Given an 8" diameter driver sheave, a 12" diameter driven sheave, and a center to center distance of 36", what is the precise length of the belt?

To determine the precise length of the belt in a pulley system, the formula used accounts for the diameters of the driver and driven sheaves, as well as the center-to-center distance between them.

The formula for the belt length ( L ) is:

[

L = 2C + \frac{\pi}{2}(D_1 + D_2) + \frac{(D_2 - D_1)^2}{4C}

]

Where:

• ( C ) is the center-to-center distance (36 inches in this case),

• ( D_1 ) is the diameter of the driver sheave (8 inches),

• ( D_2 ) is the diameter of the driven sheave (12 inches).

Plugging in the values:

1. Calculate ( 2C ):

[

2C = 2 \times 36 = 72 \text{ inches}

]

2. Calculate the second term:

[

\frac{\pi}{2}(D_1 + D_2) = \frac{\pi}{2}(8 + 12) = \frac{\pi}{2} \times 20 = 10\