The formula to calculate the belt length in a two-pulley system is:
\[ BL = \left( \frac{DL + DS}{2} \cdot \pi \right) + (2 \cdot L) + \left( \frac{(DL - DS)^2}{4 \cdot L} \right) \]
Where:
A belt length is defined as the total length of material required to wrap around and between two different pulleys. It's important to keep in mind that the belt length will be in the same units of measure as the pulley diameters. For example, if both the smaller and larger pulley diameter is measured in inches, the belt length will also be in inches.
Let's assume the following values:
Step 1: Calculate the belt length using the formula:
\[ BL = \left( \frac{10 + 5}{2} \cdot \pi \right) + (2 \cdot 20) + \left( \frac{(10 - 5)^2}{4 \cdot 20} \right) \]
Step 2: Simplify the expression:
\[ BL = \left( 7.5 \cdot \pi \right) + 40 + \left( \frac{25}{80} \right) \approx 23.56 + 40 + 0.3125 \approx 63.8725 \]
The Belt Length (BL) is approximately 63.87 inches.