Also, I've always had trouble wrapping my head around why the gravity equation suddenly has a cubic in the denominator when you make it a vector.
Mostly, how do you mathematically model a path, such that you can change the curvature of it numerically? It seems to me that there are more possible paths than there are real numbers. What are your findings on that front? I believe the optimal ascent path is related to the TWR of the rocket through time, further obfuscating the issue. I read that you were working on optimal ascent paths now. But a large part of that is optimal ascent paths, which I don't know the math for. I want to transition over to a two-dimensional model, and port my Excel program over so I can start looking at optimal atmospheric craft designs. It's currently one-dimensional, and only predicts correct results if you thrust straight upward. The other is an asparagus generator, which does the same, with extra inputs for the number of side-stacks (an even number) and the ratio of mass between the center stack and the side stacks.Īs a mostly separate project, I have a MATLAB program that takes in thrust, total mass, fuel mass, Vac ISP, and Atm ISP to numerically solve a set of three differential equations that describe the height, velocity, and mass through time. There's two parts: One is a one-stage generator, which takes in an engine type (LV-N, LV-909, etc), the number of engines, the desired TWR, and payload mass, and lists out all of the tanks you'll need, and the resulting delta-v. I designed a program that generates rocket designs that maximize delta-v in space in Excel. I've been looking for months for some of these topics.