To Calculate the Horse Power from a Diagram

In calculating the horse power of an engine, the only assistance given by the indicator is, that it provides a means of obtaining the average pressure of the steam throughout the piston stroke.

There are two methods of doing this, one by means of a planimeter or averaging instrument, and the other by means of lines called ordinates.

The ordinates or lines are drawn at a right angle to the atmospheric line, as shown in Fig. 3372, and each line is taken to represent the average height or length of one-half of the space between itself and the next lines.

Suppose, for example, that we require to get the area of that part of the diagram that lies between the dotted lines in the figure, and it is clear that the average height of this part of the diagram is represented by the height of the full line between them.

Any number of ordinates may be used, and the greater their number the greater the accuracy obtained. It is, however, usual to draw 10.

The end ordinates a and d, in the figure, should be only half the distance from the ends of the diagram that they are from the next ordinate, as will be seen when it is considered that the ordinate is in the middle of the space it represents.

The ordinates being drawn their lengths, are added together, and the sum so obtained is divided by the number of ordinates, which gives the average height of the ordinates.

Suppose, then, that the average height of the ordinate is two inches, and that the scale of the spring of the indicator that took the diagram was 30 lbs., then the average pressure, shown by the diagram, will be 60 lbs. per square inch. Or in other words, each inch in the height of the ordinate represents 30 lbs. pressure per square inch.

The mean effective pressure having been found, the indicated horse power (or I. H. P. as it is given in brief) is found by multiplying together the area of the piston (minus half the area of the piston rod when great accuracy is required) and the travel of the piston in feet per minute, and dividing the product by 33,000, an example having been already explained.

It is to be observed, however, that when great accuracy is required a diagram should be taken from each end of the cylinder, as the mean effective pressure at one end of the cylinder may vary considerably from that at the other.

This will be the case when a single valve is used with equal lap, because, in this case, the point of cut off will vary on one stroke as compared with the other, which occurs by reason of the angularity of the connecting rod.

When cut off valves or two admission valves are used, it may occur from improper adjustment of the valves. It occurs in all engines, because on one side of the piston the piston rod excludes the steam from the piston face, unless, indeed, the piston rod passes through both covers, in which case the rod area must be subtracted from the piston area.

If the expansion curve in a diagram from a non-condensing engine should pass below the atmospheric line, then the mean effective pressure of that part of the card that is below the atmospheric line must be subtracted from the mean effective pressure of that part that is above the atmospheric line, because the part below represents back pressure or pressure resisting the piston motion.

The planimeter affords a much quicker and more accurate method of obtaining the average steam pressure from a diagram.

Coffin’s averaging instrument or planimeter is shown in Fig. 3373. The diagram is traced by the point o, and the register wheel gives the area of the diagram.

A quick method of approximating the mean effective pressure (or M. E. P. as it is called) of a diagram is to draw a line a b, in Fig. 3374, touching the expansion curve at a, and so inclined that the space e is, as near as the eye can judge, equal to the space d. Then the line f drawn in the middle of the diagram, and measured on the scale of the spring that was used to take the diagram, represents the mean effective pressure, or M. E. P. of the diagram.