CHAPTER XVI

WORK, POWER, AND ENERGY; HORSE-POWER OF BELTING

103. Work.-Whenever a force causes a body to move, work is done. Unless the body is moved, no work is accomplished. A man may push against a heavy casting for hours and, unless he moves it, he does no work, no matter how tired he may feel at the end of the time. It is evident that there are two factors to be considered in measuring work-force and distance. In the study of levers, tackle blocks, and inclined planes we dealt with the problem of work. In any of these machines the work accomplished in lifting a weight is measured by the product of the weight and the distance it is moved. The work expended or put into the machine to accomplish this is the product of the force exerted times the distance through which this force must act. We found that, if we neglect the work lost in friction, the work put into a machine is equal to the work accomplished by it. The actual difference between the work put in and the work accomplished is the amount that is lost in friction. The following expressions may make these relations clearer:

Work lost in Friction = Work put in- Work got out.

104. Unit of Work.-The unit by which work is measured is called the Foot-pound. This is the work done in overcoming a resistance of one pound through a distance of 1 ft.; that is, if a weight of 1 lb. is lifted 1 ft., the work done is equal to 1 footpound. All work is measured by this standard. The work in foot-pounds is the product of the force in pounds and the distance in feet through which it acts. In lifting a weight vertically, the resistance, and hence, the force that must be exerted, is equal to the weight itself in pounds. The work done is the product of the weight times the vertical distance that it is raised. If a weight of 80 lb. is lifted a distance of 4 ft., the work done is 80×4 or 320 foot-pounds. It would require this same amount of work to lift 40 lb. 8 ft., or to lift 20 lb. 16 ft.

When a body is moved horizontally, the only resistance to be overcome is the friction. When a team of horses pulls a loaded wagon, the only resistances which it must overcome are the friction between the wheels and the axles, and the resistance on the tires caused by the unevenness of the road.

The work necessary to pump a certain amount of water is the weight of the water times the height through which it is lifted or pumped (plus, of course, the work lost in friction in the pipes). The work necessary to hoist a casting is the weight of the casting times the height to which it is lifted. The work done by a belt is the effective pull of the belt times the distance in feet which the belt travels. The work done in hoisting an elevator is the weight of the cage and of the load it carries times the height of the lift. Numerous other illustrations of work will suggest themselves to the student.

105. Power.-Power is the rate of doing work; that is, in calculating power the time required to do a certain number of footpounds of work is considered. If 10,000 lb. are lifted 7 ft. the work done is 70,000 foot-pounds, regardless of how long it takes. But, if one of two machines can do this in one-half the time that the other machine requires, then the first machine has twice the power of the second.

The engineer's standard of power is the Horse-power, which may be defined as the ability to do 33,000 foot-pounds of work per minute. The horse-power required to perform a certain amount of work is found by dividing the foot-pounds done per minute by 33,000. If an engine can do 1,980,000 foot-pounds in a minute, its horsepower would be 1,980,000÷33,000=60. An engine that can raise 66,000 lb. to a height of 10 ft. in 1 minute will do 66,000 lb. ×10 ft. = 660,000 foot-pounds per minute, and this will equal 660000=20 horse-power. If another engine takes 4 minutes to do this same amount of work, it is only one-fourth as powerful; the work done per minute will be 660000=165,000 foot-pounds per minute; and its horse-power is 185000-5 horse-power.

Example:

An electric crane lifts a casting weighing 3 tons to a height of 20 ft. from the floor in 30 seconds; what is the horse-power used?

106. Horse-power of Belting.-A belt is an apparatus for the transmission of power from one shaft to another. The driving pulley exerts a certain pull in the belt and this pull is transmitted by the belt and exerted on the rim of the driven pulley.

The power transmitted by any belt depends on two thingsthe effective pull of the belt tending to turn the wheel, and the speed with which the belt travels. From the preceding pages, it is easily seen that these include the three items necessary to measure power. The pull of the belt is the force. The speed, given in feet per minute, includes both distance and time. Force, distance and time are the three items necessary for the measurement of power.

The total pull that a belt will stand depends on its width and thickness. It should be wide enough and heavy enough to stand for a reasonable time the greatest tension put upon it. This is, of course, the tension on the driving side. This tension, however, does not represent the force tending to turn the pulley. The force tending to turn the pulley (or the Effective Pull, as it is called) is the difference in tension between the tight and the slack sides of the belt.

The effective pull that can be allowed in a belt depends primarily on the width, thickness, and strength of the leather, or whatever material the belt is made of. Besides, we must consider that every time a belt causes trouble from breaking or becoming loose, it means a considerable loss in time of the machine, of the men who are using it, and of the men required to make the repairs and, therefore, it should not be loaded as heavily as might otherwise be allowed. Leather belts are called "single,” "double," "triple," or "quadruple," according to whether they are made of one, two, three, or four thicknesses of leather. Good practice allows an effective pull of 35 lb. in a single leather belt per inch of width. In a double belt a pull of 70 lb. per inch of width may be allowed. The pull times the width gives the total effective pull or the force transmitted by the belt.

The force times the velocity, or speed, of the belt in feet per minute will give the foot-pounds transmitted by it in 1 minute. One horse-power is a rate of 33,000 foot-pounds per minute; hence, the horse-power of a belt is obtained by dividing the foot-pounds transmitted by it per minute by 33,000. The velocity of the belt is calculated from the diameter and revolutions per minute of either one of the pulleys over which the belt

travels, as explained in Chapter VII. From these considerations, the formula for the horse-power that a belt will transmit may be written

where H= horse-power

P effective pull allowed per inch of width
W = width in inches

V-velocity in feet per minute

Stated in words, this formula would read as follows: "The horsepower that may be transmitted by a belt is found by multiplying together the allowable pull per inch of width of the belt, the width of the belt in inches, and the velocity of the belt in feet per minute and then dividing this product by 33,000.

Example:

Find the horse-power that should be carried by a 12-in. double leather belt, if one of the pulleys is 14 in. in diameter and runs 1100 R. P. M.

Explanation: To get the horsepower, we must first find the values of P, W, and V. We will take P as 70 lb. since this is a double belt. W is given, 12 in. V, the velocity, is obtained by multiplying the circumference of the pulley by the R. P. M., which gives us 4032. Multiplying these three together gives 3,386,880 foot-pounds per minute, and dividing by 33,000 we have 102+ as the horse-power that this belt might be required to carry.

107. Widths of Belts.-It is possible, also, to develop a formula with which to calculate the width of belt required to transmit a certain horse-power at a given velocity.

One horse-power is 33,000 foot-pounds per minute. Then the given number of horse-power multiplied by 33,000 gives the number of foot-pounds to be transmitted per minute.

Foot-pounds per minute=33000 XH

If we know the velocity in feet per minute, we can divide the foot-pounds per minute by the velocity; the quotient will be the force or the effective pull in the belt.

Now the force can be divided by the allowable pull per inch of width of belt. The result will be the necessary width.

Stated in words, this formula would read: "To obtain the width of belt necessary for a certain horse-power; multiply the horsepower by 33,000 and divide by the product of the allowable pull per inch of width of belt times the velocity of the belt in feet per minute."

Example:

Find the width of a single belt to transmit 10 horse-power at a speed of 2000 ft. per minute.

108. Rules for Belting. 1. Belt Thickness.-It is generally advisable to use single belting in all cases where one or both pulleys are under 12 in. in diameter, and double belting on pulleys 12 in. or larger. Triple and quadruple belts are used only for main drives where considerable power is to be transmitted and where a single or double belt would have an excessive width. A triple belt should not be run on a pulley less than 20 in. in diameter, nor a quadruple belt on a pulley less than 30 in. in diameter.

2. Tension per Inch of Width.-An effective pull of 35 lb. per inch of width of belt is allowable for single belts. For double belts an effective pull of 70 lb. per inch is allowable unless the belt is used over a pulley less than 12 in. in diameter, in which case only 50 lb. per inch should be allowed. A prominent manufacturer of rubber belting recommends 33 lb. per inch of width of belt for 4-ply belts and 43 lb. for 6-ply rubber belts.

3. Belt Speeds.-The most efficient speed for belts to run is from 4000 to 4500 ft. per minute. Belts will not hug the pulley and therefore will slip badly if run at a speed of over one mile per minute. These figures are seldom reached in machine shops.