[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!

[Anthony]

A spaceship that is using wings to reach orbit does not permanently exit atmosphere until it reaches orbital velocity, or at least close enough that its thrust is able to make up for the difference, though it might make suborbital hops.

Climb rate for airbreathing engines is mostly about specific power.

[vicky_molokh]

Originally Posted by Anthony

A spaceship that is using wings to reach orbit does not permanently exit atmosphere until it reaches orbital velocity, or at least close enough that its thrust is able to make up for the difference, though it might make suborbital hops.

I was actually considering it for calculation of suborbital hops.

Originally Posted by Anthony

Climb rate for airbreathing engines is mostly about specific power.

You mean the thrust-power-to-mass ratio? If so, assuming that a winged 'spaceship' has a thrust acceleration A (with A<G) and a top velocity V (with V>stall, obviously), how do I figure the climb rate?

[Anthony]

Originally Posted by vicky_molokh

I was actually considering it for calculation of suborbital hops.

Raw climb rate isn't that relevant there -- the way you make a suborbital hop is by turning, and you don't actually need any thrust to make the hop (though you have to have somehow reached sufficient velocity, which requires thrust unless you're skipping as part of atmospheric skimming or re-entry).

[vicky_molokh]

Originally Posted by Anthony

Raw climb rate isn't that relevant there -- the way you make a suborbital hop is by turning, and you don't actually need any thrust to make the hop (though you have to have somehow reached sufficient velocity, which requires thrust unless you're skipping as part of atmospheric skimming or re-entry).

I need to get past the point of atmosphere being trace to be able to freely accelerate past maximum airspeed (also to engage any drives that don't function in atmo, if such are to be invented in the setting within observable future).

[Anthony]

Originally Posted by vicky_molokh

I need to get past the point of atmosphere being trace to be able to freely accelerate past maximum airspeed.

That's... spaceships simplifying things (maximum airspeed with altitude is a smooth curve, not a sudden change).

I don't think this will really be much of a factor, it doesn't seem to require more than a few percent climb rate (particularly in comparison to other problems with how spaceships computes things, such as max atmospheric flight speed being totally wrong).

[vicky_molokh]

Originally Posted by Anthony

That's... spaceships simplifying things (maximum airspeed with altitude is a smooth curve, not a sudden change).

I don't think this will really be much of a factor, it doesn't seem to require more than a few percent climb rate (particularly in comparison to other problems with how spaceships computes things, such as max atmospheric flight speed being totally wrong).

Well yeah, that's making things playable.

A brute-force wingless vertical climb seems to be able to handle it in a matter of 1-6 minutes or so depending on thrust. But I remember accounts that for aircraft, reaching their typical altitude can take quite a while. So I'm curious how much longer it would take, thus curious about climb rate.

[Anaraxes]

The aircraft's thrust has to counter drag to keep the plane in the air. Excess thrust can be used to climb. Divide that by the weight of the plane. ((T - D) / W).

The complexity really kicks in if you want an accurate answer to pop out of the calculations. For real aircraft, "thrust" isn't a constant you find on a spec sheet. It varies with the speed of the plane and with altitude (and other atmosphere conditions like temperature and humidity). Drag also varies with altitude, and with speed, especially once you start talking transonic and supersonic speeds. The way prop planes change with these factors varies from turboprops which vary from jets (and presumably from other high-tech sources of thrust in Spaceships).

You could also look at it from the point of view of energy. Subtract drag from the power output of the engine, and then use that power to add potential energy in the form of altitude. But again, drag and how much power you need to counter it while maintaining lift is going to vary how much excess power you have to work with.