Though a uniform clearance of 7% at each end of the stroke has been assumed as an average proportion for the purpose of compiling the table, the clearance of cylinders with ordinary slides varies considerably-say from 5% to 10%. (With Corliss engines it is sometimes as low as 2%.) With the clearance, 7%, that has been assumed, the table gives approximate results sufficient for most practical purposes, and more trustworthy than results deduced by calculations based on simple tables of hyperbolic loga. rithms, where clearance is neglected. Weight of steam of 100 lbs. total initial pressure admitted for one stroke, per cubic foot of net capacity of the cylinder, in decimals of a pound = reciprocal of figures in column 9. Total actual work done by steam of 100 lbs. total initial pressure in one stroke per cubic foot of net capacity of cylinder, in foot-pounds in column 7 ÷ figures in column 9. = figures RULE 1: To find the net capacity of cylinder for a given weight of steam admitted for one stroke, and a given actual ratio of expansion. (Column 9 of table.)-Multiply the volume of 1 lb. of steam of the given pressure by the given weight in pounds, and by the actual ratio of expansion. Multiply the product by 100, and divide by 100 plus the percentage of clearance. The quotient is the net capacity of the cylinder. RULE 2: To find the net capacity of cylinder for the performance of a given amount of total actual work in one stroke, with a given initial pressure and actual ratio of expansion.-Divide the given work by the total actual work done by 1 lb. of steam of the same pressure, and with the same actual ratio of expansion; the quotient is the weight of steam necessary to do the given work, for which the net capacity is found by Rule 1 preceding. NOTE.-1. Conversely, the weight of steam admitted per cubic foot of net capacity for one stroke is the reciprocal of the cylinder-capacity per pound of steam, as obtained by Rule 1. 2. The total actual work done per cubic foot of net capacity for one stroke is the reciprocal of the cylinder-capacity per foot-pound of work done, as obtained by Rule 2. 3. The total actual work done per square inch of piston per foot of the stroke is 1/144th part of the work done per cubic foot. 4. The resistance of back pressure of exhaust and of compression are to be added to the net work required to be done, to find the total actual work. APPENDIX TO ABOVE TABLE-MULTIPLIERS FOR NET CYLINDER-CAPACITY, AND TOTAL ACTUAL WORK DONE. (For steam of other pressures than 100 lbs. per square inch.) The figures in the second column of this table are derived by multiplying the total pressure per square foot of any given steam by the volume in cubic feet of 1 lb. of such steam, and dividing the product by 62,352, which is the product in foot-pounds for steam of 100 lbs. pressure. The quotient is the multiplier for the given pressure. The figures in the third column are the quotients of the figures in the second column divided by the ratio of the pressure of the given steam to 100 lbs. Measures for Comparing the Duty of Engines.-Capacity is measured in horse-powers, expressed by the initials, H.P.: 1 H.P. 83,000 ft.-lbs. per minute, 550 ft.-lbs. per second, = €1,980,000 ft.-lbs. per hour. 1 ft.-lb. a pressure of 1 lb. exerted through a space of 1 ft. Economy is measured, 1, in pounds of coal per horse-power per hour; 2, in pounds of steam per horse-power per hour. The second of these measures is the more accurate and scientific, since the engine uses steam and not coal, and it is indepndent of the economy of the boiler. In gas-engine tests the common measure is the number of cubic feet of gas (measured at atmospheric pressure) per horse-power, but as all gas is not of the same quality, it is necessary for comparison of tests to give the analysis of the gas. When the gas for one engine is made in one gas-producer, then the number of pounds of coal used in the producer per hour per horse-power of the engine is the proper measure of economy. Economy, or duty of an engine, is also measured in the number of footpounds of work done per pound of fuel. As 1 horse-power is equal to 1,980,000 ft.-lbs. of work in an hour, a duty of 1 lb. of coal per H.P. per hour would be equal to 1,980,000 ft.-lbs. per lb. of fuel; 2 lbs. per H.P. per hour equals 990,000 ft.-lbs. per lb. of fuel, etc. The duty of pumping-engines is commonly expressed by the number of foot-pounds of work done per 100 lbs. of coal. When the duty of a pumping-engine is thus given, the equivalent number of pounds of fuel consumed per horse-power per hour is found by dividing 198 by the number of millions of foot-pounds of duty. Thus a pumping engine giving a duty of 99 millions is equivalent to 198/99 = 2 lbs. of fuel per horse-power per hour. Efficiency Measured in Thermal Units per Minute.Some writers express the efficiency of an engine in terms of the number of thermal units used by the engine per minute for each indicated horse-power, instead of by the number of pounds of steam used per hour. The heat chargeable to an engine per pound of steam is the difference between the total heat in a pound of steam at the boiler-pressure and that in a pound of the feed-water entering the boiler. In the case of condensing engines, suppose we have a temperature in the hot-well of 101° F., corresponding to a vacuum of 28 in. of mercury, or an absolute pressure of 1 lb. per sq. in. above a perfect vacuum: we may feed the water into the boiler at that temperature. In the case of a non-condensing-engine, by using a portion of the exhaust steam in a good feed-water heater, at a pressure a trifle above the atmosphere (due to the resistance of the exhaust passages through the heater), we may obtain feed-water at 212°. One pound of steam used by the engine then would be equivalent to thermal units as follows: Pressure of steam by gauge: 50 Total heat in steam above 32° : 75 100 125 150 175 200 1172.8 1179.6 1185.0 1189.5 1193.5 1197.0 1200.2 Subtracting 69.1 and 180.9 heat-units, respectively, the heat above 32° in feed-water of 101° and 212° F., we have Heat given by boiler: Feed at 101°. Feed at 212° 1103.7 1110.5 1115.9 1120.4 1124.4 1127.9 1131.1 991.9 998.7 1004.1 1008.6 1012.6 1016.1 1019.3 Thermal units per minute used by an engine for each pound of steam used per indicated horse-power per hour: Feed at 101°...... 18.40 18.51 18.60 18.67 18.74 18.80 18.85 Feed at 212°...... 16.53 16.65 16.74 16.81 16.88 16.94 16.99 EXAMPLES.-A triple-expansion engine, condensing, with steam at 175 lbs., gauge and vacuum 28 in., uses 13 lbs. of water per I.H.P. per hour, and a high-speed non-condensing engine, with steam at 100 lbs. gauge, uses 30 lbs. How many thermal units per minute does each consume? Ans. 13X18.80 244.4, and 30 X 16.74 502.2 thermal units per minute. A perfect engine converting all the heat-energy of the steam into work would require 33,000 ft.-lbs. 778 42.4164 thermal units per minute per indicated horse-power. This figure, 42.4164, therefore, divided by the number of thermal units per minute per I.H.P. consumed by an engine, gives its efficiency as compared with an ideally perfect engine. In the examples above, 42.4164 divided by 244.4 and by 502.2 gives 17.35% and 8.45% efficiency, respectively. Total Work Done by One Pound of Steam Expanded in a Single Cylinder. (Column 7 of table.)-If 1 pound of water be converted into steam of atmospheric pressure = 2116.8 lbs. per sq. ft., it occu. pies a volume equal to 26.36 cu. ft. The work done is equal to 2116.8 lbs. X 26.36 ft. = 55,788 ft. lbs. The heat equivalent of this work is (55,788 778 =) 71.7 units. This is the work of 1 lb. of steam of one atmosphere acting on a piston without expansion. The gross work thus done on a piston by 1 lb. of steam generated at total pressures varying from 15 lbs. to 100 lbs. per sq. in. varies in round numbers from 56,000 to 62,000 ft.-lbs., equivalent to from 72 to 80 units of heat. This work of 1 lb. of steam without expansion is reduced by clearance according to the proportion it bears to the net capacity of the cylinder. If the clearance be 7% of the stroke, the work of a given weight of steam without expansion, admitted for the whole of the stroke, is reduced in the ratio of 107 to 100. Having determined by this ratio the quantity of work of 1 lb. of steam without expansion, as reduced by clearance, the work of the same weight of steam for various ratios of expansion may be found by multiplying it by the relative performance of equal weights of steam, given in the 6th column of the table. Quantity of Steam Consumed per Horse-power of Total Work per Hour. (Column 8 of table. The measure of a horse-power is the performance of 33,000 ft.-lbs. per minute, or 1,980,000 ft.-lbs. per hour. This work, divided by the work of 1 lb. of steam, gives the weight of steam required per horse-power per hour. For example, the total actual work done in the cylinder by 1 lb. of 100 lbs. steam, without expansion and with 7% of clearance, is 58,273 ft.-lbs.; and 34 lbs. of steam, is the weight of steam consumed for the total work done in the cylinder per horse-power per hour. For any shorter period of admission with expansion the weight of steam per horse-power is less, as the total work of 1 lb. of steam is more, and may be found by dividing 1,980,000 ft.-lbs. by the respective total work done; or by dividing 34 lbs. by the ratio of performance, column 6 in the table. 1,980,000 .01 100.00 50.5 34.0 25.75 20.8 17.5 15.14 13.38 12.00 10.9 10 9.91 8.17 9.82 9.08 8.46 9.73 9.00 8.39 7.86 8.92 8.31 7.79 7.33 8.83 8.15 .08 12.50 11.22 10.2 9.36 8.67 8.08 8.58 8.00 7.50 7.00 7.57 7.13 6.69 6.35 6.06 5.79 6.00 5.74 5.50 6.24 5.94 8.33 7.78 7.29 6.86 6.50 5.89 5.63 5.68 5.45 5.24 5.40 5.19 5.00 Relative Efficiency of 1 lb. of Steam with and without Clearance; back pressure and compression not considered. If the clearance be added to the stroke, so that clearance becomes zero, the same quantity of steam being used, admission being then =1+c= 32, and stroke L+c= 107. That is, if the clearance be reduced to 0, the amount of the clearance 7 being added to both the admission and the stroke, the same quantity of steam will do more work than when the clearance is 7 in the ratio 707 : 637, or 11% more. Back Pressure Considered.-If back pressure.10 of P, this amount has to be subtracted from p and p, giving p = .537, p1 = .607, the work of a given quantity of steam used without clearance being greater than when clearance is 7 per cent in the ratio of 607: 537, or 13% more. Effect of Compression.-By early closure of the exhaust, so that a portion of the exhaust-steam is compressed into the clearance-space, much of the loss due to clearance may be avoided. If expansion is continued down to the back pressure, if the back pressure is uniform throughout the exhaust-stroke, and if compression begins at such point that the exhauststeam remaining in the cylinder is compressed to the initial pressure at the end of the back stroke, then the work of compression of the exhaust-steam equals the work done during expansion by the clearance-steam. The clearance-space being filled by the exhaust-steam thus compressed, no new steam is required to fill the clearance-space for the next forward stroke, and the work and efficiency of the steam used in the cylinder are just the same as if there were no clearance and no compression. When, however, there is a drop in pressure from the final pressure of the expansion, or the terminal pressure, to the exhaust or back pressure (the usual case), the work of compression to the initial pressure is greater than the work done by the expansion of the clearance-steam, so that a loss of efficiency results. In this case a greater efficiency can be attained by inclosing for compression a less quantity of steam than that needed to fill the clearance-space with steam of the initial pressure. (See Clark, S. E., p. 399, et seq.; also F. H. Ball, Trans. A. S. M. E., xiv. 1067.) It is shown by Clark that a somewhat greater efficiency is thus attained whether or not the pressure of the steam be carried down by expansion to the back exhaust-pressure. As a result of calculations to determine the most efficient periods of compression for various percentages of back pressure, and for various periods of admission, he gives the table on the next page: Clearance in Low- and High-speed Engines. (Harris Tabor, Am. Mach., Sept. 17, 1891.)-The construction of the high-speed engine is such, with its relatively short stroke, that the clearance must be much larger than in the releasing-valve type. The short-stroke engine is, of necessity, an engine with large clearance, which is aggravated when a variable compression is a feature. Conversely, the releasing-valve gear is, from necessity, an engine of slow rotative speed, where great power is obtainable from long stroke, and small clearance is a feature in its construction. In one case the clearance will vary from 8% to 12% of the piston-displacement, and in the other from 2% to 3%. In the case of an engine with a clearance equalling 10% of the piston-displacement the waste room becomes enormous when considered in connection with an early cut-off. The system of compounding reduces the waste due to clearance in proportion as the steam is expanded to a lower pressure. The farther expansion is carried through a train of cylinders the greater will be the reduction of waste due to clearance. This is shown from the fact that the high-speed engine, expanding steam much less than the Corliss, will show a greater gain when changed from simple to compound than its rival under similar conditions. COMPRESSION OF STEAM IN THE CYLINDER. Best Periods of Compression; Clearance 7 per cent. Total Back Pressure, in percentages of the total initial pressure. Cut-off in Percent ages of the NOTES TO TABLE.-1. For periods of admission, or percentages of back pressure, other than those given, the periods of compression may be readily found by interpolation. 2. For any other clearance, the values of the tabulated periods of compression are to be altered in the ratio of 7 to the given percentage of clearance. Cylinder-condensation may have considerable effect upon the best point of compression, but it has not yet (1893) been determined by experiment. (Trans. A. S. M. E., xiv. 1078.) Cylinder-condensation.-Rankine, S. E., p. 421, says: Conduction of heat to and from the metal of the cylinder, or to and from liquid water contained in the cylinder, has the effect of lowering the pressure at the beginning and raising it at the end of the stroke, the lowering effect being on the whole greater than the raising effect. In some experiments the quantity of steam wasted through alternate liquefaction and evaporation in the cylinder has been found to be greater than the quantity which performed the work. Percentage of Loss by Cylinder-condensation, taken at Cut-off. (From circular of the Ashcroft Mfg. Co. on the Tabor Indicator, 1889.) Percent. of Feed-water accounted Percent. of Feed-water Consump for by the Indicator diagram. tion due to Cylinder-condensat'n. 5 10 15 20 30 40 84 87 90 |