V-Belt Between Two Pulleys of the Same Diameter
The simplest configuration for a V-belt is a belt stretched between two pulleys that have the same diameter. In this case, the length of the V-belt (L) is (2 x l) + (π x D), where l (lowercase letter L) is the distance between the centers of the two pulleys and D is the diameter of the pulley. The symbol "π" means pi, which equals approximately 3.141593.
V-Belt Between Two Pulleys of Different Diameters
In this case, because the two pulleys have different diameters, the calculation for the V-belt length is more complicated than if the pulleys had the same diameter. Begin with an intermittent calculation of (arcsin(D-d)), where D is the diameter of the larger pulley, and d is the diameter of the smaller pulley. For all trigometric functions in this calculation, use radians for the operation. Divide this result by 2 times l, where l is the distance between the centers of the two pulleys. Label this final result "a."
To calculate the total belt length, use the following formula:
L = (π x (D + d)/2 + 2) x (l x cos(a) + a x (D -- d)/2).
For example, if pulley 1 has a diameter of 4 inches, pulley 2 has a diameter of 3 inches, and the two pulleys are 24 inches apart, then the total belt length is 59 inches.