CHAPTER XV

HORSEPOWER OF ENGINES

103. Steam Engines. In the last chapter the meaning of the term horsepower was explained and its application to belting was discussed. We will now take up the calculations of the horsepowers of steam and gas engines.

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

FIG. 78. Simple steam boiler and engine.

Let us study the action of the steam in the cylinder of the ordinary double-acting steam engine. In Fig. 78 is shown a 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 starting point. It has thus made two strokes while the flywheel has made one complete revolution (the motion of the piston from one end of the cylinder to the other is called a "stroke"). During both strokes of the piston the steam pressure was acting on the piston,

forcing it to move; therefore, both strokes were what is called "power strokes," or "working strokes." This type of engine is known as a double-acting steam engine, since the steam acts on both sides of the piston and there are two power strokes to each revolution. In the single-acting steam engine, the steam is admitted to one end of the cylinder only, and, therefore, there is but one power stroke to each revolution.

As the piston moves from one end of the stroke to the other, the pressure of the steam in the cylinder does not remain the same, but varies according to the action of the valve in cutting off the admission of the steam. However, it is possible to obtain the average pressure per square inch throughout the stroke, or what is called the "mean effective pressure." This average pressure, or m.e.p., multiplied by the piston area in square inches gives the total average pressure or force acting against the piston. The total pressure or force exerted on the piston multiplied by the length of the stroke in feet gives the number of foot-pounds of work performed during one stroke. This result, when multiplied by the number of working strokes per minute, gives the foot-pounds of work per minute, and this divided by 33,000 gives the horsepower.

The following are the symbols generally used:

hp. = horsepower.

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.

=

=

PXAXL foot-pounds of work done per stroke.

foot-pounds of work done per minute, and

PX AXLX N

33,000 PXLXAX N

33,000

or, as usually written,

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, 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 horsepower of a 32- by 54-in. steam engine running at 94 r.p.m. with an m.e.p. (mean effective pressure) of 60 lb. per sq. in. 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 horsepower 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 m.e.p. 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. will be from 20 to 85% of the boiler pressure, depending upon the type of the engine and the load it is carrying. Horsepower calculated as explained here is called indicated horsepower because an indi

cator is used to determine it. The indicated horsepower represents the power delivered to the piston by the steam.

104. 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. Figure 79 shows in four views the operation of such an engine. Four strokes, or two revolutions, are required for each explosion that occurs in the

FIG. 79. The four strokes of a four-cycle gas engine.

cylinder. Consequently, in calculating the horsepower of a single-cylinder gas engine, the number of working strokes (or N in the horsepower 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 crankshaft and N is, therefore, the same. as the number of r.p.m.

The m.e.p. of a gas engine is from 40 to 100 lb. per square inch, depending principally upon the fuel used. For gasoline or

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

Example:

Calculate the indicated horsepower of a single-cylinder, 5- by 8-in., four-cycle gasoline engine running at 450 r.p.m. with a m.e.p. of 80 lb. per square inch.

80 lb. per sq. in.

=

=

2

19.6 sq. in.

225 working strokes per min.

PXLXA× N

105. Air Compressors. An air compressor is like a doubleacting steam engine in appearance; but, instead of delivering power, it requires power from some other source to run it. This power is stored in the air and later is recovered when the air is used. An air compressor takes air into the cylinder, raises its pressure by compressing it, and then forces it into the air line or the storage tank. When the horsepower required to drive a compressor is being calculated, the same formula can be used as for a steam engine. The value of P to use is not the pressure to which the air is raised, but the average or mean pressure during the stroke. It is usually somewhat less than half the final air pressure; for example, when an air compressor is delivering air at 80-lb. pressure, the mean pressure on the piston is about 33 lb.

Most air compressors are double-acting, though there are many small single-acting ones.

Example:

A double-acting 12- by 14-in. air compressor is running 150 r.p.m. It is supplying air at 100 lb., and the mean pressure in the cylinder is 37 lb. per square inch. Calculate the horsepower necessary to run it.