Thanks for the replies, everyone.
Yeah I am shooting for 70,000ft (~21km) as the ultimate goal, not 117km or anywhere near that record. My goal isn't fastest or highest, but something completely different: rocket launches to 21km, ditches engine, deploys retractable wings, takes sweet video on the way down as a self-guided glider, lands gently on the ground.
However... there's going to be something like 4 evolutions of the project before we get there. My job is to figure out the science (how big of an engine do we need to reach 21km? what body shape optimizes lift on the way down, but minimizes drag on the way up? How much energy do we save by stabilizing the rocket on the way up instead of letting it spin like a football? etc)
A few people told me about KSP, so I checked it out but it seems like it isn't quite as customizable as people thought, or maybe they thought I was being purely hypothetical. Also I couldn't find any information on air drag (for launch). I know it's taken into account (sort of) for heating materials on the way into an atmosphere, but I think that's it. Air drag is a VERY complicated process from what I've gathered:
Drag depends on cross sectional area, and density of air, which depends on the local pressure of air, which depends on the altitude and temperature (which depends on altitude up to the tropopause, and is ~fixed thereafter for my purposes). And it also depends on the square of the velocity.
So... solving for velocity of a rocket after burnout is really going to be a 2nd order, non-linear, non-homogeneous differential equation. I've done it for the assumption of linear drag (which is not correct, but more correct than 0 drag), but I wanted to improve on that result, which is why I was hoping KSP could help. Oh well, back to the drawing board (i.e. textbooks, mathematica, etc)
