Calculating reentry

[Mmmmyum]

So one of the big things I've been trying to teach myself the maths behind calculating reentry.

There's one hitch though, and that the coeefficent of drag changes as you slow down through the thickening atmosphere. I can get just about all the data needed from FAR, and I'm using the Earth sized Kerbin mod so the numbers should work.

Basically this is the thing I'm looking at http://www.faa.gov/other_visit/aviation_industry/designees_delegations/designee_types/ame/media/Section%20III.4.1.7%20Returning%20from%20Space.pdf, pages 8 through 12.

Could someone just show how I would do it?

EDIT: Also need to get the deceleration so a mod that shows that would be useful

Edited December 2, 2013 by Mmmmyum

[K^2]

First question. Do you actually understand all of the equations involved in computing drag and what to do with these? If so, read on. Otherwise, you need to brush up on basic mechanics.

Start with a capsule first. Besides orbital velocity, it only has one parameter to vary. Basically, re-entry angle. There might be more efficient ways to go about it, but with modern computers, just go for it. Take your ship, write equations for forces acting on it based on current velocity and altitude, and then use a numerical differential equation solver to compute trajectory. Compute loading factors and heating along trajectory, adjust re-entry angle and repeat. Do this for a range of possible entry angles, and use the data you get to establish the corridor. For the numerical solver, I'd use Mathematica. It has a lot of nifty symbolic algebra features that makes this kind of computation a lot easier.

Results probably won't be as reliable as you'd want if your life is going to depend on it, but you can definitely compute a plausible corridor for a simulation.

[Mmmmyum]

I understand the maths, some of it is a bit above my level though (currently doing IGCSE, and A levels next year). I just want to be able to mathematically calculate the trajectory of something returning from orbit, to the point that I'll be able to land at KSC

[tavert]

Cool thing to note: you can now get Mathematica for free on a Raspberry Pi: http://www.wolfram.com/raspberry-pi/

Not the fastest processor in the world, but costs a lot less than a proper Mathematica license if you don't have access to one through your school / employer.

P.S: I like your taste in music.

[diomedea]

I understand the maths, some of it is a bit above my level though (currently doing IGCSE, and A levels next year). I just want to be able to mathematically calculate the trajectory of something returning from orbit, to the point that I'll be able to land at KSC

Precision calculation of a trajectory, so to aim at a very specific point, is a well known problem in exterior ballistics (http://en.wikipedia.org/wiki/External_ballistics. A number of numerical models to achieve a good approximate solution do exist, though to achieve the required precision (e.g. as to hit a target with an artillery round at long range) corrective factors need to be found from experimental measures. But I believe you don't really need such extreme precision. Have a look at the model here, maybe you can find what you are looking for: http://www.bfxyz.nl/index.shtml.

Edited December 3, 2013 by diomedea