One G rolls: a physicist's view

"AES" wrote in message
...
As a follow-on to the discussion of "one G rolls" in this NG some time
back, an analysis of a simplified "physicist's version" of the one G
roll problem, with formulas and graphs, is available at

http://www.stanford.edu/~siegman/one_g_roll.html

I'm not sure why I was driven to do this -- maybe nothing better to do
with my time these days? -- but I was, so here it is.

I'll give a quick summary of results first, then a more detailed summary
of the assumptions behind them. Any comments on this will be welcome
(but on the NG, please; not by private email). And before anyone jumps
too hard on my approach or results, please look at the assumptions to
see what I'm claiming and what I'm not.

RESULTS:

Unless I've made some dumb mistake (always a possibility), if an
aircraft starts out in level flight and rolls through 360 degrees
clockwise about its forward axis in 10 seconds, while maintaining 1 G
force on the aircraft and the pilot, and a constant forward velocity, it
will perform a circular corkscrew "barrel roll" type of motion with a
radius of about 80 feet around a curved "guiding axis" (although the
actual orbit will not look much like a corkscrew), and will end the
maneuver displaced about 500 feet to the right, with an altitude loss of
about 1600 feet, and a screaming final downward velocity component of
300 feet/second.

snip

Good analysis. One thing you might try is running the model again at 6 or 8
seconds to complete the roll? This would be would be representative for many
GA aircraft, which have roll rates of ~45 degrees/second? I imagine it
would make a huge difference in the vertical velocity at the end of the
roll.

Also, most of us who do rolls in aircraft with non-inverted systems begin
the roll with a pull-up to a 20 degree (or so) climb. In my case (RV-6), I
pull 1.5 G's to the 20 degree upline, roll at more or less 1 G, and pull out
at 1.5 G's when the roll is complete without any net altitude loss...

KB