Path: Orbit/StraightLine
% Finds duration, ideal power-limited rocket, straight-line trajectory
This is analytic except in the case of a finite, nonzero vF, in which case
fzero is used.
Power limit is the only constraint; thrust and exhaust velocity can go to
zero or infinity. Uses Leitmann's 1961 result that the optimal
acceleration profile is linear in time. The optimal can be either:
* Constrained fuel and time, maximized distance OR
* Constrained distance and time, minimized fuel OR
* Constrained fuel and distance, minimized time.
The acceleration profile is:
a(t) = A*(tF-tau-t)
a is acceleration, A is a constant, tau is a constant, t is mission time,
tF is the final time.
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Form:
[tF,A,tau] = SLPLFindDuration( xF, Pj, vF, mDry, m0 )
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Inputs
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xF (1,:) Final distance (km)
Pj (1,:) Jet power (eta*P, eta*sigma*mE) (W)
vF (1,:) Final velocity (km/s).
Rendezvous/insertion: vF = 0.
Intercept/flyby: vF = [], unconstrained
mDry (1,:) Dry mass: Engine, payload, tanks, structure (kg)
m0 (1,:) Initial (wet) mass (kg)
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Outputs
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tF (1,:) Final time (s)
A (1,:) Acceleration scale parameter, (m/s^3)
tau (1,:) Time between turnaround and tF (s)
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Reference: Leitmann, George. "Minimum Transfer Time for a Power-Limited
Rocket." Journal of Applied Mechanics 28, no. 2 (June 1,
1961): 171-78. https://doi.org/10.1115/1.3641648.
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See also See also: SLPLTrajectory
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