff 

Superalloy standoff, based on advanced metallic NASP, Shideler. For T>1200F 

= 

ti _ s tan doff 

0. 508 

A 

ti _ s tan doff 

Titanium standoff, based on advanced metallic NASP, Shideler. For T

4.0 TPS 

Reference: 3 



M 

tps 

0.5 

⎛ M 

entry 

⎞ 

= 0.35⎜ 

⎟ Atps 

Shuttle technology. 

S 

⎝ tps ⎠ 

Space Shuttle 

Comparison 

39% 



S tps – Planform area covered by TPS 


4.0 TPS 

Reference: 4a 



M = K 

tps 

tps 

A 

tps 

TPS mass for an airbreathing booster stage using reusable metallic (inconel and columbium shingles) TPS, 

including 2% contingency. 

Space Shuttle 

Comparison 

N/A Different 

technology 

K tps = 1.42 – for maximum airbreathing Mach number of 8 

= 1.54 – for maximum airbreathing Mach number of 12 

M 

ins 

= K 

ins 

Ains 

Insulation mass for an airbreathing booster stage, including 2% contingency. 

A ins – surface area requiring insulation. 

K ins = 1.07 – for max airbreathing Mach number of 8 

= 1.23 – for max airbreathing mach number of 12 

A ins – Wetted area of vehicle covered by insulation 



4.0 TPS 

Reference: 4b 



M = 1. 51 

ins 

A body 

M = 

Mass of external insulation on a lifting body second stage. No cover panels are used. 

0.6666 

crew _ ins 

5. 

2V 

crew 

Insulation protecting the crew cabin. This reference recommends that the volume for the crew be calculated as: 

V crew = 60N crew +255 

Space Shuttle 

Comparison 

-57% 

compared to 

all TPS 

249% 

compared to 

insulation 

only 





4.0 TPS 

Reference: 6 

Derived from: Space Shuttle, ET, and Saturn launch vehicles. 


Shuttle uses the first 7 equations listed. 

Space Shuttle 

Comparison 

2% 

M 366 

M 

tps _ fuse 

= 1. Abody 

Fuselage TPS 

( ) 

tps _ wing 

= 2.845 

2Sexp 

Wing TPS 

M 2 

( S ) 

tps _ vert 

= 1.572 

vert 

Vertical control surface TPS 

M 3.468 2 

( S ) 

tps _ bf 

= 

bf 

Body flap TPS 

M 

6 

tps _ base 

= 0.82Aref 

Tvac 

N 

eng 

/ 1e 

Base TPS 

For boosters T vac N eng should be replaced with T sls . 

M 366 

tps _ sb 

= 1. Asb 

Speed brake TPS 

M = 0. 508 

Body insulation 

insulation 

A body 

M 0. 2574S 

ox _ tan k _ ins 

= 

ox 

Oxidizer tank insulation. For boosters only cryogenic oxidizer is insulated. 

M 0. 2361S 

f _ tan k _ ins 

= 

f 

Fuel tank insulation. All cryogenic fuels are insulated. Non cryogenic fuels are not. 


4.0 TPS 

M 

= 

mono _ tan k _ ins 

0. 2574 

S 

mono _ tan k 

Mono-propellant tank insulation. All cryogenic mono-propellants are insulated except on booster stages. 

A ref – reference aerodynamic area (front projected shadow area) 

A sb – exposed surface area of speed brakes 









S mono_tank – Surface area of monopropellant tank 


4.0 TPS 

Reference: 10 


Options: TPS technology. 

Shuttle comparison uses tiles, and blankets, not including wing leading edge, or nose cap RCC. 

Space Shuttle 

Comparison 

-16% 

M 

tps 

tps 

( 2 Sexp 

+ 2S 

vert 

+ 2Sbf 

) + 0. Abody 

_ tps 

= K A R + K R 

Including insulation. 

body _ tps type wtps type 

2 

R type – Percentage of TPS area covered by the type of TPS used for K tps 

K tps – Mass per area of chosen TPS type 

= 0.63 – body metallic TPS 

= 1.67 – body blanket TPS 

= 1.50 – body tile TPS 

= 2.25 – body HEX panel TPS (active cooling) 

K wtps – wing, body flap, tail, and control surface TPS mass per area 

= 1.59 – wing metallic TPS 

= 0.49 – wing blanket TPS 

= 1.50 – wing tile TPS 

2 

⎛ Dnose 

⎞ 

M 

nose ⎜ ⎟ 

max 

max 

003252 

sharp 

( 0.0002499q 

+ 1.7008 + ( 0.00003695q 

− 0. ) D ) 

= π 

nose 

(source 10a) Body or TPS 

⎝ 2 ⎠ 

For semispherical nose cap with passive TPS. 

M = 280H 

2 tan( ψ ) L 

le 

le 

le 

For thin leading edges using the sharp TPS (density = 280 lb/ft 3 ) 

M 

active 

= L le 

5.75 

For thin nose leading edge and wing and tail leading edges with active cooling. 


4.0 TPS 

A body_tps – Wetted area of TPS on vehicle body 

D nose – Diameter of base of nosecone 

H le – Height of leading edge 

L le – Length of leading edges (wing and nose if applicable) 





ψ le – Leading edge angle (? Sweep or angle of airfoil nose) 


5.0 Landing Gear 


L mg – Length of main landing gear 

L ng – Length of nose landing gear 




N land = (number of gear)*1.5 – ultimate landing load factor 

N mgw – Total number of wheels on main gear 

N ngw – Total number of wheels on nose gear 



Reference: 1 


Options: Materials, and skids or wheels. 

M 

lg 

= 

K 

lgM land 

K lg 

= 0.033 – shuttle gear 

= 0.030 – advanced composite gear 

= 0.0255 – composite skid system with no brakes 

Space Shuttle 

Comparison 

15% 




Reference: 2 



Same equation as above, but additionally the ratio of nose gear/main gear is 15%/85% 

K lg = 0.026 – advanced landing gear 

Space Shuttle 

Comparison 

-9% 



Reference: 3 



Same equation as above. 

K lg = 0.033 – shuttle technology 

Space Shuttle 

Comparison 

15% 



Reference: 4a 



M 

lg 

= 0. 0357M gross 

Gear weight for horizontal takeoff airbreathing booster vehicle 

Space Shuttle 

Comparison 

N/A 

Horizontal 

takeoff only 




Reference: 4b 

Derived from: Lifting body rocket upper stage. 


( 0.036 + 0.0061+ 

0.002 0. ) M 

land 

M = 

0008 

lg 

+ 

Landing gear for a second stage vehicle. Includes nose and main gear, gear bays, and attachment. 

Space Shuttle 

Comparison 

56% 




Reference: 5 


Options: Different gear styles. 

M = K 

maingear 

cb 

K 

tpg 

0.25 0. 973 

( M N ) L 

land 

land 

mg 

Space Shuttle 

Comparison 

-44% 

M = 

nosegear 

0.29 0.5 0. 525 

( M N ) L N 

land 

land 

ng 

ngw 

K cb 

K tpg 

= 2.25 – for cross beam (F-111) 

= 1.0 – all other gear 

= 0.826 – for tripod gear (A-7) 

= 1.0 – all other gear 

N land = (number of gear)*1.5 – ultimate landing load factor 



N ngw – Total number of wheels on nose gear 



Reference: 6 

Derived from: Space Shuttle and aircraft. 


M = 

maingear 

1.0861 

0.00927M 

land 

Space Shuttle 

Comparison 

8% 

M = 

nosegear 

1.0861 

0.001514M 

land 

For shuttle technology. 




Reference: 7 


Options: Wing location. 

Used M land instead of M glow for comparison to Shuttle. 

lg 

lg 

4 

2 

[ K + K M 

] 

3 / + K M K M 

3/ 

M = K 

+ 

Torenbeek method 

a 

b 

glow 

c 

glow 

d 

glow 

For USAF airplanes, coefficients for other civil planes with retractable gear. 

Space Shuttle 

Comparison 

37% 

K lg 

K a 

K b 

K c 

K d 

= 1.0 – low wing planes 

= 1.08 – high wing planes 

= 40.0 – main, 20.0 – nose 

= 0.16 – main, 0.10 – nose 

= 0.019 – main, 0.00 – nose 

= 1.5e-5 – nose, 2.0e-6 – nose 



Used M glow for comparison to Shuttle. Use of M land produced very low gear weight. 

10% 

M glow 

0.84 

⎛ ⎞ 

M 

lg 

= 62.61 

⎜ 

1000 

⎟ General Dynamics method 

⎝ ⎠ 

For USAF airplanes, fighter/attack aircraft. 





Used M glow for comparison to Shuttle. Use of M land produced very low gear weight. 

-17% 

M glow 

0.66 

⎛ ⎞ 

M 

lg 

= 129.1 

⎜ 

1000 

⎟ Torenbeek method 

⎝ ⎠ 

For USN airplanes, fighter/attack aircraft. 





Reference: 8 


Options: Skid or wheel gear. 

Method A 

Space Shuttle 

Comparison 

-2% 

M 

lg 

= 096 

0.9 

0. 

M 

land 

K1 

K 1 

= 0.6 – for skid gear 

= 1.0 – for wheeled gear ? 


Method B 

M 

M 

0.75 0.14 

0.44 

[ 0.001M 

( 173N 

K + 35.2L 

K )]( 1 0.06K 

) 

maingear 

= 

land mgw 1 

mg 2 

+ 

Skid gear – K 1 = 0.21, K 2 = 0.52, K 3 = 0.27 ; wheeled gear – K 1 = K 2 = K 3 = 1.0 

0.75 

0.44 

[ 0.001M 

( 18.9K 

+ 9.48L 

K )]( 1 0.08K 

) 

nosegear 

= 

land 1 

ng 2 

+ 

Skid gear – K 1 = 1.59, K 2 = 1.77, K 3 = 0.063 ; wheeled gear – K 1 = K 2 = K 3 = 1.0 

3 

3 

-41% 




Reference: 9 


Options: Development risk, number of wheels. 

For this reference use M glow even for vertical take-off vehicles. This was used for Shuttle comparison since using M land 

produces very low weight gear. 

For comparison to Shuttle, TRF=1.0 for both main and nose gear. 

Space Shuttle 

Comparison 

5% 

M = 

M 

M 

0.14 

main _ running _ gear 

9.61M 

glow0. 

001N 

mgw 

main 

main 

N mgw – rule of thumb = M glow /50,000 

0.44 

_ gear _ struct 

= ( 3.1M 

land 

0. 001Lmg 

)TRF 

⎛ 

M 

main _ gear _ struct ⎞ 

= 

⎜ M 

+ 

⎟ 

_ gear _ control 

0 . 18 

main _ running _ gear 

⎝ 

TRF ⎠ 

TRF = 0.85 – low development risk 

= 0.80 – moderate to high development risk 

= 0.70 – very high development risk 

M = 1.25M 

M 

M 

nose _ running _ gear 

nose 

glow 

0.001 

0.44 

_ gear _ struct= 

( 0.5M 

land 

0. 001Lng 

)TRF 

nose _ gear _ control 

3 

TRF 

⎛ 

M 

nose _ gear _ struct ⎞ 

= 0 . 

⎜ M 

+ 

⎟ 

nose _ running _ gear 

⎝ 

TRF ⎠ 

= 0.80 – advanced materials, all risk levels 







N mgw – Total number of wheels on main gear 



Reference: 10c 

Derived from: Aircraft from General Dynamics Study. 


M 

nose 

_ gear 

= 0.0033995M 

+ 402 

Space Shuttle 

Comparison 

19% 

M 

main 

_ gear 

= 0.02366M 

+ 1161 

The mass, M, in these equations can be either the landing mass or the GLOW depending on whether the vehicle 

is vertical or horizontal take-off. 


6.0 Main Propulsion 


A mixer – is the cross sectional area of the mixer. 



Isp sl – Specific impulse of engine at sea level 




P c – Pressure of main engine combustion chamber 

P tank – Pressure of propellant tanks 

R aox – ascent oxidizer fraction 

R eng – engine thrust to weight at vacuum conditions, installed 

R v_lo – Vehicle thrust to weight at liftoff 






V prop_tot – total volume of propellant carried. 

ε i – Expansion ratio of nozzle of engine number i 

S body 

L 

b body 



Reference: 1 


Options: Propellant type, and chamber pressure. 

M 

main _ 

⎡ 

prop 

= ⎢K 

ph 

+ K 

n 

( ε 

1 

−1) 

+ K 

⎢ 

⎣ 

Rocket engine prediction only. 

ne 

0.5 

( ε − ε ) ( ε −1) 

2 

P 

c 

1 

+ K 

na 

2 

( mP & ) 

c 

0.5 

+ K 

pf 

+ K 

ga 

I 

sp 

N 

⎥ ⎥ ⎤ 

⎦ 

eng 

m& 

Space Shuttle 

Comparison 

-15% 

Power head constants 

K ph = 5.34 – LOX/LH2, Pc = 3000psi 

= 5.18 – dual fuel engine, Pc = 3000psi 

= 2.48 – LOX/hydrocarbon staged combustion, Pc = 4000psi 

= 2.10 – LOX/hydrocarbon LH2 generator, Pc = 4000psi 

Nozzle constants 

K n = 0.01194 – LOX/LH2 

= 0.00727 – LOX/hydrocarbon 

= 0.015 – EN 155 (dual fuel) 

Nozzle extension constants 

K ne = 9.943 – LOX/LH2 


Nozzle extension actuator 

K na = 60.54 – LOX/LH2 


Pressurization and feed system constants 



K pf = 1.64 – current technology (1978) 

= 1.40 – composite/metallic feedlines 

Gimbal actuators 

K ga = 0.00129 – hydraulic system (assumed due to publish date) 




P c – Pressure of main engine combustion chamber 

ε i – Expansion ratio of nozzle of engine number i 



Reference: 2 


Options: Supercharging or not, supersonic combustion or not. 

Rocket based combined cycle engine mass. 

Rv 

_ lo 

M 

engines 

= M 

glow 

R 

eng _ ui 

R eng_ui = Engine uninstalled thrust to weight 

= 3 .99m& 

+ 114A mixer 

no inlet, no supercharging fan 

= 4 .04m& 

+ 200. 5A mixer 

no inlet, with supercharging fan 

Space Shuttle 

Comparison 

N/A 

RBCC only 

M 

press 

_ 

= 1. 616M 

feed 

glow 

R 

v _ lo 

Isp 

sl 

M 

( 0.05V 

+ 0.075V 

)( − TRF ) 

purge _ syst 

= 

f 

ox 

1 for purging lines and tanks with He 

A mixer – is the cross sectional area of the mixer. 




TRF = 0.6 – AMLS (from Lepsch) 





Reference: 3 



main _ prop 

= 

( 0. 

vac 

) N 

eng 

M 0205T 

Equation for rocket engines 

Space Shuttle 

Comparison 

-7% 





Reference: 4a 


Options: Airbreathing engine type. 

M 

engines 

Rv 

_ lo 

= M 

glow 

For airbreathing booster vehicle using composite propulsion 

R 

eng _ ui 

Space Shuttle 

Comparison 

N/A 

RBCC only 

R eng_ui – uninstalled engine thrust to weight 

= 160 – Air augmented rocket 

= 31.40 – Ejector ramjet, max internal pressure of 150 psia 

= 29.00 – Ejector scramjet, max internal pressure of 100 psia 

= 26.45 – Supercharged ejector ramjet, max internal pressure of 150 psia 

= 24.07 – Supercharged ejector scramjet, max internal pressure of 100 psia 

= 19.36 – RL, max internal pressure of 150 psia 

= 16.80 – SL, max internal pressure of 100 psia 

= 16.21 – RRL, max internal pressure of 150 psia 

= 13.95 – RSL, max internal pressure of 100 psia 

= 17.92 – SRL, max internal pressure of 150 psia 

= 14.80 – SSL, max internal pressure of 100 psia 

= 15.29 – RSRL, max internal pressure of 150 psia 

= 12.53 – RSSL, max internal pressure of 100 psia 

M 0012 

eng _ controls 

= 0. Tsls 

Mass of engine control system 

M 004 

fuel _ dist 

= 0. Tsls 

Mass of liquid hydrogen distribution, purge, and vent system 

M 003 

ox _ dist 

= 0. Tsls 

Mass of liquid oxygen distribution, purge, and vent system 








Reference: 4b 



M 0 .0146T 

N + 300 Mass of LOX/LH2 engines for a second stage vehicle. 

engines 

= 

vac eng 

M 00138T 

eng _ attach 

= 0. 

vac 

N 

eng 

Mass of engine attachment hardware. 

Space Shuttle 

Comparison 

-4% 

Uses ET 

volume 

M 445 

prop _ dist 

= 0. Sbody 

Mass of propellant distribution system for LOX/LH2 

M 

= V Mass of pressurization and vent system for LOX/LH2 

press _ vent 

0. 0672 

prop _ tot 







Reference: 6 

Derived from: Space Shuttle, ET, and Saturn launch vehicles. 

Options: Feed system type. 

Shuttle comparison uses the LOX/LH2 engines and includes engine install, subsystems, TVC, feed (K feed =2.197), purge 

(using volume of ET), and pressurization for pump fed engines. 

Space Shuttle 

Comparison 

-5% 

M 

M 

M 

engines 

engines 

Tvac 

N 

eng 

= 

min + 

( 75 : ( 5.11ln( T N ) 4.2 

) 

vac 

eng 

For rocket powered vehicles, LOX/LH2 

= 

min 

T 

vac 

N 

eng 

( 104.4 : max( 20.3 : 26.04ln( T N ) − 207 

) 

vac 

For rocket powered vehicles using LOX/RP or N2O4/MMH propellants 

eng _ install 

5. 6 

−4 

= e T N Engine installation (bolts, connectors, etc…) 

vac 

eng 

eng 

M 

eng _ subsystem 

5. 6 

−4 

= e T N Engine subsystems. 

vac 

eng 

M = 0. 001185T N Thrust vector control 

tvc 

vac 

eng 

( 1 0.04 * if ( crossfeed ,1,0) ) 

M 

feed 

= K 

feed 

m& + 

Propellant feed system 

K feed – Propellant feed system constant 

= 2.197 – Orbiter & ET configuration 

= 1.482 – Orbiter without propellant tanks 

= 0.715 – ET type tank only 



purge 

V body 

= 2.133 – Upper stage/orbiter with internal tanks 

= 1.022 – Booster or monopropellant feed system (upper or lower stage) 

M = 0. 053 Purge system 

M press 

= 0.192m& 

Booster or US type configuration, cryo propellants, autogenous system, pump-fed engines 

M 

press 

Fullage 

= 50 + 0.192m& + 0.18V 

prop _ tot 

Storable stage, ambient stored He with heat exchange system. 

26 

M = K + 

press 

press 

0.01645 

( ) 

( 0.8647 P 

1.3012 

0.99 

) tan ks 

P V 

tan k 

prop _ tot 

K press – pressure fed engine system constant 

= 0.55 – pressure fed engine, cold N2/GH2 

= 0.25 – pressure fed engine, hot N2/GH2 

= 0.19 – pressure fed engine, gas generator system 




P tank – Pressure of propellant tanks 


V body – Volume of vehicle body 




Reference: 10 



Tvac 

N 

M 

engines 

= 

R 

eng 

eng 

Space Shuttle 

Comparison 

-34% 

⎛ Tsls 

⎞ 

M 

f _ dist 

= 6.625 

⎜ ( 1− 

Raox 

)( 1+ 

0.04* if ( crossfeed,1,0) 

) 

Isp 

⎟ 

fuel distribution 

⎝ sl ⎠ 

⎛ Tsls 

⎞ 

M 

ox _ dist 

= 6.625 

⎜ ( Raox 

)( 1+ 

0.04* if ( crossfeed,1,0) 

) 

Isp 

⎟ 

oxidizer distribution 

⎝ sl ⎠ 

⎛ Tsls 

⎞ 

M = 

+ 

⎜ 

⎟ 

vppd 

0 .001366Tsls 

0. 192 Vehicle purge, pressurization, and dump system (source 10a) 

⎝ Ispsl 

⎠ 



R aox – ascent oxidizer fraction 

R eng – engine thrust to weight at vacuum conditions, installed 




7.0 RCS 

7.0 RCS 


Mdry – Dry mass of vehicle 



Mland – Landed mass of vehicle 


M rcs_propellants – Total mass of all RCS propellants 

M resid – Mass of residual propellants 

N vt – Number of vernier thrusters 

P rcs_press – Pressure of rcs pressurization system tanks 

P rcs_tank − Pressure of RCS tank 

R vt – Vernier thruster thrust to weight 

T req – Required thrust from vernier thrusters for RCS system 

T req_p – Required thrust for primary thrusters 

V rcs_f – Volume of RCS fuel 

V rcs_ox – Volume of RCS oxidizer 

V rcs_press – Volume of He required as pressurant 

V rcs_tanks – Volume of all RCS tanks 

S body 

L 

b body 


7.0 RCS 

Reference: 1 


Options: Storable or cryogenic propellants. 

M 

rcs 

= 

K 

rcs 

M 

entry 

L 

Space Shuttle 

Comparison 

10% 

K rcs 

= 1.36e-4 – based on shuttle storable system 

= 1.51e-4 – based on advanced cryogenic system 



7.0 RCS 

Reference: 2 



For shuttle comparison the larger thrusters (both front and rear) were considered primary, and the smaller were vernier. 

The actual thrust was used instead of the estimating equation provided. 

Space Shuttle 

Comparison 

-68% 

Forward RCS 

Treq 

M 

rcs _ vt 

= N 

vt 

Rvt 

Pressure fed LOX/LH2 from Rockwell IHOT study and AMLS 

⎡ M entry 

L50 ⎤ 

T req – Required thrust from vernier thrusters = ⎢ 

⎥ 

⎣147141(143) 

⎦ 

N vt = 15 – (3 in each direction plus forward) for forward RCS 

M 

M 

M 

rcs _ tan k 

0. 01295 

= P V Al 2219, yield at 140% Prcs_tank, 1.75 NOF, 5% ullage 

rcs _ tan k 

rcs _ tan k 

rcs _ press 

.0143Prcs 

_ pressVrcs 

_ press 

(1 − TRF ) + 0. 671 

( V V ) 

= 0 + Pressurization system 

rcs _ ox 

rcs _ f 

Ti 6/4 tank, 3000psia, He, yield at 400% Prcs_press, 1.25 NOF, 400 R storage temp. 

rcs _ install 

0. 74 

= M Installation hardware, lines, manifolds, etc… 

rcs _ vt 

Aft RCS 

M 

T 

req 

rcs _ vt 

= N 

vt 

+ 

Rvt 

N 

primary 

T 

R 

req _ p 

primary 


7.0 RCS 

LOX/LH2 from Rockwell IHOT study and AMLS 

T req – Required thrust for vernier thrusters = 

⎡ M entry 

L50 ⎤ 

⎢ 

⎥ 

⎣147141(143) 

⎦ 

T req_p – Required thrust for primary thrusters = 

N vt = 12 for aft RCS 

⎡ M entry 

L870 ⎤ 

⎢ 

⎥ 

⎣147141(143) 

⎦ 

Propellant tanks, pressurization system, and lines & manifolds use the same equations as for the forward RCS 

list above. 


N primary – number of primary thrusters, recommended = 10 

N vt – number of verier thrusters 

P rcs_press – Pressure of rcs pressurization system tanks, typically = 3000 psia for He 

P rcs_tank − Pressure of RCS tank = 195 – for both LOX and LH2 tanks 

R primary – thrust to weight of primary thrusters = 39.5 

R vt – thrust to weight of vernier thrusters = 9.4 

T req_p – required thrust for primary thrusters 

T req – Required thrust for RCS system 

TRF – Techology reduction factor = 0.0 for baseline, = 0.25 – for composite wound tanks 

V rcs_ox – Volume of RCS oxidizer 

V rcs_f – Volume of RCS fuel 

V rcs_press – Volume of He required as pressurant= 0.24(V rcs_ox + V rcs_f ) 

V rcs_tanks – Volume of all RCS tanks 


7.0 RCS 

Reference: 3 



M = 0. 014 Assumes shuttle technology 

rcs 

M entry 

Space Shuttle 

Comparison 

6% 



7.0 RCS 

Reference: 4b 



M = 0. 0171 Mass of attitude control system (includes OMS and RCS) for second stage. 

rcs 

M land 

Space Shuttle 

Comparison 

20% 



7.0 RCS 

Reference: 6 

Derived from: Space Shuttle. 


M = 0. 0126 Assumes shuttle technology 

rcs 

M insert 

Space Shuttle 

Comparison 

8% 



7.0 RCS 

Reference: 10 



0.434 

⎡ 

⎤ 

0.217 ⎛ L ⎞ 

M 

rcs 

= 1184⎢( M 

dry 

+ M 

pl 

+ M 

resid 

)/ 

234948) 

⎜ ⎟ ⎥ RCS system for airbreathing vehicle 

⎢⎣ 

⎝ 205 ⎠ ⎥⎦ 

Space Shuttle 

Comparison 

N/A 


M dry – Dry mass of vehicle 


M resid – Mass of residual propellants (group 20.0) 


7.0 RCS 

Reference: 10a 

Derived from: Alpha Technologies, rocket based. 


⎛ 

⎞ 

⎜ ∑ M 

rcs _ propellants 

M = 0.008 + 0.0046 

⎟ 

rcs 

M 

insert 

M 

insert 

RCS system for a rocket vehicle 

⎝ 6600 ⎠ 

Space Shuttle 

Comparison 

13% 


M rcs_propellants – Total mass of all RCS propellants 


8.0 OMS 

8.0 OMS 



M oms_prop – Mass of all OMS propellants 

N oms – Number of OMS engines 

P oms_press – Design pressure of OMS pressurization system tanks 

P oms_tank – Design pressure of OMS propellant tank 

R oms – OMS engine thrust to weight 

T oms_vac – Vacuum thrust of each OMS engine 

T req_oms – Required thrust from OMS engines 

V oms_f – Volume of OMS fuel 

V oms_ox – Volume of OMS oxidizer 

V oms_press – Volume of pressurant required 

V oms_tank – Volume of OMS tank 


8.0 OMS 

Reference: 1 


Options: Storable or cryogenic propellants. 

M 

oms 

= K 

oms 

N 

oms 

T 

oms _ vac 

+ 

K 

pps 

M 

oms _ prop 

Space Shuttle 

Comparison 

-15% 

K oms 

K pps 

– Orbital maneuver system thruster constant 

= 0.0863 – based on shuttle storable propellants 

= 0.035 – based on advanced cryogenic propellants/engine 

– OMS propellant supply system 

= 0.119 – for storable propellants including pressurization 

= 0.152 – for cryogenic propellants including pressurization and feed 


N oms – Number of OMS engines 

T oms_vac – Vacuum thrust of each OMS engine 


8.0 OMS 

Reference: 2 



M 

M 

oms _ eng 

= 

T 

req _ oms 

R 

oms 

oms _ tan k 

0. 01295 

= P V Al 2219, yield at 140% Prcs_tank, 1.75 NOF, 5% ullage 

oms _ tan k 

oms _ tan k 

Space Shuttle 

Comparison 

106% 

Not intended 

for 7 ksi tank 

pressure used 

in shuttle 

M = .0143P 

V (1 − TRF ) + 0.167( V + V ) Pressurization system 

M 

oms _ press 

0 

oms _ press oms _ press 

oms _ ox oms _ f 

Ti 6/4 tank, 3000psia, He, yield at 400% Prcs_press, 1.25 NOF, 400 R storage temp. 

oms _ install 

0. 74 

= M Installation hardware, lines, manifolds, etc… 

oms _ eng 

R oms – OMS engine thrust to weight = 22 (includes mounts, supports, igniters, etc.) 

P oms_press – Design pressure of OMS pressurization system tanks, typically = 3000 psia for He 

P oms_tank – Design pressure of OMS propellant tank 

TRF – Techology factor = 0.0 for baseline, = .25 – for composite wound tanks 

V oms_f – Volume of OMS fuel 

V oms_ox – Volume of OMS oxidizer 

V oms_press – Volume of pressurant required (He) = 0.24(V oms_ox + V oms_f ) 

V oms_tank – Volume of OMS tank 

T req_oms – Required thrust from OMS engines = M entry /16 (1/16 th g accel/decal) 


8.0 OMS 

Reference: 3 



M = 0. 0146 

oms 

M entry 

Space Shuttle 

Comparison 

14% 



8.0 OMS 

Reference: 6 



M = 0. 0121 

oms 

M insert 

Space Shuttle 

Comparison 

7% 



8.0 OMS 




⎛ 

⎞ 

⎜ ∑ M 

oms _ prop 

M = 0.0045 + 0.0076 

⎟ 

oms 

M 

insert 

M 

insert 

OMS for a rocket vehicle 

⎝ 24175 ⎠ 

Space Shuttle 

Comparison 

-5% 




9.0 Primary Power 



M 

apu_prop – mass of all APU propellants on board 

M 

av – Mass of avionics (group 13.0) 

M 

glow – Gross liftoff mass 

M 


M 

sca – Mass of surface control & actuators (group 12.0) 

N 

apu – Number of APUs 

N 

crew – Number of crew 

N 

days – Number of days on orbit 

N 

eng – Number of main engines on stage 

N 

fc – number of fuel cells 

P 

apu – Power required per APU 

P 

fc – power required per fuel cell 

S 

bf – Planform area of body flap 

S 

exp – Exposed wing planform area 

S 

tot_cont – Total planform area of all control surfaces 

S 

vert – Total planform area of vertical tail or wingtip fins 

T 

vac – Vacuum thrust per main engine 

T 

vac_gimb – Total vacuum thrust of gimbaled engines 

S body 

L 


b body 



Reference: 1 


Options: Standard or accumulators. 

M + K 

pp 

= K 

pcStot 

_ cont 

+ K 

peTvac 

_ gimb 

pb 

M 

av 

Space Shuttle 

Comparison 

-18% 

K pc 

K pe 

K pb 

= 0.712 – Standard hydraulic system 

= 0.610 – Hydraulic with accumulators for peak load 

= 0.97e-4 – Engine gimbal power demand 

= 0.405 – Battery power demand constant 

S tot_cont – Total planform area of all control surfaces 

T vac_gimb – Total vacuum thrust of gimbaled engines 

M av – Mass of avionics (group 13.0) 



Reference: 2 



M = 396 + 176.9( N + 1) + 0. 05166M 

pp 

days 

Based on NASP technology (Stanley). Assumes fuel cells are 396 lb. 

sca 

Space Shuttle 

Comparison 

-36% 

M sca – Mass of surface control & actuators (group 12.0) 

N days – Number of days on orbit 



Reference: 3 



M = 977 + 139.6N 

+ 39. 9N 

pp 

days 

days 

N 

crew 

Includes fuel cells, batteries, and associated systems. 

Space Shuttle 

Comparison 

32% 





Reference: 4a 



M = 1400 + 0. 0017 Primary power for airbreathing booster vehicle. 

pp 

M glow 

Entire power system, including conversion and distribution? 

Space Shuttle 

Comparison 

-52% 




Reference: 4b 



M 10 N + 831 Mass of auxiliary power unit for manned second stage. 

apu 

= 

crew 

Space Shuttle 

Comparison 

-57% 

M 

elec _ power 

= 800 Mass of other components, 12 people. 




Reference: 6 



N 

days 

M 

batt 

= 216 + 952 * if ( N 

crew 

> 0,1,0) Battery mass, unmanned missions only 

7 

Batteries in unmanned or manned? 

Space Shuttle 

Comparison 

-17% 

M = 216 Battery mass for manned missions 

batt 

N 

crew 

M 

fuel _ cell 

= 3030 Fuel cell mass for manned missions only 

7 





Reference: 10 



M 

pp 

L N 

apu 

0.5 

⎛ L ⎞ N 

apu 

= 227 + 18.97Papu 

+ ⎜613.8 

+ 0.66Papu 

⎟ Power system for airbreather 

205 4 

⎝ 205 ⎠ 4 

Space Shuttle 

Comparison 

N/A 


N apu – Number of APUs 

P apu – Power required per APU 




Derived from: Alhpa Technologies, rocket based. 


The following equations should be summed to get M pp for a rocket powered vehicle. 

Space Shuttle 

Comparison 

93% 

M 

batt 

⎛ N 

days ⎞ 

⎜216 + 952 * ( > 0,1,0) 

7 

⎟ if N 

⎝ 

⎠ 

= 

crew 

M 0.76 143 

fuel _ cell 

= 51.8N 

fc 

Pfc 

+ 

apu 

( 52. N N ) 

crew 

days 

1.0861 

1. 15 

( T N + 0.55S 

+ 3.4S 

+ 2.6S 

+ 0.000485M 

) 0. M 

M = 

+ 

0.118 0.00124 

vac eng 

exp vert 

bf 

land 

318 

apu _ prop 

M apu_prop – mass of all APU propellants on board 





N fc – number of fuel cells 

P fc – power required per fuel cell 






10.0 Electrical Conversion & Distribution 


S csw 



H body – Height of body 

S body 





M pascent – Mass of ascent propellants 



N gen – Number of power sources onboard 

L 

R kva – System electrical rating = Kvolts * Amps 

b 

b body 

b cthru 



Reference: 1 


Options: Advanced technology or Shuttle technology. 

M = K 

ecd 

ecd 

M 

land 

Space Shuttle 

Comparison 

-20% 

K ecd 

= 0.02 – advanced ECD system 

= 0.038 – shuttle technology ECD system 




Reference: 2 



M = 1875 + 0.324M 

+ K 8.56( L + H + b ) + 0.00043( L + b) 

M 

ecd 

sca 

ecd 

body 

Assumes use of electro mechanical actuators for control surface actuation. 

body 

sca 

Space Shuttle 

Comparison 

-65% 

K ecd = 0.6 – shape factor for RBCC SSTO (low due to proximity of payload bay and crew cabin) 








Reference: 3 



M = 0. 062 

ecd 

M dry 

Space Shuttle 

Comparison 

-1% 




Reference: 4b 



See notes under 11.0 (hydraulics) for this. 

Space Shuttle 

Comparison 

N/A 



Reference: 5 


Options: Mission redundancy. 

M = 

ecd 

0.152 0.1 0.1 0.091 

172.2K 

ecd 

Rkva 

N 

crewL 

N 

gen 

Space Shuttle 

Comparison 

-91% 

K ecd 

= 1.45 – If mission completion required after failure 

= 1.0 – Otherwise 



N gen – Number of power sources onboard 

R kva – System electrical rating = Kvolts * Amps 



Reference: 6 



M 

ecd 

M 

= 793 + 506 

1.6e 

pascent 

⎛ N 

+ 2226⎜ 

⎜ 

⎝ 7 

days 

⎞ ⎛ N 

⎟ + 7633⎜ 

⎟ 

⎠ ⎝ 

− 6 

7 




crew 

⎞ 

⎟ 

⎠ 

Space Shuttle 

Comparison 

2% 



Reference: 10 



⎛ 

L ⎞ 

M ecd 

= 1201⎜ 

0.90674 + 0.09326 ⎟ For an airbreathing vehicle 

⎝ 

205 ⎠ 

Space Shuttle 

Comparison 

N/A 







M = 793 + 3.31L 

+ 318N 

+ 1096. 4N 

For a rocket powered vehicle 

ecd 

days 

crew 

Space Shuttle 

Comparison 

6% 





11.0 Hydraulic Systems 


b 


b 

exp – Span of exposed wing (b-b body at wing root) 

M 

glow – Gross liftoff mass 

M 


N 

eng – Number of main engines on stage 

N 

hyd – Number of hydraulic functions on the vehicle 

q 

max – Maximum dynamic pressure during flight (lb/ft 2 ) 

S 

bf – Planform area of body flap 

S 

body – Planform area of vehicle body 

S 

ref – Theoretical wing planform area 

S 

tot_cont – Total planform area of all control surfaces 

S 

vert – Total planform area of vertical tail or wingtip fins 

T 

vac – Vacuum thrust per main engine 

T 

vac_gimb – Total vacuum thrust of gimbaled engines 

θ 

le – Sweep angle of leading edge 


b cthru 

S csw 

b 

C tip 

S vert 

S body 

b vert 

b body 

C root 

L 



Reference: 1 


Options: System pressure. 

M 

hyd 

= K 

hyd 

S 

tot _ cont 

+ 

K 

e 

T 

vac _ gimb 

Space Shuttle 

Comparison 

-2% 

K hyd 

K e 

= 2.10 – Shuttle technology base for hydraulic system 

= 1.23 – For a 5000 psi system 

= 3.00e-4 – Shuttle gimbal technology 

= 1.68e-4 – For a 5000 psi gimbal system 


T vac_gimb – Total vacuum thrust of gimbaled engines 



Reference: 4b 



M 

M 8 

land 

hyd 

= 15. For a lifting body rocket powered second stage. 

Sbody 

This was originally listed as support systems, and likely includes electrical conversion and distribution since the 

MBS it was included in did not have that as a separate item. 

Space Shuttle 

Comparison 

N/A 





Reference: 5 


Options: Variable or fixed sweep wings. 

M = 

hyd 

0.664 

37.23K 

vshN 

hyd 

Space Shuttle 

Comparison 

-87% 

K vsh 

= 1.425 – for variable sweep wings 

= 1.0 – for fixed wings 

N hyd – Number of hydraulic functions on the vehicle 



Reference: 6 

Derived from: Power curve from Sigma (JSC study) adjusted to Space Shuttle. 


1.1143 

qmax 

⎤ 

( S 

ref 

+ Svert 

+ Sbf 

) + 0. Tvac 

N 

eng 

⎡ 

M 

hyd 

= 0.426⎢ 

001785 

1000 

⎥ 

⎣ 

⎦ 

Space Shuttle 

Comparison 

714% 








Reference: 7 


Options: Hydraulic constant. 

For the Space Shuttle comparison K hyd = 0.0068 

Space Shuttle 

Comparison 

0% 

M = K 

hyd 

hyd 

M 

glow 

K hyd = 0.005-0.0180 







M 

hyd 

⎡ 

= 0.326⎢ 

⎢ 

⎣ 

( q S /1000) 

max 

ref 

1.3125 

( b b ) 

⎛ exp 

+ 

+ 

⎜ L + 

⎝ cos( θle 

) 

body 

⎞ 

⎟ 

⎠ 

1.6125 


b exp – Span of exposed wing (b-b body at wing root) 



θ le – Sweep angle of leading edge 

⎤ 

⎥ 

⎥ 

⎦ 

0.849 

For rocket powered vehicles 

Space Shuttle 

Comparison 

455% 


12.0 Surface Control & Actuators 






N cs – Number of flight control systems (redundancy) 

R elevon – Percent of wing that is elevon area 

R vert – Percent of vertical surfaces that are control surface 



S canard – canard planform area 



S htail – horizontal tail planform area 


S sb – speed brake planform area 



b vert 

S body 

C root 

C tip 

S vert 

b body 

b cthru 


S csw 

b 

L 




Reference: 1 


Options: System pressure. 

M = K S 

_ 

+ K based on hydraulic system from the Space Shuttle 

sca 

sca 

tot 

cont 

ms 

Space Shuttle 

Comparison 

-8% 

K sca 

K ms 

= 3.75 – for shuttle surface control and actuation technology 

= 3.80 – for 5000 psi system 

= 3.32 – for 5000 psi system using advanced materials 

= 200 – additional miscellaneous systems 




Reference: 2 



M = 0 .0163R 

M + 0. 00428R 

M Assumes EMA technology 

sca 

elevon 

entry 


vert 

entry 

Space Shuttle 

Comparison 

-58% 

different 

technology 

than shuttle 

R elevon – Percent of wing that is elevon area = 

S csw 

S exp 

R vert – Percent of vertical surfaces that are control surface = 




S 

S 

rud 

vert 



Reference: 3 



M = 0. 0048 Assumes EMA technology 

sca 

M entry 


Space Shuttle 

Comparison 

-59% 

different 

technology 

than shuttle 



Reference: 4a 



M = 640 + 0. 013 

sca 

M glow 

Control and actuation mass for airbreathing booster vehicle. May include hydraulics, though source is not clear 

on this. 

Space Shuttle 

Comparison 

51% 




Reference: 4b 



M 

M 28 

land 

sca 

= Control system and actuation mass for a lifting body upper stage. 

Sbody 

Space Shuttle 

Comparison 

-32% 





Reference: 5 



M = 

sca 

0.003 0.489 0.484 0.127 

36.28M 

Stot 

_ cont 

N 

cs 

N 

crew 

Space Shuttle 

Comparison 

-44% 

N cs – Number of flight control systems (redundancy) 





Reference: 6 

Derived from: Boeing equation adjusted to Space Shuttle. 


M 

( S + S + S ) + 3.4S 

+ 2.6( S + S ) 70 

sca 

= 

ref htail canard 

vert 

bf sb 

0 .55 

+ 

Space Shuttle 

Comparison 

29% 


S canard – canard planform area 

S htail – horizontal tail planform area 


S sb – speed brake planform area 




Reference: 7 


Options: Control surface configuration. 

M 

sca 

= K 

fcf 

⎛ M 

glow ⎞ 

⎜ 

⎝ 1000 ⎟⎟ ⎠ 

0.581 

Space Shuttle 

Comparison 

-1% 

K fcf 

= 106 – for airplanes with elevon control, and no horizontal tail 

= 138 – for airplanes with a horizontal tail 

= 168 – for airplanes with a variable sweep wing 







( 0.55Sexp + 30) + ( 3.4S 

+ 30) + ( 2.6S 

+ 10) 

M For rocket powered vehicles 

sca 

= 

vert 

bf 

wing vert. tail body flap 

Space Shuttle 

Comparison 

4% 





13.0 Avionics 

13.0 Avionics 







N pil – number of pilots 


13.0 Avionics 

Reference: 1 


Options: 1978 or 1990 technology. 

M = K 

av 

av 

M 

0.125 

dry 

Space Shuttle 

Comparison 

-7% 

K av = 1350 – for current technology (~1978) 

= 710 – for 1990 technology 



13.0 Avionics 

Reference: 2 



M 

av 

= 3300 

Constant based on NASP technology AMLS SSTO 

Space Shuttle 

Comparison 

-50% 

not shuttle 

technology 


13.0 Avionics 

Reference: 3 



M 

av 

= 6564 

Constant based on Space Shuttle avionics mass 

Space Shuttle 

Comparison 

0% 


13.0 Avionics 

Reference: 4a 



M 

av 

= 670 + 440 + 240 

Includes 670 lbs for instruments, 440 lbs for guidance and navigation, and 240 lbs for communication. For an 

airbreathing booster vehicle. 

Space Shuttle 

Comparison 

-79% 


13.0 Avionics 

Reference: 4b 



Compared to Space Shuttle avionics mass less instruments and displays. 

Space Shuttle 

Comparison 

-85% 

M 

av 

= 261 + 302 

Includes 261 lbs. for guidance and navigation, and 302 lbs. for communications. No instruments. 


13.0 Avionics 

Reference: 6 

Derived from: Data from EHLLV, Shuttle C studies, and Space Shuttle. 


N N 

7 7 

Includes range safety weight. 

days 

crew 

M 

av 

= 544 + 1067 + 3027 + 0. 27 

A 

body 

Space Shuttle 

Comparison 

-2% 





13.0 Avionics 

Reference: 7 



Compared to only the instruments and displays for the space shuttle. 

⎡ ⎛ M 

glow ⎞⎤ 

⎡ ⎛ M 

glow ⎞⎤ 

⎛ M 

glow ⎞ 

M 

inst 

= N 

pil ⎢15 + 0.032 

⎜ N 

eng ⎢5 

0.006 ⎥ + 0.15 + 0. 012M 

1000 

⎟⎥ 

+ + 

⎜ 

1000 

⎟ 

⎜ 

1000 

⎟ 

⎢⎣ 

⎝ ⎠⎥⎦ 

⎢⎣ 

⎝ ⎠⎥⎦ 

⎝ ⎠ 

Mass for instruments and displays only. 

glow 

Space Shuttle 

Comparison 

23% 

only 

instruments 

and displays 



N pil – number of pilots 


13.0 Avionics 




M = 544 + 1067 * if ( N > 0.1,1,0) + 3012 * if ( N > 0,1,0) + 0. 27A 

For rocket vehicle 

av 

days 

crew 

body 

Space Shuttle 

Comparison 

-2% 





14.0 Environmental Control & Life Support System 


b 


H 

body – Height of body 


M 

av – Mass of avionics (group 13.0) 

M 

ecd – Mass of electronic conversion & distribution (group 10.0) 

N 

crew – Number of crew 

N 

days – Number of days spent on orbit 

V 

crew – Volume of crew cabin 

S body 

L 

b body 



Reference: 1 



M = K V + K N N + K 

eclss 

pv 

0.75 

crew 

os 

crew 

days 

ah 

M 

av 

Space Shuttle 

Comparison 

5% 

K pv = 5.85 – pressurized volume constant 

K os = 10.9 – oxygen supply tank constant 

K ah = 0.44 – avionics heat load constant 







Reference: 2 



M 

( L + b + H ) + 512 163 

eclss 

= 

htl 

body body 

141 + 729 + K 6.79 

+ 

Space Shuttle 

Comparison 

-60% 

K htl = 0.6 – Shape factor for RBCC SSTO (Payload bay close to crew cabin with radiators in payload bay doors). 

This equation is composed of: 

141 lb – personnel systems 

729 lb – equipment cooling system 

512 lb – radiators 

163 lb – flash evaporators 

All masses are based on AMLS SSTO study by Stanley 


H body – Height of body 




Reference: 3 



M = 2652 + 54. 1N 

eclss 

crew 

N 

days 

Space Shuttle 

Comparison 

0% 





Reference: 4a 



M 

eclss 

= 550 

Constant mass for environmental control. System is designed for a booster, so is for short duration and small 

crew to pilot the vehicle only. 

Space Shuttle 

Comparison 

N/A 

Short duration 

only 



Reference: 4b 



M 

eclss 

= 464 + 20N crew 

Mass of environmental control system. 

Space Shuttle 

Comparison 

-89% 

Maybe add long term facilities 




Reference: 6 



Shuttle comparison to the cooling system mass only. 

Space Shuttle 

Comparison 

1% 

( N N ) 1. 18 

M 

cooling 

= 32.24 

crew days 

Cooling system mass only 








For rocket powered vehicles. 

M 0 .3M 

+ 0.15M 

+ 1410* if ( N > 0,1,0) + 870* if ( N > 0,1,0) + 15.4 N N + 3 

( ) ( ) ( ) [ ( )] 1. 18 

eclss 

= 

av 

ecd 

crew 

crew 

crew days 

Equipment cooling Crew controls Crew displays Crew Env. Cooling 

Space Shuttle 

Comparison 

53% 

For airbreathing vehicles. 

3 

⎪⎧ 

⎛ L ⎞ ⎡⎛ 

L ⎞ ⎤⎪⎫ 

M eclss 

= 1235⎨1 

+ 0.27⎜ 

−1⎟ 

+ 0.069⎢⎜ 

⎟ −1⎥⎬ 

⎪⎩ ⎝ 205 ⎠ ⎢⎣ 

⎝ 205 ⎠ ⎥⎦ 

⎪⎭ 




M ecd – Mass of electronic conversion & distribution (group 10.0) 


15.0 Personnel Equipment 






Reference: 1 


Options: Mission duration. 

M = K + K 

pe 

fww 

furn 

N 

crew 

Space Shuttle 

Comparison 

-17% 

K fww – food, waste, and water management system: for 1 to 4 crew 

= 0 – for missions less than 24 hours 

= 353 – for missions greater than 24 hours 

K furn – seats and other pilot/crew related items = 167 




Reference: 2 



M = 502 + 150 

pe 

N crew 

Based on NASP technology AMLS (Stanley) 

Space Shuttle 

Comparison 

-15% 




Reference: 3 



M = 555 + 164 

pe 

N crew 

Space Shuttle 

Comparison 

-7% 




Reference: 4b 



M 

pe 

= 52N crew 

Mass of cabin furnishings. 

Space Shuttle 

Comparison 

-80% 




Reference: 5 



Compared only to space shuttle personnel accommodations and furnishings and equipment. 

Space Shuttle 

Comparison 

34% 

M = 217. 6 

furn 

N crew 

Furnishings and seats only, no galley or water or waste management 




Reference: 6 



For space shuttle comparison the mass of the personnel group was added to the mass of the personnel equipment. 

Space Shuttle 

Comparison 

38% 

N 

N 

days 

7 

Includes personnel in addition to personnel equipment. 

crew 

M 

pe 

= 2444 + 645N 

crew 

+ 86. 4 




16.0 Dry Weight Margin 




M i – Total mass of group i in MBS 




Reference: 1 



M 

m arg in 

= K 

m arg in 

K margin = 0.10 

( M − N M ) 

dry 

eng 

eng 

Space Shuttle 

Comparison 

N/A 






Reference: 2 



M 

m arg in 

= K 

15.0 

∑ 

m arg in 

i= 

1.0 

M 

i 

Space Shuttle 

Comparison 

N/A 

K margin – Margin percentage 

M i – Total mass of group i 

Recommends K margin = 10% margin 



Reference: 3 



M 

m arg in 

= K 

15.0 

∑ 

m arg in 

i= 

1.0 

M 

i 

Space Shuttle 

Comparison 

N/A 






Reference: 4b 



M 

m arg in 

= K 

15.0 

∑ 

m arg in 

i= 

1.0 

M 

i 

Space Shuttle 

Comparison 

N/A 






Reference: 6 

Derived from: Data developed by Program Development PD24 (80-22). 


M 

m arg in 

= K 

15.0 

∑ 

m arg in 

i= 

1.0 

M 

i 

Space Shuttle 

Comparison 

N/A 



Recommended margin based on development status: K margin = 

0% - masses based on existing structures, hardware, engines, which require no modification 

5% - masses based on existing structures, hardware, engines, which require some modification 

10% - masses based on new designs which use existing type materials and subsystems 

15% - masses based on new designs which use existing type materials and subsystems which require limited 

development in materials technology 

20%-25% - weights based on new designs which require extensive development in materials technology 



Reference: 10 



M 

m arg in 

= K 

15.0 

∑ 

m arg in 

i= 

1.0 

M 

i 

Space Shuttle 

Comparison 

N/A 






Reference: 11 

Derived from: Program data from space hardware. 

M 

m arg in 

= K 

15.0 

∑ 

m arg in 

i= 

1.0 

M 

i 

Space Shuttle 

Comparison 

N/A 



Hawkins shows that historically dry weight growth from proposal to first flight is 25.5%. 



Reference: 12 

Derived from: NASA space programs. 

Talay shows a 30% historical increase in vehicle weight from first concept documentation to time of proposal. The 

following chart also shows dry weight growth for NASA programs only. 

Space Shuttle 

Comparison 

N/A 

Chart showing dry weight growth of NASA space vehicle programs from [ref. 12]. 


17.0 Crew & Gear 






Reference: 1 



M = 400 + 560 

cg 

N crew 

N crew is limited to between 1 and 4 people. 

Space Shuttle 

Comparison 

18% 




Reference: 2 and 3 

Derived for: Airbreathing horizontal takeoff vehicle, and from a rocket. 


cg 

( 311 

days 

) N 

crew 

M = 1176 + + 23N 

Includes crew consumables (food), personal items, crew, and suits (Talay) 

Space Shuttle 

Comparison 

23% 





Reference: 4a 



M 

cg 

= 650 

Constant mass, for a small crew to pilot a booster stage. 

Space Shuttle 

Comparison 

N/A 



Reference: 4b 



cg 

( 220 + 35. ) N 

crew 

M = 5 

Space Shuttle 

Comparison 

-51% 




Reference: 6 



Equations under group 15.0 includes crew. 

Space Shuttle 

Comparison 

N/A 




Derived from: Alpha Technologies. 


M = 2550 * if ( N > 0,1,0) + 645N 

+ 77. 6N 

cg 

crew 

crew 

days 

Space Shuttle 

Comparison 

109% 




18.0 Payload Provisions 








M 

payp 

= 0.0 

Mass of provisions included in payload mass. 

Space Shuttle 

Comparison 

N/A 



Reference: 6 



M = 0. 025 

payp 

M pl 

Space Shuttle 

Comparison 

431% 



19.0 Cargo (up and down) 

19.0 Cargo (up and down) 

Reference: All 

Fixed value based on mission. 

For worst case the payload must be assumed to be returned for sizing re-entry and landing loads. 

Space Shuttle 

Comparison 

N/A 


20.0 Residual Propellants 


M main_usable_prop – Usable main propellant, typically M pascent 

M oms/rcs_usable_prop – Usable OMS and RCS system propellants 

M pascent – Mass of ascent propellants (group 27.0) 







Reference: 1 



M = 

resid 

0.79 

0.05M 

pascent 

Includes main propellant tank pressurization gas. 


Space Shuttle 

Comparison 

-98% 

Orbiter 

-15% 

ET 






Shuttle comparison only uses equation for OMS/RCS residuals. 

M 

M 

oms / rcs _ resid 

= 0. 05 

M 

mainprop _ resid 

= 0. 005 

oms / rcs _ usable _ prop 

M 

main _ usable _ prop 

Space Shuttle 

Comparison 

-37% 

Orbiter 

OMS/RCS 

70% 

ET 

M main_usable_prop – Usable main propellant, typically M pascent 





Reference: 4a 



M 

ox _ resid 

0. 027 

= M Residual liquid oxygen for an airbreathing booster vehicle 

tot _ ox 

Space Shuttle 

Comparison 

816% 

ET 

M 

f _ resid 

0. 027 

= M Residual liquid hydrogen for an airbreathing booster vehicle 

tot _ fuel 





Reference: 4b 



M 

ox _ resid 

0. 005 

= M Residual liquid oxygen for a rocket second stage 

tot _ ox 

Space Shuttle 

Comparison 

195% 

ET 

M 

f _ resid 

0. 03 

= M Residual liquid hydrogen for a rocket second stage 

tot _ fuel 





Reference: 10 



Shuttle comparison only uses equation for OMS/RCS residuals. 

M 

M 

oms / rcs _ resid 

= 0. 05 

resid _ ascent _ fuel 

= 4 

M 


( 0.00529V 

) 

K 

f 

f _ package 

Space Shuttle 

Comparison 

-37% 

Orbiter 

18% 

ET 

M 

resid _ ascent _ ox 

= 2 

K 

( 0.11V 

) 

ox 

ox _ package 

K f_package – Fuel tank internal packaging efficiency, takes into account baffles, spars, etc.. 

K ox_package – Oxidizer tank internal packaging efficiency, takes into account baffles, spars, etc.. 





21.0 OMS/RCS Reserve Propellants 


g – Gravitational acceleration at the surface of the Earth 

Isp oms – Specific impulse of OMS engines 

Isp rcs – Specific impulse of RCS engines 




∆V oms – Total velocity change possible using OMS engines (fps) 

∆V rcs – Total velocity change possible using RCS engines (fps) 



Reference: 1 



For shuttle comparison maximum ∆V was calculated from the maximum usable propellants available. For OMS ∆V = 

700 fps, RCS ∆V = 200 fps. 

M 

oms / rcs _ res 

= M 

land 

⎡ 

⎢e 

⎢ 

⎣ 

⎛ 0.005∆V 

⎜ 

⎝ Ispoms 

g 

oms 

⎞ 

⎟ 

⎠ 

+ e 

⎛ 0.005∆V 

⎜ 

⎝ Isprcsg 

rcs 

⎞ 

⎟ 

⎠ 

⎤ 

− 2⎥ 

⎥ 

⎦ 

Space Shuttle 

Comparison 

-94% 

OMS/RCS 

residual only 












M 


= 0. 1 

M 


Space Shuttle 

Comparison 

43% 




Reference: 10 



M 0. 0075M 


= 

pascent 


Space Shuttle 

Comparison 

-98% 

Using ascent 

propellant in 

shuttle only 

595% 

Using ascent 

propellant in 

ET 


22.0 RCS Entry Propellants 





∆V rcs_entry – entry velocity change required 



Reference: 1, 2, and 10 

Derived from: Physics based. 


M 

rcs _ entry 

= M 

entry 

⎡ 

⎢e 

⎢ 

⎣ 

⎛ ∆Vrcs 

⎜ 

⎝ Isp 

_ entry 

rcsg 

⎞ 

⎟ 

⎠ 

⎤ 

−1⎥ 

⎥ 

⎦ 

Space Shuttle 

Comparison 

8% 




∆V rcs_entry – entry velocity change required (Shuttle = 40 fps) 



Reference: 3 



M 0. 00336M 

rcs _ entry 

= 

entry 

Assumes approximately 40 fps of ∆V. 

Space Shuttle 

Comparison 

-16% 



23.0 OMS/RCS On-Orbit Propellants 












Reference: 1 

Derived from: Physics based. 


For shuttle comparison maximum ∆V was calculated from the maximum usable propellants available. For OMS ∆V = 

700 fps, RCS ∆V = 200 fps. 

M 

oms / rcs _ orbit 

= M 

entry 

⎡ 

⎢e 

⎢ 

⎣ 

⎛ ∆V 

⎜ 

⎝ Isp 

oms 

oms 

⎞ 

⎟ 

g 

⎠ 

+ e 

⎛ ∆V 

⎜ 

⎝ Isp 

rcs 

rcs 

⎞ 

⎟ 

g 

⎠ 

⎤ 

− 2⎥ 

⎥ 

⎦ 

Space Shuttle 

Comparison 

-4% 

Using actual 

shuttle Isp and 

∆V 

Isp oms – OMS propulsion specific impulse 

= 313s – storable 

= 440s – cryogenic 

Isp rcs – RCS propulsion specific impulse 

= 289s – storable pulsing system 

= 398s – cryogenic pulsing system 








Derived for: Physics based. 


For shuttle comparison maximum ∆V was calculated from the maximum usable propellants available. 

For OMS ∆V = 700 fps, RCS ∆V = 200 fps. 

M 

oms _ orbit 

= M 

entry 

⎡ 

⎢e 

⎢ 

⎣ 

⎛ ∆V 

⎜ 

⎝ Isp 

oms 

oms 

⎞ 

⎟ 

g 

⎠ 

⎤ 

−1⎥ 

⎥ 

⎦ 

Space Shuttle 

Comparison 

-4% 

Using actual 

shuttle Isp and 

∆V 

M 

rcs _ orbit 

= M 

entry 

⎡ 

⎢e 

⎢ 

⎣ 

⎛ ∆Vrcs 

⎞ 

⎜ 

⎟ 

⎝ Isprcs 

g ⎠ 

⎤ 

−1⎥ 

⎥ 

⎦ 

∆V rcs – Typically 15 fps for front RCS, and 35 fps for aft RCS 

∆V oms – Typically 500-800 fps for ascent, 50 fps for on orbit maneuvers, and 200 fps de-orbit 

Isp rcs = 420s – LOX/LH2 pressure fed thrusters based on Rockwell IHOT work, O/F=4.0. 

Isp oms = 462s – LOX/LH2 pump fed engines based on Rockwell IHOT work, O/F=6.0. 









Reference: 4b 



M 0. 0215M 

rcs _ prop 

= 

land 

All RCS propellant, including entry, for a rocket powered lifting body second stage. 

Space Shuttle 

Comparison 

-76% 

M 30N 

apu _ prop 

= 543 + 

crew 

Propellant required for APU while on orbit. 




24.0 Cargo Discharged 

24.0 Cargo Discharged 

Reference: All 

Constant value dependent on the mission. 

Mass of payload carried to orbit, and not back to Earth. 

Space Shuttle 

Comparison 

N/A 


25.0 Ascent Reserve Propellants 



Isp vac – Vacuum specific impulse of main engines 


∆V ideal – Ideal ∆V for ascent 



Reference: 1 



Space Shuttle comparison uses ascent propellant in the ET. ∆V is based on Orbiter and ET together (no SRBs). 

Space Shuttle 

Comparison 

64% 

M 

⎡ 

⎛ ∆Videal 

0.005 ⎞ 

⎜ 

⎟ 

Ispvacg 

pascent _ res 

= M ⎢ ⎝ 

⎠ 

insert 

e −1⎥ 

+ 

⎤ 

0.004M 

pascent 

⎢ 

⎥ 

⎣ 

⎦ 

∆V ideal – Ideal ∆V for ascent = 24,994 fps calculated from maximum usable propellant load on Space Shuttle and 

ET combination. 


Isp vac – Vacuum specific impulse of main engines 


∆V ideal – Ideal ∆V for ascent 



Reference: 2, 3, and 4b 

Derived for: Airbreathing horizontal takeoff vehicle, and from a rocket, and lifting body upper stage. 


Space Shuttle comparison uses ascent propellant in the ET. 

Space Shuttle 

Comparison 

50% 

M 0. 005M 

pascent _ res 

= 

pascent 

Main propellant reserves are vented to orbit or transferred off-board before entry. 




Reference: 10 



Space Shuttle comparison uses ascent propellant in the ET. 

Space Shuttle 

Comparison 

125% 

M 0. 0075M 

pascent _ res 

= 

pascent 



26.0 Inflight Losses & Vents 






Reference: 1 



Shuttle comparison uses ascent propellant in the ET, and compares to losses in the Orbiter. 

Space Shuttle 

Comparison 

83% 

M = 0. 0043 

plosses 

M pascent 







M = 0. 01 

plosses 

M entry 

Includes waste, purge gasses, excess fuel cell reactants, vented and lost propellants. 

Space Shuttle 

Comparison 

-35% 

Note: Reference 10 includes this mass after the insertion weight, meaning that it is treated as propellant lost 

during ascent. 



27.0 Ascent Propellants 


M f_ascent – Total ascent fuel 


MR – Mass ratio for ascent 

R f – Fuel ascent propellant fraction: M f_ascent over M p_ascent 



Reference: 2 

Derived for: Physics based. 


2 

⎛ 1 ⎞ 

M 

f _ ascent = R 

f 

M 

glow ⎜1 

− ⎟ Ascent fuel mass 

⎝ MR ⎠ 

⎛ ⎞ 

⎜ 

1 

M ⎟ 

ox _ ascent 

= M 

f _ ascent 

−1 

Ascent oxidizer mass 

⎝ R 

f ⎠ 

M f_ascent – Total ascent fuel 



R f – Fuel ascent propellant fraction: M f_ascent over M p_ascent 

Space Shuttle 

Comparison 



Reference: 4b 



Use the same equations as reference 2, but add 60 lbs. of total propellant lost during thrust decay. 

Space Shuttle 

Comparison 

4b 



Reference: 10 



M 

MR −1 

= 

MR 

pascent 

M glow 

Space Shuttle 

Comparison 

10 




28.0 Startup Losses 






M prop_tot – Total propellant onboard 


T start – Main engine startup time 



Reference: 1 


Options: Startup loss factor. 

M 

start _ loss 

= 

M 

prop _ tot 

K 

su 

K su – startup losses = 0.001 to 0.002 

Space Shuttle 

Comparison 

-22% using 

K su =0.002 

M prop_tot – Total propellant onboard 



Reference: 2 



M 

Rv 

_ lo 

M 

gross 

Ispsl 

Assumes a 4 second ramp up of engines before hold down is released. 

start _ loss 

= 2 

Space Shuttle 

Comparison 

44% 






Reference: 3 



M 0. 01M 

start _ loss 

= 

pascent 

Space Shuttle 

Comparison 

291% 




Reference: 4b 



M 00128 

start _ loss 

= 0. M 

pascent 

Startup losses. 

M = 210 30 Propellant lost during thrust buildup (210 lbs. LOX and 30 lbs. LH2) 

buildup _ loss 

+ 

Space Shuttle 

Comparison 

-44% Using 

ET ascent 

propellant 




Reference: 10 



M 

start 

Rv 

_ lo 

_ loss 

= Tstart 

M 

gross 

Losses while starting the engines 

Isp 

sl 

Abody 

M 

boiloff 

= K 

boil 

Boiloff while waiting on the pad or runway 

21357 

Space Shuttle 

Comparison 

351% Based 

on 6s from 

ignition to 

release 

1% at 1.4s 

K boil 

= 4359 – for LH2 

= 104 – for LOX 





T start – Main engine startup time 


Technology Reduction Factors 

Reference: 3 

These TRFs represent near term improvements. For example AMLS or NASP. 

Near term mass reduction by system. The technology reduction factor (TRF) is listed on the right. The new mass (improved technology) 

is found using the following equation: 

M new = M original (1-TRF) 

1.0 Wing 44% 

2.0 Tail 44% 

3.0 Body & secondary struct. 38% 

Crew cabin 38% 

Body flap 44% 

Thrust structure 38% 

LOX & LH2 tank 0% 

4.0 TPS 35% 

5.0 Landing gear 9% 

6.0 Main Propulsion 15% 

7.0 RCS 0% 

8.0 OMS 0% 

9.0 Primary Power 0% 

10.0 ECD 18% 

11.0 Hydraulics 0% 

12.0 Surface Control (EMA) 0% 

13.0 Avionics 50% 

14.0 ECLSS 10% 

15.0 Personnel Equipment 0% 


TRF-1

Reference: 6 

Derived from data provided by Airframe Team, September 1999. 

Technology mass reduction factors by material. The TRF is listed on the left. The new mass (improved technology) is found using the 

following equation: 

M new = M original (1-TRF) 

0% - Structural designs based on current aluminum alloy, ie. Saturn V, original ET 

10% - Structural designs based on aluminum lithium alloy, ie new lightweight ET 

20% - Wing structural designs based on advanced composites and materials 

25% - Propellant tanks structural designs based on advanced composites and materials 

30% - Interstages and body structural designs based on advanced composites and materials 


TRF-2

Development of a Mass Estimating Relationship Database for ...

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