MINIMUM STOPPING-DISTANCE OF AN AUTOMOBILE ¹ 250043

Claims and counter-claims as to the deceleration possible under certain conditions, especially when applied to the legal questions arising at the time of an accident, induced the author to make an investigation of the subject. An attempt has been made to include all the variables that are of significance or of sufficient magnitude to affect appreciably the performance of a car under a given set of conditions of the vehicle or of the environment. Inasmuch as the calculations are simplified by doing so and because the difference between the amounts of deceleration and of power involved are small, the assumption is made that the maximum deceleration occurs when the wheels are locked, rather than when they are still rotating. The stopping-distances, theoretically obtained, apply to level-road conditions only.

Through a series of mathematical equations, based on the weight of the car, the proportion of the weight on the front and on the rear wheels, the height of the center of gravity above the road, the length of the wheelbase, the coefficient of friction between the tires and the road, the velocity and the like, conclusions are reached that:

1. (1)
   With two-wheel brakes, the transfer of effective weight from the rear to the front wheels is directly proportional to the rate of deceleration
2. (2)
   With four-wheel brakes, this effect can be neglected, for the retarding force exerted by the front wheels is increased by the same amount as that of the rear wheels is reduced
3. (3)
   The maximum deceleration is independent of the weight of the car and increases with the coefficient of friction between the tire and the road
4. (4)
   In cars with two-wheel brakes only, the maximum deceleration increases as the percentage of weight on the rear wheels increases, as the height of the center of gravity above the road becomes less and as the wheelbase becomes longer
5. (5)
   The extent to which the maximum deceleration of two-wheel-brake cars is affected by a change in the ratio of the height of the center of gravity above the road to the length of wheelbase is shown to be as the square of the rate of deceleration and in the opposite direction; that is, as the ratio becomes greater, the deceleration becomes less in proportion to the square of its rate
6. (6)
   Although the maximum deceleration in cars with four-wheel brakes is to be obtained when all four wheels are locked, better control is secured when the front wheels are rotating; consequently, most brakes are adjusted to this manner