Launch Vehicle Economics Worked Examples

In Defense of External Tanks



By Chris Y. Taylor

42nd AIAA/ASME/SAE/ASEE Joint

Propulsion Conference

July 11, 2006









chrisytaylor@yahoo.com

External Tanks on Aerospace Vehicles









a.k.a. drop tank, tip tank, belly tank, expendable tank

c=RΓ

c = specific cost ($/lb.)

= Launch Cost/Payload Mass



R = structure - payload mass ratio

= Structure Mass/Payload Mass

Driven by Technology & Physics



Γ = structure cost ($/lb.)

= Launch Cost/Structure Mass

Driven by Management & Economics

c = R ( Γvehicle + Γops

+ Γrisk + Γpropellant) + RD(Γnr/a)

Recurring Cost

Γvehicle = Cost of Vehicle Hardware

Γops = Cost of Operations

Γrisk = Cost of Risk

Γpropellant = Cost of Propellant



Non-Recurring Cost

RD = Developed Structure–Payload Mass Ratio

Γnr = Non-recurring Structure Costs

a = Amortization Factor

Current Specific Launch Cost Estimate

$10,000

$9,000

$8,000

Costs/Payload Mass ($/lb.)









$7,000

$6,000

$5,000

$4,000

$3,000

$2,000

$1,000

$0

R&D Vehicle Ops Risk Prop.

R&D costs must be lowered!



Launch costs >$1000/lb. payload to LEO

with current development & flight rate

even if all recurring costs are zero!



How can RD(Γnr/a) be lowered?



a Γnr RD

SSTO vs. SSTO+ET

Pure SSTO

low hardware costs

low operations costs

high development

costs!



Adding E.T.

lowers development

Pegasus/Ithaca Launch Vehicle Concept







cost a lot, for a little

more hardware & a.k.a. stage-and-a-half,

ops cost tip tanks plus reusable

core, RAS, ILRV

RocketCost.xls (beta)

1 stage simple linear cost analysis + risk to Contents



Summary Structure Propellant Total Vehicle Description

Payload Mass (lbs.) n/a n/a 8,100 Mass Ratio R 6.752 dimensionless

Vehicle Masses (lbs.) 6,706 85,162 99,969 Structural Mass Ms 6,706 lbs.

Specific Cost ($/lb) 1,161 Propellant Mass Mp 85,162 lbs.

Structural Ratio R 0.828 dimensionless

Rocket Equation Variables Initial Mass Mi 99,969 lbs.

Specific Impulse Isp 415 s Final Mass Mf 14,806 lbs.

Change in Velocity ΔVbo 23,500 ft/s Production Vehicle Cost Cs $6,706,409

Velocity Loss due to Gravity & Drag ΔVloss 2,000 ft/s Program Development Cost Cd $670,640,947

Ideal Change in Velocity ΔV 25,500 ft/s Fraction of Theoretically Possible ΔV Vratio 0.729682972 dimensionless

Propellant Mass Fraction η 0.927 dimensionless

Payload Mass Mpl 8,100 lbs. Total Cost of Launch

Cost of Hardware Expended Ch $134,128

Vehicle Cost Characteristics Cost of Propellant Cp $10,816

Fraction of Hardware Expended f 0.020 dimensionless Cost of Operations & Refurbishment Co $502,981

Combined Propellant Price Cp 0.127 $/lb Cost of Risk Cr $2,045,723

Specific Cost of Hardware cs 1,000 $/lb TOTAL COST w/o Development Ct $2,693,647

Hourly Cost of Labor cl 75 $/hr Development Cost Assigned to ea. Launch Cd $6,706,409

Labor Intensity L 1 hr/lb Total Cost including Development $9,400,057

Vehicle R&D Cost per lb. of Ms cr&d 100,000 $/lb

Cost per lb. of Vehicle of Additional Facilities cf 0 $/lb Cost per unit Mass of Payload

Fraction of Development Attributed to ea. Launch d 0.01000 dimensionless Payload Mass Mpl 8,100 lbs.

Non-Vehicle Cost Mission Failure Cfail $198,000,000 Specific Cost of Hardware Expended ch 17 $/lb

Probability of Mission Failure pfail 0.01000 dimensionless Specific Cost of Propellant cp 1 $/lb

Specific Cost of Ops & Refurb co 62 $/lb

Specific Cost of Risk cr 253 $/lb

Specific Cost of Developoment cd 828 $/lb

SPECIFIC COST ct 1,161 $/lb









http://www.jupiter-measurement.com/research/rocketcost.xls

SSTO+ET Specific Cost vs. ET Size

4000



3500



3000

Specific Cost ($/lb.)









2500



2000

Total Cost

1500

R&D Cost

1000

Hardware Cost

500



0

0 5,000 10,000 15,000 20,000

ET Separation Velocity (ft/s)



Isp=450s, T/W=50, ηT=.0.96, Γcore=$100k/lb, Γet=$20k/lb,

Ch,core=$2.5k/lb, Ch,et=$1k/lb, fcore=0.02, a=27

Range of SSTO+ET Tech Levels

5000 Isp=430s,

T/W=40,

4500

ηT=.0.95,

4000 a=27



3500 Baseline

Specific Cost ($/lb)









3000

Isp=460s,

2500 T/W=60,

ηT=.0.95

2000 a=72

(monthly)

1500



1000 As blue, except

a=312,

500 Ch,et=$300/lb

(weekly)

0

0 5000 10000 15000 20000

ET Separation Velocity (ft/s)

SSTO+ET vs. SSTO+SRB Specific Cost

5000

Pure SSTO

4500



SSTO+SRB

Specific Cost ($/lb)









4000

(5k fps)

3500



SSTO+ET

3000

(5k fps)



2500



SSTO +ET

2000

35 40 45 50 55 60 (18k fps)

Core Engine Thrust/Weight

SSTO+ET Conclusions

Adding external tanks to an SSTO reduces

development cost



At existing conditions external tanks are more

economical than SRBs for boosting SSTOs



Conditions where pure SSTOs are cheaper than

SSTO+ET aren’t likely to happen soon.



If you are dreaming of an SSTO, consider adding

external tanks to it.

R&D costs must be lowered!



Launch costs >$1000/lb. payload to LEO

with current development & flight rate

even if all recurring costs are zero!



How can RD(Γnr/a) be lowered?



a Γnr RD

Using Identical Stages for

Reduced Development Cost



With Identical stages

RD < R

even for an entirely

new launch vehicle.



Identical stages

increases development

cost (Γnr) and has

inefficient staging

Bimese velocities. Trimese

Image from:

THE BIMESE CONCEPT: A STUDY OF

MISSION AND ECONOMIC OPTIONS by Dr.

John R. Olds and Jeffrey Tooley, 1999

Reusable Bimese + ET

2STO Bimese Bimese 3STO Tri-

Adding an ET to +ET mese

a bimese Amort. $1,676 $1,151 $857 $1,535 $713

reduces R&D



orbiter ΔV Hardware $36 $41 $197 $33 $39



requirement Ops $68 $78 $94 $83 $96

substantially Other $61 $63 $59 $60 $61

for small Recurring $165 $182 $350 $176 $196

additional Total $1,841 $1,333 $1,207 $1,711 $909

development

cost. R 0.905 0.52 0.386 0.829 0.321

RD 0.905 1.03 0.944 0.829 0.963



Isp=440s, T/W=40, ηT=.0.95, η=.0.918, Γnr,xsto=$50k/lb, Γnr,xmese=$60k/lb,

Γnr,et=$15k/lb, Ch=$2k/lb, Ch,et=$500/lb, fcore=0.02, a=27

Expendable Bimese + ET

2STO Bimese Bimese 3STO Tri-

Adding an ET +ET mese

to a bimese Amort. $750 $468 $444 $697 $297

reduces R&D



system cost Hardware $694 $843 $659 $645 $803



even if Ops $56 $63 $80 $70 $80

bimese Other $52 $53 $52 $52 $52

vehicles are Recurring $802 $959 $791 $767 $935

completely Total $1,552 $1,427 $1,235 $1,464 $1,232

expendable!

R 0.75 0.843 0.799 0.697 0.803

RD 0.75 0.421 0.400 0.697 0.268



Isp=440s, T/W=40, ηT=.0.96, η=.0.928, Γnr,xsto=$27k/lb, Γnr,xmese=$30k/lb,

Γnr,et=$15k/lb, Ch,xsto=$925/lb, Ch,xmese=$1k/lb, Ch,et=$500/lb, fcore=1, a=27

Reusability is for Lower Stages

2 Stage Case, subscripts indicate stage number



c  c1  c 2

 η2 

c  R11  R 2R11  

1- η  R 2R11  R 22

 2 





If Γ 1 ≈ Γ 2, then changes to R1 or R2 have the same effect.



Changes to Γ 1 have bigger effect than Γ 2.



Therefore, 2nd stage should be expensive and light weight

while 1st stage is heavier and cheaper (big&dumb or reusable).

Expendable Tank on Lower Stage

Partially 550

Expendable

reusable 500 Partially Reusable

lower stage

Specific Cost ($/lb)

Reusable

with 450

expendable

400

tanks

becomes









Original Boeing EELV Concept

350

economical

before fully 300

reusable 250

lower stage. 10000 20000 30000 40000 50000

Base Development Structure Cost ($/lb)

Isp=315s, T/W,reuse=87, T/W,exp =100, ηT,reuse=.0.948, ηT,exp=.0.955,

Ch,engine=$1000/lb, Ch,et=$500/lb, f=1/0.05, a=27, ΔV=12,500 ft/s

Conclusions

Adding ETs to SSTO designs lowers specific cost for

most current and likely future design conditions.



Adding ETs to a bimese design lowers the systems

specific cost, even if the bimese vehicles are fully

expendable.



Partially reusable lower stages using expendable

tanks and reusable engine pods will become

economical before fully reusable stages.



By any name, external tanks are still a useful

feature in aerospace conceptual design.

Selected Bibliography

• Griffin, M. D., and Claybaugh, W. R., “The Cost of Access to Space,” JBIS, Vol. 47,

1994, pp. 119-122.

• Claybaugh, W. R., AIAA Professional Study Series Course: Economics of Space

Transportation, Oct. 12-13, 2002, Houston TX.

• Carton, D.S., and Kalitventzeff, B., “Effect of Engine, Tank, and Propellant Specific

Cost on Single-Stage Recoverable Booster Economics,” JBIS, Vol. 20, 1965, 183-196.

• Taylor, C.Y., “Propulsion Economic Considerations for Next Generation Space Launch,”

presented at the 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit,

AIAA-2004-3561, Ft. Lauderdale, FL, 2004.

• Griffin, M.D., “Heavy Lift Launch for Lunar Exploration,” presented at the U. of

Wisconsin, Madison, WI, Nov. 9, 2001,

http://fti.neep.wisc.edu/neep533/FALL2001/lecture29.pdf.

• Isakowitz, S. J., Hopkins, J., and Hopkins, J. P., International Reference Guide to

Space Launch Systems, 4th ed., AIAA, Reston, VA, 2004.

• Ross, D.M., “Low Cost Booster Production – Technology and Management,” Reducing

the Cost of Space Transportation: Proceedings of the American Astronautical Society

7th Goddard Memorial Symposium, edited by George K. Chacko, American

Astronautical Society, Washington, D.C., 1969.

• Kiersarsky, A. S., “Assessment of Expendable Tankage for Low Cost Transportation

Systems,” NASA-CR-107139, Nov. 5, 1969.

• Rocketcost.xls spreadsheet, Rev. K., Jupiter Research and Development, Houston,

TX, 2006.