(66)
which is useful in determining the original tension required to enable a belt to transmit a given force between two pulleys.
The equations 65 and 66 are applicable to a kind of brake called a friction-strap, used to stop or moderate the velocity of machines by being tightened round a pulley. The strap is usually of iron, and the pulley of hard wood.
Let α denote the arc of contact expressed in turns and fractions of a turn; then
θ = 6.2832a
eƒθ = number whose common logarithm is 2.7288ƒa
(67)
See also [Dynamometer] for illustrations of the use of what are essentially friction-straps of different forms for the measurement of the brake horse-power of an engine or motor.
§ 104. Stiffness of Ropes.—Ropes offer a resistance to being bent, and, when bent, to being straightened again, which arises from the mutual friction of their fibres. It increases with the sectional area of the rope, and is inversely proportional to the radius of the curve into which it is bent.
The work lost in pulling a given length of rope over a pulley is found by multiplying the length of the rope in feet by its stiffness in pounds, that stiffness being the excess of the tension at the leading side of the rope above that at the following side, which is necessary to bend it into a curve fitting the pulley, and then to straighten it again.
The following empirical formulae for the stiffness of hempen ropes have been deduced by Morin from the experiments of Coulomb:—