Source: Reports of the United States Commissioners to the Paris Universal Exposition, Vol III
Title: Machinery and Processes of the Industrial Arts, and Apparaturs of the Exact Sciences
Author: Frederick A. P. Barnard, United States Commissioner
Another machine was exhibited in model, at the Paris Universal Exposition of 1855, so-ingenious in its conception that it has been made the subject of an elaborate theoretic discussion by Mr. Combes, of the Imperial School of Mines, in his excellent work on the mechanical theory of heat. This was the invention of Mr. Franchot, of Paris.
It consisted of two cylinders, entirely equal, and both of double effect, of which the pistons were connected with cranks on the same working shaft. One of these cylinders was to be kept constantly at the maximum temperature, and the other at the temperature of the ambient air. The mode of maintaining the superior temperature was not perhaps satisfactorily settled, since Mr. Franchot has never executed his project on a large scale.
Between the two cylinders communication was always free, both above and below their respective pistons; the air passing from one to the other alternately, as the pistons moved. But the body of air above the pistons was permanently separated from that below them. These two bodies of air, therefore, having been originally equal in mass, always remained so, though their volumes were constantly changing.
Regenerators were placed both at top and bottom, in the space through which the air had to pass in its passage from cylinder to cylinder.
In these regenerators it was designed that the air should leave its heat in passing from the hot cylinder to the cold; and it was presumed that it would take the same heat up again, in its return from the cold cylinder to the hot.
Finally, in the attachment of the pistons to the working shaft, the arrangement was such that the crank of the hot cylinder piston was always ninety degrees, in the direction of revolution, in advance of the other.
By considering the movements of the piston under these circumstances, we may easily discover what must be the maxima and minima of the effective force of the engine, and the progress of the ﬂuctuations of the force. For convenience, let the piston of the hot cylinder be called A, and the other B.
Then if A is in the middle of its course, descending, B will be at the uppermost limit of its course, and about to descend. All the superior mass of air will be in the cylinder A, and in the upper regenerator; and, disregarding the regenerator, we may say that it is reduced to one half its normal bulk. By the law of Mariotte, its pressure would be doubled; but by the added effect of the elevated temperature which, for facility of illustration, we will suppose to be suﬂicient to double its elasticity, it will be quadrupled; so that, at the instant in which B begins to descend, there will be a downward pressure on both pistons of four atmospheres.
At the same time the inferior mass of air will be expanded to once and a half its normal bulk, and its pressure would be equal to two thirds of an atmosphere only, but for the high temperature of the part which occupies the lower half of the cylinder A. The actual inferior pressure will be something more than four-ﬁfths of an atmosphere, and the excess of downward over upward pressure will be upward of three atmospheres.
At this time, however, the motion of the piston A is much more rapid than that of piston B, so that the downward pressure will rapidly diminish, and the upward pressure increase. When the revolution has advanced sixty degrees from the position ﬁrst considered, or when the crank of A is one hundred and ﬁfty degrees from the vertical, the two pressures will balance; and when the piston A reaches its lower limit, the piston B being then at the middle of its course, the inferior body of air will occupy half its normal space in the lower half of the cylinder B, while the superior mass will ﬁll the entire cylinder A, and half the cylinder B also.
The upward pressure will now be two atmospheres, and the downward pressure less than two. During the preceding thirty ,degrees of revolution, therefore, the efffective force of the engine will have been negative, and the same will continue to be the case until the crank A shall have passed forty-ﬁve degrees beyond its lowest point, or two hundred and twenty degrees from the vertical. The two cranks will then be equally inclined to the vertical on opposite sides of it, and their efforts to turn the shaft will be opposed to each other.
These efforts being necessarily equal, and acting at equal distances from the centre of motion, will neutralize each other, and, for a moment, the effective force wil1 be zero. When the piston B reaches the bottom, and the piston A is half advanced upward, the circumstances are the same mechanically as those with which the movement commenced, only now it is the inferior mass of air which is compressed into half its normal bulk in the hot cylinder, while the superior mass is dilated into once and a half the same bulk.
It is further evident that this position is not that in which the difference of bulk of the two masses is absolutely the greatest, though it is here that the effective force is maximum; for, owing to the greater rapidity of movement of that piston which is nearest the middle of its course, it will be evident that, while the piston B is approaching the limit of the stroke, and the piston A receding from it, the volume of the inferior mass of air is, on the whole, enlarging, so that the point of minimum volume must occur before the completion of the stroke of B.
It actually occurs for the two bodies of air alternately, when the crank B is within thirty degrees of its culminations, upper or lower, and approaching them. This machine, if it could be realized, would possess two important advantages.
In the ﬁrst place, its negative effect, or total active resistance, instead of consuming, as is usual in air-engines, two-thirds of the positive power, amounts to less than one-third. In the second place, it admits of increase of power without increase of dimensions, by the simple expedient of condensing the air within the cylinder in advance. In this case, indeed, some leakage might occur; but compensation for such a leakage could be provided without a great expenditure of force. In the third place, it gives, theoretically, the largest amount of work for the heat expended that it is practicable under any form to attain.
But all these advantages are dependent for their realization upon the eﬂiciency of the heating apparatus and the satisfactory performance of the regenerators. It encounters here the same diﬂiculties which have impeded as yet the complete success of every form of hot-air engine.