#### APPENDIX F

COMPOSITE VARIABLES FOR SSPS AND ADDITIONAL COLONIES

Due to the nature of the calculations discussed in appendix D it was necessary to construct composites by making separate aggregates for each. One is for the nonlabor, nonchemical processing and fabricating plant costs, and is expressed in dollars (the dollar costs). Three of the aggregates are for the number of man-years of labor needed at L5, on the Moon, and elsewhere in space. The final aggregate is a charge for the amount of chemical processing plants used at L5.

The dollar cost aggregate is the sum of three parts. These are: the present value, with respect to the time at which the item was completed, of all future costs associated with maintenance and operation; a capital charge for the use of any capital other than chemical processing and fabricating plants at L5; and the costs of the actual physical components. As a simplification, construction is assumed to take place within a year, thus allowing interest charges on components used in the early phases of construction to be ignored. The error introduced (because in actuality construction, especially in the case of colonies, takes longer than a year) is small.

A capital charge is defined as the constant amount that must be paid every year of the life of some capital good so that the present value of these payments is equal to the cost of the capital good. This definition assumes that the productivity of the capital good is the same for every year of its life. It follows that if the life of a capital good is infinite and the real discount rate is X percent, then the capital charge is X percent of the cost of the capital. The capital charge is higher when the lifetime is finite but not very much higher if the lifetime is long (30 years or more), as is the case in essentially all of the capital in this program. In particular, for a real discount rate of 10 percent and a lifetime of 30 years, the capital charge is 10.37 percent. As a simplification, all of the capital charges assume an infinite lifetime.

The three labor and the chemical processing and fabricating plant aggregates are calculated in precisely the same way as the dollar cost aggregate, except that instead of using dollars of cost, man-years of location specific labor or plants are substituted.

The costs of the components along with other costs are given in table 6-13.

TABLE 6-13 (gif format)

#### TABLE 6-13.- COSTS OF VARIOUS ITEMS 1

(1)2
Item
(2)
Capacity
(3)
Costs at purchase of parts bought on Earth
(4)
Transportation for parts bought on Earth when oxygen and the 2nd- generation shuttle system are available, 3
\$10^9
(5)
Costs & location of labor for construction, man-years
(6)
Number of chemical processing & fabricating plants
needed 4
(7)
Annual maintenance & operation costs
SSPS5 10 GW at
busbar
on Earth
4.6100 0.6600 2950 at L5 1.9900 \$30 million 30 man-yr not at L5, not on Moon
2nd & later colonies 10,000
persons
.2595 7.3090 19,820 at L5 5.0000 6
Interlibrational
transfer vehicle
500 kt/yr
delivered to L5 6
.0300 .0055 100 at L5 .0035 11 man-yr at L5
Mass catcher Catches
313 kt/yr
.0060 .0011 100 not at L5,
not on Moon
.0033 13 man-yr, not on L5, not on Moon
Mass driver 7 625 kt/yr .4507 .1367 700 on Moon 0 75 man-yr on Moon
Moon base 100 persons .0721 .0219 25 on Moon 0 6
Lunar rectenna 448 GW at
busbar
17.4312 5.2875 2777 on Moon 0 6
Construction shacks 100 persons .0300 .0055 25 at construction
shack location
.0045 at L5 6

1 All costs are in 1975 dollars.
2 Indicates columnar numbers referred to in text
3Transportation costs from Earth to those places denoted as not at L5 and not on the Moon are assumed to be the same as transportation costs from Earth to L5.
4 In order to work at full capacity, a chemical processing and fabricating plant requires an input of 1,000 kt of lunar rock annually.
5 All costs for these items are before the effects of learning curves have been taken into account. These effects are discussed in appendix D. Do not overlook footnote 6 of table 6-12.
6 An ILTV must start at the mass catchers with 625 kt of lunar rock in order to deliver 500 kt to L5.
7 A mass driver requires 0.12 GW to run at full capacity.

It may be expected that costs will fall with time. To simplify, all of the component costs which enter the dollar aggregate are assumed constant, purposely chosen somewhat lower than costs would initially be and considerably higher than they would eventually be. Note also that all of the components in table 6-13 are produced at least partly in space. Besides component costs, the table also gives the direct costs for SSPS's and second and later colonies. It is the transformation of these direct costs into dollar costs, location-specific labor costs, and plant costs, which gives the composite variables.

There are two SSPS composite variables; one for when oxygen is available in space but the second generation shuttle system is not; the other for when both are available and hence transportation costs are lower. To show in some detail how the composite variables are made, a rough derivation of the second of the two composite variables mentioned above is given here.

Essentially, all of the data needed are in table 6-13 and its footnotes. The cost of material bought on Earth is, from column 3, \$4.61 billion. This includes \$1.01 billion for the rectenna on Earth. The transportation cost of the material bought on Earth is, according to column 4, \$0.66 billion. The annual nonlabor costs for maintenance and operation are, as stated in column 7, equal to \$30 million. The present value at the time of construction of this, assuming as an approximation an infinite lifetime for the SSPS's, is \$0.3 billion. Total dollar costs thus far are \$5.57 billion.

Column 5 shows that the direct labor costs are 2950 man-years, all at L5. Labor costs of maintenance and operation are obtained (as in the case of the nonlabor costs) from the present value by multiplying the annual figure by 10. This gives 300 workers at a location other than L5 or the Moon. To be precise, the 300 are at geosynchronous orbit where the people attend to the SSPS once it is in operation. The cost of the housing accommodations for the workers at L5 is not included in the composite variable. This is dealt with by the methodology described in appendix D. Workers not at L5 have their housing costs counted into the variable. The 300 geosynchronous orbit workers are assumed to live in construction shacks. From the information provided in table 6-13, this costs \$0.09 billion for parts bought on Earth, \$0.0165 billion for transportation, 75 man-years at geosynchronous orbit, and 0.0135 of a chemical processing and fabricating plant.

Transportation costs from Earth to every place of relevance for these calculations are assumed to be the same as the costs from Earth to L5. Taking 10 percent of all of the costs of construction shacks given above in order to obtain the appropriate capital charges gives \$0.0107 billion, 8 man-years, and 0.00135 plants. The 8 man-years require housing, and the 0.00135 plants require lunar rock as input. The costs of these are small enough to ignore. Everything is now included within the SSPS aggregate except for a direct chemical processing and fabricating plant capital charge of 0.199 plants and 11990 kt of lunar rock needed as input to these plants.

To get the lunar rock within a year requires 4.0 interlibrational transfer vehicles (ILTVs). From table 6-13, the capital charges for these are: \$0.0142 billion for parts bought on Earth and transportation, 40 man-years at L5 for construction, 0.0014 plants, and a negligible amount of lunar rock. In addition, annual maintenance and operations costs are 44 man-years at L5. The present value of this is 440 man-years, and the capital charge, which is the relevant number, is 44 man-years. Twenty percent of the mass coming off the Moon is used as fuel for the ILTVs. Thus, 2488 kt are needed from the Moon. To catch it, 8.0 mass catchers are needed. The resulting charges are \$0.0057 billion, 184 man-years not at L5 or on the Moon, 0.00264 plants, and negligible lunar rock. The 184 man-years of labor are derived from workers housed in construction shacks for which is charged \$0.0065 billion, 5 man-years which are not at L5 or on the Moon, and 0.00083 plants.

On the Moon 4.0 mass drivers are required. The charges for these are \$0.235 billion and 580 man-years on the Moon. All of the plants discussed thus far were at L5. Their costs are converted to dollar costs by the algorithm given in appendix D. The costs of the plants on the Moon are measured in terms of dollars needed to purchase parts on Earth and the dollars needed to pay for the transportation of these parts to the Moon. These dollar costs are included in the amounts given in columns 3 and 4 of table 6-13.

The power used by 4.0 mass drivers is 0.48 GW. This is 0.1071 of the 4.48 GW that an SSPS with lunar rectenna can deliver. The capital charge for this fraction of a rectenna is \$0.2433 billion and 30 man-years on the Moon. Thus far, there is a total lunar labor charge of 610 man-years. The capital charge for the lunar base additions that these people require is \$0.0573 billion and 15 man-years of labor on the Moon.

One final item is needed: 0.1071 of an SSPS beaming power to the Moon. The costs of such an SSPS are the same as the costs of the SSPS being evaluated, except that the \$1.01 billion for a rectenna on Earth need not be paid. Thus, building one SSPS requires 0.1071 of a second SSPS plus (0.1071)^2 of a third SSPS plus (0.1071)^3 of a fourth, and so on. The sum of this series is 1.1199. Therefore multiplying all the previous costs by 1.1199 and subtracting \$0.1211 billion for the Earth-based rectenna correction gives the final result of a cost of \$6.76 billion, 3398 man-years at L5, 700 on the Moon, 557 not at L5 or the Moon, and 0.2298 chemical processing and fabricating plants.

These costs of the SSPS variable are for when both oxygen in space and the second-generation shuttle are available. To obtain the costs of the SSPS variable when only oxygen is available, the transportation costs given in column 4 of table 6-13 are adjusted in accordance with the information given in table 6-10. The result is a cost of \$9.73 billion with the nondollar costs remaining the same.

Colony composite variable costs are found by a similar method. A somewhat rougher calculation than that for the SSPS yields \$9.24 billion, 20,946 man-years at L5, 1759 on the Moon, and 626 elsewhere. From table 6-13 it is seen that the direct dollar costs are \$7.57 billion. This direct cost may be broken down as follows: plants and animals cost, including transportation, \$0.68 billion; nitrogen in the atmosphere and H 2 for H2O cost, including transportation, \$2.42 billion; high technology equipment from Earth and personal belongings cost, \$2.88 billion. Finally, \$1.6 billion is needed to pay for transportation for 10,000 colonists.