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I'm trying to use Jool as Ulysses used Jupiter to insert itself into an extremely inclined polar solar orbit with a fairly modest amount of delta-V (direct solar polar insertion from Kerbin escape would take something like 15000 m/s of delta-V).

However, regardless of how I seem to tweak my Jool encounter, I can only get up to about ~40 degrees of orbital inclination (it seems happy to kick me 300 million km away from Kerbol, but not tip me any more). What's the key to have Jool give me an extreme orbital inclination?

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I'll have a video demonstration up hopefully tomorrow showing how I got a probe in a Kerbol circular polar orbit with an orbital radius close to the mean orbital radius of Jool. Suffice it to say, gratuitous use of maneuver nodes was had. – MBraedley Mar 8 '13 at 3:08
I have no idea what this game is, but it sounds amazing! – Ian Mar 8 '13 at 10:54
Yeah, so about that video I promised. My editing software has been fighting me all weekend. I would need a breakthrough to make it happen. Sorry. – MBraedley Mar 11 '13 at 0:03

So you're correct in using Jool for a gravitational slingshot into a high inclination, and you're also correct in assuming that you can only get about 40° from an encounter prior to switching the spheres of influence. Trying to set up burns prior to switching SoI is an exercise in futility. What you do want to do is set up your encounter so that you're coming in close to over a pole. 200m/s early (about a month out from switching SoI) can save a lot down the road.

Getting your trans-Joolian burn correct is actually one of the biggest factors for saving fuel. Not only do you minimize delta-V on the transfer burn, but you'll also minimize delta-V on the polar injection burn. You want to start your transfer about 65° after crossing the terminator into night when Jool is leading Kerbin by about 95°. When it comes to the phase angle, burning too early is really bad, as delta-V costs go up exponentially with the amount of time before optimal. Burning late isn't so bad, as costs go up much slower (quadratically maybe? Don't know for sure). This is a utility for determining optimal burn patterns.

So you've done your transfer burn, and you've done your final correction burn before switching SoI, and you're just waiting those last few seconds before that Jool orbit line changes from yellow to green. When that happens, you'll want to immediately plop down a maneuver node not too far in front of you. You're basically going to be doing a bunch of min-maxing to get your inclination into the high eighties. First, set your incoming inclination for best result inclination. Next, add about 500m/s of prograde velocity. You're doing this because you essentially have to kill something like 4000m/s of horizontal velocity and turn that into vertical. Next, reduce your periapse using the ground vector until optimal. Rinse and repeat, adding the most velocity in the prograde direction. Eventually, you'll get to a point where the inclination of the resulting orbit is correct, but the periapse will be in the sun, or the apoapse will be way out of the system. You're three options are to try and fix it now, try to fix it at Jool periapse, or (easily) fix it once you achieve polar orbit.

It's a tough operation, but with patience and experimentation, you should be able to get it every time.

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I saw this video that made the case for switching to conic draw mode 0. I'd suggest watching that to see how early course adjustments can really reduce delta-V later down the line. – MBraedley Apr 2 '13 at 17:24

if you're no stickler for transit time you can do a multi-planet banking shot from an inclined orbit around kerbin. each shot, provided it's angled right, will put you closer to polar insertion at jool.

the maneuver controls(click on your orbit path and it'll say 'add maneuver') have a predictive pathing feature. learn to love it. it makes reaching other planets incredibly easy, no mechjeb needed. if you're really good a bare few hundred meters/sec delta shift can easily punt you around the entire system.

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