ShyTorque:
>One thing that occurred to me earlier is that a "rigid" rotor is not actually completely rigid in the literal sense <
Agreed. My description was not expressed clearly enough. The use of the expressions "totally rigid rotor" and "really rigid rotor" are intended to represent a non-existent and theoretical rotor. A rotor that is able to achieve absolute rigidity. This theoretical rotor should exhibit gyroscopic precession. As a rotor's rigidity decreases from this absolute state, so will the amount of gyroscopic precession that it exhibits.
At the other extreme, we have the teetering rotor that probably exhibits no gyroscopic precession. Between these two extremes will be the so-called rigid rotors.
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heedm;
Thanks for a very elaborate description of gyroscopic precession.
>>Also, “In [ShyTorque’s] first instance, because the rotor is rigidly attached to the helicopter, the mast and helicopter will be pried (rolled) to the right” <<
>Actually, gyroscopic precession is a very good way of describing the rigid rotor. The mast and the helicopter would roll right only if the rotor wasn’t turning. With the rotor turning, everything pitches nose down. <
Like ShyTorque, perhaps your statement above is also based on my unclear description of 'absolute rigidity'. The rotor above must be turning to obtain both aerodynamic precession and gyroscopic precession. I agree that gyroscopic precession will pitch the nose down. But also, because this extremely rigid rotor does not flap, aerodynamic precession (maximum downward force on the right, assisted by maximum lift on the left) will want to roll the craft to the right.
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There appears to be one major difference between the gyroscope and the rotor of a helicopter. The gyroscope has a large amount of relative mass and its moment arm is approximately 98% of its radius. The helicopter has a very small amount of relative mass and its moment arm is approximately 45% of its radius. To me, this implies that, if gyroscopic precession does play a part in rotor dynamics, its part will be very small.
The following is a graph that has been used by Prouty and by Stepniewski & Keys.
http://www.synchrolite.com/0941.html#Phase_Angle It shows that as the rotor's stiffness increases, the phase angle of the rotor decreases. The hypothetical absolutely rigid rotor that is mentioned above, can be seen to have a theoretical phase angle of 0-degrees.
To achieve this rigidity, the weight of the rotor will be quite heavy and therefore gyroscopic precession must become a factor. The aerodynamic precession of 0-degrees will work in conjunction with the gyroscopic precession of 90-degrees and a resultant phase angle of say 4-degrees will result.
Theoretically speaking.
[ 07 August 2001: Message edited by: Dave Jackson ]