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I'm trying to figure out how to turn TWR through the flight of a stage into a function for programming purposes. Clearly TWR as a function of time must follow the form F(t, y) = Aert + Besy Note that I'm talking about a single stage; there are discontinuities upon staging. Also, I'm assuming instantaneous ignition and a fixed throttle. t is time, y is altitude, taking the launchpad as zero (for ease of calculation). The coefficient A is clearly an expression of the throttle, so let's set it aside. The B term is likewise a scalar relating to the Isp at sea level. The s term is fairly easy. It's a coefficient to altitude, intended to represent change in Isp with thinner atmosphere. But I'm still having some trouble with understanding how to use it; how does the atmosphere decay? It's clearly ln(something) depending on the celestial body, which means we could rewrite the second term as Bsy Similarly, the r term is related to the mass-flow rate of the engine(s), or, if you like, the mass-loss rate of the rocket. F is in Newtons. t is in seconds. y is in feet. This means r must be in Newtons/second and s must be in Newton-seconds. And at this point I'm lost. How do I go about giving specific values to my r and s terms? For example, let's say I have a rocket that at F(0,0) = 300kN. Therefore 300kN = A + B. Easy, but unhelpful. What else do I know about this rocket? I know the mass-flow rate. I know the specific impulse at sea level and in a vacuum. How do I derive the rest? For background (and because perhaps there's an easier way to do this), I'm trying to take a given, arbitrary rocket and calculate, to a rough approximation, a zero-lift ascent from Earth (or another celestial body, but let's skip that). Thanks to anyone who can help.
