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.