[TRANSACTIONS OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS.] HIGH RATIOS OF EXPANSION AND DISTRIBUTION OF UNEQUAL PRESSURES IN SINGLE AND COMPOUND ENGINES. BY J. C. HOADLEY, C. E. Read at the Annual Meeting, 1880. Although my ultimate theme, as will appear later, is the compound engine, the first part of my remarks may seem to be almost irrelevant, so elementary is the mode of elucidation which I propose to adopt, and for which I have prepared numerous diagrams, although circumstances have not afforded me the time necessary to write out my ideas as embodied in the drawings. It has seemed to me that the considerations, hitherto taken into account in making comparisons between the performance of compound engines and that of single cylinders, fail to explain in a satisfactory manner the considerable advantage which generally appears in favor of the former, notwithstanding the obvious increase of frictional resistance caused by the introduction of the second cylinder, and the loss, by expansion between the cylinders without doing work. That such a preponderance of advantage generally appears will, I think, be admitted, although in a few instances single cylinders have closely rivaled the best performance of compound engines. Why is it, then, that the production of power by the transformation of the molecular motion of heat into the kinetic energy of moving masses, through the expansive force of steam in a steam engine, can be more economically conducted in two cylinders than in one, the ratio of expansion being the same? Dividing the fall of temperature between the boiler and condenser is, doubtless, analagous to the introduction of a separate condenser. Interposing an intermediate temperature of 200° F. between the 300° of the boiler and the 100° of the condenser, serves as a "heat trap" to keep the low temperature of the condenser away from the surfaces which have to come into contact with high-pressure steam. This is a true cause, effective as far as it goes, but falls short, as it seems to me, of fully accounting for the observed facts. There is another cause, unnoticed hitherto, so far as I know, although vaguely hinted at under the general term of "better distribution of pressure," which seems to me to exert no little influence, and to deserve more attention than has been bestowed upon it hitherto. In order to make my meaning perfectly clear, I will go rapidly over the diagrams here exhibited, and explain the transformations they undergo, and the influence of these transformations upon the useful effect of the horizontal pressure on the piston of a horizontal engine. Fig. 1.-Let the horizontal medial line S S, represent the stroke of a piston, and let the circle described about its middle point represent the orbit of the crank. Let the height S A S B, from this medial line to the top of the figure represent, on any scale whatever, uniform effective steam pressure upon the piston during a forward stroke; and let the equal distance from the same line downward to the bottom of the figure S B', S' A'. in the same manner represent the uniform effective pressure during the return stroke. Draw any number of co-ordinates to the medial line-there are nine in the figure-and produce them beyond the circle to a distance equal to that intercepted between the circle and the medial line, that is, to a distance equal to the natural sines of the respective crank angles, radius or crank being taken equal to unity. Then, a continuous curve, drawn through the extremities of these lines, will be an ellipse, of which the major axis will represent twice the uniform piston pressure throughout the stroke, and the minor axis, half the length of the major axis, will represent the stroke of the piston. Then will the area of this ellipse represent, on the scale of pressure adopted, the rotative effect, or the tangential component of the horizontal pressure, equal to zero at the beginning and end of the stroke, and to unity at mid-stroke, and the ratio of this area to the area of the parallelogram will equal the ratio of the rotative effect to piston pressure, namely, the ratio of to unity, or about 78.5 per 4 cent. Supposing, now, this circle to be revolved upon the medial line as an axis, through one-fourth of a revolution, until its plane is perpendicular to the plane of the paper, and the ordinates of the ellipse exterior to the circle to be erected upon the medial line. We shall then have our ellipse reduced to a circle, and our parallelogram to a square. Fig. 2. Our rotative effect is now represented by a circle, and the piston pressure of an entire revolution, by a circumscribing square to this circle; and the ratio of rotative effect to piston pressure, as before, to unity. 4 Fig. 3. We have hitherto neglected the influence of the angular vibration of the connecting rod, as if it remained constantly parallel to the axis of the engine. We see in this figure, resembling somewhat the horizontal section of a human skull, the effect of a connecting rod of a length five and one-third times the length of the crank. The area representing the rotative effect is no longer a circular area, and although symmetrical on each side of the medial line, it is no longer so, if divided vertically by the middle ordinary, since more rotative effect appears to be developed in the portion towards S', to the right of the middle ordinate, which represents the end of the cylinder farthest from the crank, than in the other end. This inequality results from the unequal velocity of the piston near the two ends of the stroke, which, in turn, is caused by the angular vibration of the connecting rod. But the whole area of this unsymmetrical figure is equal to the arc of the circle in Fig. 2, and notwithstanding that the curve transcends the square of mid-stroke, the ratio of this area to the square, representing piston pressure, remains as 7 to unity as at first. Fig. 4. We here see the effect of the inertia of the reciprocating parts in modifying the horizontal pressure upon the crank pin. Still supposing the piston pressure to be uniform, and equal on any scale whatever, to the radius of our circle, and assuming that the weight and velocity of the reciprocating parts are such that their inertia is just equal at dead center to the piston pressure, one square of piston pressure is transformed at the crank pin into a lozenge, SCS' C", of area equal to the square; one circle of rotative effect is transformed into the curvilineate figure here seen, symmetrical as divided by the line of stroke, and still bearing the ratio to the lozenge of to unity, π 4 since every ordinate bears the same ratio to the whole height of the lozenge at its position, that the line at the same position bears to radius or unity. Fig. 5. We here see a further modification of the areas under consideration, by the vibratory motion of the connecting rod. The top and bottom lines are no longer straight, but are curves of peculiar character-alike, but disturbing the symmetry of our areas, to preserve which, one of the lines would have to be reversed. But the shaded figure SACS C'S, is equal to the square of Fig. 2 and to the lozenge of Fig. 4; the area of rotative effect is still equal to that of π the circle of Fig. 2, and their ratio still remains as to unity, not 4 withstanding that the curves of rotative effect transcend, at and near mid-stroke, the lines of horizontal pressure on crank pin. |