What role does terminal velocity play in a rocket launch?
The section about terminal velocity on the KSP wiki says that terminal velocity “represents the speed at which a ship should be traveling upward during a fuel-optimal ascent.” It also has a table of terminal velocities at various altitudes, calculated based on gravity. In particular, it says that terminal velocity in Kerbin’s atmosphere at 10km is about 240m/s.
In a few places on KSP-related forums, I’ve seen people claim that for fuel efficiency, one should reduce throttle in the lower, thicker parts of the atmosphere to avoid exceeding terminal velocity; in particular, I’ve seen people say that one should avoid going faster than 240m/s below 10km altitude. I suspect that this advice is wrong, but I’d like to make sure my own understanding is correct.
Terminal velocity is the speed where drag equals thrust. Drag is proportional to speed while thrust typically isn’t, so as you go faster, drag increases until it cancels out all the thrust and you can’t go any faster. Drag is also proportional to atmospheric density, so terminal velocity varies with altitude. But crucially, terminal velocity is also proportional to thrust.
If you’re a skydiver and you jump out of an airplane, you can fall until you reach terminal velocity based on your body’s drag coefficient. When you open your parachute, you’ll slow down since you’ve greatly increased your drag without changing your “thrust” (the downward force of gravity), reducing your terminal velocity below your current speed. But if you’re wearing a rocket pack instead of a parachute, and you point it at the ground and ignite the rocket, you’ll speed up: you have more downward thrust now, and it takes more speed to produce enough drag to balance it out. Your terminal velocity has increased.
This tells me two things:
- It’s impossible to accelerate past terminal velocity; you can only asymptotically approach it. It makes no sense to reduce throttle to avoid exceeding it, because that can’t happen. (Reducing throttle during flight will actually reduce your terminal velocity, possibly below your current speed, causing you to exceed it.)
- The 240m/s number (and the rest of that table on the wiki) is only applicable to an unpowered fall through the atmosphere, where the “thrust” is just gravity. It’s not relevant to a rocket-powered ascent.
However, Kerbal Engineer has a readout that shows terminal velocity during flight, and it seems to be proportional to thrust, but with a high-enough thrust-to-weight ratio I’m able to exceed it by a significant margin. I don’t know whether that readout is correct, and if it is, how it’s possible.
Speaking of TWR, my understanding is that higher is better for fuel efficiency, since more thrust gets you to orbit faster and you spend less fuel on just counteracting gravity. But if I reduce throttle to try to stay below 240m/s until I reach 10km, this results in a rather low TWR, barely above 1.0 at liftoff.
In light of all that, what I’d like to know is: for optimal fuel efficiency, is there a specific speed vs. altitude profile that I should try to follow during a launch? Or should I just get my TWR as high as possible to get into orbit fast, and ignore my actual speed (as long as I don’t go so fast that I burn up)?
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Basically, you are reading about an old rule of thumb from the original aerodynamics model where terminal velocity was roughly the ideal ascent speed. This is no longer true under the new aerodynamics model, because of how drag is now calculated as you move. Here’s a related discussion
on reddit. Ideal ascent speed is now variable by stage and angle and should be determined via testing and possibly math
The ideal ascend speed is still the terminal velocity of the rocket. This hasn’t changed. However, what did change is that calculating the terminal velocity isn’t as trivial anymore with the new aerodynamics model, because now it doesn’t depend on altitude alone but also on how aerodynamic your vessel is designed and how it is oriented.
But in my experience, as long as you try to build your rockets aerodynamically (nose-cones on everything, any radially-mounted equipment in service bays, more complex payloads hidden in aerodynamic shells), you will have a hard time getting even close to terminal velocity in most flight phases. So just go for maximum thrust.
Look at the equation for terminal velocity:
terminal velocity = sqrt(2*mass*acceleration / (area * air density * drag coefficient))
Pressure drops exponentially with altitude, so even if you were stuck at terminal velocity, just wait a while. The very next instant your altitude will increase linearly, your pressure/density will drop exponentially, and your terminal velocity will increase faster than linear. If terminal velocity does become an issue, your altitude will still increase exponentially, but it will be capped to a certain exponential curve. By the time you reach vacuum, your velocity at that altitude will be invariant to increases in thrust.
As with Lawton, I too believe terminal velocity is not very useful here. I tried some of my own tests with sounding rockets (I encourage anyone to do the same). Using KSP version 1.2, I put 9 vector engines on a small rocket, flew it straight up at different throttle levels, and when I reached the height of Kerbin’s atmosphere, I recorded my apoapsis. I never saw a cap to apoapsis, not even a sign I was reaching one. Apoapsis increased linear to throttle level, maybe even subtly exponential. However, I did burn up a bunch of rockets in the process, so there are good reasons to reduce thrust, just none concerning terminal velocity.