LENGTH OF BELTS 71 



0.0349, adding TT to the product and multiplying the sum by 

 the radius of the pulley. Or 



Length = radius X(TT +0.0349 sin- 1 - 

 \ * 



If the length of belt in contact with the smaller pulley is 

 desired, the formula will be 



Length = radius X ( TT 0.0349 sin - x - ) . 

 \ ** / 



Length of Belts. Whenever possible the length of belt 

 required for a pair of pulleys should be determined by actual 

 measurement by means of a steel tape passed around the 

 pulleys. Where this is impracticable, the length of an open 

 belt can be determined by calculation, using one of the three 

 formulae below published by Carl G. Barth in the American 

 Machinist, March 12, 1903: 



'+C*+2C. (i) 



T 1 



+Cx- 



12 X 



L is the length of the belt, D the diameter of the larger pulley 

 and d the diameter of the smaller pulley, and C is the center 

 line distance of the pulleys, all in the same unit, inches or feet 



as the case may be, TT = 3.1416, and x = ( - - ) . The accuracy 



\ 2C / 



of the formulae is as follows, testing them by the limiting case 

 where d=o and C- , giving L=Dir: Formula (i) gives a 



2 



result somewhat over 2 per cent short; formula (2) gives a 

 result about i per cent short; formula (3) gives a result under 

 0.4 per cent short. 



