Should I do the inclination burn closer or farther from the parent body?

[Themohawkninja]

This is a question that I have wondered for a long time. Is it better do to the inclination burn when in a very high orbit, or a very low orbit, or does it not matter at all?

Edited August 7, 2013 by Themohawkninja

[LameLefty]

The delta-v requirements to change the inclination of an orbit vary significantly with orbital height. Doing the burn at a very high apoapsis is a LOT cheaper, fuel-wise, than doing it at a low orbital altitude.

[Stochasty]

The slower you're moving, the cheaper it is to change inclination. As for whether or not "higher is better" it depends on how steep the inclination change you need to make is; sometimes it's more efficient to do it where you stand, sometimes it's more efficient to boost yor orbit first and then make the change. This is obvious for the case of a 180 degree inclination change; it'd take about 4500 m/s to manage in LKO, but you can do it for under 2000 m/s by boosting your orbit to the edge of Kerbin's SoI, making the change, and then dropping your orbit back down.

The math here is very similar to the math for bielliptic transfers. Sometimes they're efficient, sometimes they're not; it depends on how large a difference there is between your current orbit and yourtarget orbit, although I don't remember the exact formula off of the top of my head.

[King Arthur]

Generally speaking, most orbital manuevers are better done at a higher altitude if you're flying there as the associated slower velocities mean you spend significantly less dV than you would at lower orbits.

[asmi]

Generally speaking, most orbital manuevers are better done at a higher altitude if you're flying there as the associated slower velocities mean you spend significantly less dV than you would at lower orbits.

True, but that's not always possible - for example inclination changes need to happen when the vessel cross equator, otherwise only higher inclinations are available and LAN will change as well, LAN changes have to happen in most nothern/southern points of orbit - otherwise inclination will also change.

[purpletarget]

The cut-off is generally around 60 degrees. If you're torquing/inclining your orbit more than 60, then you'll save dV by boosting your Ap and doing the change way out there. Anything under 60ish, just stick altitude you're at.

[Mr Shifty]

The formula for an impulse inclination change cost is simple:

2 * current_velocity * sin (change_in_inclination_angle/2)

If I want to change my inclination by 45 degrees and I'm currently going 2246 m/s, it will cost 2 * 2246 * sin (45/2) = 1719 m/s.

So you can see that the cost scales directly with velocity. The break-even point will vary with initial and final altitudes, but for an initial altitude of 100km, it costs ~ 920 m/s to raise your apoapsis to the edge of Kerbin's SOI and a similar amount to lower it again. Your speed at apoapsis would be about 25 m/s, so inclination changes would be trivial. So working backward, somewhere around 55 degrees of inclination change is where it's more efficient to raise your orbit to change inclinations.

[arq]

If you don't care about lowering your final orbit altitude on the opposite side of the body, you can get away with as little as

delta_V = current_velocity * sin(inclination_change)

by burning at double the angle by which you wish to change your orbit, but this will quickly leave you on a suborbital trajectory so this is rarely useful unless you are parked in a high circular-ish orbit and wish to move to a lower orbit at a different inclination. Note that for angles >=90deg this just means burning full retrograde to a full-stop (a 0km*Xkm orbit can change inclination for free at X), which will just have you plummet to the surface.

[Umlüx]

so its not only the height, but the speed too...

say, if i want to visit Bop... given the high orbital speeds in low jool orbit (i usually aimed my probes for a 200-300km orbit).. i should better aim for a higher orbit (when aerobraking) and then make the inclination change?

[blizzy78]

so its not only the height, but the speed too...

No. It is only about your velocity. Orbiting at higher altitudes just means your orbital velocity is lower.