Launching from high latitudes into high inclination orbits.

[Kobymaru]

Hi!

I have a base on Duna, that is at a latitude of 37° North,and a Space Station on an inclination of 45°.

The way that I currently launch is..."visual". I pick a good perspective in the Orbital view, wait until the base is under the stations orbit, and then launch onto a heading of around 45°.

Then I use KER to correct the inclination "on-the-fly".

This works "well enough", I end up within 2° of the target orbit.

 

I was wondering however, is there a better way? Could I calculate (or have a mod tell me) when exactly I have to launch? And which heading I have to put it into? I'd have to account for the velocity of the planet rotation.

Does anyone have nice math for this, or a mod that would help me with these launches on higher latitudes/inclinations?

 

Edit: Bonus points for an easy way to pick the launch time so that I end up rendez-vous'ing with the station with doing phasing orbits for ages.

Edited December 29, 2016 by Kobymaru

[FancyMouse]

Nope the whole thing is ascent path dependent, so there isn't any nice formula that can work in general case - even it's the same ship, if you fly differently you would need a different formula if there exists one.

However, since you mentioned Duna - my experience for Duna ascent is that Duna spins so slowly (~1/3 angular velocity of Kerbin's) so that it will just work to launch below the target orbit. So your launch spot should just work. 45 degree heading is also ok. But you probably want to watch for KER's "inclination to target" number (if you didn't have it on your KER panel you should set it up) once you get to about 100m/s. Then you should be able to manually steer the ship to keep that number well within 0.1 degree until in orbit. That should do the job.

[MaxL_1023]

Inclination matching is more complicated than launching at a heading matching the suggested inclination. Assuming you launch when you are directly under the space station, you have to match two velocities:

1. The Prograde orbital velocity (the component in the east/west direction)

2. The Normal orbital velocity (the component in the north/south direction)

If you hyperedit your spaceship to the stations radial altitude, find your relative velocity and cancel it, you will end up in the same orbit. However, this is not how you normally launch into orbit. The vector you need to cancel your relative velocity (assuming a gravity turn in the radial direction gets you to the right altitude) will NOT be equal to your target inclination. The planet's rotation will give you an initial velocity which you need to take into account. Over time, this initial velocity will deflect your course away from the proper heading. 

My rule of thumb is to try and launch from the latitude matching the inclination of the target - this lets you launch due eastwards and match inclinations once per planetary day. This is why you can launch to the moon from Cape Canaveral fairly easily (at least at certain times) - the moon almost passes over that latitude at its farthest northward excursion from the equator. 

If you are at 37 north and your target inclination is 45 degrees, you should launch about 9 degrees south of east when the station passes overhead (and is approaching its decending node). Burning at -8 will put you a little under 45 degrees of inclination due to the extra starting velocity from Duna's rotation - you need to burn a little farther southwards to cancel this out. Matching just after the ascending node will be more expensive and require a launch significantly north of east, with more of a normal component than the alternative path. 

I try to put space stations in polar orbits - it is a little more expensive to get into that orbit but much easier to rendezvous and allows any surface site to have two equal launch windows. 

[bewing]

If you know (by testing once) how long it takes your ship to get to orbit, and you know how fast the station is going (by looking on the map view) -- then multiply the speed by the time and divide by 2 to get the relative distance it will cover while you are ascending. After you've done the following maneuver once, see how much extra distance there was, and subtract that off your initial distance.

Target the station. Watch on the map view until it reaches this distance on a fairly close approach, then launch. Get your Ap up close to the orbital altitude with a bit of gravity turning and your standard 45 degree heading -- suborbital.

Now treat the entire rest of the exercise as a super high speed docking maneuver. Go to target mode, click Retrograde, and burn at full thrust. Each time you've knocked off maybe 50% of the relative speed or distance, go slightly off retrograde to push your retrograde marker reasonably close to being on top of the antiTarget marker, repeatedly, as necessary -- just as you would normally do. No need for KER. When I am burning locked to retrograde, I like to roll my ship in advance, so that (for example) the D direction is away from the antiTarget. So when I want to push my retrograde marker around, all I have to do it click SAS off and hit one button -- then click SAS on again.

And when your nose touches the station's docking port, dock.

I swear this method works great!

 

Edited December 29, 2016 by bewing