Space Settlements - A Design Study 1977

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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 H₂ 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.

TABLE 6-13 — COSTS OF VARIOUS ITEMS¹

  1. All costs are in 1975 dollars.
  2. Indicates columnar numbers referred to in text.
  3. Transportation 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.

APPENDIX G

CONCEPTS FOR ESTIMATING PROFITS FOR THE COLONY

The total benefit (revenue plus consumer savings) is 14.1 mils per kW-hr for electricity which is sold to Americans. For an SSPS that has a capacity of 10 GW and an assumed utilization of 95 percent, this produces annual benefits of $1.173 billion. Power sold to foreigners yields 13.6 mils of benefits per kW-hr which amounts to $1.132 billion annually for each SSPS. All the power produced in the first 2 years after the initial terrestrial SSPS is built is sold to the U.S. Afterwards one-third of the power produced is sold abroad. An SSPS is assumed to begin to produce power the year after it is completed. As an example, table 6-12 shows that in year 20, 5 terrestrial SSPS's are producing power. The benefits obtained are therefore $5.783 billion.

Subject to certain qualifications discussed below a project should be undertaken if and only if the value of its benefits exceeds the value of its costs (see ref. 9). It is important to include all benefits and all costs, even those which are not normally expressed in monetary terms, such as the value of any damage done to the environment. In our society there is usually a positive interest rate. This is a reflection of the fact that society values the consumption of a commodity today at a higher value than the consumption of the same commodity in the future. This fact must be taken into consideration when the value of benefits and amount of costs are determined. To do this the benefits and costs which occur in the future must be discounted. For example, if a project pays as benefits or has costs amounting to $B in every one of n + 1 consecutive years, then the value of the benefits or what is technically called the present value of the benefits is equal to:

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where the benefits and costs are measured in real dollars (that is, dollars of constant purchasing power) and where r is the real discount rate.

Under certain idealized conditions the real discount rate is the same as the real rate of interest. The latter is essentially the rate of interest observed in the marketplace less the rate of inflation. Empirically the idealized conditions needed to make r equivalent to the real rate interest do not hold, resulting in a considerable divergence between these two parameters. The size of this divergence and hence the appropriate value of r is the subject of an extensive, unresolved debate among economists. The value of r which is currently used by the Office of Management and Budget is 10 percent. This is considered by most economists to be reasonable if not conservative.

Having introduced several concepts, it is now possible to be precise about what is meant by the benefit-to-cost ratio. It is the present value of the stream of benefits divided by the present value of the stream of costs. When this ratio is greater than one, then the project, subject to certain qualifications, is worthwhile. It is worth noting that if a benefit-to-cost ratio is, for example, 1.2, then if the costs in every year of the program were increased by as much as a factor of 1.2, the project would break even in the sense that the benefits would equal the costs where the costs include a real rate of interest equal to the real discount rate.

There is no reason why a project cannot be of infinite length having an infinite stream of benefits and costs. Normally, the present value of these streams and hence the benefit-to-cost ratio is finite. In the space colonization program a 70-year period is selected, not because a finite period is needed but for other reasons. In particular, if one goes too far into the future, various assumptions begin to break down. For instance, a 5 percent growth rate in electrical power cannot continue forever, especially since much of this growth rate is due to a substitution of electricity for other forms of energy. An additional consideration is that when employing a real discount rate of 10 percent, whatever happens after 70 years has little impact on the benefit cost ratio.

The term payback has been applied to a number of differing concepts. The most common form of usage is adopted for this study; namely, that payback occurs when the principal of the original investment has been repaid.

APPENDIX H

ENVIRONMENTAL IMPACT OF MICROWAVE POWER TRANSMISSION

The proposed system to transmit solar power to the Earth's surface involves microwaves as the conduit of energy beamed from Earth-orbiting solar power stations through the atmosphere. Primary concerns about the impact upon the environment of such a system are:

  1. Beam drift
  2. Biological effects of radiation
  3. Electromagnetic interference

The microwave beam from the satellite solar power station (SSPS) is triggered by a pilot signal beamed from the center of the receiving antenna to provide the necessary phase control to produce a coherent beam. Otherwise, if the beam were to drift, its coherence would be lost, the energy dissipated, and the resulting power density would approximate normal communication signal levels on Earth (ref. 10).

Radiation effects depend on the power density of the transmitted beam which in the present system is designed for a peak of 10-100 mW/cm². In the United States and other nations of the Western world, 10 mW/cm² is an accepted standard for radiation exposure, while the Eastern European nations have placed acceptable exposure limits as low as 10 µW/cm² (ref. 4). It is noted (ref. 11) that the U.S. Department of Health, Education and Welfare has set a limit for new microwave ovens of 1 mW/cm² at a distance of 5 cm. The major biological effect of continuous microwave irradiation at levels between 10 and 100 mW/cm² is believed to be heating. Human exposure can be minimized by providing shielding for the personnel stationed in the rectenna area and by limiting public access to regions in which the Gaussian power distribution is below acceptable radiation levels. The system could be designed so that the microwave power density at 10-15 km from the center of the beam would be at most 10 µW/cm², meeting the lowest international standards for continued exposure to microwaves. Passengers in aircraft flying through the beam should be more than adequately protected by the metallic skin as well as the short transit times involved. By fences and a metallic screen under the rectenna, plant and animal life can be protected. Birds flying through the beam would experience elevation of body temperature (ref. 4). Radiation effects do not appear to present substantial problems to transmission of power from space, but more research is required.

System efficiency and lack of atmospheric attenuation suggest 10 cm as the wavelength for transmission. The corresponding frequency, 3 GHz, can be controlled to within a few kHz (ref. 11). Due to the high power involved, electromagnetic noise could potentially interfere with radar, microwave and radio frequency communications, and possibly with radio astronomy. This will necessitate further restrictions near the rectenna.

REFERENCES

  1. U.S. Atomic Energy Commission, Office of Information Service, Technical Information Center: Nuclear Reactors Built, Being Built or Planned in the U.S. as of June 30, 1974, Prepared by the Office of the Assistant Manager for Energy and Development Programs, May 1, 1975 (TID 8200-R30).
  2. Energy Research and Development Administration: A National Plan for Energy Research, Development, and Demonstration; Creating Energy Choices for the Future, (Vol. 1: The Plan), 1975, U.S. Govt. Printing Office, Washington, D.C. 20402, ERDA-48.
  3. Public Utilities Fortnightly, Feb. 28, 1974.
  4. Glaser, P. E., Maynard, O. E., Mackovciak, J., and Ralph, E. L.: Feasibility Study of Solar Power Stations, NASA CR 2357, 1974.
  5. Asher, H.: Cost-Quantity Relationships in the Airframe Industry, Rand Corporation Report R-291, Santa Monica, Calif., 1956.
  6. Hirsch, W. A.: Firm Progress Ratios, Econometrics, 1956.
  7. Manne, Alan S., and Yu, Oliver: Breeder Benefits and Uranium Availability, Nuclear News, vol. 18, no. 1, Jan. 1975, pp. 46-52.
  8. Hudson, Edward, and Jorgenson, Dale: Tax Policy and Energy Conservation, Discussion paper no. 395, Harvard Institute of Economic Research, Harvard University, Jan. 1975.
  9. Prest, A. R., and Turvey, R.: Cost Benefit Analysis: A Survey, The Economic Journal, vol. 75, Dec. 1965, pp. 683-735.
  10. Glaser, Peter E.: The Satellite Solar Power Station — A Focus for Future Space Activities, Presentation to the Subcommittee on Space — Science and Applications of the Committee on Science and Technology, U.S. House of Representatives, July 22, 1975, in its Future Space Programs, vol. 2, 1975, pp. 431-459. (Also issued as American Astronautical Society paper 75-281.)
  11. Ehricke, K. A.: The Power Relay Satellite, a Means of Global Energy Transmission Through Space, E74-3-1, Rockwell International Corporation, El Segundo, Calif., 1974.
  12. The costs in this article are in terms of 1974 dollars. All costs referenced as coming from it were adjusted to 1975 dollars by taking into account the inflation that occurred in the energy market during 1974. These adjusted prices were obtained from Manne by personal communication on Nov. 17, 1975.
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