Path of an airplane in a 1G roll

Chris W wrote:
Do we have any who is a math whiz here? I want to find a formula to
calculate the position of an airplane throughout a 1G roll. The reason
I'm doing this is so I can build a "roll track" for a remote control car
so the car will alway have a positive g force on it to keep it on the
track. Anyone have any ideas? So far my attempts have have all come up
short. They don't pass what my college calculus instructor called the
"warm and fuzzy" test. I think it has been too long since I took those
classes.

Most folks who do this do it with a system of differential equations.
It's not a simple thing to do, if you want to model the whole thing:
http://www.aoe.vt.edu/~durham/AOE5214/
But, then again, I'm the sysadmin for aoe.vt.edu (and not an aero
engineer) so I may not have looked at the simple solutions. A general
(in the mathematical sense) answer to your question is in "Chapter 7:
Equations of Motion". The previous 6 chapters are background knowledge.

I think I'd just try it in a flight simulator -- maybe you can use an
simulated-aircraft that has a G-meter.

One way to approach the calculation might be to model the aircraft as if
it were weightless. Then, have the aircraft accelerate with 1g worth of
lift (pitch-up, slam you into your seat). The model you've developed
should show the airplane looping in one way or another. Then, add a
roll at the maximum roll-rate of the aircraft into the model. And,
after that, wrap the resulting shape around a parabola. Some calculus
and a lot of vectors should do it. Or, you could just do a lot of
vector summing in a program like Mathematica or a program of your own
devising should do it.

But, please take what I have to say with a spoonful of salt since I am
merely an IT guy who gets really excited around airplanes.

-Luke