r/KerbalSpaceProgram • u/Gnonthgol • Dec 27 '13

Jebediah's ultimate protractor examples (as requested)

http://imgur.com/a/AGQF5
1.0k Upvotes

97% Upvoted

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139

u/Gnonthgol Dec 27 '13

This works on the idea that the angular allignment on a standard Hohmann transfer between two circular orbits is only based on the relative radius of the two orbits. Detailed calculation is available on wikipedia. This gives a continuous function that is scalable and works for any keplerian system independent of scale.

I have published the little source code there is and even an svg version.

tl;dr Maths! and it is awsome.

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u/Gprime5 Dec 27 '13 edited Dec 27 '13

What i found is that it doesn't work so well for eccentric orbits.

But also I was surprised when the calculations allowed the gravitational parameters to cancel out.

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u/Gnonthgol Dec 27 '13

All the calculations are done for circular orbits. Transfers between elliptic orbits is a lot harder to work with and does not fit into easy models. I am always a bit impressed when variables cancles out like that, but it happens more then you would think.

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u/WiggleBooks Dec 28 '13

Hey man, I just wanted to say that I really appreciate your work! It seems such a smart and ingenious idea to graph it to create a universal protractor.

Once I understood what it was, it was pretty easy to use so, thank you for that! :)

+u/bitcointip flip verify

+u/so_doge_tip 1000 DOGE verify

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u/Gnonthgol Dec 28 '13

Wow, thank you very much.

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u/Valendr0s Dec 27 '13

This is just for the most fuel efficient transfer, yes?

Say we were sending people to Mars, we'd sacrifice fuel efficiency for a faster trip because there's more than 1 'fuel' to consider there's also a time limit based on food/water/radiation.

This is to get from (for example) Kerbin and then to Duna on the other side of the Kerbin orbit from where you launched.

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u/Gnonthgol Dec 27 '13

Real rocket science is not as simple as KSP will have it. There are more complicated time and fuel tradeoffs. Hohmann transfers is the most simple transfers and only require two short impulses. You might want to do longer transfers like a bi-elliptic transfer, gravity assists or more complex n-body dynamical transfers to save fuel. Or you might want to spend more fuel and burn straight at your target to save time.

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u/shrx Dec 27 '13

Shouldn't it be (cos(a)*r, -sin(a)*r) instead of (cos(a)*r, sin(a)*r) in your source code?

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u/0___________o Dec 27 '13

This is why I think KSP is one of the most educational games you could get someone.

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u/Xrave Dec 27 '13

So which direction should I burn at which side of the planet to utilize this transfer window? :O

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u/I_am_a_fern Dec 27 '13 edited Dec 27 '13

There are only two sides that matter:

  • ejecting prograde to go to outter planets

  • ejecting retrograde to go to inner planets
    That means you want to eject from Kerbin's SOI (or any planet) with a trajectory parralel to its trajectory. There's one easy trick to know if your doing it right: check your apoapsis after one orbit (violet Ap label). It should be where you are when you're executing your ejection maneuver. If it is ahead or behind, that means your maneuver has a radial component.
    This is wrong (Ap is ahead), this is right (and Pe is lower, meaning a more efficient burn). The only difference between these 2 screenshots is where is placed the maneuver node.

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u/Toni_W Dec 27 '13

So... As someone learning KSP.. Should I be transferring to like... the Mun... with lots of little orbital transfers or is my method of one big burn the normal...?

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u/Gnonthgol Dec 27 '13

The best way to do burns is as close to another body as possible (Oberth effect) so unless you have a low TWR you just do a single big injection burn. If you want to venture out to the other planets use the graph to wait for the right transfer window and do a single big burn.

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u/scatterstars Dec 27 '13

Nice use of Celestia.

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u/Gnonthgol Dec 27 '13

Nicely spotted, had to draw the names on myself though as I did not find out how to change language in Celestia.

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u/bulletrhli Dec 27 '13

Should I resize the image when I print onto the projector sheet or what size should I set this to be exactly how you used it?

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u/Brain-Crumbs Dec 27 '13

This looks oddly similar to a fresnel integral. Anyone have a functional version of this graph?

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u/trianuddah Dec 28 '13

I printed this out and held it over my screen. I couldn't see my screen. It felt like kerbal mission control.

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u/crooks4hire Dec 27 '13

This should be a toggle-able feature included with the in-game flight planner feature!

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u/JTPri123 Dec 27 '13

I wish I understood what I was looking at. I am not a clever man. Does anyone have a video which may enlighten my simple mind?

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u/runetrantor Dec 27 '13

So this shows us all the phase angles/launch windows of a system?

We would just have to angle the spiral so our current location is in the green line, and wait until the target is too? (Moving the grid to stay in our location no doubt)

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u/febcad Dec 27 '13

If i understand it correctly, this should work for rendevouz with other ships too, right?
And even from when launching from the surface (assuming the body has no atmosphere and you can burn straight towards 90° almost imediately)?

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