A logistics model for large space power systems

Acta Astronautica Vol. 13, No. 6/7, pp. 411-423, 1986 Printed in Great Britain. All rights reserved

0094-5767/86 $3.00+0.00 © 1986 Pergamon Journals Ltd

A LOGISTICS MODEL FOR LARGE SPACE POWER SYSTEMSt H. H. KOELLE Aerospace Institute, Technical University of Berlin, Salzufer 17-19, D-1000 Berlin I0, F.R.G. (Received 28 January 1986)

Abstract--Space Power Systems (SPS) have to overcome two hurdles: (1) to find an attractive design, manufacturing and assembly concept and (2) to have available a space transportation system that can provide economical logistic support during the construction and operational phases. An initial system feasibility study, some five years ago, was based on a reference system that used terrestrial resources only and was based partially on electric propulsion systems. The conclusion was: it is feasible but not yet economically competitive with other options. This study is based on terrestrial and extraterrestrial resources and on chemical (LHJLOX) propulsion systems. These engines are available from the Space Shuttle production line and require small changes only. Other so-called advanced propulsion systems investigated did not prove economically superior if lunar LOX is available! We assume that a Shuttle derived Heavy Lift Launch Vehicle (HLLV) will become available around the turn of the century and that this will be used to establish a research base on the lunar surface. This lunar base has the potential to grow into a lunar factory producing LOX and construction materials for supporting among other projects also the construction of space power systems in geostationary orbit. A model was developed to simulate the logistics support of such an operation for a 50-year life cycle. After 50 years 111 SPS units with 5 GW each and an availability of 90% will produce 100 x 5 = 500 GW. The model comprises 60 equations and requires 29 assumptions of the parameter involved. 60-state variables calculated with the 60 equations mentioned above are given on an annual basis and as averages for the 50-year life cycle. Recycling of defective parts in geostationary orbit is one of the features of the model. The state-of-the-art with respect to SPS technology is introduced as a variable Mg mass/MW electric power delivered. If the space manufacturing facility, a maintenance and repair facility for operational units and a space logistics operation center are included in the GEO complex, the standard computer run indicates a value of 17 Mg/MW in the (lst) year and 7.1 Mg/MW in the 50th year. Total personnel requirements in GEO are 245 (lst) and 600 in the 50th year. The average mass flow from the Moon to GEO is 55,000 Mg p.a., from the earth come 42,000 Mg p.a. These flows require about 500 lunar bus launches and 540 HLLV average launches p.a. The use of lunar resources reduce the logistic cost to 67% compared to an all earth resources scenario!

i. INTRODUCTION The energy d e m a n d will grow d u r i n g the next decades due to a n increasing p o p u l a t i o n o n this planet. C o n t r a r y to this trend, the supply o f fossil fuels will be diminished since theses energy reserves are constantly used up a n d they are not renewable. Nuclear energy fills the gap, but the storage o f nuclear waste remains as a n unsolved p r o b l e m a n d u n p o p u l a r issue. Fusion energy remains a distant hope, but it is still uncertain if a n d w h e n this source o f energy becomes available to replace fossil fuels. The near future energy alternative is solar energy. It is feasible, it is being developed t h o u g h in small applications not very attractive as far as e c o n o m y goes. But it is the m o s t attractive energy source as far as the environm e n t is concerned. Therefore, we are obliged to search for m o r e economical applications of solar energy. 1"Paper presented at the 36th Congress of the International Astronautical Federation, Stockholm, Sweden, 7-12 October 1985. 411

One o f the available options is the conversion o f solar power in space into electric energy a n d sending this energy via microwaves to the user o n the surface o f the earth. A detailed study ( D O E / N A S A ) [ 1 ] ) has shown t h a t this alternative " a fleet o f solar space power stations" in the geostationary o r b i t is technically feasible. The reference model selected for this feasibility study was oriented towards advanced propulsion a n d limited to e a r t h resources only. W i t h these model a s s u m p t i o n s it was s h o w n t h a t the space power systems were at this time n o t economically competitive with c o n t e m p o r y power plants o n the earth surface. This study shows t h a t the use of l u n a r resources a n d available chemical p r o p u l s i o n technology can lead to a substantial reduction of the logistics cost to build a n d operate a fleet o f space power systems. This analysis shows also that this c o n s t r u c t i o n activity could c o m m e n c e early in the next century a n d lead to a b o u t 100 5 - G W space power units providing a b o u t 15% o f the world energy d e m a n d by the middle of the next century.

H.H. KOELLE

412

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L4LoglshCS{ socops ) center

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F._~[-M-'~:~r' ~]nd repa ~r fa,~,l ~ T Spores, consur;oDle%

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Spares, consum(:]bles foe,lily extensions f "1

._driQr bus JQ,Jrlches 'Tota! number of--Jndr bJS Iounchefl r~o j rPa P Q ~-. . . . . . . . . . . .

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Fig. I. Macro structure of space power system logistics model.

2. S Y S T E M S

DEFINITION

A manned "Space Manufacturing Facility (SMF)" in geostationary orbit builds with the help of semiautomatic production processes "space power units" with an increasing annual production rate. The life cycle considered is 50 years, the production goal is 1 II 5-GW units with a 90% availability rate. This "space power system" (Fig. 1) will thus deliver 100 x 5 = 500 GW electric power to the consumer on earth or elsewhere. For the purpose of this study it is not necessary to make detailed assumptions how exactly the electric power is produced in space. It sufficies to assume that a certain mass is required for these power units to produce 1 MW of power. It is also logical to assume that the technology will improve greatly in the 50-year life cycle time period; thus we will introduce a function of time for the specific mass per unit power Mg/MW =f(t). Closely connected with this assumption is the size of the crew to run the Space Manufacturing Facility. There will be learning involved which we take into consideration by an exponential law. Of particular interest within this study is the optimization of the logistics burden on this system. We allow the feedstock, spares, equipment and consumables required for the con-

struction and operation of this SPS to come either from the lunar surface or earth surface. But we also allow recycling of defective equipment replaced by spares at an increasing rate with life time. This share is not negligible. We use the number of launches of the "Lunar Bus" which transports the lunar feedstock to the GEO construction site as the driver of the logistics system (independent variable). We also assume a function for the share of the construction material which comes from lunar or GEO sources, the rest has to come from earth. Aside from the "Space Manufacturing Facility (SMF)," the GEO complex consists of a "Maintenance and Repair Facility (MRF)" with the task to keep the operational power units functioning but we also require a "Space Operation Center (SOC)" for the logistics side of the operation to support the space transportation system (unloading, tanking and servicing of arriving space ferries). All of them have a crew, its size varying with the amount of activities taking place. The effectiveness of the logistics system can then be defined as the ratio of "transportation cost of construction materials and supplies to the geostationary orbit and the power output of the space power system." This effectiveness can be measured as an

Large space power systems annual factor but also for the whole life cycle. This allows us to compare the overall effectiveness of a logistics system that uses lunar resources with a logistics system that uses only resources from earth as done in the reference system used in the previous analysis (Glaser[2]). This will give us the opportunity to make a judgement whether or not we should develop lunar resources for this purpose. The problem to be solved by this study can now be formulated as follows: Find through systems simulation that combination of earth and lunar space transportation systems which leads to the minimum logistics burden on a geostationary space power system. This optimization of the space logistics system should also try to come up with the earliest possible availability of the SPS and produce acceptable rates of change throughout the system! To solve this problem, we need to develop a functional model of mass flows and personnel required as a function of time for the life cycle specified. These requirements will result in launch rates for the rocket vehicles involved and these in turn will determine the manufacturing rate of the space power units. The scenario used for this model starts from a point where we have already a small lunar research station that is supplied by a HLLV based, fully reusable space transportation system. This lunar research station will have to be expanded towards a lunar factory which produces large amounts of lunar LOX and construction material for the space manufacturing facility in the geostationary orbit. The scenario also assumes the existence of space stations in low earth and lunar orbits which can support the logistics operation. It is conceivable that the life cycle analysed here begins about the year 2010! The next point is a mathematical description of the model and includes the assumptions made.

413

from the earth surface R2:

CME (%) = 100 - CML (%) - CMG (%) = (%) = f ( t ) =(A31)

(A32)

If CML is the independent variable and given a s f ( t ) by eqn (R 1), we can calculate the total construction material arriving at GEO: R3:

CMG (%) 1-1 C M L ( % )

CM(Mg)=CML

CME (%)~

-+ CML (%)] = (R1) {1

t

A032

R2

+ A ~ + g---03i)

and in terms of mass delivered we obtain R4:

CMG (Mg) -

CMG (%) 100

x CM

(A032) -

R5:

100

x (R3)

CME (%) CME(Mg)- - × CM 100 -

(n2) 100

x (R3)

It should be noted that the mass obtained through recycling in GEO cannot be larger than the mass of spares delivered to GEO! Not all of the CM arriving at the GEO space manufacturing facility (SMF) will be converted into SPS hardware, there will be some losses during the manufacturing process. Thus we have to deduct these residuals (RESCM). During one time period we now add to the SPS the mass R6: DELTAMSPS -- CM (1 - RESCM) = (R3) x (1 - A10)

3. M A T H E M A T I C A L

MODEL

3.1 Relationships to calculate the numerical values of the state variables of the geostationary complex (GEO ) Lunar construction material CML to be transported from the lunar surface through LUOSOC with refueling to GEOSOC: RI:

CML = MPLB x NLB = Mg payload (Mg p.a.)

We will accumulate these residuals in a GEO depository; it can be used for radiation shielding. Thus we add to the depository R7:

x CM (Mg) This leads to the total mass invested in operational SPS R8: CUMMSPS = CUMMSPS(t - 1) + DELTAMSPS(t)

x no. lunar launches p.a. = MPLB x lAID + (A1B + A l E × T ) Alc - A 1 F x T 2]

The construction material arriving at GEO can originate from the lunar surface, earth surface or from recycling processes in GEO. If the shares of CM from the moon (CML) and from GEO (CMG) are given (by estimating), then the rest of the CM has to come

DELTAMRES = (RESCM x 100)

and to the total residual mass deposited R9:

CUMMRES = CUMMRES(t - l) + DELTAMRES(t)

(Mg)

If we know the mass required to build one SPS unit in terms of specific mass (Mg/MW), assumption A1 l, and the power level of a single SPS unit (MW/unit), assumption A12, we obtain the number of SPS units

414

H . H . KOELLE

built in that time period R 10: D E L T A N O S P S = D E L T A M S P S / S M S P S

In case these differences are negative they are set = 0; otherwise they are s u m m e d up to R20:

x LSPS

DELTAMFEX = DELTAMSMF + DELTAMMRF

= (R6)/(AI1 x A t 2 )

+ D E L T A M S O C (Mg)

The total n u m b e r of SPS units d u r i n g the entire c o n s t r u c t i o n period at any time t is then Rll:

C U M N O S P S = C U M N O S P S ( t - 1) + DELTANOSPS =(RI1 +R10)

a n d in terms of additional power installed we o b t a i n R 12:

DELTALSPS = DELTANOSPS x LSPS ( M W ) =(R10 x AI2)

= (R 17) + (R 18) + (R 19) These additional mass requirements in G E O are assumed to come at 100% from the e a r t h space port which is a conservative a s s u m p t i o n but simplifies the model. All G E O facilities require a certain a m o u n t of spares to replace defective equipment. These spare rates are p r o p o r t i o n a l to the mass o f these facilities a n d are given by a s s u m p t i o n A13. This leads to a n n u a l mass flows as follows R21:

S M S P S = SRSPS x C U M M S P S = ( A I 3 1 A )

a n d with respect to total power installed R13:

C U M L S P S ( M W ) = C U M L S P S ( t - 1)

x (R8) (Mg p.a.) R22:

S M S M F = S R S M F x M S M F = (A132A) x (R 14) ( M g pro.)

+ DELTALSPS R23:

=(R13+R12) T o h a n d l e the i n c o m i n g c o n s t r u c t i o n material (R6) the space m a n u f a c t u r i n g facility needs to be of a certain size. If we can estimate the specific mass of this S M F , A4, then it must have a mass of R14:

M S M F = C1 + C2 × C M = (A41) + (A42) x (R 3) (Mg)

In a similar way we arrive at the mass of the G E O m a i n t e n a n c e a n d repair facility ( M R F ) which takes care o f the o p e r a t i n g SPS R15:

a n d also of the G E O space t r a n s p o r t a t i o n o p e r a t i o n center (SOC) R16:

x (R 15) ( M g p.a.) R24:

M S O C = C5 + C6 x C M = (A61)

These spare parts can come from the l u n a r surface, from G E O recycling processes a n d from earth. The total spare parts r e q u i r e m e n t is R25:

R17: D E L T A M S M F = M S M F ( t ) -MSMF(t

- 1) (Mg)

= (R 14)t - (R 14)t - 1 R 18: D E L T A M M R F

= MMRF(t) -MMRF(t

= (R21) + (R22) + R23) +

R24)

they are delivered f r o m R26:

SML=CII

R27:

SMG=C12xTOTSM=(AI42A)

R28:

SME=TOTSM-SML-SMG=(R25i

xTOTSM=(A141A)

xlR25) x(R251

- (R26) - (R27] In addition, all G E O facilities need people to operate them. In case o f the m a n u f a c t u r i n g process we will have a significant a m o u n t of learning estimated to be p r o p o r t i o n a l o f the square root o f the c o n s t r u c t i o n material processed. A great deal of a u t o m a t i o n will be involved. T h e m a i n t e n a n c e a n d repair as well as the loading a n d u n l o a d i n g activities are assumed to be p r o p o r t i o n a l to the a m o u n t of material h a n d l e d R29: P S M F = C14 + C M c1~ = (A71) + (R3) I'x7z~ R30: P M R F = C16 + C17 x C U M M S P S = (A81) + ( A 8 2 ) x (R8)

DELTAMSOC = MSOC(t) -MSOC(t

+ S M S O C ( M g p.a,)

- 1) (Mg)

=(R15)t-(R15)t-I R19:

TOTSM = SMSPS + SMSMF +SMMRF

+ ( A 6 2 ) x (R3) (Mg) These three facilities have to be e x p a n d e d with increasing mass flow of c o n s t r u c t i o n material by the a m o u n t s of

SMSOC = SRSOC x MSOC = (AI34A) x (R 16) ( M g p.a.)

M M R F (Mg) = C3 + C4 x C U M M S P S ( t ) = (A51) + (A52) x (R8)

SMMRF=SRMRFxMMRF=(A133A)

- 1) (Mg)

= (R16)t - (Rl6)t - 1

R31:

PSOC=CI8+C19xCM=(A91) + ( A 9 2 ) x (R3)

Large space power systems Thus the total personnel requirements in GEO are R32:

R42: D E L T A M L = CML + SML + CSL = (R 1) +(R26) + (R39) (Mg)

TOTPGEO = PSMF + P M R F + PSOC = (R29) + (R30) + (R31)

R43: D E L T A M E = CME + SME + CSE = (R5)

Since these people have an average duty cycle of less than one year (assumption 17), we need the following number of roundtrips between earth and GEO R33:

NTRIPS = T O T P G E O : T D U T Y = (R32):(A17)

This requirement will result in a certain number of launches from earth with the HLLV or other shuttle vehicles. They will be calculated later. Aside from spare parts and personnel, these GEO facilities require a certain amount of annual consumables for operation. These are primarily propellants to move materials and personnel around but also for attitude and orbit control. They are lost in space and need to be replenished. Supplies that can be recycled (such as food and water for the crew) are considered as part of the facility mass or spares. The consumables are calculated by the following equations R34:

CSSPS = CRSPS x CUMMSPS = (AI51) x (R08)

R35:

R36:

R37:

CSSOC = CRSOC x MSOC = (A154) × (R16)

This adds up to the total amount of consumables required TOTCS = CSSPS + CSSMF + C S M R F + CSSOC (Mg) = (R34) + (R35) + (R36) + (R37) These consumables originate from various sources as follows CSL = C24 x TOTCS = (A16.1) x (R38) (Mg) R40:

CSG = C25 x TOTCS = (A16.2) x (R38) (Mg)

R41:

CSE = TOTCS - CSL - CSG = (R38) - (R39) - (R40) (Mg)

The primary mass flows to the GEO complex to be transported from the moon and the earth by the space transportation systems can now be summed up to AA

+ D E L T A M F E X + (R20). Through recycling processes of spares and other suitable material, we regain R44: D E L T A M G = C M G + SMG + CSG = (R4) +(R27) + (R40) However, we have to observe that the material gained through recycling cannot be larger than the amount of defective equipment replaced by spares accumulated in the depository (R53). To calculate the number of HLLV launches required to transport D E L T A M E from the earth surface to GEO, we have to make a little correction to include the supplies required by the lunar factory to produce DELTAML. This will be done by a correction factor given in assumption A20. Knowing the GEO payload capability of the HLLV (A19) we now obtain the minimum number of successful launches required R45:

[ 316~7--K

N M I N H L L V --- DELTAME: (A19) + 0,025 DELTAML: (A24)

CSMRF = CRMRF x MMRT = (A153) × (R15)

R39:

+(R28) + (R41) (Mg)

CSSMF = C R S M F x M S M F = (A152) × (R14)

R38:

415

Since we need hydrogen on the lunar surface and in lunar orbit that has to be transported there by the HLLV and is proportional to DELTAML, we need additional HLLV launches to the amount of R48:

N T A N K E R H L L V = MLH2 : MP LU O = (R47):(A24)

with the hydrogen requirement of R 4 7 : M L H 2 = D E L T A M L × C29 = (R42) × (A23) Considering the effects described above, we obtain for the total number of HLLV launches p.a. R49:

NTOTHLLV = NMINHLLV + NTANKERHLLV = (R45) + (R48)

The number of lunar bus launches can also be calculated but we have to take into consideration the LOX requirements in lunar orbit which have to be transported by the lunar bus, too. If this has a payload capability as given in assumption (A22), we obtain R46: N T O T L U B U S = D E L T A M L x C28 : MPLUBUS = (R42) x (A25) : (A22) (No. p.a.)

416

H . H . KOELLE

We can also estimate now the total lunar LOX requirement which amounts to R50:

This is added to the G E O depository R52:

DELTAGEODEP = DELTAMRES

M L U L O X = D E L T A M L x C29

+ DE LTAGEOSCRAP

= (R42) x (A21)(Mg p.a.) N o t yet taken into consideration is the LOX needed for lunar imports and for the rotation of the lunar crew and local lunar transportation requirements. There is one more influence factor that could be taken into consideration. If we replace defective equipment in our G E O facilities, this will at least partially be of higher performance and/or of smaller mass. This results in an upgrading of the facilities, If we consider only the operating SPS this would lead to a reduction in mass (at a very low rate) during the 50-year life cycle but also to a higher power output per Mg installed mass. This is not negligible if this continuous over 50 years. If we assume that a certain amount of the annual replacements of defective equipment will be lighter (A26) we can replace equation R8 by R8':

(Mg p.a.) = ( R 7 ) + (R51) The cumulative amount as a fimction of operational lifetime is R53: C U M G E O D E P -- C U M G E O D E P ( t - i ) + DELTAGEODEP

=(R53)t - 1 + ( R 5 2 ) This mass is available for potential recycling at a later date or for radiation protection purposes, We can also estimate the number of H L L V launches required for the rotation of the G E O crew provided that a modification of the H L L V is available for earth - G E O passenger transport. The number of passenger flights becomes R54:

NOPHLLV = NTRIPS: ( H L L V M P G E O : SMP)

C U M M S P S = C U M M S P S ( t - 1) -MUPR

= ( R 3 3 ) : ( A 1 9 : A I 8 ) (No. p.a,)

x SRSPS

x C U M M S P S ( t - 1)

(Mg)

This increases the number of launches lbr cargo plus passenger of the H L L V to

+ DELTAMSPS(t) = (R8),_~ - (A26) x (A131)

R55:

NCPHLLV = NTOTHLLV + NOPHLLV (No. p.a.) = (R49) + ~R54)

x(R8), ~+(R6) We have also a slightly increased power output which allows us to replace eqn R 13 by

A measure of the effectiveness of using lunar resources is then the ratio of H L L V launches required for a given SPS with and without lunear resources. This is given by

R 13': C U M L S P S (MW) = C U M L S P S ( t - 1)

R56: L U R E S E F F = N C P H L L V x 100

x PUPR

NOHLLV + (DELTAML + DELTAME): HLLVMPGEO

+ DELTALSPS = (R 13) x (A27) + (R 12)

(R55) x 100 These are the most important relations for the logistics system required for the deployment and operation of space power systems. But we can obtain more relevant information with little effort. We calculated the amount of spares required by the G E O facilities to keep them operable T O T S M (R25). We also determined the amount of spares and consumables won from the defective parts replaced by spares S M G (R27) and C S G (R40). This leaves a certain amount of scrap in G E O

(R54) + [(R42) + (R43): (A 19)] Other measures of system effectiveness are the total mass invested in G E O ( C U M M S P S ) (R8) plus the mass of the S M F + M R F + SOC = D E L T A F E X (R20) divided by the number of operational SPS C U M N O S P S (R 11) R 57:

S P E C U N I T M = [(R8) + (R 20)] : (R 11) (Mg/unit)

R51:

DELTAGEOSCRAP = TOTSM - SMG - CSG - C M G = (R25) -- (R27) -- (R40) - (R4)

or even better divided by the total power installed C U M L S P S (R 13) R58:

S P E C P O W M = [(R8) + (R20)]:(R 13) (Mg/MW)

Large space power systems The number of HLLV launches required per unit power installed is also of interest R59:

SPECLVPOW = NOCPHLLV:

R60:

417

TRSPTCOST = NOCPHLLV x CHLLV (Mio. Dollar)

CUMLSPS

+NTOTLUBUS x CLUBUS

1000

(R55) x (A28) + (R46)

(R 13) (launches GW) = (R 55): 1000

x (A29)

If we have a reasonable estimate for the cost of a HLLV and a lunar bus (A28) and (A29), we obtain a rough estimate for the overall logistics cost of the SPS operation described in this model. It is given by the equation

The following flowchart (Fig. 2) illustrates the rather complex structure of the relationships between the elements of the logistics system investigated. Not shown are the selected indicators of system effectiveness because the number of lines to be added

,!

~,-~+~/ J-~ r-~-~-LF~ ~S~£ r F~iz~MFEXi i SMSOCj-~ I sMr

r

--@ .-@ !

I ~oMon J i Earth launches

@_t_ ]® R-46bus Lunar launches

Fig. 2. Micro structure of model.

J ,.,

418

H . H . KOELLE

would result in a considerable reduction of trans-

11. Specific mass of SPS ( M G / M W )

parency.

All=SMSPS:10-0.08x

3.2 Assumptions

12, P o w e r level for single SPS unit ( M W )

1. L a u n c h rate of l u n a r bus t r a n s p o r t i n g c o n s t r u c t i o n material from LS t h r o u g h L E O to G E O ( N L B ) (no. p.a.) A1NLB =0+(10+0.4T)x

T°-6°s- 0.01 T 2

T=AllB-AIIAx

T

LSPS = 5000 ( M W ) 13, Spare rates required to m a i n t a i n G E O facilities m o p e r a t i o n (SR) - ( M g s p a r e s / M g facility) AI31 = SRSPS = 0,015 -- 0.0001 x 1"

2. Single payload ( M P L B ) - (Mg)

capability

of

Lunar

Bus

=A131B-AI31A

x I'

A132 = S R S M F = 0.030 --0.0002 x T

A22 M P L B = 319 (Mg)

= A 1 3 2 B - A I 3 2 A x 1" 3. Shares of sources from which the G E O construction materials come from (percent) A31 C M L = 3 0 + 0 . 8 × T A32 C M G = 0.5 x T

from the m o o n ( % ) from G E O recycling ( % )

4. Specific mass of Space M a n u f a c t u r i n g Facility ( S M F ) in G E O required to h a n d l e the flow o f c o n s t r u c t i o n materials ( S M S M F ) - ( M g / C M p.a.) S M S M F : A41; A42; = 5000; 0.1 5. Specific mass of M a i n t e n a n c e a n d R e p a i r Facility ( M R F ) in G E O required to serve all o p e r a t i n g SPS ( S M M R F ) (Mg/MSPS) -

S M S O C : A61; A62 = 100; 0.002 6. Specific mass of the G E O Space T r a n s p o r t a t i o n O p e r a t i o n C e n t e r ( G E O S O C ) to h a n d l e logistics to, f r o m a n d within the G E O complex SM SOC : A61; A62 = 1000; 0.01 7. Personnel factor o f the S M F ( P / C M p.a,) S P S M F : A71; A72 = 100; 0.5 (exponent) 8. Personnel factor of the M R F ( P / M S P S ) S P M R F : A81; A82 = 10; O.O0002 9. Personnel factor of the G E O S O C ( P / C M p.a.) SPSOC: A91; A92 = 3O; 0.0001

A133 = S R M R F = 0.010 -- 0.0001 x T = A133B- AI33A x T A134 = S R S O C = 0.020 --0.0002 x 7' = AI34B-

A134A x I

14. D i s t r i b u t i o n of sources from which spares are delivered (percent) - (SSR) A141 = S S R L = 0.007 x T = A141A x 7" A142 = S S R G = 0.005 x T = A142A x T 15. C o n s u m a b l e s p.a. a n d per mass unit required to operate G E O facilities ( M g p . a . / M g fac.) AI51 = C R S P S = 0.0i)5 A152 = C R S M F = 0,05 A153 = C R M R F = 0,J A154 = C R S O C = 0.15 16. D i s t r i b u t i o n of sources from which c o n s u m a b l e s are delivered to G E O facilities ( p e r c e n t ) - (SCR) AI61 = S C R L = 0.1 + 0 , 0 1 x T =A161B+A161A

x 7"

A162 = S C R G = 0.05 17. Average duty cycle of crew m e m b e r s in G E O ( T D U T Y ) - (YRS) T D U T Y = 0,25 18. Equivalent mass e a r t h - G E O (Mg/P)

per

person

per

roundtrip

S M P = 1.0 19. H L L V payload capability to G E O (Mg/flight) H L L V M P G E O = 110 M g

10. Share o f the i n c o m i n g c o n s t r u c t i o n material t h a t is leftover from the p r o d u c t i o n process in the S M F a n d will n o t become part of the SPS

20. H L L V multiplier for lunar i m p o r t requirements as a function o f export mass ( M g i m p o r t s / M g exports)

R E S C M = A10 = 0.01

H M L I = 1~025

Large space power systems 21. Multiplier for number of lunar bus launches due to lunar LOX requirements for refueling in lunar orbit

419

2 0 0 --

160

Annual moss flow

from the M o o n /

BMLUOREF = 2.88 22. Lunar bus single flight payload capability LBMP = 319 Mg

Z LJ

;20

% 80

23. Multiplier for HLLV launches to LUO resulting from LH2 requirements for logistics system in LUO and on lunar surface (Mg LH2/Mg exports) HLLVMLH = 0.28 24. HLLV single flight payload capability to LUO (Mg) HLLVMPLUO = 110 Mg 25. Multiplier for lunar LOX production (Mg LOX/ Mg export) LOXM = 1.88 26. Multiplier for mass reduction of SPS inventory due to replacement of defective equipment with lighter spares MUPR = 0.1 (mass uprating) 27. Multiplier for power increase of SPS inventory due to replacement of defective equipment with more efficient space parts (power uprating during life cycle) PUPR = 1.001 28. Average launch cost of one HLLV during life cycle CHLLV = 15 Mio. Dollar (1985) 29. Average launch cost of one lunar bus launch CLUBUS = 6.2 Mio. Dollar (1985) 4. R E S U L T S O F T H E S I M U L A T I O N

4.1 Standard computer run Some twenty computer runs were made to find one strategy which results in a stable system with an acceptable number of launches of the HLLV, a reasonable growth rate in terms of deliverable power and smooth functions of the sensitive parameters of the system. The results obtained by this model serve the primary purpose to provide input data to the lunar base model and to the overall space transportation model. The interfaces of all three models have to be matched to produce a consistent longrange space program. Before this can be,done other missions than this "Space Power System Construction and Operation Program" have to be added to obtain the complete mission spectrum. Due to these restrictions, the data presented on the following pages have only preliminary character. Nevertheless, they are typical for such a program and can serve a discussion in depth. Lacking at this time is a model that describes the manufacturing and assembly pro-

0

I fO

I 20

from Earth (R-43) . L 30 40

L 50

Yeors

Fig. 3. Annual mass flows from Earth and moon. cess of the space power units proper. This task remains to be done. As soon as such a model becomes available, this logistics model can be adapted and together they will provide the answer if and when such a system might become economically viable. The following pages give the most important trends of the system parameters using the assumptions of Section 3.2 as a function of time for the chosen life cycle of 50 years. A close examination of these time series will provide some insight into the behaviour of the system investigated. It also will result in ideas on where, when and how the system effectiveness can be improved. The interpretation of the data presented on a selected basis will conclude this Section. 4.2 Interpretation of results The complete results are available upon request. Some 19 of the 60 parameters investigated are presented in l0 diagrams which follow and are explained in some detail. Figure 3 gives an indication of the mass flows involved from the earth surface to the construction site in GEO and from the lunar surface respectively. One would attempt to increase the mass flow from the moon as rapidly as possible because the transportation cost is about 1/3 as compared to the mass to be transported from earth. The peak mass flow from earth occurs at about half of the life cycle. Figure 4 illustrates the distribution of the original supplies in terms of percent of the annual rates. It is easy to see that recycling in geostationary orbit is worthwhile, the share of mass regained by this activity is not neglibible. Figure 5 shows the nonlinear growth of the space power system in terms of accumulated mass and power installed as a function of time. Due to the learning processes, it would be unrealistic to plan for a constant construction rate of space power units. The amount of actual power delivered is about l0 to 12% smaller than the total power installed. At the end of the time period considered in this model more than 500 GW of electric po~wer would be made available by this space power system.

420

H. H, KOELLE !00

g

/

=o o I

share from

Earth

//_

0

10

This is a logistic task which is often overlooked in studies of this nature. Where this is feasible these supplies will come from the m o o n due to economic reasons. Figure 8 indicates the amount of scrap and residuals accumulating in G E O for later recycling or used for purposes of radiation shielding. These 100,000 tons are valuable raw material. Figure 9 is a plot of launch rates of the lunar bus and the heavy launch vehicle as a function of time with the payload capabilities assumed (lunar b u s = 3 1 9 M g ) to GEO; H L L V = l l 0 M g to G E O and to LUO). These rates can grow only in a modest and smooth way, they determine pretty much the growth of the space power system. They have to be

7

Share of mass ~on irdr~

20

3C

4C

t:

Years

Fig. 4. Origin of mass flows in percent.

{D

:~S spare

,~, 3o

20

40C u~

10

C.

. . . . .

~

~C,Jrn

p. . . . o

consumables

-

j ~Or .

20

10

ao

,40

50

Years O0

0

10

20

30

40

50

-

-

Fig. 7. Spares and consumables required by SPS.

Yea rs j r'~'iU I0 *i / e

Fig. 5. Cumulative mass and power installed in SPS.

....

. /

R-55) i-© ~ 2O

/

R-14 Space

%

~

/ /

2

manufacturing

facd~ty 1

6

~0

Maintenance and repair facd t v

4

x

F~ !6 SLiaCe

:

~C

2C

?

.

.

.

.

C

4L

5

Yea rs

Fig. 8. Scrap and manuf, residuals ace. in GEO dep. C

10

20

3C'

4C

E,C

Years

!

1000 !-

Fig. 6. Cumulative masses of SMF, MRF and GEO-SOC. Figure 6 gives an overview of the growth rates and total masses of the other facilities required in G E O to build and service the space power units in operation. The mass required for the space manufacturing facility in G E O will depend to a large extent on the degree of automation built into this system. This requires a more detailed study to come up with better assumptions as made in this analysis. Figure 7 shows the amounts of supplies in terms of spare parts, propellants and other consumables required by the facilities stationed in GEO. These are almost proportional to the mass installed at any time.

2

80C

600

i I

HLLC ~ (R-55)

/

LJBdS (R-46)

.~ 200

a=

i

Z

0

10

20

30

40

50

Years

Fig. 9. Number of annual launch rates of lunar bus and heavy lift launch vehicle.

Large space power systems

8 E

S

I

R-52

l_

pers

6o0 ~-

0

400

ro~a~ GEO 8O

500

4 0 0 --

R -31

3oo - / / /

~-30

/~/"

100 --

n

60

Pets m o n' and rep fac

2 O O --~R-29

E

Personnel m space manJ f a g f J r m g faClhfy 2O

0

i

i

1

t

I

~C,

20

30

40

50 0

Years

matched to the capabilities of the lunar factory producing LOX and construction materials and to the launch vehicle production rates possible. Particularly the production of SSME engines used for all stages of the HLLV might prove to be the driver of the system. The purpose of using lunar resources extensively is of course to keep the HLLV launch rate down! The peak of the HLLV launch rate turns out to be 35 years after the beginning of this project, much later than hoped for. Figure 10 illustrates the size of the crew required to operate the facilities in GEO. The order of magnitude is probably right, but it can be considered as a rough estimate only. Most of the personnel is required for the construction and assembly of the individual space power units. Figure 11 gives us the trend of the specific mass per unit power of the space power system over system life. All facilities in GEO (operating units, SMF, M R F and s a c ) are included. Considering the fact that 50 years are a long time period where many improvements will find their way into the SPS this trend appears reasonable. However, the designers and developers of the power units have now to compare these trends with their own data. If this trend appears too pessimistic or optimistic we can easily change this parameter which is of an assumption basis to this logistic model. The same

:E "x c:~ 18

o ConstQnt

co

0O3 ~4

14

"6 Vorlable o

10

~o

.o- r'a tn "a~"

oo

g~

o

a u')

m

if3

z --

& 0

I 10

I 20

l 30

l 40

I 50

Yeors

Fig. 10. Number of personnel required in GEO.

E

421

I

I

I

]

10

20

30

40

2

i

50

Y e a rs

Fig. 11. Specific mass of SPS and logistic support cost.

Fig. 12. Effectiveness of lunar resources.

diagram shows a curve of relative cost which assumes constant launch vehicle cost. In reality these will be higher in the first years and be lower towards the end of the life cycle. This correction leads to the dotted curve! Figure 12 finally gives an indication of the effectiveness of using lunar resources. It shows that the number of HLLV launches is reduced to about 50% by using lunar resources. In terms of cost preliminary estimates indicate that over the system lifetime we can hope to save about 1/3 of the logistic cost by using an optimum mix of lunar and earth resources.

5. CONCLUSIONS AND RECOMMENDATIONS

The only way to gain some insight into the behaviour of complex systems is the simulation. Even if the knowledge of the interrelationships within the system is incomplete, one should develop the best possible simulation model at that time. Running the simulation model will lead to its improvement, the learning process has to be started. Our knowledge about space power systems today is far from complete. But we know how to develop a simulation model of a space power system and the logistics system to support it. We have started with the logistics system because we have a very good knowledge of space transportation systems. To develop a good base to depart from, we started out with conventional space transportation systems, e.g. such that are derived from Space Shuttle hardware. Thus, we have structured a SPS logistics (sub)system model, have made plausible assumptions and also a great number of runs. All of this did not take more than one hundred man-hours. Nevertheless, we have learned a lot: 1. The build-up of a SPS can proceed only in a fairly slow pace because the launch rate of the HLLV cannot make jumps. 2. Life cycles with less than 50 years do not seem appropriate for the analysis of space power systems. 3. Lunar resources in terms of construction material and lunar oxygen will lead to a reduction of the logistic cost by 1/3.

422

H.H. KOELLE

4. The use of lunar resources will cut the annual launch rate of the earth-based Heavy Lift Launch Vehicle by half. 5. The use of lunar oxygen within the logistics system will make it possible to live with available launch vehicle technology (SSME engine in particular). Advanced propulsion systems in this case do not offer any operational or economical advantage. 6. The use of available technology within the logistics system reduces the risk of such an undertaking considerable and leads to more reliable cost estimates. 7. Several hundred people will be needed in geostationary orbit, adequate life support systems and economical passenger transportation systems will be pacing items in the development of space power systems. 8. We have to develop our know-how to launch large rockets by an order of magnitude. Launch rates required for the SPS go as high as two per day, the U.S.S.R. launches two per week at the present time. This is not an unsurmountable problem. An equatorial launch site for such an operation will be very beneficial. 9. Recycling of defective parts and scrap left over from manufacturing processes offer a great potential for economical savings and should be considered seriously. 10. Laser propulsion systems should be considered for the orbital maneuvering vehicles providing transportation within the space power system. Electrical power will be available in large quantities at all points of departure and arrival. Distances will be relatively short. Laser driven OMV's will reduce the supply rate of consumables. The following recommendations seem to be justified at this point in time: 1. A reevaluation of the economical viability of space power systems should be completed by the end of this decade. 2. The structure of this logistics model as well as the assumptions entering it should be refined. 3. This model must be complemented by another model that can simulate the manufacturing and assembly process of space power units. Also the cost estimating procedure for the development of the SPS must be refined. 4. A market model for other space missions than the SPS must be developed. This will make it possible to integrate in a feasible and efficient manner all likely space missions of the next 50 to 60 years into one cohesive program. 5. Improve existing simulation models for space transportation systems which can handle such integrated space programs in a consistent manner with a high degree of confidence. 6. Use all means of communication available to relay relevant information between interested individuals and groups.

6. SUMMARY OF THE REPORT

This paper describes a logistics model of a typical space power system as it may come into being in the first half of the next century. The primary inputs for this logistics model are 1. Life cycle duration (e.g. 50 years) 2. Power level of the SPS at the end of the life cycle assumed (e.g. 500 GW) 3. Availability of space power units (e.g. 88.5%) 4. Specific mass (Mg/MW) of SPS as a function of time (e.g. SMSPS = 1 0 - 0.08 7-) 5. Power level for single SPS unit (e.g. 5 GW) If such a space power system is to be built and operated in geostationary orbit or anywhere else. a logistics system has to transport construction materials, space parts, consumables and also people from various points of origin to the construction site and to the positions the units of the SPS are located. This model allows earth and lunar resources as well as recycling in geostationary orbit. The space transportation system consists of a Heavy Lift Launch Vehicle and a Lunar Bus, both of which can transport supplies and people between the transportation nodes. The launch rates of these space vehicles are determined by this logistics model if the payloads are known. Also the cost per launch of these vehicles must be known if the logistics system is to be optimized under certain boundary conditions. The simulation model presented in this report comprises 60 equations describing the interrelationships between the system variables and parameters. Aside from the five input parameters for the SPS stated above and the four-space-vehicle data (cost per launch and payload capability of two vehicles) 20 other assumptions are required to run this model. These are listed in Section 3.2 for the reference model presented in this paper. The computer code developed for this simulation model is available upon request, also the computation results, e.g. the printout of all 60 system variables calculated as functions of time. Nineteen of the 60 system variables are presented in diagrams along with some interpretation in Section 4.1. A system of t00 operating space power units in geostationary orbit with an output of 500 GW in its 50th year requires in this year a total mass flow of 155,000 metric tons. To operate the system, this model projects a crew size in GEO of 600 people. The total mass installed in the GEO SPS amounts to slightly more than 4 million metric tons! To get this material to the GEO from earth and from the moon, we need average annual launch rates of 490 for the lunar bus and 540 for the heavy lift launch vehicle during the 50-year time period considered. It should not be overlooked that not only construction material has to arrive at GEO but there is a considerable flow of spare parts and consumables needed by the SPS. These amount to some 60,000 metric tons in the 50th year of operation.

Large space power systems It is too early to come up with realistic cost figures at this time. But we can make an attempt to estimate the order of magnitude of the logistics part of the SPS system not including development costs. The reference model indicates for the standard run of February 1985 average annual cost of about 11.132 billion $ (1985) during the 50-year time period. The launch vehicle cost estimates were obtained from simulation runs of another model available at our institute and are the best available at this time. The average annual output of the SPS over 50 years is calculated to be 2 0 0 . 8 G W × 0.885 availability x 8 760h p.a. = !,556,740 GWh. Dividing the annual logistics costs of 11.132 billion $ by the power output of 1,556,740GWh we obtain 0.715cents/KWh as the logistics burden for this model of a typical SPS. This is not the whole story. We have now to develo p a model for the construction of the SPS units and all those things which are not part of the logistics model presented in this paper. Such a model wilt be developed by this institute in the near future. Then and only then we can make a comparison with other power systems. One conclusion can be drawn already now. It does payoff to use lunar resources. If you do, chemical propulsion systems of the S S M E type are hard to beat. That reduces and risk and' the development time.

423 REFERENCES

1. DOE/NASA (1980), Program assessment report statement of findings--satellite power systems and evaluation program. In DOE/ER-0085, November (1980). 2. P. E. Glaser, Solar power via satellite. Astronautics & Aeronautics, August (1973). 3. G. M. Hanley, Satellite power systems concept definition study (Exhibit D), Vol V. In NASA Contractor Report 3396 (1981). 4. K. P. Heise, SPS: An economic outlook. J. Space Solar Power Rev. 2, 62 (1981). 5. B. Johenning and H. H. Koelle, Recent advances in lunar base simulation. Paper IAA 83-237, Budapest, October, 1983. Acta Astronautica 11, 819-824 (1984). 6. H. H. Koelle and B. Johenning, A logistic scenario for an early lunar base. TN 143/1984, Aerospace Institute, Technical Univ. of Berlin, Dec. 10 (1984). 7. R. H. Nansen, Potential for future space solar power systems. Paper presented at the International Meeting on Utilization o f Space Shuttle & Space Lab., June 4, Bonn, Germany (1976). 8. R. Ress, Stimulation of reusable space transportation systems for cis-lunar missions with emphasis on chemical propulsion systems. Doctorial thesis, Technical Univ. of Berlin (1984). 9. U. Thomas, Analysis of cis-lunar transportation systems using unconventional propulsion systems with special consideration of life cycle cost. Doctoral thesis, Technical Univ. of Berlin (1984).