The Long Burn Revisited : Departure Orbit Achieved!

[Brainlord Mesomorph]

The Long Burn Revisited : Departure Orbit Achieved

- or -

“It’s not the size of your thruster, it’s how you use it.â€Â

by Brainlord Mesomorph

A 70 ton rocket delivered on a direct Kerbin/Jool transfer using only one nuclear thruster.

Final departure burn was 1700 m/s and took 45 minutes. Departure altitude: 100km. No staging (after orbit). Burned 30 tons of fuel. All stock, no mods. (except Alarm Clock).

Continuing our conversation from this thread: http://forum.kerbalspaceprogram.com/threads/97459-Help-with-plotting-interplanetary-trajectories

We were discussing the problem of large underpowered ships being unable to achieve interplanetary transfer orbits from LKO. The issue being that the planet Kerbin is so small and LKO is so tight, that within 15 minutes you’re changing direction 90°. So if your ship can’t complete its departure burn within 10 or 15 minutes, you just can’t do it.

It was explained that NASA’s solution to this problem would be a series of short perigee burns carefully placed to extend the apogee in the direction of the spacecraft’s final departure all the way up to SOI, creating a highly elliptical orbit the Earth at one end. Then one final burn at perigee to send the craft on its way.

The problems (we thought) this created in KSP were twofold; first, we don’t know our departure angle until we’re in our launch window and we’ve actually plotted our course. And two, building up the orbit all the way to SOI would take too long and the final orbit would take almost a month and you’ve missed you launch window.

One reader, metaphor, pointed out you didn’t need to get apogee all the way up to the edge of the SOI, just within lunar orbit would be enough. And that you would have time to do that within your launch window. And he was right. An apogee of 9,000 km is a 10 hour orbit. And you do have time to plot a course to your destination, use that node as perigee, build up your departure orbit, plot your final burn to your destination, and execute it, for one ship. If you hurry. But you don’t have to.

Because our second misconception was that you don’t know the angle of the departure burn.

Of course we do!

This isn’t rocket science, OK actually it’s precisely rocket science, but this part is easy:

If you’re using a launch window calculator to find the launch window with a minimum delta V, then your final departure angle will always be basically prograde or retrograde to Kerbin’s orbital track. Indeed, that’s why it’s minimum delta V. (right?)

This means our departure orbit simply must be parallel to Kerbin’s orbit at the time of departure. With apogee prograde of Kerbin if you’re going to the outer solar system, and retro grade if you’re going in.

How does this information help us?

Well, Kerbin’s orbital period is approximately 106 Earth days. This means at 26 ½ earth days before your departure window, your departure orbit points directly at the sun.

All you have to do is,26 ½ earth days before your departure window, line up your perigee and apogee points with the sun. You don’t even need to establish the departure orbit yet, you just need to mark your perigee and apogee points in space.

Then you have 26 ½ lengthy earth days to build up your departure orbit, and once it’s marked in space, you can park other ships in it!

You can park 10 ships 1 hour apart in this orbit weeks ahead of departure, and when your departure window opens you’ll have a full 10 hours to plot all 10 departure burns, and a full hour for each one, secure the knowledge that nothing will overlap. And that you’re using minimum delta V for everything.

I want thank everyone who helped me figure this out.

I hope I have paid the community back by telling you about my 26 ½ Days-Ahead-Point-Your-Orbit-At-The-Sun Trick.

Should we have a new official abbreviation?

KDO: Kerbin Departure Orbit. Defined as an orbit with a perigee of 100 km, an apogee of 9,000 km, parallel to Kerbin orbit at the time of departure.

Edited October 22, 2014 by Brainlord Mesomorph

[mhoram]

The problems (we thought) this created in KSP were twofold; first, we don’t know our departure angle until we’re in our launch window and we’ve actually plotted our course. And two, building up the orbit all the way to SOI would take too long and the final orbit would take almost a month and you’ve missed you launch window.

Another solution would be to build up the final elliptical orbit before the departure burn.

If you’re using a launch window calculator to find the launch window with a minimum delta V, then your final departure angle will always be basically prograde or retrograde to Kerbin’s orbital track. Indeed, that’s why it’s minimum delta V. (right?)

You talk about the ejection angles here. And they differ for all target planets.

So I believe that the 26 1/2 day rule you suggest does not provide the optimal efficiency. Probably the number of days would have to be adjusted for each target planet.

Here is a picture that shows the ejection angles. (Source: http://forum.kerbalspaceprogram.com/threads/47133)

[Brainlord Mesomorph]

Another solution would be to build up the final elliptical orbit before the departure burn.

is exactly what I'm saying...

You talk about the ejection angles here. And they differ for all target planets.

So I believe that the 26 1/2 day rule you suggest does not provide the optimal efficiency. Probably the number of days would have to be adjusted for each target planet.

Here is a picture that shows the ejection angles.

Yes, and all of those departure angles will work with a basic prograde or retrograde Departure Orbit. (maybe not the absolute minimum delta V, but it does work)

and what you just called the 26 day 1/2 rule just shows you what will be prograde or retrograde in 26 days.

(as a matter of fact that's exactly where my Jool burn was)

Edited October 23, 2014 by Brainlord Mesomorph

[el_coyoto]

Nice and clear, thanks for sharing.

Long burns have always been hard for me to do without tons of calculus and I really like the assumptions you make to simplify the problem and the 26 day 1/2 rule, it's smart.

[Streetwind]

Now the question is - how far can you push this? At which point does even this method become impractical?

In KSP, it's very rare to have burns longer than an hour. But some electric propulsion probes IRL can burn for months on end to escape Earth. I'm kind of interested in the kind of trajectory (and planning strategies) they require.

[el_coyoto]

But some electric propulsion probes IRL can burn for months on end to escape Earth. I'm kind of interested in the kind of trajectory (and planning strategies) they require.

IRL constant low thrust trajectories are very hard to solve analytically from what I remember : numerical applications and constraint solving are often used, as well as the Interplanetary Space Network, which makes analytical computations kinda moot (I'm no physicist, so I may be wrong).

There are a few resources dealing with low thrust trajectories in general or spiral "circle to circle" trajectories...

I guess a more thorough search could bring a detailed ion probe mission report/planning from a space agency explaining the challenges faced when dealing with low thrust engines, the trajectory they used and why.

[Brainlord Mesomorph]

Now the question is - how far can you push this? At which point does even this method become impractical?

Well, if the original problem was a 90° change in direction in 15 minutes in LKO, in KDO you have a 90° change in direction in 2 ½ hours. Is that our upper limit?

Probably not. Because 200 m/s into the burn you already have escape velocity, you are interplanetary, and your trajectory is basically a straight line, so there may not be an upper limit. Torch ships anyone?

One thing I forgot to mention:

The departure burn starts at perigee regardless of where your final node is (that is, for a long burn).

In my example, my Jool departure node was exactly where it is on that guys chart. The burn was 46 minutes, so I should’ve started 23 minutes early. But that would have been 10 minutes before perigee and wouldn’t have worked.

So I started to burn precisely at perigee, and it ran 10 minutes long, but like I said by that point your course is basically a straight line so it doesn’t matter.

Edited October 23, 2014 by Brainlord Mesomorph

[Streetwind]

IRL constant low thrust trajectories are very hard to solve analytically from what I remember : numerical applications and constraint solving are often used, as well as the Interplanetary Space Network, which makes analytical computations kinda moot (I'm no physicist, so I may be wrong).

There are a few resources dealing with low thrust trajectories in general or spiral "circle to circle" trajectories...

I guess a more thorough search could bring a detailed ion probe mission report/planning from a space agency explaining the challenges faced when dealing with low thrust engines, the trajectory they used and why.

Thanks for the links! That gives me some reading for the time being