Horse-power per Pound Mean Effective Pressure. Area in sq. in. X piston-speed Formula, 33,000 8 1523 82 1720 9 .1928 916 .2148 10 2380 .3046 .4570 .6093 .6444 11 .2880 .5760 12 .3427 .7616 .9139 1.0662 1.2186 1.3709 .6878 .8598 1.0317 1.2037 1.3756 1.5476 .7711 .9639 1.1567 1.3495 1.5422 1.7350 .8592 1.0740 1.2888 1.5036 1.7184 1.9532 .9520 1.1900 1.4280 1.6660 1.9040 2.1420 .8639 1.1519 1.4399 1.7279 2.0159 2.3038 2.5818 .6854 1.0282 1.3709 1.7136 2.0563 2.3990 2.7418 3.0845 .8044 1.2067 1.6089 2.0111 2.4133 2.8155 3.2178 3.6200 .9330 1.3994 1.8659 2.3324 2.7989 3.2654 3.7318 4.1983 .5355 1.0710 1.6065 2.1420 2.6775 3.2130 3.7485 4.2840 4.8195 .6093 1.2186 1.8278 2.4371 3.0464 3.6557 4.2650 4.8742 5.4835 .6878 1.2756 1.9635 2.6513 3.3391 4.0269 4.6147 5.4026 6.1904 .11 1.5422 2.3134 3.0845 3.8556 4.6267 5.3978 6.1690 6.9401 .8592 1.7184 2.5775 3.4367 4.2959 5.1551 6.0143 6.8734 7.7326 .9520 1.9040 2.8560 3.8080 4.7600 5.7120 6.6640 7.6160 8.5680 1.0496 2.0992 3.1488 4.1983 5.2479 6.2975 7.3471 8.3966 9.4462 1.1519 2.3038 3.4558 4.6077 5.7596 6.9115 8.0634 9.2154 10.367 1.2590 2.5180 3.7771 5.0361 6.2951 7.5541 8.8131 10.072 11.331 1.3709 2.7418 4.1126 5.4835 6.8544 8.2253 9.5962 10.967 12.338 1.4875 2.9750 4.4625 5.9500 7.4375 8.9250 10.413 11.900 13.388 1.6089 3.2178 4.8266 6.4355 8.0444 9.6534 11.262 12.871 14.480 1.7350 3.4700 5.2051 6.9401 8.6751 10.410 12.145 13.880 15.615 1.8659 3.7318 5.5978 7.4637 9.3296 11.196 13.061 14.927 16.793 2.0016 4.0032 6.0047 8.0063 10.008 12.009 14.011 16.013 18.014 2.1420 4.2840 6.4260 8.5680 10.710 12.852 14.994 17.136 19.278 2.2872 4.5744 6.8615 9.1487 11.436 13.723 16.010 18.297 20.585 2.4371 4.8742 7.3114 9.7485 12.186 14.623 17.060 14.497 21.934 2.5918 5.1836 7.7755 10.367 12.959 15.551 18.143 20.735 23.326 2.7513 5.5026 8.2538 11.005 13.756 16.508 19.259 22.010 24.762 2.9155 5.8310 8.7465 11.662 14.578 17.493 20.409 23.324 26.240 3.0845 6.1690 9.2534 12.338 15.422 18.507 21.591 24.676 27.760 3.2582 6.5164 9.7747 13.033 16.291 19.549 22.808 26.066 29.324 3.4367 6.8734 10.310 13.747 17.184 20.620 24.057 27.494 30.930 3.6200 7.2400 10.860 14.480 18.100 21.720 25.340 28.960 32.580 3.8080 7.6160 11.424 15.232 19.040 22.848 26.656 30.464 34.272 4.0008 8.0016 12.002 16.003 20.004 24.005 28.005 32.006 36.007 4.1983 8.3866 12.585 16.783 20.982 25.180 29.378 33.577 37.775 4.4006 8.8012 13.202 17.602 22.003 26.404 30.804 35.205 39.606 4.6077 9.2154 13.823 18 431 23.038 27.646 32.254 36.861 41.469 4.8195 9.6390 14.459 19.278 24.098 28.917 33.737 38.556 43.376 5.0361 10.072 15.108 20.144 25.180 30.216 35.253 40.289 45.325 5.2574 10.515 15.772 21.030 26.287 31.545 36.802 42.059 47.317 5.4835 10.967 16.451 21.934 27.418 32.901 38.385 43.868 49.352 5.7144 11.429 17.143 22.858 28.572 34.286 40.001 45.715 51.429 5.9500 11.900 17.850 23.800 29.750 35.700 41.650 47.600 53.550 6.1904 12.381 18.571 24.762 30.952 37.142 43.333 49.523 55.713 6.4355 12.871 19.307 25.742 32.178 38.613 45.049 51.484 57.920 53 6.6854 13.371 20.056 26.742 33.427 40.113 46.798 53.483 60.169 54 6.9401 13.880 20.820 27.760 34.700 41.640 48.581 55.521 62.461 7.1995 14.399 21.599 28.798 35.998 43.197 50.397 57.596 64.796 7.4637 14.927 22.391 29.855 37.318 44.782 52.246 59.709 67.173 7.7326 15.465 23.198 30.930 38.663 46.396 54.128 61.861 69.594 8.0063 16.013 24.019 32.025 40.032 48 038 56.044 64.051 72.057 8.2819 16.570 24.854 33.139 41.424 49.709 57.993 66.278 74.563 18.5680 17.136 25.704 34.272 42.840 51.408 59.976 68.544 77.112 55 56 57 58 59 60 To draw the Clearance-line on the Indicator-diagram, the actual clearance not being known.-The clearance-line may be obtained approximately by drawing a straight line, cbad, across the compression curve, first having drawn OX parallel to the atmospheric line and 14.7 lbs. below. Measure from a the distance ad, equal to cb, and draw YO perpendicular to OX through d; then will TB divided by AT be the percentage of clearance. The clearance may also be found from the expansion-line by constructing a rectangle efhg, and drawing a diagonal gf to intersect the line XO. This will give the point O, and by erecting a perpendicular to XO we obtain a clearance-line OY. Both these methods for finding the clearance require that the expansion and compression curves be hyperbolas. Prof. Carpenter (Power, Sept., 1893) says that with good diagrams the methods are usually very accurate, and give results which check substantially. The Buckeye Engine Co., however, say that, as the results obtained are seldom correct, being sometimes too little, but more frequently too much, and as the indications from the two curves seldom agree, the operation has little practical value, though when a clearly defined and apparently undistorted compression curve exists of sufficient extent to admit of the application of the process, it may be relied on to give much more correct results than the expansion curve. M B To draw the Hyperbolic Curve on the Indicator-diagram.-Select any point I in the actual curve, and from this point draw a line perpendicular to the line JB, meeting the latter in the point J. The line JB may be the line of boiler-pressure, but this is not material; it may be drawn at any convenient height near the top of diagram and parallel to the atmospheric line. From J draw a diagonal to K, the latter point being the intersection of the vacuum and clearance lines; from I draw IL parallel with the atmospheric line. From L, the point of intersection of the diagonal JK and the horizontal line IL, draw the vertical line LM. The point M is the theoretical point of cut-off, and LM the cut-off line. Fix upon any number of points 1, 2, 3, etc., on the line JB, and from these points draw diagonals to K. From the intersection of these diagonals with LM draw horizontal lines, and from 1, 2, 3, etc., vertical lines. Where these lines meet will be points in the hyperbolic curve. FIG. 140. Pendulum Indicator Rig.-Power (Feb. 1893) gives a graphical representation of the errors in indicator-diagrams, caused by the use of in correct form of the pendulum rigging. It is shown that the "brumbo " pulley on the pendulum, to which the cord is attached, does not generally give as good a reduction as a simple pin attachment. When the end of the pendulum is slotted, working in a pin on the crosshead, the error is apt to be considerable at both ends of the card. With a vertical slot in a plate fixed to the crosshead, and a pin on the pendulum working in this slot, the reduction is perfect, when the cord is attached to a pin on the pendulum, a slight error being introduced if the brumbo pulley is used. With the connection between the pendulum and the crosshead made by means of a horizontal link, the reduction is nearly perfect, if the construction is such that the connecting link vibrates equally above and below the horizontal, and the cord is attached by a pin. If the link is horizontal at mid-stroke a serious error is introduced, which is magnified if a brumbo pulley also is used. The adjoining figures show the two forms recommended. FIG. 141. Theoretical Water-consumption calculated from the Indicator-card.-The following method is given by Prof. Carpenter Power, Sept. 1893): p = mean effective pressure, I length of stroke in feet, a area of piston in square inches, a 144 area in square feet, c = percentage of clearance to the stroke, b = percentage of stroke at point where water rate is to be computed. n = number of strokes per minute, 60n number per hour, wweight of a cubic foot of steam having a pres sure as shown by the diagram corresponding to that at the point where water rate is required, w' that corresponding to pressure at end of compression. + c α Number of cubic feet per stroke = 10 100 141 Corresponding weight of steam per stroke in lbs. 1 'b+c α ) ・W. 144 100 The indicated horse-power is plan÷ 33,000. Hence the steam-consump tion per hour per indicated horse- power is 60nla (b + c)w -cw' 14,400 33,000 Changing the formula to a rule, we have: To find the water rate from the indicator diagram at any point in the stroke. RULE. To the percentage of the entire stroke which has been completed by the piston at the point under consideration add the percentage of clearance. Multiply this result by the weight of a cubic foot of steam, having & pressure of that at the required point. Subtract from this the product of percentage of clearance multiplied by weight of a cubic foot of steam hav ing a pressure equal to that at the end of the compression. Multiply this result by 137.50 divided by the mean effective pressure.* NOTE. This method only applies to points in the expansion curve or between cut-off and release. *For compound or triple-expansion engines read: divided by the equiva lent mean effective pressure, on the supposition that all work is done in one cylinder. The beneficial effect of compression in reducing the water-consumption of an engine is clearly shown by the formula. If the compression is carried to such a point that it produces a pressure equal to that at the point under consideration, the weight of steam per cubic foot is equal, and w = w'. In this case the effect of clearance entirely disappears, and the formula 137.5 becomes (bw). p In case of no compression, w' becomes zero, and the water-rate = Prof. Denton (Trans. A. S. M. E., xiv. 1363) gives the following table of theoretical water-consumption for a perfect Mariotte expansion with steam at 150 lbs. above atmosphere, and 2 lbs. absolute back pressure: The difference between the theoretical water-consumption found by the formula and the actual consumption as found by test represents "water not accounted for by the indicator," due to cylinder condensation, leakage through ports, radiation, etc. Leakage of Steam.-Leakage of steam, except in rare instances, has so little effect upon the lines of the diagram that it can scarcely be detected. The only satisfactory way to determine the tightness of an engine is to take it when not in motion, apply a full boiler-pressure to the valve, placed in a closed position, and to the piston as well, which is blocked for the purpose at some point away from the end of the stroke, and see by the eye whether leakage occurs. The indicator-cocks provide means for bringing into view steam which leaks through the steam-valves, and in most cases that which leaks by the piston, and an opening made in the exhaust-pipe or observations at the atmospheric escape-pipe, are generally sufficient to determine the fact with regard to the exhaust-valves. The steam accounted for by the indicator should be computed for both the cut-off and the release points of the diagram. If the expansion-line departs much from the hyperbolic curve a very different result is shown at one point from that shown at the other. In such cases the extent of the loss occasioned by cylinder condensation and leakage is indicated in a much more truthful manner at the cut-off than at the release. (Tabor Indicator Circular.) COMPOUND ENGINES. Compound, Triple- and Quadruple-expansion Engines. -A compound engine is one having two or more cylinders, and in which the steam after doing work in the first or high-pressure cylinder completes its expansion in the other cylinder or cylinders. The term "compound" is commonly restricted, however, to engines in which the expansion takes place in two stages only-high and low pressure, the terms triple-expansion and quadruple-expansion engines being used when the expansion takes place respectively in three and four stages. The number of cylinders may be greater than the number of stages of expansion, for constructive reasons; thus in the compound or two-stage expansion engine the low-pressure stage may be effected in two cylinders so as to obtain the advantages of nearly equal sizes of cylinders and of three cranks at angles of 120°. In triple-expansion engines there are frequently two low-pressure cylinders, one of them being placed tandem with the high-pressure, and the other with the intermediate cylinder, as in mill engines with two cranks at 90°. In the triple-expansion engines of the steamers Campania and Lucania, with three cranks at 120°, there are five cylinders, two high, one intermedi. ate, and two low, the high-pressure cylinders being tandem with the low. Advantages of Compounding.-The advantages secured by divid ing the expansion into two or more stages are twofold: 1. Reduction of wastes of steam by cylinder-condensation, clearance, and leakage; 2. Dividing the pressures on the cranks, shafts, etc., in large engines so as to avoid excessive pressures and consequent friction. The diminished loss by cylinder-condensation is effected by decreasing the range of temperature of the metal surfaces of the cylinders, or the difference of temperature of the steam at admission and exhaust. When high-pressure steam is admitted into a singlecylinder engine a large portion is condensed by the comparatively cold metal surfaces; at the end of the stroke and during the exhaust the water is re-evaporated, but the steam so formed escapes into the atmosphere or into the condenser, doing no work; while if it is taken into a second cylinder, as in a compound engine, it does work. The steam lost in the first cylinder by leakage and clearance also does work in the second cylinder. Also, if there is a second cylinder, the temperature of the steam exhausted from the first cylinder is higher than if there is only one cylinder, and the metal surfaces therefore are not cooled to the same degree. The difference In temperatures and in pressures corresponding to the work of steam of 150 lbs. gauge-pressure expanded 20 times, in one, two, and three cylinders, is shown in the following table, by W. H. Weightman, Am. Mach., July 28, 1892: "Woolf" and Receiver Types of Compound Engines.-The compound steam-engine, consisting of two cylinders, is reducible to two forms, 1, in which the steam from the h.p. cylinder is exhausted direct into the 1. p. cylinder, as in the Woolf engine; and 2, in which the steam from the h. p. cylinder is exhausted into an intermediate reservoir, whence the steam is supplied to, and expanded in, the 1. p. cylinder, as in the "receiverengine." If the steam be cut off in the first cylinder before the end of the stroke, the total ratio of expansion is the product of the ratio of expansion in the first cylinder, into the ratio of the volume of the second to that of the first cylinder; that is, the product of the two ratios of expansion. Thus, let the areas of the first and second cylinders be as 1 to 3%, the strokes being equal, and let the steam be cut off in the first at stroke; then Expansion in the 1st cylinder.... 66 66 2d 46 .................. 1 to 2 1 to 3% Total or combined expansion, the product of the two ratios... 1 to 7 Woolf Engine, without Clearance-Ideal Diagrams.— The diagrams of pressure of an ideal Woolf engine are shown in Fig. 142, as they would be described by the indicator, according to the arrows. In these diagrams pq is the atmospheric line, mn the vacuum line, cd the admission |