(42S) Solver: Length of a V Belt

[Eddie W. Shore]

Blog Entry:

The following equation relates the length of a V belt, the center to center distance between two pulleys or sheaves:

L = 2 * C + 1.57 * (D + d) + (D - d)^2/(4 * C)

where:

L = length of the V belt, the belt that wraps around two pulleys (or sheaves)
C = center to center distance
D = diameter of the large pulley/sheave
d = diameter of the small pulley/sheave

Use the SOLVER function win calling VBELT.

LPULLEY: large pulley/sheave diameter
SPULLEY: small pulley/sheave diameter

Code:

LBL "VBELT"
MVAR "LENGTH"
MVAR "CENTER"
MVAR "LPULLEY"
MVAR "SPULLEY"
2
RCL * "CENTER"
RCL "LPULLEY"
RCL + "SPULLEY"
1.57
*
+
RCL "LPULLEY"
RCL - "SPULLEY"
X ↑ 2
4 
÷
RCL ÷ "CENTER"
+
RCL - "LENGTH"
END

Example 1:
Large Pulley Diameter = 1 in
Small Pulley Diameter = 3/4 in
Center to Center Distance = 1.5 in
Result: V Belt Length ≈ 5.7579 in

Example 2:
Large Pulley Diameter = 1 in
Small Pulley Diameter = 7/16 in
V Belt Length = 6.24 in
Result: Center to Center Distance ≈ 1.975 in

Source:

Gladstone, John "Air Conditioning Testing and Balancing: A Field Practice Manual" Van Nostrand Reinhold Company: New York. 1974 ISBN 0-442-22703-5