The fact that new technology offers more risks than established technology results in fewer sales than the market size indicates. This occurs, even though the new technology is cheaper, because some potential customers who would otherwise be buying hold back, waiting to see if the new technology actually works. The percentage of the U.S. market size assumed obtainable for each of the first 10 years after the initial terrestrial SSPS is operational is: 10, 12, 16, 20, 25, 32, 40, 45, 50, 60. From then on it is 100 percent.
A 30-year lifetime is assumed for an SSPS. This is the typical lifetime of Earth-based electric power plants. At a 5-percent growth rate for 30 years, the market grows by a factor of 4.3. Therefore, the market for new plants due to growth is taken as 4.3 times as large as the market for replacement.
The number of new terrestrial SSPS's that can be sold per year and the ways in which this changes over time is calculated and given in column 3 of table 6-12. An example is to calculate the number for year 20. In 1975 the U.S. consumed 224 GW of electricity. At a 5 percent growth rate this will be 594.34 GW by year 20. The additional power needed for growth in year 20 is 5 percent of this. In addition, there is the replacement market which is such that the growth market is 4.3219 times as large. To take into account the foreign market, multiply by 1.5. Finally, since this is only the sixth year in which terrestrial SSPS's have been produced, take 40 percent of the foregoing to correct for market penetration. This gives 21.96 GW. SSPS's are assumed to be utilized 95 percent of the time, with the remainder being required for maintenance. Thus, to provide this level of power, 2.31 power stations of 10 GW are needed.
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. 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.
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.
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.
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.
TABLE 6-12 — COSTS AND BENEFITS OF A PROGRAM OF SPACE COLONIZATION IN 1975 DOLLARS¹
- The analysis runs for 70 yr. The numbers for the last 25 yr corresponding to table 6-12 are not given. They may, however, be calculated by the reader if desired. All of the required data are given within this chapter.
- Indicates columnar numbers referred to in text.
- These costs are obtained by summing the costs in table 6-9.
- All learning curves with respect to SSPS's, colonies, and chemical processing and fabricating plants, have the first unit given in the table as the second unit in a learning curve since one colony, one SSPS, and one plant were produced previously and have their costs accounted for as part of the adjusted costs of figure 6-2.
- Second and later colonies which are finished in year X are assumed to provide their full complement of labor in year X-1. The first colony is assumed to be complete except for 37.5 percent of its radiation shield by the beginning of year 20. The colony is then slowly occupied. One-sixth of its full complement of export labor being available in year 20, one-half in year 21, five-sixths in year 22, and all of it thereafter. By the beginning of year 23 the colony has been completed.
- The initial SSPS dollar costs can be divided into a constant cost of $2.48 billion and a variable cost of $7.26 billion. The introduction of the second-generation shuttle system reduces these numbers to 1.99 and 4.77, respectively. The variable cost falls in accordance with an 80 percent learning curve until it has decreased by a factor of six. (See footnote 4.)
- All numbers in this column can be calculated from information given in table 6-12 except for the entries for years 15 through 22. These use as additional inputs the amount of labor related directly or indirectly to the first colony. In chronological order these inputs are 2671, 3010, 3214, 3316, 3486, 1375, 1375, and 1375 man-years.
- To help maintain a reasonably smooth pattern of expenditures, $4 billion which, according to the algorithm, should have been spent in year 20 is moved to year 19. For similar reasons $2 billion is moved from year 25 to year 24. In practice these changes could be accomplished by purchasing on Earth some of the components for SSPS's the year before they are actually needed.
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.