rotational velocity question

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Hi everyone,

I'm working on an Artificial Intelligence algorithm for a hobbyist video game project involving aircraft. I'm trying to figure out how to limit my aircraft pitch rotational velocity (radians per second) by G-force.

My fwd speed varies, my G force limit does not, let's say 10 to round it off.

As units of measure, I'm using feet, seconds, & radians.

If we can, let's ignore gravity,lift, drag & aircraft weight vectors effects at the moment so we can just concentrate on a apparent G-force as the aircraft pitches around a loop. (I know there would be one  more g-force on the bottom of the loop and one less on the top due to actual gravity, but I'd like to ignore that factor at the moment).

Also, let's say the the pilot is very good & the rotational velocity is constant throughout the loop.

So all I know is my fwd speed in feet per second, and my desired Gforce-limit, I do not know the radius of the loop. Do I have enough information to determine rotational velocity? & if so, how?

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acceleration = fwd speed *   rotational velocity


So, obviously I'm no math genius here. Thanks for being patient.

since I'm solving for rotational velocity, I'll re-write as rv = a/fs

if my acceleration is feet/sec/sec & my fwd speed is feet/sec,

what units of measure will the result be? I'm assuming its ??/sec. Is it automatically radians unless converted to something else?
Centripetal acceleration = (speed^2)/r.

To get the gs divide centripetal acceleration by the acceleration due to gravity in the units you use (feet, seconds) Therefore the magnitude of the acceleration due to gravity is = 32.

Thus your         g = ((speed^2)/r)/32
Hence    r = (speed^2)/(your max g times 32)
 Speed = (r *your max g *32)^0.5

You have to know either the radius of the loop or the speed.

Rotational velocity = speed/r

If you just want to know the rotational velocity use ozos equation

acceleration = fwd speed *   rotational velocity

thus    rotational vel = acceleration / fwd speed.
The acceleration in the equation is your max g times the acceleration due to gravity in the units you are using (feet, sec). In your case 32.
rotational vel (in radians per second) = (max gs * 32)/ fwd speed            
where fwd speed is in feet/sec
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acceleration = v^2 / r

I'm assuming you're using meters, since you say G is 10.

So let's say you want to limit acceleration to 5G.
5G = v^2 / r
r = v^2 / (5G) = v^2 /50

Let's say v is 100 m/s.
r = (100^2) / 50 = 10000/50 = 200 m.

So the minimum radius would be 200m.
Whoops, you came right out and said you were using feet.

G = 32 f/s^2

5G = v^2 / r
r = v^2 / (5*32) = v^2 / 160
If your v is 300 f/s, then
r = (300^2) / 160 = about 560 feet.


Thanks guys, most points to ozo for quickness, Thanks to aburr for explaination, some points to Nova even though I wasn't looking for radius, it'll come in handy someday.

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