Calculating the Horse Power of an Engine

The horse-power of an engine may be calculated as follows:

Rule.—Multiply the area of the piston by the average steam pressure upon the piston throughout the stroke, and by the length of the stroke in inches, which gives the number of inch pounds received by the piston from the steam during one stroke.

As there are two piston strokes to one revolution of the engine, we multiply by two, and thus get the number of inch pounds received by the piston in one revolution.

By multiplying this by the number of revolutions the engine makes in a minute, we get the number of inch pounds of power received by the piston in a minute.

By dividing this by 12, we get the number of foot pounds the piston receives per minute, and dividing this by 33,000 lbs. we get the horse-power of the engine.

It has already been stated that Watt determined that a horse was capable of exerting a power equal to the raising of 33,000 lbs. one foot high in a minute, hence, having foot pounds of the engine per minute, dividing them by 33,000 gives the horse power.

This gives the amount of power received by the piston, but it is evident that the engine cannot exert so much power, because part of it is expended in overcoming the friction of the moving parts of the engine.

The amount of the piston power expended in overcoming the friction depends upon the fit of the parts, upon the lubrication and the amount of the load.

Thus, the friction of the cross head guides, of the cross head pin, of the crank pin and of the crank shaft bearings will increase with the amount of resistance offered to the piston motion.

The average pressure on the piston is a difficult thing to find, however, for several reasons.

First, because the pressure in the cylinder may, during the live steam period, vary from that in the steam chest because of the ports being too small or from the passages being choked from a defective casting.

Second, because the steam is wire drawn during the time that the slide valve is closing the port to effect the cut off.

Third, because the live steam in the port and passage at the time the cut off occurs gives out some power during the period of expansion.

Fourth, because there is some condensation of the steam in the cylinder after the point of cut off, and there is no means of finding by calculation how much loss there may be from this cause.

During the live steam period there is also loss from condensation in the cylinder, but this is made up for by steam from the steam chest.

Fifth, the loss from condensation after the cut off has occurred will vary with the speed of the engine, and is greater in proportion as the piston speed is less, because there is more time for the condensation to occur in.

Sixth, there is some pressure on the piston between the time that the exhaust begins and the piston ends its stroke.

Seventh, because the compression absorbs some of the piston power.

Assuming the average pressure on the piston to be known, however, we may calculate the horse power as follows:

Example.—What is the horse power of an engine whose piston is 20 inches in diameter, and stroke 30, the revolutions per minute being 120, and the average pressure on the piston 60 lbs. per square inch?

Diameter of piston 20

Diameter of piston squared 400

.7854

400

Area of piston = 314.1600 ( these two ciphers neglected.)

60 average steam pressure.

lbs. pressure on piston 18849.60 ( this cipher neglected.)

30 length of stroke in inches.

565488.0 inch lbs. per stroke.

2 two piston strokes per revolution.

12 ) 1130976 inch lbs. per revolution.

94248 foot lbs. per revolution.

120 revolutions per minute.

1884960

94248

11309760 foot lbs. per minute.

33000 ) 113097 60 ( 342.72 = horse power of engine.

99000

14097 6

13200 0

897 60

660 00

237 600

231 000

6 6000

In working out the calculation, the ciphers that are decimals and are on the right hand are neglected or taken no account of, because they represent no value and may therefore be discarded.

Thus the area of the piston is 314.1600 inches, the two right hand ciphers having no value. Again the lbs. pressure on the piston is 18849.60 lbs., and the right hand cipher, having no value, is discarded. The inch lbs. per stroke is 565488.0, and the decimal cipher, representing nothing, is discarded when multiplying by the 2.

We have in this case taken no account of the fact that the piston rod prevents the steam from acting against a part of the piston area during one stroke; hence for correct results we must subtract from the area of the piston one half the area of the piston rod.

The horse power thus obtained is that which the engine receives from the steam, and is more than the engine is capable of exerting to drive machinery, because a part of this power is consumed in overcoming the friction of the working parts of the engine.