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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).
Technical analysis of the forces and torques involved in front wheel shimmy.

Identifier  ExFiles\Box 170\3\  img031
Date  5th June 1935 guessed
  
-3-

The car is shown shimmying with the right front wheel down. This wheel has just met the ground (at A) toed in at a considerable angle (5° or 10°). It is now being swung out by a couple which consists of :-

First : the outward torque produced by the angle of camber of the wheel plane relative to the ground.

Second : the rolling resistance of the (highly compressed) tire multiplied by the distance d between the centre of the wheel plane and the kingpin.

At B, the lowest point of the swing of the axle, the front wheel is pointing straight ahead. Its rotary velocity about the kingpin is at a maximum. Therefore the gyroscopic acceleration of the axle clock-wise (direction of arrow C) is a maximum. Consequently the right front wheel is thrown up into the air toed out (as at B) and the left front wheel meets the ground toed in repeating the cycle.

The description is not yet complete however :-

Outward precession torque due to camber is maximum at B when outward velocity of precession is maximum. The torque thus leads the wobble displacement by 90° and satisfies the condition for a damped oscillation at or near resonance. This condition also provides a maximum feed-in of energy to the wobble motion. But maximum clock-wise torque on axle from gyroscopic effect is at B, when the axle has maximum counter-clockwise displacement. This only satisfies a condition for a very slightly damped oscillation running above resonance.

However this is not the only torque on the axle.
  
  


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