The real question is this: What is the figure representing the acceleration of the motion of a piston, controlled by a crank which revolves with a uniform velocity? I stated it to be a right-angled triangle, and indicated, as I supposed, clearly enough, a simple method by which this could be shown. Your correspondent claims that the calculation, according to my own rule, gives a figure of a totally different form, and one that shows the acceleration, as well as the motion, to be reduced to zero at the commencement of the stroke. Let us see. Let the straight line, AJ, in the following figure, represent half the stroke of the piston, and let the distances, AB, AC, etc., on this line, represent the versed sines of 10°, 20°, etc., up to 90°, or the motion of the piston while the crank is moving through these arcs. At the points A, B, C, etc., erect the perpendiculars, Aa, Bb, Cc, etc., and let the length of each of these ordinates represent the acceleration imparted in a given time at that point of the stroke. Then will AJ be to Aa as IJ is to Ii, as HJ is to Hh, etc., showing that the straight line, aJ, connects the extremities of all the ordinates, and that the triangle, AJa, represents the acceleration of the motion of the piston, from the commencement to the middle of the stroke.
The following table will enable any one to make the calculations proving the truth of the above proposition:
| Degrees. | Versed sine. | Motion for 10° | Acceleration during 1°. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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The method of obtaining the decimals representing the acceleration for 1°, at any point, was fully explained in the paper, and compared with the similar method of showing the uniform acceleration of a body acted on by a constant force. The ordinary tables in the hand-books, going only to five places of decimals, are of no use for these computations.
I would suggest a practical experiment. Let any one having an engine running at a good speed, loosen the crank pin brasses a little, so that, at starting, it will thump heavily. Let the engine be lightly loaded, so that only a small portion of the boiler pressure will need to be admitted to the cylinder. As its speed increases, the thump will die away; and, if at its full speed, the pressure of the steam admitted is not so great as to overcome the centrifugal strain of the reciprocating parts on the crank, as it passes the centers, the engine will revolve in silence. Any one can ascertain, by the rule given in the note to the paper, just what pressure can be admitted without causing a thump, or this can be found by a little experimenting. I am running an engine which does not thump with loose crank pin brasses, under eighty pounds pressure, admitted sharply on the centers.
Charles T. Porter.
