9.7 factor, M,, to be explained later; and the mass of the payload carried outbound, MPLO" These masses are then related to the outbound propellant mass MPO by: In similar form,using the mass of payload carried inbound, MPLI' the corresponding equation for inbound propellant is found to be: It has been found by examing past aerospace systems that empirical curve fitting of known systems allows good approximation of vehicle component masses for preliminary design studies (9.5). From chis reference, tank mass can be found as a function of total vehicle stored propellant mass. The maximum propellant stored in the OTV exists at predeparture from low earth orbit,and consists of both MPO and MPI" Using empirical sizing factors T and M,, tank mass is found to be: There now exists above three equations with three unknowns, which will permit solving for the values of MPO' MPI' and M, in terms of known variables y, T, MPLI' MPLO' MF, and M,. However, explicit solutions of these equations are overly complex,and it is more convenient to write and solve the equations using matrix techniques. The three equations then condense to: The value of y has been fixed by the necessary transfer 6V. The magnitude of T is dependent on the contents of the propellant tank: .1129 for liquid hydrogen, and .0153 for liquid oxygen.
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