Fig. 6. I now introduce a very ordinary pair of indicator diagrams, just such as any ordinary locomotive or other link-motion engine will produce any day when in good order and working with two and one-half fold expansion. The blank space which serves as a background is bounded at the bottom by the vacuum line, at the top by the line of boiler pressure, and at the ends by lines representing clearance in terms of stroke. These diagrams show the effect of wire-drawing on the admission line-of early release, corresponding to compression, upon the expansion line, and of compression up to initial pressure, upon the exhaust line. So ordinary are they, that some master mechanics might be tempted to adopt the vernacular, and style them "'ornery." But such as they are, just such diagrams as these have to do the greater part of the steam-engine duty of the world. Let us, then, see what they are doing, and can do. A scale of pressures is here introduced for the first time, namely, 50 pounds per square inch to one inch in height. Boiler pressure is 130 pounds above atmosphere, say 144.7 absolute; initial pressure is 105 pounds above the atmosphere, say 119.7 absolute, and back pressure up to closure of exhaust, 16 pounds absolute; and including compression, 17.91 pounds absolute. Cut-off takes place at 30 per cent. of stroke from clearance line, or at about 28 per cent. of stroke from dead center, the absolute ratio of expansion is 3.3,-mid-stroke pressure is 50 lbs. above back pressure, terminal pressure,-expansion supposed to be continued to the end,36.11 pounds, and mean effective pressure in the cylinder, all deductions made for wire-drawing and early exhaust, 52.25 pounds. Fig. 7. The diagrams shown in the preceding figure, are here seen enlarged vertically to a scale of 20 pounds per square inch to one inch of vertical height, or two and one-half times, so that midstroke pressure is now equal to the radius of our circle. The forward and return stroke diagrams are placed base to base, their common base-line being their respective lines of back pressure, 16 lbs. above vacuum line. Compression is indicated by heavy shading. We have here, we see at a glance, pretty nearly our lozenge of Fig. 4, as indicated by the dotted lines CS', C'S; but reversed, the highest pressure being at the beginning of each stroke. It will be observed, however, that the figure formed by the two diagrams is a little larger than the lozenge. This is because compression is not only a deficiency to be made up, but also a resistance to be overcome. Let us now see what effect will be produced upon this approximate lozenge by the causes which so greatly modified our square of uniform pressure, and our circle of rotative effect. Fig. 8, exhibits all the lines shown on the five succeeding figures, and the auxiliary lines used in tracing them, introduced for refer ence, but not requiring special comment. Fig. 9. Here is seen the effect of the inertia of the reciprocating parts, reproducing very nearly our original square of uniform piston pressure; that is, the same cause which transformed one square to a lozenge, now re-transforms our approximate reversed lozenge back to almost a square. It is a little larger than the square, for the reason already explained, namely, to compensate for the resistance of compression, which is indicated by the dark shading. Fig. 10. The rotative effect on the crank-pin, in a tangential direction, is seen in this figure, in direct comparison with the square of uniform horizontal pressure A B A' B', darkly shaded around it, save where portions of it project beyond. Fig. 11. Here this same rotative effect is shown in direct comparison with the circle of rotative effect due to uniform pressure, horizontally upon the crank pin. By comparing this figure with the last, it will be seen that the rotative effect produced by the varying piston pressure of these diagrams, is more nearly uniform than would be the corresponding effect of equal, mean, effective pressure uniformly exerted upon the piston throughout the entire revolution. Fig 12 is similar to Fig. 9, but is modified by introducing the disturbing effect of the angular vibration of connecting rod. Notwithstanding the slight departure from symmetry due to this cause, the approximation to the original square A B A' B', is quite close, and the horizontal pressure on the crank pin is still nearly uniform. Fig. 13 shows the rotative effect under the same modifying influence of the vibration of the connecting rod, in direct comparison with both the square of uniform horizontal pressure, and the circle of rotative, tangential pressure corresponding thereto. Now, before applying the principles here illustrated to the action of steam pressure in a compound engine, let us see what such a pair of ordinary diagrams would be capable of doing. Suppose the engine, represented in action by them, to be a locomotive engine, with cylinders 15 inches diameter and 24 inches stroke, piston rod 21⁄2 inches diameter; the mean net area of piston will then be 180 square inches, equal to 14 square feet, the volume swept through by a single piston at one stroke will be 2 cubic feet, and by both pistons during one entire revolution of the driving wheels, 10 cubic feet. If these driving wheels be 5 feet diameter, and if the speed be 25 miles per hour, the rotatory speed will be 125 revolutions per minute, and the piston speed 500 feet per minute. Our initial pressure is 104 pounds above atmosphere, say 118.7 absolute; cut-off is at 28 per cent. of the stroke from dead center, terminal pressure, if expansion were carried to the end of stroke, would be 36.11 pounds, the ratio of expansion 3.3, mid-stroke pressure 50 pounds; back pressure, exclusive of compression, 16 pounds, and including compression, 17.91 pounds; and mean effective pressure, all allowances made for wire drawing, early release and compression, is 52.25 pounds. It follows that the indicated power of both cylinders will be 285 horse power. The quantity of steam expended per hour, compression allowed for, will be 6,120 pounds, equal to 21.4 pounds per horse power per hour; and allowing for steam condensed in doing work, 624 pounds per hour, we shall have a total of 6,762 pounds per hour, equal to 23.7 pounds per horse power per hour. This is, of course, a very good result, rarely much surpassed by more complicated engines; and it is due, of course, to the assumption of dry steam. "Put your trust in God," said Cromwell to his Ironsides, "and keep your powder dry." I can recommend no safer place of trust, but to the engineer would say, "By all means keep your steam dry!" Returning now to the action of steam in a cylinder, with ultimate reference to the compound engine: If the circle in Fig. 14 represents the orbit of a crank, and the horizontal diameter SS', the stroke of a piston; and if the square be taken to represent uniform piston pressure, and the circle the corresponding rotative effect, then will the diagonals of the square divide the revolution of the crank into quadrants, two of which may be called mid-stroke quadrants, and the other two, end quadrants; in the former 90.9 per cent. of the pressure is rotative, and only 9.1 per cent. non-rotative; in the latter only 48.7 per cent. is rotative, and 51.3 per cent. non-rotative, Of the whole pressure throughout the revolution, 64.3 per cent. in midstroke quadrants is rotative, and 6.4 per cent. non-rotative, and 14.3 per cent. in end quadrants rotative, and 15.0 per cent. non-rotative. These results which are geometrically accurate, as far as the third place of decimals (tenths of one per cent.), may be tabulated thus: In the figure, the dark shading shows the non-rotative pressure; the light shading shows the rotative effect in the end quadrants, and the white space shows the rotative effect in the mid-stroke quadrants. Fig. 15 represents the above ratios by the relative surface of the black and white areas. Fig. 16. One-tenth of the circular area of rotative effect is here covered by the black annulus, the white space within, which shows the net rotative effect, upon the assumption that frictional resistance, per pound of piston pressure, is uniform throughout the revolution, and is equal to 10 per cent. of the indicated power.* It also shows the relative value of this net rotative effect in the mid-stroke quadrants and in the end quadrants. The inequality is now greater than before. Of the whole net rotative effect, 85.2 per cent. is in the mid-stroke quadrants, and only 14.8 per cent. in the end quadrants. Of the gross rotative effect, 76.7 per cent. is usefully exerted in the mid-stroke quadrants, 13.3 per cent. in the end quadrants, and 10 per cent. is consumed in friction, about equally divided, upon our assumption, among all the quadrants. Of the whole power, as estimated by steam pressure, multiplied by piston area and by piston velocity, 29.3 per cent. is expended in the end quadrants in producing 14.8 per cent. of the net rotative effect and in overcoming one-half of the friction, and 70.7 per cent. is expended in the midstroke quadrants in producing 85.2 per cent. of the net rotative effect and in overcoming the other half of the friction. Relatively to the power developed in the cylinder, the net rotative effect is 2.4 times as great in the mid-stroke quadrants as in the end quadrants. But this is upon the assumption that the friction, resulting from steam pressure on the piston, is substantially uniform throughout each entire revolution. Now, this resistance is probably considerably greater in the end quadrants than in the mid-stroke quadrants. Steam pressure on the piston produces frictional resistance at four places, and in varying degrees in each, the value of this resistance, per unit of pressure, being directly as the velocity of the frictional surfaces, the co-efficient of friction being assumed to be uniform, say, as for unctuous surfaces, 8 per cent. At the cross-head pin the motion is small, being inversely as the length of connecting rod to radius of cross-head pin; but it is most rapid at dead centers, and 70 per cent. of the whole motion takes place in the end quadrants. On the slides, the pressure is reduced from piston pressure in the ratio of crank to connecting rod, and the velocity is a maximum at mid-stroke, 70 per cent. of the motion falling within the mid-stroke quadrants. Rotary motion being supposed to be uniform, pressure on piston uniform, and frictional resistance per pound of pressure also uniform, it follows that the piston, moving more slowly near the dead center, will require longer time and a larger arc of crank motion to develop power equal to frictional resistance than at mid-stroke. It is believed that the black circle-the area covered by which, bears to the area embraced by its outer boundary, the same ratio that frictional resistance bears to the total rotative effect-fairly integrates the result of these conditions. There may be, I admit, some fallacy in this, but I don't see it if there is. J. C. H. The crank-pin moves with velocity substantially uniform, in a path longer than the piston path, in the ratio of one-half to unity, say, 57 per cent. longer. The friction here is uniform per unit of pressure, and varies with varying piston pressure, or, strictly speaking, with varying horizontal pressure on the crank-pin, as modified by the inertia of the reciprocating parts. It is much greater in total amount in the end quadrants, with any considerable degree of expansion, and the inequality increases with the ratio of expansion. The vertical component of the inertia of the connecting rod also goes to augment friction on the crank-pin. The frictional pressure on the crank-shaft is a resultant of the horizontal pressure acting through the crank at a varying angle, and the weight of the shaft, balance wheel, etc. On account of the considerable diameter of the crank-shaft, the velocity of its surface is, in shortstroke engines, generally about as great as that of the piston, and frictional resistance, uniform per unit of pressure, is, in fact, greatest at dead center. With uniform pressure, and uniform friction per unit of pressure, one-half of the frictional resistance at crank-pin and crank-shaft journals, falls within the mid-stroke quadrants, and the other half within the end quadrants. After some consideration of the above elements of the problem, I am almost convinced that there is, in all actual conditions of steamengine practice, a good deal more frictional resistance in the end quadrants; and, with very high ratios of expansion, a very great deal more. I have not, I confess, completely worked out the train of calculation necessary to verify this if true, or to refute it if fallacious, so that I am not prepared to present, as I have done hitherto, absolute numerical results which cannot be attacked. The next figure (No. 17) is, therefore, presented as an illustrative diagram of a probable relation, and not as a geometric representation of an ascertained fact. Fig. 17. The black border of the circle representing rotative effect is, as in Fig. 16, equal in area to one-tenth of the area of the circle, which forms its outer boundary; but its greater breadth at dead center, and its diminished breadth at mid-stroke, representing greater frictional resistance in the end quadrants and less in the mid-stroke quadrants, reduce the white area within the border to an ellipse with its major axis vertical, to represent the net rotative effect, transmissible beyond the crank shaft. Measured by the planimeter, this area shows that eighty-seven per cent. of the net rotative effect is produced within the mid-stroke quadrants, and only thirteen per cent. within the end quadrants; and that of the whole power developed in the cylinder by the mean effective pressure, sixty-one per cent. is |