place the belt on the pulleys, and force the shaft back into place. Of other methods of fastening belts, the leather lacing is undoubtedly the best when properly done. In lacing a belt, begin at the center and lace both ways with equal tension. Fig. 69 shows an excellent method of lacing belts. The lacing should be crossed on the outside of the belt. On the inside, the lacing should lie in line with the belt. Holes should be about 1 in. apart and their edges should be at least in. from the ends of the belt. The holes should be punched, preferably with an oval punch, the long dimension of the oval running lengthwise of the belt so as not to weaken the belt too much.

PROBLEMS

181. A casting weighs 300 lb. How much work is required to place it on a planer bed 3 ft. 5 in. above the floor?

182. How much work is required to pump 5000 gallons of water into a tank 150 ft. above the pump?

183. Find the horse-power that may be transmitted per inch of width by a single belt running at 2500 ft. per minute. How does this compare with a double belt running at the same speed?

184. A 6 in. double belt is carried by a 48 in. pulley running 250 R. P. M. Find the horse-power that may be transmitted.

185. A shop requires 50 horse-power to run it. The main shaft runs 250 R. P. M. Select a main driving pulley and determine width of double belt to run the shop.

186. A foundry fan runs 3145 R. P. M., and requires 24 horse-power to run it. There are two single belts on the blower running over pulleys 7 in. in diameter. Determine the necessary width of belt.

Note.-(Each belt should be wide enough to drive the fan so that in case one breaks, the other will carry the load.)

187. A belt is carried by a 36 in. pulley running at 150 R. P. M. The effective pull in the belt is 240 lb. Find the horse-power.

188. A pumping engine lifts 92,500 gallons of water every hour to a height of 150 ft. What is the horse-power of the engine?

189. If a freight elevator and its load weigh 5000 lb., what horse-power must be exerted to raise the elevator at a rate of 2 ft. per second?

190. A touring car is travelling on a level road at a rate of 45 miles an hour. If it is shown by actual test that a force of 200 lb. is required to maintain this rate of speed, what horse-power must the engine deliver at the wheels?

CHAPTER XVII

HORSE-POWER OF ENGINES

109. Steam Engines. In the last chapter, the meaning of the term horse-power was explained and its application to belting was discussed. We will now take up the calculations of the horse-powers of steam and gas engines.

One horse-power was given as the ability to do 33,000 footpounds of work in 1 minute. From this we see that the best way to get the horse-power of any engine is to find out how many foot-pounds of work it does in 1 minute and then to divide the number of foot-pounds delivered in a minute by 33,000.

Let us study the action of the steam in the cylinder of the ordinary double-acting steam engine. In Fig. 70 is shown a

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FIG. 70.

section of a very simple boiler and engine. We find that steam enters one end of the cylinder behind the piston and pushes the piston toward the other end of the cylinder. Meanwhile, the valve is moved to the other end of the valve chest. The operation is then reversed and the piston is pushed back to the startingpoint. It has thus made two strokes, or one revolution. The steam pressure on the piston is not the same at all points in the stroke, but varies according to the action of the valve in cutting. off the admission of steam into the cylinder. However, it

is possible to obtain the average or "mean effective pressure" per square inch during a stroke, and, if we multiply this by the piston area in square inches, we will have the average total pressure or force exerted during one stroke. Now reduce the length of the stroke to feet and multiply this by the total pressure just found, and we have the number of foot-pounds of work done during one stroke. This result, when multiplied by the number of working strokes per minute, gives the foot-pounds per minute and this divided by 33,000 gives the horse-power. The following are the symbols generally used:

P= Mean pressure in pounds per square inch.
A = Area of piston in square inches.
L=Length of stroke in feet.

N = Number of working strokes per minute.
PXA=Total pressure on piston.

PXAXL ft. lb. of work done per stroke.
PXAXLXN=ft. lb. of work done per minute, and hence

PXLXAXN

33000

In the latter form, the letters in the numerator

spell the word Plan and the formula is thus easily remembered. In the common steam engine, there are two working strokes for every revolution of the engine, that is, the engine is what is called double acting, and N is twice the revolutions per minute. A few steam engines, like the vertical Westinghouse engine, are single acting and, hence, have only one working stroke of each piston per revolution. Unless otherwise stated, it will be assumed in working problems that a steam engine is double acting. Example:

Find the horse-power of a 32 in. by 54-in. steam engine running at 94 R. P. M. with an M. E. P. (Mean Effective Pressure) of 60 lb. Note. In giving the dimensions of an engine cylinder, the first number represents the diameter and the second number the stroke.

Notice particularly that the area of the piston is expressed in square inches, because the pressure is given in pounds per square inch; but that the stroke is reduced to feet because we measure work in foot-pounds and, consequently, must express in feet the distance which the piston moves.

If an engine has more than one cylinder, the horse-power of each can be calculated and the results added; or, if the cylinders are arranged to do equal amounts of work, we can find the horsepower of one cylinder and multiply this by the number of cylinders.

The mean effective pressure can be obtained for any engine by the use of a device called an "indicator," which draws a diagram showing just what the pressure is in the cylinder at each point in the stroke. From this diagram, we can calculate the average or mean effective pressure for the stroke. This pressure must not be confused with the boiler pressure or the pressure in the steam pipe. For instance, when the steam comes from the boiler to the engine at 100 lb. pressure, the mean pressure in the cylinder will not be 100 lb., as it would be very wasteful to use steam from the boiler for the full stroke. Instead, the M. E. P. (Mean Effective Pressure) will be from 20% to 85% of the boiler pressure depending on the type of the engine and the load it is carrying. Horse-power calculated as explained here is called Indicated Horse-power because an indicator is used to determine it. The indicated horse-power represents the power delivered to the piston by the steam.

110. Gas Engines.-The most common type of gas or gasoline engine works on what is called the four stroke cycle. Such an engine is called a four-cycle engine. Fig. 71 shows in four views the operation of such an engine. Four strokes, or two revolutions, are required for each explosion that occurs in the cylinder. Consequently, in calculating the horse-power of a single cylinder gas engine, the number of working strokes (or N in the horse-power formula) is one-half of the R. P. M. There is another type of gasoline engine called the two-cycle engine. A single cylinder two-cycle engine has one working stroke for each revolution of the crank shaft and N is therefore the same as the number of R. P. M.

The mean effective pressure of a gas engine is from 40 to 100 lb. per square inch, depending chiefly on the fuel used. For

gasoline or natural gas or illuminating gas it is usually between 80 and 90 lb. per square inch.

What horse-power could be delivered by a single cylinder 5 in. by 8 in. four-cycle gasoline engine running 450 R. P. M.?

Note.-Use a value of P=80 lb. per square inch.