throughout the stroke, due to the expansion of the steam, while the back pressure remains constant, except for the effect of compression at the end of the stroke. The theoretical back pressure in a non-condensing engine (one exhausting into the atmosphere) is that of the atmosphere or 14.7 pounds per square inch above a vacuum, but in actual practice it is about 2 pounds above atmospheric pressure, or 17 pounds absolute, due to the resistance of exhaust ports and connecting pipes. In the case of a condensing engine (one exhausting into a condenser) the back pressure depends upon the efficiency of the condenser, averaging about 3 pounds absolute pressure in the best practice.

Effective Pressure.—This is the difference between the pressure on the steam side of the piston and that on the exhaust side, or in other words, the difference between the working pressure and the back pressure. This value varies throughout the stroke with the expansion of the steam.

Mean Effective Pressure.—It has just been stated that the effective pressure varies throughout the stroke. The mean effective pressure (M. E. P.) is the average of all the effective pressures, and this average multiplied by the length of stroke, gives the work done per stroke.

Line of Absolute Vacuum.—In the diagram shown in Fig. 6, the line OX is the line of absolute vacuum; that is, it is assumed that there is no pressure on the exhaust side of the piston. In other words, the engine is exhausting into a perfect vacuum.

Atmospheric Line.—This is a line drawn parallel to the line of absolute vacuum at such a distance above it as to represent 14.7 pounds pressure per square inch, according to the scale used.

Construction of Ideal Diagram

Fig. 7. Constructing a Steam Engine Work Diagram

One of the first steps in the design of a steam engine is the construction of an ideal diagram, and the engine is planned to produce this as nearly as possible when in operation. First assume the initial pressure, the ratio of expansion, and the percentage of clearance, for the type of engine under consideration. Draw lines OX and OY at right angles as in Fig. 7. Make OR the same percentage of the stroke that the clearance is of the piston displacement; make RX equal to the length of the stroke (on a reduced scale). Erect the perpendicular RA of such a height that it shall represent, to scale, an absolute pressure per square inch equal to 0.95 of the boiler pressure. Draw in the dotted lines AK and KX, and the atmospheric line LH at a height above OX to represent 14.7 pounds per square inch. Locate the point of cut-off, B, according to the assumed ratio of expansion. Points on the expansion curve BC are found as follows: Divide the distance BK into any number of equal spaces, as shown by a, b, c, d, etc., and connect them with the point O. Through the points of intersection with BP, as a´, b´, c´, d´, etc., draw horizontal lines, and through a, b, c, d, etc., draw vertical lines. The intersection of corresponding horizontal and vertical lines will be points on the theoretical expansion line. If the engine is to be non-condensing, the theoretical work, or indicator diagram, as it is called, will be bounded by the lines ABCHG.

The actual diagram will vary somewhat from the theoretical, as shown by the shaded lines. The admission line between A and B will slant downward slightly, and the point of cut-off will be rounded, owing to the slow closing of the valve. The first half of the expansion line will fall below the theoretical, owing to a drop in pressure caused by cylinder condensation, but the actual line will rise above the theoretical in the latter part of the stroke on account of re-evaporation, due to heat given out by the hot cylinder walls to the low-pressure steam. Instead of the pressure dropping abruptly at C, release takes place just before the end of the stroke, and the diagram is rounded at CF instead of having sharp corners. The back pressure line FD is drawn slightly above the atmospheric line, a distance to represent about 2 pounds per square inch. At D the exhaust valve closes and compression begins, rounding the bottom of the diagram up to E.

The area of the actual diagram, as shown by the shaded lines in Fig. 7, will be smaller than the theoretical, in about the following ratio:

Large medium-speed engines, 0.90 of theoretical area.
Small medium-speed engines, 0.85 of theoretical area.
High-speed engines, 0.75 of theoretical area.

CHAPTER II

RATING AND GENERAL PROPORTIONS OF STEAM ENGINES

The capacity or power of a steam engine is rated in horsepower, one horsepower (H. P.) being the equivalent of 33,000 foot-pounds of work done per minute. The horsepower of a given engine may be computed by the formula:

in which

The derivation of the above formula is easily explained, as follows: The area of the piston, in square inches, multiplied by the mean effective pressure, in pounds per square inch, gives the total force acting on the piston, in pounds. The length of stroke, in feet, times the number of strokes per minute gives the distance the piston moves through, in feet per minute. It has already been shown that the pressure in pounds multiplied by the distance moved through in feet, gives the foot-pounds of work done. Hence, A × P × L × N gives the foot-pounds of work done per minute by a steam engine. If one horsepower is represented by 33,000 foot-pounds per minute, the power or rating of the engine will be obtained by dividing the total foot-pounds of work done per minute by 33,000. For ease in remembering the formula given, it is commonly written

in which the symbols in the numerator of the second member spell the word “Plan.”

Example:—Find the horsepower of the following engine, working under the conditions stated below:

• Diameter of cylinder, 12 inches.
• Length of stroke, 18