Measure the distance between the centres of the pulleys, the diameters of the pulleys, and the thickness of the belt. Add the thickness of the belt to the diameter of a pulley, and this gives the effective diameter. Half this is the effective radius, and it is to be noted that the effective radius, or the effective diameter, of a pulley should generally be used in all calculations relating to belts and pulleys. In making such calculations, care must be taken, also, to have all the dimensions in the same unit, feet or inches. In general, it is well to reduce all dimensions to feet.

To illustrate the preceding remarks, suppose that the diameter of a pulley is 10 inches, and that the thickness of the belt passing over it is 3/8 of an inch. What is the effective radius, in feet? Ans. The effective diameter is 10-3/8 inches; hence the effective radius is 5-3/16 inches. 5 inches is 0.417 ft. 3/16 of an inch is 0.016 ft. Hence 5 -3/16 inches is 0.433 ft.

There are two cases to be considered, one in which the belt is crossed, and the other in which it is open.

To find the length of a crossed belt passing over two pulleys:

(1) Divide the sum of the radii of the two pulleys by the distance between their centres, and find from the table of factors the factor corresponding to this quotient.

('.') Multiply the factor so found by the sum of the radii.

(3) Multiply the sum of the radii by the number 3.1416.

(4) Subtract the square of the sum of the radii from the square of the distance between centres, and take the square root of the remainder. Multiply the quantity bo obtained by 2.

(5) Take the sum of the quantities obtained by (2), (3), and (4).

Example.-The radius of one pulley is 42 inches, of the other 36; the distance between centres of pulleys is 1- feet, and the thickness of the bell is 1/4 of an inch; required, the length of the belt.

'I he effective radii are 3.51 feet and 3.01 feet.

(1) Sum of radii, 6.520. Distance between centres, 12. Quo tient of first quantity divided by second, 0.54. Factor in table corresponding to this quotient, 1.141.

(2) 1.141 multiplied by 6.52, 7.439+ .

(3) 6.541 multiplied by8.1.416.20.483+

Square root of difference, 10.074 + . 10.074 multiplied by 2, 20.148.

(5) Sum of 7.439, 20.483. and 20.148, 48.07 feet, or 48 feet and 27/32 of an inch, length of belt required.

Table Of Factors For Determining The Length Of Belts

To find the length of an open belt passing over two pulleys: (1) Divide the difference of the radii by the distance between centres, and find from the table of factors the factor corresponding to this quotient.

(2) Multiply the factor so found by the difference of the radii.

(3) Multiply the sum of the radii by the number 3.1416.

(4) Subtract the square of the difference of the radii from the square of the distance between centres, and take the square root of the remainder. Multiply the quantity so obtained by 2.

(5) Take the sum of the quantities obtained by (2), (3), and (4). It will be observed that these rules require only simple arithmetical operations.

Example.-Given, diameter of driving-wheel, 36 inches; of driven wheel, 9 inches; distance between centres, 5 feet; thickness of belt, 1/8 of an inch; what is the length of the belt?

Effective radii, 1.505 and 0.330 feet. (1) Difference of radii, 1.125. Distance between centres, 5. Quotient, 0.23. Factor in. table corresponding to this quotient, 0.464. (2) 0.464 multiplied by 1.125, 0.522. (3) Sum of radii, 1.885. 1.885 multiplied by 3.1416, 5.922, Square root of difference, 4.872. 4.872 multiplied by 2, 9.744. (5) Sum of 0.522, 5.922, and 9.744, 16.188 feet, or 16 feet 2 1/4 inches, length of belt. B.