I haven't done any calculation of precession of stunt planes. I also don't know what you guys have done in the treatment of the propeller in that regard. I'm going to assume that it has been treated as rigid rotating body such as a gyroscope. While that is a good first order approximation it is only roughly valid under certain constraints such as blades which are rigidly attached to the hub or rather as rigid as blades can be. My background is in rotary wing aerodynamics, helicopters. Flying rotor systems.
For our purposes, it has always been treated as a rigid body, which for any maneuvering purposes, is almost certainly true, the natural frequency of the blades flexing is much higher than the maneuvering rate, as it the rotation rate of the prop. Sometimes, the fact that the inertia changes between the axes as it rotates can cause or permit some vibration (which a big difference between two- and three-blade props) matters, but has no direct effect on the maneuvering, assuming the inertia is the otherwise the same.
Almost all the inertia is in the propellor, you can ignore the crankshaft, spinner, rotor, or nose weights on the shaft as far as that goes. Figure that the radius of gyration around the spin axis is approximately .225*diameter (an approximation, but quite good for a surprising number of cases, regardless of number of blades). I
xx= mr
2.
Precession routinely works in two dimensions. For a conventional rotation engines, the continuous left yaw rate caused by going around the circle causes a "nose up" pitch torque in the airplane's body frame, that is, nose up from the ground in level upright flight, and nose down in level inverted flight, as if the pilot was continually pulling a small amount of "up" elevator. That is generally dealt with in trimming, either positive stab incidence, downthrust, or most of the time, "down" elevator with neutral flap.
As I recall, the example in my SN article was about 33 in-oz
* of nose-up for my particular case. Pete Soule' came up with a value for a team racer on his website, but he had a unit conversion error, which he may have corrected since the last time I looked.
The other direction is in maneuvers, "inside" corners inducing right/nose-out yaw, and outside corners inducing left/nose-in yaw. It's about 5x as large at the pitch torque for very tight corners, since the pitch rate for an inside turn is about 5x the rate for going around in a circle. So it's not nothing. At the same time, in most cases, there is also some p-factor that operates in the other direction, which is hard to calculate, but appears to be something like 1/10th the magnitude of the precession for most cases.
This can be dealt with a number of ways, but for the most part, people use passive stabilization (positive yaw stability), and Al Rabe invented a movable rudder that has the capability to compensate for it. It amounts to a feed-forward. The rudder moves to "nose-right" yaw on outside maneuvers, and "nose-left" yaw on inside maneuvers, although you need less inboard movement than outboard movement, since the restoring force from the line goes up nose-out and down nose-in.
In practice, you can trim it out to NATs-level quality without any active control and virtually all of the Rabe-rudder systems end up *grossly maladjusted*, although there is nothing wrong with the idea. Igor also uses his Rabe rudder system to, to first approximation, to rotate the airplane around an axis displaced from the principle axes, so you can hold a more-or-less constant outboard yaw angle, which would otherwise cause wild roll and yaw motion due to the dynamics and kinematics.
I would strongly suggest reviewing Al Rabe's Bearcat or Mustunt article, my SN discussion from about 2005-early 2006s (about "positive incidence"). I have lost the link to Pete Soule's old site, it is somewhere, but I have lost track of it.
Note that the inertia of the prop matters in another way, unrelated to precession - the more inertia, the more torque it takes to spin it up or down, or for a fixed amount of torque, how fast it accelerates or decelerates in RPM. I don't know and haven't carefully considered how much it matters for IC engine systems, but Igor told us it matters a lot in how well his feedback system works, the key problem being a rate slew limit that limits the response enough to inhibit the maximum permissible gain to maintain stability.
Certainly, a big part of being an engineer is knowing where to rip off good ideas.
That's a joke. I got every neat trick I know from various big names, having ripped off Paul Walker more than is seemly.
People are not out to try to get you, me least of all. If they were, you would know. But you can't really expect someone to write a 5000-word report summarizing all the work done to date over the last 70 years, in a few hours, when you fly off the handle at the slightest setback, and haven't done any research. Calm down.
Brett
*12.5" prop, 34 grams, 11000 rpm, 5.4 second laps
r=.225*12.5" = 2.81"=.234 feet
m=34 grams=.075 lb = .00233 slugs
I
xx=.00233 slugs*(.234feet)
2=0.000128 slug-ft
2 omega= 11000 rpm=1151 rad/sec
H=I
xx omega=0.000128 slug-ft
2*1151 rad/sec=.147 ft-lb-sec
yaw rate = 6.28 rad/5.4 seconds = 1.185 rad/sec (5.4 seconds/lap)
Nose-up pitch torque = H*pitch rate=.147 ft-lb-sec * 1.185 rad/sec=0.1742 ft-lb=
33.6 in-ozpitch rate (hard corner) ~ 6.28 rad/sec (360 degrees/second)
Nose-out yaw torque = .147 ft-lb-sec * 6.28 rad/sec = .923 ft-lb =
177 in-ounces