:D​

As it currently is (or was, I'm not clear on if this was implemented yet), ISP (engine efficiency) increases linearly with atmospheric pressure - which decreases exponentially with height. This means at very low altitudes, the engine uses a value close to the atm ISP, while it very quickly uses higher ISP as it gets above 15k. In the actual physics code, though, the current ISP controls how much fuel is used per unit of force - in effect, the fuel flow rate. This is governed by the following equation: dm = T/(((IF-II)*atm-IF)*G); where 'dm' is the instantaneous change in mass of the rocket, T is thrust, IF is ISP final, II is ISP initial, atm is current atmospheric pressure, and G is 9.82. This will change. Instead of fuel flow changing, the rocket will just be able to generate more thrust. However, they are basically isomorphic.

Found it. return Mathf.Clamp((float)(90.0 - Math.Pow((altitude - VerticalAscentEnd()) / (turnEnd - VerticalAscentEnd()), turnShapeExponent) * (90.0 - turnEndAngle)), 0.01F, 89.99F);

What does 'path shape' refer to, mathematically? I know it is not the speed of a linear increase in angle based on altitude or time. How would I obtain the angle as a function of height, given the start and end altitudes, and the path shape?

Mhoram, you are a wizard and scholar. I've been looking for months for some of these topics. I designed a program that generates rocket designs that maximize delta-v in space in Excel. 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. 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. As 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. It's currently one-dimensional, and only predicts correct results if you thrust straight upward. It includes gravity, drag, and thrust... just like you said in your paper. 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. But a large part of that is optimal ascent paths, which I don't know the math for. I read that you were working on optimal ascent paths now. 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. 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. 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. Do you know why it is?

Yo all, I really enjoy KSP and thought I'd come here since all of my friends look at me oddly when I try to tell 'em about my newest build. I've been playing KSP for around two years now, almost since it first released. But I still have a lot to learn. Welp, that's it.