Path of an airplane in a 1G roll

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.

--
Chris W

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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

On Sun, 19 Jun 2005 11:04:39 -0500, 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.


IIRC, There is a computer sim game for building roller coasters with some
realistic physics. While not exactly what you were looking for, maybe you
could build the coaster with the forces you want and then immitate the
shape produced for your track without going thru all the math?

peace,
chris

You can't do a roll and retain 1 G positive throughout the roll.


BJC

"zaphod" wrote in message
news
On Sun, 19 Jun 2005 11:04:39 -0500, 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.


IIRC, There is a computer sim game for building roller coasters with some
realistic physics. While not exactly what you were looking for, maybe you
could build the coaster with the forces you want and then immitate the
shape produced for your track without going thru all the math?

peace,
chris

"Byron Covey" wrote:
You can't do a roll and retain 1 G positive throughout the roll.

Actually, you can't do ANY maneuver and maintain exactly 1G. The G's you
feel are the sum of the Earth's gravity and your acceleration. Since the
Earth's gravity is always 1G, if your total G force is always 1G, then your
acceleration must be zero, and you can not change your flight path.

You can certainly maintain positive G's through maneuvers (even inverted),
and you can certainly maintain something close to 1G though maneuvers, but
you cannot maintain exactly 1G through the whole thing.

Not quite true. Start a coordinated turn, decending at the same time
and you can keep the bathroom scale you're sitting on reading your
weight. At 45 degrees of back I think you'll find the airplane has to
be accelerating downward too, so the .707 horizontal G and the .707
vertical G combine to provide 1 G into the pilot's seat. At inverted,
you'll have to pull back pretty hard on the yoke to provide a relative
to the pilot upward acceleration of 64.4 f/sec*2 to keep pasted into
the seat at 1 g.

"Tony" wrote in message
oups.com...
Not quite true. Start a coordinated turn, decending at the same time
and you can keep the bathroom scale you're sitting on reading your
weight.

Only if that descent involves a vertical acceleration. That is, it's not a
constant rate descent.

A constant rate descent would require 1G of *vertical* lift, which means
greater than 1G of actual lift from the wing (where I blatantly misuse "1G"
as a way of describing the amount of lift equal to the weight of the
airplane ). Using your 45 degree bank angle example that comes to about
1.41G.

Alternatively, maintaining 1G of lift would mean that the descent rate would
be increasing throughout the turn. Depending on the bank angle, this could
turn into a pretty dramatic descent rate in short order.

Pete

"BC" == Byron Covey writes:

BC You can't do a roll and retain 1 G positive throughout the
BC roll. BJC

There's supposed to be a video of the great Bob Hoover doing a barrel
roll with a glass of water on the panel...not a drop spilled. If
anybody knows where a copy of the video is (or if it even exists) that
would be a worth addition to Jay Honeck's collection.

I've seen it. It was years ago. I borrowed the 8 mm tape from EAA for a
chapter program. Not only was the glass sitting there, Bob poured water
into it during the roll.


BJC

"Bob Fry" wrote in message
...
"BC" == Byron Covey writes:

BC You can't do a roll and retain 1 G positive throughout the
BC roll. BJC

There's supposed to be a video of the great Bob Hoover doing a barrel
roll with a glass of water on the panel...not a drop spilled. If
anybody knows where a copy of the video is (or if it even exists) that
would be a worth addition to Jay Honeck's collection.

In article , Bob Fry
wrote:

"BC" == Byron Covey writes:

BC You can't do a roll and retain 1 G positive throughout the
BC roll. BJC

There's supposed to be a video of the great Bob Hoover doing a barrel
roll with a glass of water on the panel...not a drop spilled. If
anybody knows where a copy of the video is (or if it even exists) that
would be a worth addition to Jay Honeck's collection.

All that shows is that he maintained positive G's and coordination.