Calculating Re-entry Angle from Orbit

[Scrogdog]

This won't be an issue or concern for most, but I need advice from someone a bit more talented than myself.

I've started using the Deadly Re-entry add-on, and it's pretty brutal. Exactly why I like it.

But here's the thing. It seems that the only way to calculate the correct angle is by eyeballing it which isn't very precise.

There must be some way to do this. Some data that I can make sense of that I am not currently. I do also have Engineering Redux, but the description doesn't make it seem like adding the chip would help me out in this case.

Any advice would be greatly appreciated! At this point it seems all I can do is trial and error runs and even then, any success would only work with the same ship at the same altitude.

[iamaphazael]

It seems like arctan( (ap-pe) / (circumference of planet/2) ), while not completely accurate, should give you a ballpark idea of how steep or shallow you're going to be, and at least be a repeatable calculation that you can calibrate against

[SunJumper]

I'm sure it might be possible to be use implicit differentiation for this, but I'm not sure.

[Scrogdog]

Thanks for the ideas!

Ultimately I'm going to need to set up a spreadsheet that allows me to enter some data. I'm going to need to get my head around this to make that happen.

I found this at faa.gov. Pretty comprehensive and deals with a lot including designs.

In addition, I found this formula on wiki (the idea being that "re-entry" angle is the same as any other flight angle);

The flight path angle is the angle between the orbiting body's velocity vector (= the vector tangent to the instantaneous orbit) and the local horizontal. Under standard assumptions the flight path angle \phi satisfies the equation:

h\, = r\, v\, \cos \phi

where:

h\, is the specific relative angular momentum of the orbit,

v\, is orbital speed of orbiting body,

r\, is radial distance of orbiting body from central body,

\phi \, is the flight path angle

I'm certainly no math major, but it occurs to me that I don't even know how to determine some of those parameters! Looks like I'll need working spreadsheet formulas to determine some of those, and then take that information to the other formula!

Hoo boy. I've got work to do.

[maltesh]

If you know your orbit's semimajor axis (a), your orbit's eccentricity (e), and your radial distance from the center of the planet you're orbiting ®, you can find the true anomaly of your position on your orbit at any time (theta) with the following equation:

Knowing the True Anomaly, you can then find your flight path angle (phi) which is the angle above or below the horizontal your spacecraft is travelling at that time:

[Scrogdog]

Wow! Looks like you nailed it!

Of course, how would I know?

Where can I see my eccentricity in-game? I saw it in one of the tutorials in the help window, but don't think I've seen it since.

[RoboRay]

MechJeb and Kerbal Engineer will display your orbital parameters for you. Otherwise, you'll have to calculate it from your Ap and Pe heights.

[Scrogdog]

Great; I have Engineer I just haven't yet flown the chip.

Thanks for all the help folks!

Hmmm, one more thing, I suppose. Still not sure how I'll actually calculate the burn, but I'll chew on this for a while.

Edited May 21, 2013 by Scrogdog