Question to the physics junkies out there !

[aNewHope]

Hi there,

since a few months I've been playing around with the kOS scriptable autopilot (mod). In case you don't know it, try it out, it's awesome!

Now that I installed FAR, I want to adjust my rocket launching program to do an almost perfect gravity turn.

The program should check the TWR of the craft, and find the fitting trajectory.

The thing that's missing is the right formula to get a trajectory always following the prograde marker.

I even found a paper on "Computational algorithm for gravity turn maneuver" that should contain the required maths.

Until equation II it's easy going, but the following 3 are the problem I can't solve.

What do they describe? What is this variable "z"? And can I use them to get a perfect gravity turn for e.g. a constant TWR of 2.5?

Edited March 11, 2014 by aNewHope

[capi3101]

You'd probably need to look up the source material to get a full description of the equations. Fortunate for you that I work at a research library.

Gimme a sec and let's see what we can do here...expect edits.

EDIT 1814Z: We do have electronic access to that particular book -

Go to libraries.ou.edu

Type in "Introduction to Space Dynamics" in the Discover box. It should be the first thing that comes up.

Question becomes whether or not you can access it based on your location. I'm assuming not and will continue searching for the equations in question.

EDIT 1819z: The equations are on Chapter 8, page 257.

Z is the tangent of 1/2 the angle of the rocket's acceleration trajectory from the vertical.

The equations give you that angle in terms of t (time) and C (initial conditions of velocity and Z angle), so yes you should be able to use them to get a perfect gravity turn.

That's if I'm understanding the equation's correctly; it mostly looks Greek to me...

Anyways, I hope you have luck accessing the materials yourself. There's some good stuff in there.

Edited March 11, 2014 by capi3101

[Kasuha]

I may be reading it wrong but it seems to me that paper assumes zero aerodynamic drag. That may not be what you're looking for.

[aNewHope]

So Z is tan (1/2 Ψ) ?

Thank you very much! That's exactly what I wanted to know!

Damn, I love the KSP community!

PS.: Sadly I can't log into the library but z was pretty much all that's missing.

PPS.: (to Kasuha) Due to the limited power of kOS I wont be able to model the drag accurately (without FAR, yes ; with it certainly not). Hopefully this wont be necessary to give a good trajectory.

PPPS.: It works! It ********** works! Thank you so much Capi3101! I tried all week to solve this darn problem and now I have a very good solution. Maybe I'll post the program, when it's finished

Edited March 11, 2014 by aNewHope

[capi3101]

Glad to have been of assistance.

[Yasmy]

Strange. I've not run across these junk science journals before. A little snooping around turns up tons.

Lots of plagiarism from the Wikipedia article for Gravity Turn,

from versions predating this article. I'm guessing that you will find that same for the other listed sources.

The good news is that we (the world) are slowly are gaining some legit open-access journals. It is unfortunate that publicly funded science sits largely a) behind paywalls and in the copyright hands of private corporations.

Anyway, sorry to dampen the mood.

Congratulations on getting it to work!

Edited March 12, 2014 by Yasmy

[Phylan]

Did you ever finish this script? I'd be interested to see what you came up with if you're up for sharing it.

[Amaroq]

PPPS.: It works! It ********** works! Thank you so much Capi3101! I tried all week to solve this darn problem and now I have a very good solution. Maybe I'll post the program, when it's finished

Oooh, please do!