Combining plane change with transfer burns

[guitarxe]

I read that supposedly the best way to arrive at a different inclination at a target body is to combine plane change together with the transfer burn, because that way the amount of dV you burn to change your inclination goes towards the transfer burn, and you pretty much get your inclination change "for free".

I've tried doing this with the Mun, but looks like either I didn't understand it or it doesn't work? If I try to place a node such that I arrive at Mun orbit at 90 degree inclination from Kerbin's orbit, I'm actually paying a very large amount of dV. About the same as the sum of inclination change at Kerbin and then the transfer dV amount.

But if I first burn to the Mun, and then do inclination change right at the border of the Mun's SOI, then the dV for that in total is much less. This makes sense since the cheapest way of changing inclination is at highest orbit, but why doesn't the combination method work?

[KarateF22]

One reason for this is because the Mun is moving. You do not need to shift your plane a full 90 degrees relative to Kerbin to achieve a polar Munar orbit, you only have to shift your plane between 10 and 20 degrees in tandem with an entry into the Mun's SOI while at maximum deviation from its plane distance-wise.

Additionally, plane changes are cheaper the closer to the Apoapsis you are as plane changes are a percentage modification of your total speed, you are slowest at your Apoapsis so it is cheapest there. This is why it seems cheapest to do as you enter the Mun's SOI, because it effectively is. The only time a plane change is guaranteed to be cheaper in tandem with a rendezvous setup burn is when at Apoapsis, however the closer to it you are the more likely it is that this is the case.

Edited June 13, 2015 by KarateF22

[FancyMouse]

Combining gives you good only if the two burns are close enough. Otherwise the Oberth effect will be much more important than the vector combining.

EDIT: I don't even know what I was talking about...

Edited June 13, 2015 by FancyMouse

[Orbital Vagabond]

The trick is to find the "sweet spot" where the dV cost is the lowest. On the one hand, the closer you are to semilatus rectum (line through the focus of the orbit and perpendicular to the semi-major axis), changes along the normal vector are most effective at changing the elevation at the apoapsis. However, normal burns are pretty expensive at the semilatus rectum because you're still pretty low, and hence moving pretty fast. So you've got to balance the effectiveness of a normal burn, which goes down as you approach the Mun (in your example) and the cost of the burn, which is also going down as you approach the Mun.

The good news is, it sounds like you've found a good spot near the transition. I'd bet you could save some dV by making the burn an hour or two before the Munar intercept.

Making the inclination change when you're initiating the transfer for a fair to good hohmann transfer is a bad place to make the normal burn for two reasons: It's where you're moving fastest, and it won't lead to much elevation change at the target.

Edited June 13, 2015 by Orbital Vagabond