[Spaceships] Calculating Climb Rate

[vicky_molokh]

Greetings, all!

I'm trying to estimate the time required for a spaceship to exit atmosphere. For reasons of tech available, exiting atmosphere is more important to me than attaining a stable Newtonian orbit. Thing is, unlike the usual Blast Off calculation, the time spent overcoming air and climbing is no longer negligible. So I'm trying to refine the calculations. Some of them seem straightforward, others less so.

The simplest case seems to be a wingless high-thrust craft doing a vertical liftoff, in which case aerodynamic lift is effectively zero. At which point I can subtract local gravity from the drive's acceleration rating, and calculate top airspeed based on the remaining rating, calculate time required to accelerate and distance passed, then divide the remaining distance by top speed to get the approximate time taken.

However, what happens in cases of a winged craft blasting off with an acceleration comparable to or less than the local gravity? Or an atmospheric craft climbing using wings and thrust in general? We can easily calculate horizontal top speed that can be achieved by a winged craft (at which it maintains enough aerodynamic lift to compensate against gravity), but the more one pulls one's nose up, the less efficient aerodynamic lift becomes, at some point resulting in a negative climbing rate if thrust is less than local gravity.

So . . . how do I calculate that?

Thanks in advance!