By the aid of the accompanying tables, now published for the first time, it will be easy for any one to ascertain the amount of power that can be safely transmitted by good leather belts under ordinary circumstances. It is scarcely necessary to add that the power transmitted by a belt in any special case can only be ascertained by experiment. All that can be done by the most elaborate rales is to show what power ought to be transmitted if a belt is properly arranged. The tables and accompanying rules will be useful, therefore, in calculations of the width of belt required to do a definite amount of work under given circumstances. With these preliminary explanations, the use of the tables will be illustrated.

I. Other things being equal, the power transmitted by a belt depends upon the arc of contact and the speed of the belt.

II. To find the arc of contact between a belt, and a pulley, by the aid of the accompanying table.

First Method. Measure the length of the portion of the circumference of the pulley that is in contact with the belt, and the diameter of the pulley. Divide the first measurement by the radius of the pulley, which gives the length of the arc of contact for a circle whose radius is 1. Find the number nearest to this in the column of the table headed "Length of arc for a radius of 1, " and the required angle will be found in the Same horizontal line of the next column, to the left, headed "Arc of contact."

Table For Finding The Arc Of Contact Of A Belt With A Pulley

Example.-Suppose the length of the circumference of a pulley in contact with a belt is 8-1/2 feet, and the diameter of the pulley is 4 feet. The quotient arising from dividing 8-1/2 by 2 (the radius of the pulley)is 4.25, and the number in the table nearest to this is 4.26, showing that the required arc of contact is about 244°.

[It is to be noted that, in calculations of this kind, the effective radius of the pulley should be used (see page 110), and all dimensions must be referred to the same unit of measurement.]

Second Method

Measure the effective diameters of both pulleys, and the distance between their centres. There are two cases to be considered:

(a) To find the arc of contact for a crossed belt.

Divide* the sum of the radii of the two pulleys by the distance tween their centres; find in the column of constants the nearest number to the quotient, and pick out the corresponding angle.

Example.-Diameter of driven pulley, 20 inches; of driving pulley, 24; distance between centres, 8 feet. What is the arc of contact on each pulley of a crossed belt passing over them? Sum of radii, 1.8333 feet. 1.8333 divided by 8 is 0.23, nearly. From the table, it appears that the angle required is 207°.

(b) To find the arc of contact for an open belt.

Divide the difference of the radii of the two pulleys by the distance between their centres, and find the angles corresponding to the constant nearest to the quotient, in the table.

Example.-In the case of an open belt passing over two pulleys, the following dimensions are given: Diameter of driving pulley is 5.25 feet; diameter of driven pulley is 3.5 feet; distance between centres is 9 feet. The difference of radii (0.875) divided by 9 is 0.097+. Nearest constant in table, 0.1, corresponding to an angle of contact of 192' on the driving, and 168' on the driven pulley.

[These rules are founded on the assumption that the belt is drawn perfectly tight between the pulleys. Where there is much deviation from this, in practice, it is better to employ the first method.]

III. To find the speed of a belt, in feet, per minute.

Multiply the diameter of either pulley, in feet, by 3.1416 times the number of revolutions that it makes per minute.

Example.-A. belt passes over a pulley that is 3 feet in diameter, and makes 200 revolutions a minute. The speed of the belt is the product of 3, 3.1416, and 200, or about 1885 feet per minute.

IV. To find the power that can be safely transmitted by a good leather belt of given width, passing over smooth iron pulleys, and running at a given speed, the arc of contact being also given.

This is determined by means of the second table. Find the horse-power for a belt one inch in width, for the nearest arc of contact in the table, and the nearest speed of belt, and multiply this by the width of the belt. If the belt is open, and the pulleys have different diameters, take the angle of contact made by the belt with the smaller pulley.