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From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Page discussing precession torque on wheels, illustrated with a diagram of right front wheel motion.

Identifier  ExFiles\Box 170\3\  img040
Date  14th July 1933 guessed
  
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RIGHT FRONT WHEEL
LOOP SHOWING WHEEL MOTION
ROTATION OF SPOT IS CLOCKWISE
ANGLE OF ABOUT 10°.

This means that the point of maximum wheel swing actually occurs less than 90° of phase before the maximum position of corresponding car displacement.

Precession Torque on Wheels.

1. Since the maximum swing angle of the wheels actually occurs at points A' and C', it will seem that during the greater part of the movement from A to C the wheels are pointing to the left of their path of travel and therefore are subjected to a precession torque tending to swing them to the right. The maximum swing to the right occurs at C'. Therefore the precession torque leads the corresponding wobble displacement by something more than 90° of phase. This suggests that the wheel motion occurs at some point above the "natural" wobble frequency of the wheels. The above precession torque is obviously increased as caster is increased and explains the observed dependence of wobble excitation on caster.

2. The rocking axis of the car is inclined and therefore has some of the qualities of vertical axis and some
  
  


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