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Rocket calculations



1. My understanding is that the parameter used is the "Exhaust Velocity" of
the propellant, as measured from the thrust generated on a static test stand,
Ve = F/ (dm/dt) , where the derivative is the rate of mass flow of the
propellants.
For a pulsatile rocket (discrete exhaust pulses), Ve is the velocity in
the rest frame of the rocket just before each pulse.

2. I have toyed with a few simple models of generating thrust by prpelling
masses backward, and find that Ve is NOT constant.
Models used were (a) massless compressed spring between m and M,
(b) Fixed change of energy E, from rest system, and (c) Fixed force over a
distance d (as measured along mass M).
These all give Ve of the form Ve^2 = K ( M )
__ __________
m ( M + m )
where (M + m) is the total mass before the pulse and m is the mass projected
backard. THe relative velocity is also a function of both masses.
Model (c) fits the case of a constant pressure gas acting on the mass m
over a fixed length exhaust tube ( or pea shooter).
Is the assumption that Ve is constant an approximation used xhen M >> m ?