Theoretical Studies in Braking

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Abstract
In Part I of this paper, after a simple description of the basic properties of a pneumatic tyre, a highly simplified vehicle consisting of a pneumatic-tyred wheel bearing a load is considered mathematically during braking and during the release of brakes. By inserting numerical estimates it is shown that, among other results, from 15 mile/h a wheel may lock within 18 ms. It is also shown that under perfectly uniform conditions the stopping distance is appreciably less when the brake-shoe torque is approximately equal to the moment of the maximum frictional force that is possible between the tyre and the road, than for both greater and lesser brake-shoe torques. In Part II of the paper a commercial device—the Maxaret—designed originally to release the brakes of an aeroplane before the wheels lock on landing and then later to reimpose the brakes is briefly described and the mathematical equations of its operation, both in itself and in application to a highly simplified road vehicle, are set up. A numerical investigation, making use of the results given in Part I of this paper, was executed and the results are given. These show in detail the mode of operation of the device. These highly simplified calculations suggest that in its present form a much longer braking distance will result from using the device than would be obtained with locked-wheel braking. This is in conflict with experimental results and may be due to both the simplifications that had to be made for the numerical work and some of the empirical data used. Some of the former could be avoided if an electronic computer were available. Further investigation is desirable and this should enable the device to be adjusted to give the shortest stopping distance consistent with the avoidance of locked wheels.

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