all costs, we only need assign some portion of the fixed cost to each mission. Since price should be fairly constant over the lifetime of the vehicle, we assign an equal portion of this cost to each mission. This places a term in the formula for the price of the vehicle cost times the time taken for a mission (the longer a mission, the fewer the number of missions to share the fixed cost). There is also another factor in this term from taking the present value of the costs over the lifetime of the vehicle. This factor is k in the formula below. The per mission fixed cost is where 7^ is the time for a single mission (measured in years), Cris the cost of a single vehicle, and k converts the quantity to the present value. The time taken in a mission is the transfer time for the mission plus the time for maintenance of the vehicle. The transfer time is calculated from the velocity change for the mission and the exhaust velocity and thrust to mass ratio for a given propulsive technology. Adding in the time spent waiting for a bum plus the time that will be spent in refurbishment between flights gives where tm is the time between taken for refurbishment, RTM is the thrust to mass ratii and ntprop is the mass of the propulsion system. The (2/365) term arises as an averag time spent waiting for a bum. RESULTS Combining the above expressions, we are able to arrive at the break-even price for a given technology. Slightly different equations arise for aerobraked versus nonaerobraked case. The formulae for an unmanned orbital transfer vehicle for both a conventional and an aerobraked system are given below. (Because of the nature of the calculation of present value, time quantities should be converted to years.) Areobraked case: Nonaerobraked case:
RkJQdWJsaXNoZXIy MTU5NjU0Mg==