I’ll reiterate. I am not an expert on helicopter theory. My explanation was merely a description of gyroscopic precession. I discussed helicopters just to illustrate where the gyroscopic precession breaks down.
vorticey, I suspect your theory would work on some helicopters and not on others. Many things that affect gamma are dynamic and do not apply to steady state conditions. Delta 3 appears to be one of them, it comes into play only when the tip path plane and swashplate are not parallel. I’m definitely not the one to ask for this.
Nick said, “Some proofs for your consideration that the blade is bouncing up and down, and not precessing”
You’re right, the blade is bouncing up and down. At some point prior to max upwards deflection, the blade pitch is at a maximum. This is obvious if you think about it. We apply a force to a blade that causes an acceleration, which in turn causes displacement. Although it is an instantaneous process, we don’t see what we consider to be the full result of the maximum force until a number of degrees later.
The blades are rotating. They are constrained to either pivot about a flapping hinge or to bend over their length when subject to forces parallel to the rotor axis. Because of this you can’t just push on the blades and expect them to move under your finger. They will start moving immediately, but you won’t see max deflection until later on. It won’t always be 90 degrees because of the geometry of the system, notably the flapping hinge, and because of the complexity of rotors.
The blade doesn’t “spin…with a motion in which the axis of rotation sweeps out a cone” (Encarta World English Dictionary) so by definition it does not precess.
The ways that you can change gamma are consistent with what I’ve written. Adding the mass to the blade changes the moment of inertia of the blade which changes it’s resonant frequency. That will definitely change gamma. Keep in mind that all the forces on the blade are not necessarily in phase with cyclic input. The net result could change gamma even on a system that exhibits a true 90 degree phase lag.
I can give you a fairly simple rotating system that shows a precession of 45 degrees, and can be adjusted for other precession angles. However, it doesn’t fit into the definition of a gyroscope so it doesn’t qualify as a gyroscope that changes it’s precession angle. You’re right that you’d have to go to Bizarro world to see that.
I’m not sure what you mean when you discussed the dynamic response and the blades resonating. The equations of motion can fully describe the motion of the blades without ever talking about conservation of angular momentum. That does not negate what I’ve said. Conservation of angular momentum is buried inside the equations of motion. Also, the resonant frequency of the blade is dependant on geometry and mass distribution, not any dynamic factors.
For the bifilar pendulum dampers, I bow to your knowledge.
ShyTorque said, “…does gyroscopic precession result in aerodynamic effects or rather aerodynamic effects resulting in gyroscopic precession?”
Neither. Aerodynamic effects control the rotors. Gyroscopic precession is a close explanation of why the aerodynamic forces appear to be out of phase with their result.
I need a good helicopter aerodynamics textbook. Anyone have a recommendation?
Matthew.
"In this philosophy particular propositions are inferred from the phenomena and afterwards rendered general by induction.", Sir Isaac Newton
[ 06 August 2001: Message edited by: heedm ]