Selecting Launch Azimuth and Predicting Delta-V and Time to Rendezvous

[dlrk]

I've been playing KSP for years, and I can rendezvous routinely, but not with a consistent use of delta-v and timing, and launching to inclined orbits is still a bit of a challenge.

So, specifically, I'm looking for some guidance on picking a launch azimuth and predicting how much delta-v and time is required to rendezvous. The specific situation I have is launching from the Mun to rendezvous with a spacecraft out of the plane I'm launching into. How would I determine what heading will take me closest to the desired inclination, and what apoapsis would be the most efficient for the plane change? The main question here is the azimuth, I realize that balancing altitude change and plane change delta-v is probably pretty complex.

[A_name]

Lol I wish I knew what azimuth means.

[Tyko]

3 hours ago, dlrk said:

I've been playing KSP for years, and I can rendezvous routinely, but not with a consistent use of delta-v and timing, and launching to inclined orbits is still a bit of a challenge.

So, specifically, I'm looking for some guidance on picking a launch azimuth and predicting how much delta-v and time is required to rendezvous. The specific situation I have is launching from the Mun to rendezvous with a spacecraft out of the plane I'm launching into. How would I determine what heading will take me closest to the desired inclination, and what apoapsis would be the most efficient for the plane change? The main question here is the azimuth, I realize that balancing altitude change and plane change delta-v is probably pretty complex.

Lots to answer there. The easy one is "what apoapsis would be the most efficient for the plane change?".

The answer to that one is as high as possible. The higher it is the slower you're moving and that makes plane changes less expensive. In some cases it's actually cheaper to increase your AP above your target altitude, execute your plane change way out, then bring your AP back down afterwards.

[Plusck]

The rule for "what apoapsis would be the most efficient for the plane change" is pretty simple: as high as possible!

And the maths for plane changes on circular orbits is also (relatively) simple trigonometry. 90° plane change = sq.root(2) x orbital velocity (because it's a 1:1:root 2 right-angled triangle). 60° = 1x orbital velocity (because with a 60° angle, the vectors form an equilateral triangle).

There's a good thread on plane change here:

So basically, for a 60° plane change it'll be cheaper if you raise Ap to SOI edge. For a 30° plane change you stay where you are (it'll cost slightly more than half your orbital velocity since it's the base of an isosceles triangle therefore 2x sin(15)).

 

As for launching into a different plane from the target orbit: first question is why? Second question is what's the angle difference?

If you're launching from somewhere other than the equator that is less than 60° north or south, and want to reach an equatorial orbit, the best seems to be to launch due east, get Ap up to the equator at the target altitude, and circularise there. You'll therefore do the plane change a quarter orbit after your lift-off point.
So the same goes for any orbit on a different plane: if for some reason you can't simply wait to launch into that plane, then launch as close as possible to it so that you reach Ap just as you cross the target plane a quarter orbit later.
And if it's more than 60° difference, you definitely want to raise Ap well above the target altitude and just raise Pe to the target altitude while changing plane, then burn retrograde to circularise at Pe.

Since you are definitely not wanting to get up to orbital velocity before the plane change, the maths is going to be a lot more complicated, but the principle is relatively simple if you compare to the most efficient way to land at that same point from your target orbit: just try to do the exact reverse manouvre.

 

And finally, to rendezvous with a craft on another plane, that really depends on how much of an angle difference there is.

When doing LKO rescue contracts, I've found that ideally, you want to take off when the target is about 300-350km away. That means the target is near the end of the sea crossing before the land mass where KSC is located. Or when looking at Kerbin, it's about an eighth of the span of the globe.
And I've found that that sort of relative distance works well on all of the moons and planets.

To meet a craft in orbit, you really have to rely on the map view once you're sure you've cleared the terrain. Adjust your ascent so that AN/DN is located where your path will cross your target's orbit. Use radial in/out to get the target intercept markers to line up.

And then once you've lined up, the absolutely most efficient way to get into the exact same orbit as the target is to fire exactly along the target retrograde marker. No need for nodes or anything. By reducing relative velocity to zero exactly at the time you meet your target craft, you are making the most efficient burn possible by definition.

 

edit: oh yeah, didn't really answer the question about predicting dv and time from launch. To be honest I don't know and I'd be interested to know if anyone has good rules of thumb.
That will obviously change a lot depending on your TWR. In my experience, the place that I end up doing lots of refuelling, and therefore lots of ascents to orbit with fuel to join the orbiting station, is Moho. TWR on the way down to the surface is high, so I can consistently get from orbit to my desired spot on the surface for about 1050 m/s (approx 900 m/s actual dv cost, plus 150 m/s gravity losses and steering to land next to my miner). On the way back up, with much lower TWR, I seem to spend about 1200 m/s. So if I had a rule of thumb, it would be approximately 120% of orbital velocity without a major plane change.
Time to rendezvous is approximately one quarter of the orbital period of whatever you're meeting.
And I'd guesstimate that the cost of matching velocity with the target would be about 80% of whatever it would be if you were already in a circular orbit.

So for the Mun, with a 30° plane change, I'd guess 120% x 600 m/s to orbit and rendezvous, plus 250 m/s plane change (80% x 0.52 x 600) at the rendezvous, giving a total of 870 m/s.

Edited December 8, 2017 by Plusck

[Snark]

17 hours ago, A_name said:

Lol I wish I knew what azimuth means.

Compass heading, i.e. do you launch north, south, east, or west?  In other words, the angle measured around a vertical (i.e. perpendicular to the ground) axis.

20 hours ago, dlrk said:

The specific situation I have is launching from the Mun to rendezvous with a spacecraft out of the plane I'm launching into.

So, if I understand correctly, your situation is this?

• You have a craft that is on the surface of the Mun.
• Your target is in an inclined orbit around Kerbin.
• You want to launch from the Mun surface for a direct intercept of the target.

Correct?  Or is it something else, e.g. you're in orbit around the Mun, and/or the target is orbiting the Mun instead of Kerbin?  Or what?

Can you be more specific?

If the above understanding is correct (i.e. from Mun surface to Kerbin-orbiting target), then your optimal-dV strategy will be:  wait until the Mun has orbited to the point where it's sitting at its AN/DN versus the target's orbit.  Then launch at an azimuth that takes you directly into the plane of the target orbit.  Calculating that azimuth will involve some trig that is based on doing math about the inclination of the target, coupled with the Mun's orbital velocity around Kerbin.

Would prefer not to get into the gory mathematical details, though, until there's confirmation that this is indeed what you're trying to do.

[dlrk]

@Snark

Thanks for the reply, no need to get into that gory math, it's not the situation I'm in, I'll copy your bullet pointing for clarity.
 

• I have a craft on the surface of the Mun
• My target is an inclined orbit of the Mun
• I want to launch from the Mun surface to intercept the target, without waiting for the launch site to be in the plane of the target

@Plusck

Thanks for the info, I'll try aiming for a high apoapsis over the ascending node before circularizing.

As for why, it's pretty simple:

I have a lander on the Mun's surface with a day of supplies (USI-LS), and need to launch to rendezvous with a larger orbiter to return to Kerbin. The orbiter is in a very close plane, but not in plane enough to launch directly into the right inclination.

So, the question that really remains here is, how I determine the launch azimuth that will be closest to the target plane/inclination?

[Plusck]

10 hours ago, dlrk said:

So, the question that really remains here is, how I determine the launch azimuth that will be closest to the target plane/inclination?

Eyeballing it?

Basically what I said about that roughly eighth of a diameter of the body is the first thing.

So in this pic, if you really can't wait for the body to revolve under you, and the space station you're aiming for is about to come up on you, you'll want roughly this spacing (actually, I think you'd probably want to launch a touch earlier... you'll probably average about 3/4 of the velocity of the space station as you ascend... so therefore 1/8th of a diameter —meaning 1/4 of a quarter orbit difference in distance travelled— is only just enough to catch it) and you'd want to start heading in the direction of the orange arrrow (basically 45°). However, remember that that 45° apparent angle is mapped onto a sphere. In reality, where you lift off it will be a bit more than 45° and it will fall as you climb. So I'd aim for about 30° compass heading on lift off and expect it to settle down to 45° by the time I'd got up to a couple of hundred m/s.

If you switch to map view as soon as you've cleared terrain, you'll see AN/DN on your orbit as it starts lifting out of the ground. You just need to adjust your flightpath slightly so that AN/DN (in this case, DN) hits the target orbit where you expect your Ap to be.

And you don't want to hit the other orbit more than a quarter of an orbit around. Or less, but you'll probably always end up doing that...

 

Edited December 9, 2017 by Plusck

[bewing]

I think it's more about the timing, rather than the trig. Launching due east on the mun doesn't get you much, but you always want to launch due east anyway.

The orbiter is going to be coming around in its orbit in a nice regular fashion. So it all depends on how high the orbiter is, and how long it takes for your lander to get to that altitude.

So you launch east, burn until your lander's orbit intersects the orbiter's orbit (don't circularize), and find out how long it takes to get to that intersection point.

Then you subtract that time to find out exactly where your orbiter needs to be when you launch your lander from the surface.

Then (if you did that all correctly) both ships will be at the same spot at the same time. Go to target mode, hit the brakes really hard and dock.

And even if the timing is a little off -- it's still just a high-speed docking maneuver that you need to pull off.

 

Edited December 9, 2017 by bewing