Here are a few more ideas about your theories:
The weight of the propellor is such a small fraction of the total airframe weight that precessive forces are negligible. The WWI planes with rotary engines had a much greater percentage of their total weight spinning, a pilot who ignored precession in one of those often quickly became dead.
It has been a while since somebody told me about gyroscopes, but I believe the quantity one is concerned with is not the mass of the prop, but the angular momentum; after all, it isn't the mass of the wheel that keeps a bicycle upwright! it is the rotation of that mass. So, even though the prop is very light, it is also spinning very fast, and can thus has a high angular momentum, and its votes count more ("the lefts have it!" nevermind, that was a bad one) You might not notice it on your favorite sport plane, since it accellerates through the takeoff roll so quickly; but underpower a nice senior telemaster, or perform a reduced power takeoff with a sport plane, and you can certainly see the effects if you look for them.
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point number 3: The critical engine is determined almost entirely as a result of p-factor, since p-factor is what displaces the center of thrust further away from the longitudinal axis of the plane...
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Absolutely wrong, sir. The center of thrust is displaced by mounting the engines to either side of the airplane. And if you fly a twin engine out at a high angle of attack you too, will soon be a statistic. Offset thrust, rudder authority, and torque are the determinants of VMC, P-factor has nothing to do with it.
Oh, I think I'm going to have to stand my ground on this one, but because I figured I could get away with omitting a word or two, I can see how you disagree. I meant to say that the p factor is what displaces the center of thrust further away from the airplane's longitudinal axis
on the non-critical engine; of course the center of thrust is displaced for both engines by the distance from the long. axis, but the center of thrust on the non-CE is displaced further away because of the p-factor. The key to the CE theory is that there is an
asymetric displacement of the center of thrust. This is why counter-rotating twins have no critical engine; the center of thrust is still displaced from the
longitudinal axis of the engine just like it is on almost all prop-aircraft. But, (in most counter-rotating cases) the center of thrust is displaced to the left on the right engine and the right on the right engine, and it all evens out, because there is no dissymetry between the distance from the aircraft long. axis and the center of thrust.
I will admit my 15 degree prop blade angle was a simplification, but it was sufficient to convey the needed information. A real propellor has a blade angle that changes from the root to the tip, since the tip travels a much greater distance per revolution than the root, it needs much less angle to have the same true pitch. If the blade were extended all the way to the root, the blade angle at the root would be 90 degrees regardless of the actual pitch, since the root has effectively zero rotation.
I think the interesting thing is that all of this discussion, and most aerodyamic discussions, are over-simplifications. The key to learning aerodynamics for a pilot is for him to be able to predict what will happen to his craft; he doesn't have to know formulas, etc. Instead, we teach pilots little "thought models" that help describe how airplanes fly. From time to time, we realize that those models are a bit too much of a simplification, and we have to add to them. Lets face it, I'm a pilot, not an engineer; I've never been in a wind tunnel, but I can tell you how a plane is going to react in most of its flight envelope.
Here is my next point:
You still overlook torque.
On the critical engine. the left, torque tends to counteract the offset thrust, making it easier to fly than with the right only, where the torque and offset thrust effects add.
With the CR version the torque and offset thrust are counteractive on both engines.
With either version, in a dive, VMC still holds. And in that dive the airflow into the props is as close as axial as you can get it making P-factor absent by definition. And you still can't hold yaw at full throttle until your speed comes back up. Torque and offset thrust, yes. P-factor, a resounding no.
On my side of the river, the feds like to hear that critical engines are determined by four factors; p-factor, torque, accellerated slipstream (more lift further out on the wing) and spiralling slipstream. Critical engines are not determined by just one thing, but several factors; we don't have to decide on one and vote him "senior air marshal of all critical engine factors
. Although, the spiralling slipstream and accellerated slipstream concepts rely on good ole' p-factor to displace the center of thrust further away on the left side (in america). The feds over here also like for pilots to know that VMC is very much affected by p-factor; VMC is almost never a problem, except in a high angle of attack, high power situation... "I've just got to clear those trees-mountains-clouds-ground-towers-runway-cows," or "lalalala see no airspeed indicator, hear no airspeed indicator, speak no airspeed indicator... Hey mr. airspeed indicator, if I can't see you you can't see me; after all, I'm busy trying to figure out why there's oil all over the wing" etc. After all, if you are going so fast that you have a low angle of attack, then you are going fast enough to have sufficient rudder effectiveness. VMC really matters at high power settings and high angles of attack; you remember that in what you call normal flight aoa is related to airspeed, right? Slow airspeed means more aoa to maintain altitude; you can't have a high power setting and a low aoa without building up airspeed (the stuff that makes your rudder able to do the job). Think about it, the only reason that an airplane will have a low speed when the engines are humming is because we are flying slow (high aoa in this case), and induced drag is high. When we reduce aoa, induced drag goes away, and the "brakes" that were keeping us slow are released. The airplane accellerates, and "away go vmc worries, down the drain." That is, unless you have an airplane with an extraordinarily high VMC; there are lots of factors that impact VMC, but the most obvious ones in a model might be high output engines, insufficient rudder, etc. Once again, I personally don't feel obligated to name one of those many factors "vice air marshall of all VMC," or "president of the VMC club." Or, "can't we aerodynamic-tendancies all just get along?"