What is the most efficient way to make large orbital plane changes?

[Meithan]

NJC2:

Your orbit cleanup initiative is impressive for someone that just started playing KSP! In my opinion orbital rendezvous is one of the hardest skills to acquire when you're starting out. Kudos on achieving that.

As for reducing inclination change delta-v, you can certainly do the "raise apoapsis" trick, but I felt like adding that the best way to save on delta-v is to launch directly into an orbit with the desired inclination (as somebody else already mentioned). You may lose the "free" delta-v from Kerbin's rotation (174 m/s), or even may be required to pay it (if you're launching west), but that's peanuts compared to the inclination change delta-v while in orbit (and it can be paid for by the launch rocket anyway, which lifts off the burden to your final spacecraft).

Launching from the equator, you can reach any orbital inclination (including retrograde orbits) by simply pointing your rocket in that direction when starting the gravity turn (well, approximately at least; Kerbin's rotation will alter the final result a bit).

Is it really necessary to go as far out as the Mun or Minmus for an efficient inclination change

The higher the apoapsis, the more the delta-v saving. Push it all the way to the limits of Kerbin's SOI (~80,000 km) if you want the minimal delta-v requirement and don't mind timewarping a lot (and having to be careful to avoid encounters with the moons). Yup, even factoring in the cost of raising the apoapsis that high, you'll end up saving delta-v in the end. It may be counterintuitive, but it's due to one thing (which is the lesson to be learned here, I suppose): inclination change maneuvers are very darn expensive!

One thing to note, though, is that you get diminishing returns (in delta-v saving) as you raise the apoapsis more and more. The difference in delta-v saved between using a 4000 km apoapsis and a 80,000 km apoapsis is less than 200 m/s. Probably not worth it. What you did (raising the apoapsis to ~ keosynchronous altitude) was probably pretty efficient.

Edited November 24, 2013 by Meithan

[NJC2]

I just finished some minor cleaning up tonight. I refueled the de-orbiter with just fuel and whatever monopropellant was left from the refueling craft after docking. When I designed the MODO, the first one I sent up had a "manufacturing defect" that I didn't catch until it was in orbit and trying to dock with the module. Somewhere in the VAB while re-arranging the bottom set of RCS thrusters, the symmetry reset to single, so it went into orbit missing 3 RCS thrusters. I fixed the design and launched a second one, but left the old defective one in orbit since it had precious fuel on it. I had already sucked it's main tank dry, but it had almost a full tank of mono-propellant. That's why I only refueled the main tanks and a tiny bit of RCS. I intercepted the defective MODO and docked to retrieve its monopropellant before de-orbiting it (removing the last of the debris from orbit), which proved to be a little tricky since the refueling ports are on the sides of the craft. I managed to pull it off though.

NJC2:

Your orbit cleanup initiative is impressive for someone that just started playing KSP! In my opinion orbital rendezvous is one of the hardest skills to acquire when you're starting out. Kudos on achieving that.

Thanks for the kind words. I did watch a video of someone doing an orbital rendezvous and docking before I tried on my own. It only showed one method of intercepting from a lower orbit and to something in a higher circular orbit. It did teach me enough to figure out how to do other intercepts on my own. After doing it a few times I don't find it that hard. I couldn't do it without having a map view showing ascending/descending nodes and intercept points, along with using the maneuver node to play with.

While I like to try and do things efficient, sometimes you just have to strike a balance between efficiency and time. I know I don't do the intercept maneuver the most efficient way by accelerating time and waiting for the two objects to orbit several times and get a close encounter before making the final intercept burn. The way I'm doing it is by first matching inclination, then putting my one of my apsides (I'm not that smart, I had to look up the plural of apsis) on the target's orbit, make a burn at the intercept node to raise my Ap up so I swing out and catch it on the next orbit. I play around with the maneuver node a bit to find out about how much I'll need to burn, but I don't use the node to make the burn. Whenever I've relied on the maneuver node, it never comes out right, so I manually start the burn before the intercept node and watch for the target's position at intercept node to move around in real time. I stop the burn when it gets close to the intercept node, and then tweak it a bit with small pulses of RCS to get it as close as possible (I usually get it within 500m or less). It saves time and doesn't require a large burn, at least for things in circular orbits. When intercepting those objects in highly elliptical orbits, I had to wait an orbit or two to get a good intercept without an insanely long burn.

As for reducing inclination change delta-v, you can certainly do the "raise apoapsis" trick, but I felt like adding that the best way to save on delta-v is to launch directly into an orbit with the desired inclination (as somebody else already mentioned). You may lose the "free" delta-v from Kerbin's rotation (174 m/s), or even may be required to pay it (if you're launching west), but that's peanuts compared to the inclination change delta-v while in orbit (and it can be paid for by the launch rocket anyway, which lifts off the burden to your final spacecraft).

Launching from the equator, you can reach any orbital inclination (including retrograde orbits) by simply pointing your rocket in that direction when starting the gravity turn (well, approximately at least; Kerbin's rotation will alter the final result a bit).

Launching things into matching orbits so far gives me more trouble than an orbital rendezvous. My first attempt was a total failure when I had to refuel the MODO in near polar orbit. I checked the heading of the target craft before launch, it was ~165° descending. So when I launched the refueling craft, I made the gravity turn to 165°. When I switched to the map to see my orbit forming, the orbit was drifting off to the east at what looked more like around 140°. As I was making heading corrections trying to save the launch I had to drop a booster stage which collided with my main engine. I realized the orbit being off must have been to do with the rotation of Kerbin, so on the second try I guestimated and turned farther south, which put me closer, but I still had to keep making heading changes as I ascended. I got lucky though and was able to make it directly into a matching orbit only off by 0.5° of inclination. There has to be a way to calculate what heading to launch in to achieve a specific orbital heading. I was going to make another post if I couldn't find an answer by searching (which I haven't done yet).

It probably would have been more efficient/economical to launch another craft into the offset, retrograde orbit of the last two pieces of debris, but I designed the MODO to stay in orbit and be re-useable so I wanted to make use of it instead of launching something else. All but two of the things I was de-orbiting were in low equatorial orbits, so I cleared them first. Counting the fuel required to launch another craft into that orbit with what I would have used if I had done the inclination changes right, it may have be close. Considering that after I refueled, I made the last 70° of inclination change, intercepted and de-orbited two pieces of debris, then returned to within 5° of an equatorial orbit on one Rockomax-32 tank. Doing it the sloppy way I did, it required re-fueling two times, but if I had done it right to begin with, I think I could have performed the full inclination change, de-orbited both debris and returned to equatorial orbit without re-fueling, or at least one re-fueling which may have been equal to the fuel required to launch a separate craft. I may just test that out of curiosity. I can backup my save and see how large of an inclination change I can make with the fuel on board compared to what it would take to launch another de-orbiter in a retrograde orbit.

I didn't need to return it to an equatorial orbit after finishing it's mission. I considered leaving it where it was until I needed it again, but I decided to go ahead and bring it back to an equatorial parking orbit. I can detach the de-orbiting module and re-task the craft for something else. I'll leave the de-orbiting module in orbit in case I need it though. I'm thinking I may use it to go to the Mun, since all I would have to do is design the lander and send it up to attach to the already fueled giant rocket in orbit.

[Meithan]

Launching things into matching orbits so far gives me more trouble than an orbital rendezvous. My first attempt was a total failure when I had to refuel the MODO in near polar orbit. I checked the heading of the target craft before launch, it was ~165° descending. So when I launched the refueling craft, I made the gravity turn to 165°. When I switched to the map to see my orbit forming, the orbit was drifting off to the east at what looked more like around 140°. [...] There has to be a way to calculate what heading to launch in to achieve a specific orbital heading. I was going to make another post if I couldn't find an answer by searching (which I haven't done yet).

Technically, the launch direction (called the launch azimuth, β) for a given desired orbital inclination i depends on latitude Õ as follows (according to the Orbiter wiki):

From the equator (Õ=0), the launch direction is intuitively "the same" as the desired inclination. If you want a 30° prograde orbit, launch 30° north of east, which is equivalent to a launch azimuth of 60° (remember azimuth is measured clockwise from North=0°).

But even this is assuming that (1) the launch is an impulsive maneuver that occurs instantaneously and (2) the planet isn't rotating. Of course, neither of these is true in practice. Point (2) can be factored in the calculation (see the Orbiter wiki article for the full details), but taking care of (1) would require a much more complicated trajectory planning that would depend on the parameters of the rocket and computer precision to execute it.

An alternative approach is to use KER or MechJeb to have a readout of the orbital inclination as you launch. A formula like the above can give you a general idea of the launch direction. Then, as you climb, you can adjust your trajectory by looking at the real-time updates of the current orbital inclination. That's enough to generally get within a couple degrees of the intended orbit. Then you can do the final correction at the next ascending/descending node.

By the way, I was investigating the efficiency of orbital inclination adjustment yesterday and I found out that for inclination changes below about 48°, doing the "increased apoapsis trick" is actually more expensive than doing the inclination change in your initial orbit. The trick is only good for large inclination changes, it seems. I'll make a post about it in the Science Labs subforum when I have some time to check the calculations and write it up.

[KvickFlygarn87]

Bi-elliptical all the way. And a bit further.

[Bug_]

Just posting this picture, just with a bit of fumbling around with the orbits I came across this, so it's one way to do it (it was about a 3 second burn to get out of the kerbin polar orbit, into the kerbin eliptical orbit, using the moon)

[Specialist290]

While the effort is undoubtedly appreciated, I think NJC2 has more than likely either solved his problem or since moved on in the intervening year and a half since this question was originally posted. Therefore I'll be locking this up.