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or 25 foot-pounds of work done.

The object of Figs. 3, 4 and 5 is to show how foot-pounds of work may be represented graphically by the areas of diagrams, and also to make it clear that this remains true whatever the form of the diagram. It is also evident that knowing the area, the average height or pressure may be found by dividing by the length, and vice versa.

Fig. 6. The Ideal Work Diagram of a Steam Engine

Fig. 6 shows the form of work diagram which would be produced by the action of the steam in an engine cylinder, if no heat were lost by conduction and radiation. Starting with the piston in the position shown in Fig. 2, steam is admitted at a pressure represented by the height of the line OY. As the piston moves forward, sufficient steam is admitted to maintain the same pressure. At the point B the valve closes and steam is cut off. The work done up to this time is shown by the rectangle YBbO. From the point B to the end of the stroke C, the piston is moved forward by the expansion of the steam, the pressure falling in proportion to the distance moved through, until at the end of the stroke it is represented by the vertical line CX. At the point C the exhaust valve opens and the pressure drops to 0 (atmospheric pressure in this case).

As it is always desirable to find the work done by a complete stroke of the engine, it is necessary to find the average or mean pressure acting throughout the stroke. This can only be done by determining the area of the diagram and dividing by the length of the stroke. This gives what is called the mean ordinate, which multiplied by the scale of the drawing, will give the mean or average pressure. For example, if the area of the diagram is found to be 6 square inches, and its length is 3 inches, the mean ordinate will be 6 ÷ 3 = 2 inches. If the diagram is drawn to such a scale that 1 inch on OY represents 10 pounds, then the average or mean pressure will be 2 × 10 = 20 pounds, and this multiplied by the actual length of the piston stroke will give the work done in foot-pounds. The practical application of the above, together with the method of obtaining steam engine indicator diagrams and measuring the areas of the same, will be taken up in detail under the heading of Steam Engine Testing.

Definitions Relating to Engine Diagrams

Before taking up the construction of an actual engine diagram, it is first necessary to become familiar with certain terms which are used in connection with it.

Cut-off.—The cut-off is the point in the stroke at which the admission valve closes and the expansion of steam begins.

Ratio of Expansion.—This is the reciprocal of the cut-off, that is, if the cut-off is 1⁄4, the ratio of expansion is 4. In other words, it is the ratio of the final volume of the steam at the end of the stroke to its volume at the point of cut-off. For example, a cylinder takes steam at boiler pressure until the piston has moved one-fourth the length of its stroke; the valve now closes and expansion takes place until the stroke is completed. The one-fourth cylinderful of steam has become a cylinderful, that is, it has expanded to four times its original volume, and the ratio of expansion is said to be 4.

Point of Release.—This is the point in the stroke at which the exhaust valve opens and relieves the pressure acting on the piston. This takes place just before the end of the stroke in order to reduce the shock when the piston changes its direction of travel.

Compression.—This acts in connection with the premature release in order to reduce the shock at the end of the stroke. During the forward stroke of an engine the exhaust valve in front of the piston remains open as shown in Fig. 2. Shortly before the end of the stroke this closes, leaving a certain amount of steam in the cylinder. The continuation of the stroke compresses this steam, and by raising its pressure forms a cushion, which, in connection with the removal of the pressure back of the piston by release, brings the piston to a stop and causes it to reverse its direction without shock. High-speed engines require a greater amount of compression than those running at low speed.

Clearance.—This is the space between the cylinder head and the piston when the latter is at the end of its stroke; it also includes that portion of the steam port between the valve and the cylinder. Clearance is usually expressed as a percentage of the piston-displacement of the cylinder, and varies in different types of engines. The following table gives approximate values for engines of different design.

A large clearance is evidently objectionable because it represents a space which must be filled with steam at boiler pressure at the beginning of each stroke, and from which but a comparatively small amount of work is obtained. As compression increases, the amount of steam required to fill the clearance space diminishes, but on the other hand, increasing the compression reduces the mean effective pressure.

Initial Pressure.—This is the pressure in the cylinder up to the point of cut-off. It is usually slightly less than boiler pressure owing to “wire-drawing” in the steam pipe and ports.

Terminal Pressure.—This is the pressure in the cylinder at the time release occurs, and depends upon the initial pressure, the ratio of expansion, and the amount of cylinder condensation.

Back Pressure.—This is the pressure in the cylinder when the exhaust port is open, and is that against which the piston is forced during the working stroke. For example, in Fig. 2 the small space at the left of the piston is filled with steam at initial pressure, while the space at the right of the piston is exposed to the back pressure. The working pressure varies