Burning Straight Up and Out

[Archgeek]

I had a bit of mind-thought regarding kerbin escape burns and whether it's feasible to just burn straight up just before sunset or dawn, depending on where you're going. Ostensibly the Oberth effect should favour craft doing their acceleration nearer the planet, and one has to climb out of the entire gravity well anyway, so gravity drag shouldn't be any more of an issue than it is for escaping from a circularized orbit. Experiments did not support that hypothesis, though.

To test the Thomas Foolery I slapped a kerbal flight engineer chip on the side of the Kerbal-X, gave myself an arbitrary target of 9Gm solar periapse, and tried three techniques, then recorded the delta-v left aboard:

1. gravity turn => low, circular orbit (around 70km) => escape parallel to kerbin's orbit
   
2. straight up and out, just before the sun hit the top of the VAB to make up for kerbin's rotation and give a good ejection angle
   
3. pre-noon launch => gravity turn => go east, no circularization
   

The first two were method one--first launch left 1717m/s left in the tank after a rather sub-optimal burn, and KE got mad on my second test, so I had to calculate the 1747m/s based on ship mass and fuel remaining.

Next I tested straight up and out--1532m/s, 1544m/s, 1538m/s remaining...seems like straight up and out sucks butts, even with a very good ejection angle.

Finally the gravity turn with aggressive escape--1698 w/ suboptimal launch timing, then 1770 w/ better timing. 'Seems the Oberth portion of the hypothesis holds.

So I see that there's something to getting orthogonal with the gravity field as soon as one can, but I'm not too sure why. Does burning orthogonally at periapse avoid gravitational losses climbing out of the gravity well altogether, rather than just delaying them? Does climbing straight up make too much of the burn happen further out from the planet, reducing the Oberth effect significantly?

I'm beginning to sense a brain fart on my part.

Edited December 14, 2014 by Archgeek

[GoSlash27]

It seems you've actually got it pretty-well indexed.

Were you to check your velocity at fixed times through the burn, you would find that your velocity is much higher during the prograde burn than the vertical at any point after you've gotten into the gravity turn.

In fact, even going *retrograde* will be more efficient than escaping vertical!

So you get a boost from having gone prograde and picking up the free velocity from the rotation, but that's not where the profit comes from.

The profit comes from expending your fuel while going as fast as possible (the Oberth effect) because changes in periapsis are ultimately dependent on your kinetic energy, not your change in velocity. And kinetic energy is proportional to the *square* of velocity.

So changing your velocity (i.e. accelerating) when you're going fast has a bigger effect than when you're going slow.

And since you were going prograde instead of up, your acceleration was much more rapid because you weren't having 10 m/sec^2 stolen from you by the gravity fairy during the whole burn.

Happy Saturday!

-Slashy

[Mesons]

[DATA!!]

So I see that there's something to getting orthogonal with the gravity field as soon as one can, but I'm not too sure why. Does burning orthogonally at periapse avoid gravitational losses climbing out of the gravity well altogether, rather than just delaying them? Does climbing straight up make too much of the burn happen further out from the planet, reducing the Oberth effect significantly?

I'm beginning to sense a brain fart on my part.

I wouldn't say so, I think you have gathered the data to back up the sensibility of Hohmann transfers. You've pretty much hit the nail on the head with your last comment (quoted) about climbing straight up--if you could instantaneously add velocity in any direction, they'd all result in the same energy change. Burning orthogonal to the direction of the gravity vector at periapsis maximizes the time spent burning with a high speed, which is restating the benefits of exploiting the Oberth effect.

[Pecan]

All these current threads discuss essentially the same topic:

http://forum.kerbalspaceprogram.com/threads/102606-Transfering-to-Mun-First-to-LKO-or-Directly-to-Mun

http://forum.kerbalspaceprogram.com/threads/102794-straight-up-vs-LKO-Oberth-effect

http://forum.kerbalspaceprogram.com/threads/102755-Does-brute-force-rendezvous-%28surface-to-target%29-save-on-dV

[Renegrade]

I did similar testing quite some time ago, although I was using an SRB-powered Jeb joyride of a rocket instead of the (hideous) Kerbal X.

My results were opposite: taking off at sunrise/sunset took significantly less delta-v overall to reach interstellar space. And by significantly less, I mean the rocket didn't have enough delta-v to reach escape velocity using a traditional launch, and reached past Duna's orbit with the sunrise launch.

One important difference (aside from my significantly greater launchpad TWR -- it was somewhere around four) is the use of FAR.

[Vanamonde]

This question about how to play the game has been moved to gameplay questions.

[Kryxal]

Oberth is about the relationship between speed, acceleration, and energy ... the faster you're moving, the more your kinetic energy changes by speeding up or slowing down, and an orbit (or hyperbolic flight path) is a path of constant total energy.

The gravity turn, on the other hand, is about getting more net acceleration from force: consider a TWR of 2.0 ... straight up, your effective acceleration is 1.0 G upward, while at a 30 degree angle your acceleration is sqrt(3) = 1.73 G horizontally, a fair bit more net force.

[Archgeek]

Okay, brainfart it is. Burning straight up and out does indeed eat more gravity drag, and going sideways benefits more from Oberth. (Gravity turn FTW)

All these current threads discuss essentially the same topic:

[uSEFUL THREADS I SOMEHOW AVOIDED FINDING]

Well well, 'not surprised by that, but the search system here leaves a bit to be desired--it likes to glom onto one individual word rather than the whole phrase. Pathetically, I see one of those was yesterday, with another one before that! And with similar science! This just keeps happening! Such absurdium.

Welp, that answers the heck out of a question that probably turns up too often around here. Thanks, everyone!