are more or less autonomous. For some of the subsystems their contributions and their costs can also each be considered independently of the other subsystems. In our case, we are interested in whether the choice of technologies to be used in the subsystems is independent of one another. This independence allows us to measure the costs of these subsystems, and in particular, the costs that are added (or subtracted) by using a particular technology for a subsystem. These costs are the basis of the comparison. The comparison is made based on the effect the use of a technology has on the break-even price charged for a single LEO to GEO and return trip. The break-even price is the price that must be charged such that the costs, both fixed and variable, match the revenue of the vehicle over its lifetime. Not all costs and revenues occur at the same time. The value of money is dependent on the time when it exists. To see this, consider the value of one thousand dollars now and the value of one thousand dollars one year from now. By taking that thousand dollars now, one can make it into more than one thousand dollars one year from now by buying a government bond. Then in one year one would have one thousand dollars plus interest. Clearly then, one thousand dollars this year is worth more than one thousand dollars next year. The present value is a way of normalizing the value of money at different points in time to the value of money now. This method is used to normalize all costs and revenues of our transfer vehicle. The formula for the present value of all the revenues generated by our vehicle over its lifetime is where / is the income for one year, r is the rate of interest, and L is the lifetime of the vehicle. The formula for the present value of the costs is where Cr is the cost of the vehicle and V is the variable cost accrued over one year. Using our requirement that costs and revenues are equal over the vehicle lifetime gives us Below, we expand this equation and convert to per mission costs and revenues. Now we will calculate the fixed and variable costs. The variable costs will be per mission maintenance and fuel requirements for the mission. Since vehicle maintenance will be highly sensitive to the specific design of the vehicle, we do not try to deal with it, but instead, hide it in a single variable vm. Approximating the At? requirements as independent of the propulsion system used, we can find the fuel requirements for the mission in terms of the mass of the vehicle and payload. where tnzis the fuel mass, m„ is the mass of the OTV, mu is the mass of the payload, and Au is the velocity change between orbits. The fixed costs arise from the cost of the vehicle itself. Since we are normalizing
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