The conclusion to be drawn from this series of experiments is the great importance of high speed in the economy of belt transmission. The friction of belts on pulleys is evidently dependent on the velocity of sliding, and, as a general rule, the greater the velocity the greater the friction. There are but few apparent exceptions to this rule, and investigation of them has led to the inference that in all such cases, the condition of the belt or pulley surface had undergone a change either by heating or by deposit from the belt on the pulley. The percentage of slip is the measure of the power lost in transmission by the belt itself, and the higher the speed the less this becomes. There is a limit, however, to the power which may be transmitted as the speed is increased, and this limit is caused by the reduction in pressure against the pulley arising from the action of centrifugal force.

This point has been clearly demonstrated in a paper read before this Society by Mr. A. F. Nagle on the “Horse Power of Leather belts,”[43] and the formula there developed is written thus:

HP = CVtw(S - .012 V2) ÷ 550,(1.)

in which C is a constant to be determined from the arc of contact and coefficient of friction as expressed in the equation:

C = 1 - 10-.00758fα,(2.)
V = velocity of belt in feet per second.
t = thickness of the belt in inches.
w = width„„
S = working strength of leather in lbs. per square inch.
f = coefficient of friction.
α = arc of contact in degrees.

[43] Transactions A. S. M. E., Vol. II., page 91. See also Mr. Nagle’s Tables I., II., and III., in Appendix VI. to this paper for values of C and H.P.

The velocity at which the maximum amount of power can be transmitted by any given belt is independent of its arc of contact and coefficient of friction, and depends only upon the working strength of the material and its specific gravity.

From equation (1.) we obtain for the maximum power of leather belts the condition:

V = √(28S),(3.)