Oberth and potential energy when ascending

[NikkyD]

Help me out here,

i am playing around with http://forum.kerbalspaceprogram.com/threads/123114-Single-Turbojet-SSTO-Spaceplane and some question popped into my head.

because of the design and other limitations i end up with a trajectory that has an AP of 100km. When my jets top out its at 25km with about 1400 velocity.

Now some things are puzzling me.

The orbital speed is given as 1400 at 25km and as i get to the AP, which is about 2 to 3 min away it slows down to below 1100. This is not due to drag but because i am exchanging E_kin with E_pot (its what i am thinking, plz correct me if i am wrong).

Now if i want to follow oberth, i should thrust prograde asap at about 35 km when the drag is almost zero. However prograde now is about 20° up and if i thrust there, my AP rises and wastes energy.

If i aim down at -20° i can lower the AP and move it a bit away from me, buying me time with low TWR engines. But then i am about 40° off prograde making oberth less effective.

If i wait until about 1 min from AP and then do my about 2 min thrust it would be the standard but my AP will stay at 100km and for the challenge i only need 70.

The initial 100km AP is a given, so lets assume i can't do anything against that, only maneuvers after 25km are possible and the deltaV budget ofc is tight.

I know the theory about all the stuff... but i am lost right now and don't know where to start.

Edited June 6, 2015 by NikkyD

[Orbital Vagabond]

The orbital speed is given as 1400 at 25km and as i get to the AP, which is about 2 to 3 min away it slows down to below 1100. This is not due to drag but because i am exchanging E_kin with E_pot (its what i am thinking, plz correct me if i am wrong).

Primarily, yes, you're exchanging KE for PE, but you are still losing some orbital energy to drag as you ascend up to 70 km alt.

Now if i want to follow oberth, i should thrust prograde asap at about 35 km when the drag is almost zero. However prograde now is about 20° up and if i thrust there, my AP rises and wastes energy.

If i aim down at -20° i can lower the AP and move it a bit away from me, buying me time with low TWR engines. But then i am about 40° off prograde making oberth less effective.

If i wait until about 1 min from AP and then do my about 2 min thrust it would be the standard but my AP will stay at 100km and for the challenge i only need 70.

The initial 100km AP is a given, so lets assume i can't do anything against that, only maneuvers after 25km are possible and the deltaV budget ofc is tight.

I know the theory about all the stuff... but i am lost right now and don't know where to start.

It's always most efficient to add energy into your orbit by thrusting directly prograde, regardless of what the prograde direction relative to the horizon, so you're correct in being concerned about thrusting off prograde (in this case, radial). This isn't so much an issue with the Oberth effect as it is that you're canceling out velocity with a non-parallel thrust (basically vector math).

While thrust in your direction of travel is the most efficient way to add energy, it won't necessarily put you in the orbit that you want to be in. If you want a circular 70 km orbit, I would perform your orbital insertion right at 70 km thrusting mostly prograde, and slightly radial in (below the horizon). That way you won't go any higher than you need to, and will minimize losses due inefficient radial burning since your radial/vertical velocity vector will be lower (less vertical velocity to cancel).

If the suborbital trajectory with a 100 km Ap is locked in stone, I think this is the most efficient method to get a 70 km x 70 km orbit.

Hope that helps.

Edited June 4, 2015 by Orbital Vagabond

[Snark]

One thing you need to bear in mind here is that you have not just one, but two things you need in order to make a stable circular orbit. Energy is one (you've already got that covered in your post above), but the other is angular momentum. To be in an orbit that has a periapsis that's high enough, you need both "enough energy" and "enough angular momentum."

In an ideal world where you don't have to worry about aerodynamics at all (i.e. if Kerbin had no atmosphere), then your theoretical optimum minimum-dV way to get in a circular orbit at some altitude would be:

1. Have a craft with insanely high TWR (the higher the better)

2. Take off nearly horizontally, using a single momentary burst at extremely high acceleration (the higher the better), powerful enough to raise your apoapsis to the desired orbit height

3. Coast to apoapsis, then make a single prograde burn to raise your periapsis

When you have a gradual ascent with gradual gravity turn, or spaceplane that "starts" its rocket burn when it's already pretty high up, then the picture gets a bit messier. But essentially, you want to follow these rules:

- Always burn exactly prograde; this optimizes energy efficiency.

- To raise your apoapsis, do as much of your burn at as low an altitude as possible; this optimizes Oberth effect.

- To raise your periapsis, wait until apoapsis and then burn prograde (this optimizes angular momentum efficiency).

When I say "angular momentum", I'm referring to this:

http://en.wikipedia.org/wiki/Specific_relative_angular_momentum

Does this help?

[Orbital Vagabond]

In an ideal world where you don't have to worry about aerodynamics at all (i.e. if Kerbin had no atmosphere), then your theoretical optimum minimum-dV way to get in a circular orbit at some altitude would be:

1. Have a craft with insanely high TWR (the higher the better)

In theory, the "more thrust is better" is true, but in practice, TWR > 3 provides almost no dV savings.

[Snark]

In theory, the "more thrust is better" is true, but in practice, TWR > 3 provides almost no dV savings.

Oh yes, but I did say "in theory." The theoretical infinite TWR would be accompanied by zero-mass engines, which are also kinda scarce in KSP. In practice, even without atmosphere to get in the way, a too-high TWR would actually be bad, because it would mean you're wasting too much mass on engines.

It's also the case that in the theoretical, atmosphere-free ideal, you'd do your gravity turn pretty much immediately and do all your thrusting sideways, which eliminates much of the Oberth-effect benefit that you'd get from higher TWR.

However, all of that is kinda moot, and not directly germane to the OP's question, which is "how/when/in what direction should I burn optimally," which I think we're all pretty much agreed on. Thrust prograde to raise your apoapsis to the desired height, coast to apoapsis, thrust prograde to raise periapsis.

[NikkyD]

@ snark, i kinda know the standard procedure, question is more:

what if i have a rather high AP, should i coast and do the usual or can i somehow profit from it or even turn PE into KE, sacrifice AP for PE.

[ajburges]

If you are still in atmo, you can use lift to accelerate radially at the cost of prograde momentum. While horridly inefficient, radial thrust here can raise Pe at the cost of Ap.

Better is to coast. The higher the Ap the less dV needed to boost Pe out of the atmosphere. You can even leave it on the edge to aerobrake Ap to desired height.

There were some crazy .90 space planes that made orbit with crazy high Ap from jets then using jets with air trapped in intakes to raise Pe at that high Ap.

Edited June 4, 2015 by ajburges

[Snark]

what if i have a rather high AP, should i coast and do the usual or can i somehow profit from it or even turn PE into KE, sacrifice AP for PE.

Depends what your goal is. For example, if your goal is simply "have a periapsis above atmosphere," then your best course of action is still to coast to apoapsis and then thrust prograde to raise periapsis.

If your goal is something different (such as "be in a circular orbit above atmosphere" or "have periapsis above atmosphere, and also have an apoapsis lower than it already is"), then the answer might be different. What's the exact problem you want to solve?

[Slugy]

I can provide no maths, but while a steady max thrust burn at (or very near) prograde will be most efficient for a rocket that needs that time to build speed, burning below prograde (and even as low as below 0 degrees) can be the best option with vehicles that have excess thrust (which most do in KSP).

It really does depend on the thing you are flying.

[DarkGravity]

It might be helpful to look at an extreme situation. Imagine you have a very high AP, and the trajectory is nearly straight up. Let's say once you reach 10km, your AP is 225km and your projected crash site is right next to the launch pad. If you wait until you are at AP to start your burn, you won't have enough time to circularize your orbit. So you will want to start your burn before AP. But the problem here is that even a short while before AP in this scenario, the prograde direction is essentially radial-out (straight up) and won't do much to circularize your orbit. So you need to aim for a more radial-in trajectory rather than true prograde on approach to AP and slightly radial-out after passing AP. Only during the center of the burn should you be heading directly prograde, and even then only if you are interested in keeping your AP where it is. This scenario is present (too a much less extreme degree) in many launches, so keep it in mind when you try to find a balance between getting more energy into the orbit vs. shaping the orbit to your desired specifications.

At least, that's the way things appear to me. I'm not a rocket scientist.

[NikkyD]

I'm not a rocket scientist.

Then what the hell are you doing here ?

[Snark]

It might be helpful to look at an extreme situation. Imagine you have a very high AP, and the trajectory is nearly straight up. Let's say once you reach 10km, your AP is 225km and your projected crash site is right next to the launch pad. If you wait until you are at AP to start your burn, you won't have enough time to circularize your orbit. So you will want to start your burn before AP. But the problem here is that even a short while before AP in this scenario, the prograde direction is essentially radial-out (straight up) and won't do much to circularize your orbit. So you need to aim for a more radial-in trajectory rather than true prograde on approach to AP and slightly radial-out after passing AP. Only during the center of the burn should you be heading directly prograde, and even then only if you are interested in keeping your AP where it is.

Again, it completely depends on what your goal is. For example, if your only goal is "be in orbit" (i.e. raise periapsis above atmosphere, and you don't care what the orbit looks like otherwise), then sticking to prograde is still the best option.

Taking your example, where you're currently at 10 km and your apoapsis is already up at 225 km:

If you just coast up to 225 km and then thrust prograde to raise periapsis to 70km, you'll need to do a burn of 1958 m/s.

However, if you do a prograde burn while still at 10 km to raise your apoapsis to, say, 50,000 km, then you only need a dV of 1645 m/s to do that... and then once you're up at 50,000km, a dV of only 43 m/s will raise your periapsis to 70 km, for a total burn of 1688 m/s.

So even in that case, sticking to prograde-burns-only will save you a few hundred m/s of dV.

That said, there can be cases where burning off prograde can make sense, depending on the goal. Getting to a particular desired orbit can mean adjusting both your angular momentum and your energy, and while it's always most desirable to do burns at periapsis/apoapsis to maximize efficiency for both, sometimes you don't have that choice (e.g. if burning at periapsis would be the theoretical ideal, but you're on a suborbital trajectory and your periapsis is deep underground, then you may have to compromise if you're not a fan of lithobraking).