**HP Prime and HP 42S/DM42/Free42: Length of V Belts Solver**

**Introduction**

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

**HP Program VBELT**

This program creates four global variables:

beltlength = L

centerdist = C

lrgpulley = D

smpulley = d

The program then takes you to the Num page of the Solve app. This allows us to create descriptive variables to help us in the Solve app.

Global variables are created outside the main program.

// create global variables

// outside the main program

EXPORT beltlength;

EXPORT centerdist;

EXPORT lrgpulley;

EXPORT smpulley;

EXPORT VBELT()

BEGIN

// 2019-04-28 EWS

STARTAPP(“Solve”);

// uncheck E0-E9

LOCAL k;

FOR k FROM 0 TO 9 DO

Solve.UNCHECK(k);

END;

// enter equation to E1

E1:=”beltlength=2*centerdist+

1.57*(lrgpulley+smpulley)+

(lrgpulley-smpulley)^2/

(4*centerdist)”;

Solve.CHECK(1);

// go to Num View

STARTVIEW(2);

END;

**HP 42S/DM42/Free 42 Solver Program VBELT**

Use the SOLVER function win calling VBELT.

LPULLEY: large pulley/sheave diameter

SPULLEY: small pulley/sheave diameter

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

**Examples**

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

Eddie

All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.