Path: StraightLine/ConstantThrust
% Optimal velocity ratio for straight-line mission This is the ratio of exhaust velocity to characteristic velocity, uE/Vc, to produce the given payload fraction. This is for a propulsion system characterized by a specific power in W/kg, exhaust velocity, and time of flight, so that Vc = sqrt(2*eta*P/m*tF) and the defining ratio is uE/Vc. This relation is independent of distance traveled, depending only on the rocket equation and the mass fractions. This formulation ignores the tankage mass fraction. The rocket equation is expressed via mass fractions, DV = uE*log( (1 + mE/mF) / (mP/m0) ) where mE is the engine mass, mF is the propellant mass, and the payload fraction lambda is mP/m0. Noting that mE/mF = (uE/Vc)^2 Vc = sqrt(2*eta*P/m*tF) we have the result that exp(DV/uE) = (1 + (uE/Vc)^2)/(lambda + (uE/Vc)^2) For every DV there is an optimum (uE/Vc) which maximizes lambda. This function saves the solution in persistent variables and interpolates the solution. It will generate the data on the first call of each MATLAB session. -------------------------------------------------------------------------- Form: cVc = OptimalCharacteristicVelocity(lambda); lambda = OptimalCharacteristicVelocity(cVc,true); [cVc,lambda] = OptimalCharacteristicVelocity; % return internal data -------------------------------------------------------------------------- ------ Inputs ------ lambda (1,:) Payload fraction, mP/m0 doInverse (1,1) Invert operation ------- Outputs ------- cVc (1,:) Ratio, uE/Vc -------------------------------------------------------------------------- Reference: Craig Williams, An Analytic Approximation to Very High Specific Impulse and Specific Power Interplanetary Space Mission Analysis, AAS Space Flight Mechanics Meeting, 1996 --------------------------------------------------------------------------
Common: Graphics/Plot2D
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