Most Efficient Way to Kerbin Escape?

[Wait- Was That Important?]

I'm curious as to whether flying in a straight line away from Kerbin is most efficient or rather is making orbit and burning at the Periapse most efficient?

I'm launching Ion driven probes and have been wondering, since they don't need any servicing in Kerbin Orbit, if I should change how I've done it in the past.

I really don't have the physics background to do the equations for this myself, despite playing KSP. Common sense would dictate that since Escape Speed is independent of direction, flying straight away would let you put the most energy into escaping Kerbin, rather than putting the horizontal energy, perpendicular to where you want to go, into making an orbit.

Assume that you're not using a Munar/ Minmus assist, as that just complicates things further.

[Malaugrym]

For ion powered devices, I generally make use of the Oberth effect and make several orbits, adding a little juice each time.

As for your assumptions based on common sense, I would revisit them, and think hard (no offense intended). Try to imagine the effect of gravity on a straight line.

[Nullspace250]

No,in fact you want to go as fast as you can horizontaly,because of the Oberth effect

I dont know the technical stuff,but Scott manley made a VERY OLD video on how to get the most efficient way to escape velocity

[Wait- Was That Important?]

I just can't seem to work it out- it is late here, and a Monday at that. I'll take your advice for now and then watch some videos about it, do some experimenting in the game later. Thanks for the help guys.

[Jason Patterson]

If you burn straight upward then you are fighting the force of gravity the entire time - your engine's thrust is being opposed by it and a fraction is simply canceled out. By burning horizontally you can add velocity without fighting gravity at all. On Kerbin you have to get above the atmosphere, so you can't simply burn horizontally straight off of the launch pad, but on the Mun (or other small bodies with no atmosphere) this sort of approach is viable. Check out gravity drag for more information.

The most efficient escape profile is to make a gravity turn exactly as you would when getting to orbit, but keep burning until you have escaped. If you need to escape in a particular direction (very likely) then a very slightly less efficient method is to launch into a low altitude orbit (70-80km) and then finish your escape from that orbit. With a good ascent profile this is only a bit less efficient than a direct ascent, and it is far easier to get right.