How many G's ?

[Allan Perret]

Now counting the one G of gravity, how many G's of acceleration is the typical 60 size stunter seeing while flying the round loops ?  [Assuming a constant speed]

[Tim Wescott]

Lap time = t = 5.5 seconds

Effective radius of hemisphere = r_h = 69 feet = 21 meters

Speed = s = r_h * (2 * pi / t) = (21m) * (6.283) / (5.5s) = 24m/s (which is about 48 mph -- maybe 5.5 seconds/lap is unreasonable).

Level flight centripetal acceleration = s^2 / r_h = (24m/s)^2 / (21m) = 27m/s^2 or so, or about 2.8g

Effective radius of 45 degree circle = r_l = sin(22.5 degree) * r_h = (0.38)(21m) = 8m

looping centripetal acceleration = s^2 / r_l = 72m/s^2, or about 7.3g

I tried to give enough detail here so that you can play with speeds and line lengths.

At least on the airplanes that I have instrumented and flown, the assumption of constant speed is just a bit more true than the old assumption that the earth was flat.  On a Sig Banshee pulled by an all-stock LA 46, I was seeing about a 3:1 difference in speed between the top and bottom of a loop.

However, for the purposes of calculating wing loadings, the 7.3g is probably fair.

[Allan Perret]

Lap time = t = 5.5 seconds

Effective radius of hemisphere = r_h = 69 feet = 21 meters

Speed = s = r_h * (2 * pi / t) = (21m) * (6.283) / (5.5s) = 24m/s (which is about 48 mph -- maybe 5.5 seconds/lap is unreasonable).

Level flight centripetal acceleration = s^2 / r_h = (24m/s)^2 / (21m) = 27m/s^2 or so, or about 2.8g

Effective radius of 45 degree circle = r_l = sin(22.5 degree) * r_h = (0.38)(21m) = 8m

looping centripetal acceleration = s^2 / r_l = 72m/s^2, or about 7.3g

I tried to give enough detail here so that you can play with speeds and line lengths.

At least on the airplanes that I have instrumented and flown, the assumption of constant speed is just a bit more true than the old assumption that the earth was flat.  On a Sig Banshee pulled by an all-stock LA 46, I was seeing about a 3:1 difference in speed between the top and bottom of a loop.

However, for the purposes of calculating wing loadings, the 7.3g is probably fair.

Seems like I remember reading that we pull about 15 G in the square corners. [probably based on the old 5' radius]
So I was thinking the round loops would only be something like 3~4 G.   

Am I right in thinking that the 7.3 G you calculated would be the same for a loop flown between 0 & 45° [like in the pattern] and also a loop flown directly overhead [a level lap at 67.5° elevation].

[Tim Wescott]

It's always possible I'm getting my math wrong.  Ignoring gravity, though, the canopy-ward acceleration will always be the same.

[Howard Rush]

We had a discussion like this awhile back.  It's at http://stunthanger.com/smf/index.php/topic,25255.0.html .  Down at the bottom of the discussion I plotted lift at constant speed and at constant power.

 

[Tim Wescott]

I'm looking at some collected flight data.  I'm seeing accelerations on the order of 8g for the round maneuvers (which bears out my calculations), but only 10g for the square corners, with some peaking at around 14g.  The rotation rate is fairly constant in the corners of the squares, but the bottom corners show significantly more acceleration than the top ones.

Dunno why -- but I suspect airplane slowing is part of it.

[Steve Helmick]

I'm looking at some collected flight data.  I'm seeing accelerations on the order of 8g for the round maneuvers (which bears out my calculations), but only 10g for the square corners, with some peaking at around 14g.  The rotation rate is fairly constant in the corners of the squares, but the bottom corners show significantly more acceleration than the top ones.

Dunno why -- but I suspect airplane slowing is part of it.

Maybe that's just your square corners, Tim?   Steve

[Howard Rush]

The flap movies we took last week showed a surprising amount of control input variation in round loops. 

[Tim Wescott]

Maybe that's just your square corners, Tim?   Steve

It could be, but in a prior round of airplane tests with a gyro but no accelerometer, I couldn't get the rotation rate nearly as fast as you'd expect for a "rule book" square loop -- the best I could do was to kind of get the airplane to flop over from the rising line to the upper line.

We need some good movies, and someone willing to dissect them frame-to-frame.

[Howard Rush]

We need some good movies, and someone willing to dissect them frame-to-frame.

Guess who's done that.

[Tim Wescott]

I know you recently did some with the camera on the plane -- have you done any with the camera on the ground?

One could find some existing flights on YouTube, I suppose, and try to measure from that.

[Mark Scarborough]

Hey Howard,, have you had any luck reducing the size of the movie file of my plane,, I want to disect it to try and come to terms with whats actually going on,, and finalize a solution,, (aside from building a new plane that is)