metrical on both sides as a probability curve and shaped very much like it. The lower curve of fig. 67 is a similar plotting of the number of efficiency 72* values for the same tests falling within each group, the curve being drawn through the points. It lacks the symmetry of the upper curve, and the points do not fall so near the peak. The symmetry of the upper curve and its similarity to a mathematical probability curve suggest that the true boiler efficiency (E,) is much more nearly constant than efficiency 72*, and that the attempt made to find a constant true boiler efficiency is along the right track. But the curves of fig. 66, discussed on page 143, show that this "constant" true boiler efficiency is subject to variations when capacity FIG. 67-Probability curves: A, Approximate curve based on true boiler efficiency; B, attempt at approximate curve based on boiler efficiency 72*. Tests 89-401. and furnace temperature are changed, although they are comparatively slight. By referring to the upper curve of fig. 67, it will be seen that most of the tests fall between 77 and 87 per cent, the greater number being close to 83.7 per cent, the position of the peak. This means that under average conditions the boilers at the fuel-testing plant will absorb about 83.7 per cent of the heat available to them. The meaning of constant-capacity curves for boiler efficiency (E) could perhaps be made plainer by taking from the chart (fig. 65, p. 141) four specific examples: Example 1. Taking the furnace temperature at 2,500° F., and moving from left to right on the chart, we cut lines of higher capacity and lower boiler efficiency (E); with a capacity increase from 70 to 120 per cent, the boiler efficiency drops from 71 to 67 per cent. Inasmuch as the furnace temperature remains constant the quantity of heat received by the lower row of tubes by conduction through the encircling tiles and by radiation from the hot brickwork is perhaps the same. Therefore the decrease in boiler efficiency must be charged to the tubes which are farther from the furnace and receive their heat from the gases by convection and conduction. A possible explanation of lower boiler efficiencies with higher capacities is that a steeper temperature gradient is required to transmit more heat through the soot, metal, and scale. There is also a thicker layer of steam bubbles on the heating surface, which increases the resistance to the passage of heat. These effects cause the flue gases to leave the heating surface of the boiler at higher temperatures as the capacity increases Example 2. Using the scale at the foot of the chart and following the line of 15,000 pounds of gas passing over the heating surface per hour, we find that with a calculated furnace temperature of 2,100° F. the boiler efficiency (E) is about 67 per cent and the capacity about 70 per cent. Moving vertically upward the pounds of air must be slightly reduced and more coal burned in order to obtain higher furnace temperature and at the same time keep the pounds of gas per hour constant. By doing this more heat becomes available for raising the temperature of the gases, as shown by the ordinate on the right of the chart. At a furnace temperature of 3,300° F., the capacity is 130 per cent and the boiler efficiency (E) 75 per cent, an increase of 8 per cent over the efficiency with a temperature of 2,100° F. Example 3. Taking the curve of 100 per cent rated capacity we find that rated capacity can be obtained with many conditions. The first extreme is with a furnace temperature of 2,100° F., when passing 21,000 pounds of gas through the boiler per hour; obtaining a boiler efficiency (E) of 64 per cent. The second extreme is with a furnace temperature of about 3,500° F., and a boiler efficiency of 76 per cent, when passing about 11,000 pound of gas through the boiler per hour. Example 4. A boiler efficiency of 70 per cent can be attained under many conditions. The lowest temperature on the chart with which this efficiency can be obtained is 2,400° F. at a capacity of 70 per cent, when passing about 12,000 pounds of gas through the boiler per hour. In order to maintain this high efficiency when working at 130 per cent of rated capacity, it is necessary to increase the furnace temperature to 2,800° F. by burning more coal with decreased air supply. The curves of fig. 66 (p. 144) differ from those of fig. 65 (p. 141) in that true boiler efficiency (E,) is used instead of boiler efficiency (E). The true boiler efficiency is based on the heat available to the boiler, considering only that part of the heat in the gases as available which is above the temperature of the steam. If the steam and water in the boiler were at atmospheric temperature, the two efficiencies, E and E, would be the same; but as the temperature of the water in the boilers is always from 150° to 200° F. above the atmospheric temperature less heat is available for the boiler. The general significance of the chart is (1) that true boiler efficiency increases with initial temperature, perhaps because an increasing amount of heat is absorbed by the lower row of tubes on account of conduction through the encircling tiles and of radiation on them, where they are bare in the rear, from the brickwork of the combustion chamber, and also because the higher temperature of the gases causes a steeper temperature gradient through the soot, metal, and scale, so as to cause a higher rate of flow of heat. All these causes are apart from the simplest statement of Perry's suggested theory of constant true boiler efficiency and are modifying factors of it in practice. The further general significance of this chart is (2) that at the same initial temperature. the true boiler efficiency decreases as the mass of gases passed over the heating surface increases that is, as the capacity increases. The explanation of the fact that the true boiler efficiency (E) is lower with these conditions is that inasmuch as capacity is proportional to the rate of heat absorption by the boiler the temperature difference between the water in the boiler and the first layer of gases on the outside must be greater in order that more heat be transmitted into the water in the same length of time. This increase in the temperature gradient causes the gases to leave the heating surface of the boiler at a higher temperature than in the cases of low capacity. The efficiency range of this chart is not very large-only from 77 to 85 per cent--and few points are near the extremes. MISCELLANEOUS. RELIABILITY OF OBSERVATIONS AND DATA. The following remarks are given to facilitate the utilization of the actual data of the tests which are discussed in this volume: Item 2: Duration of trial. This item is important for its effect on the water level in the boiler, which is easily changed several inches by opening or closing the steam valve, or by starting or stopping a large engine. Perhaps the usual error on this account was a fraction of 1 per cent of the evaporation. The item also enters into the errors of estimating the amount of fuel on the grate at starting and stopping. This estimating was always done with care, but the error on ten-hour tests may have been sometimes as much as 1 per cent of the coal burned, especially if the amount was small. As regards the fuel, when estimating accuracy, the real question is, How much coal was burned? not, How long did the test last? Item 3: Grate surface, square feet. Boiler No. 1 was equipped with a plain grate, having an area of 40.55 square feet. Boiler No. 2 was equipped with a McClave rock " ing grate, having an area of 36.4 square feet. These areas were maintained constant during the 1905 tests. Item 11: Barometer, inches of mercury. This observation was always obtained from the Weather Bureau, and no correction was made for difference in elevation between the Weather Bureau station and the fuel-testing plant, which was only a few feet. Item 11.1: Steam pressure. This reading was sometimes taken from a calibrated steam gage and sometimes from a recording-instrument chart. It is correct within a pound. Items 12 and 13: Draft readings. These readings are accurate to 0.02 inch. Item 17: Temperature of steam, calculated. Item 18: Correct unless otherwise noted. Item 20: Correct unless otherwise noted. Item 21: Generally low, owing to air leakage, and apt to be in error in extreme instances, as much as 100° F., this error being the aggregate of the thermometer error and the greater error due to the difficulty of obtaining a true average temperature in the stack by the use of a single thermometer. Large errors are noted in their respective tests. Item 21.1: Average temperature of furnace. Read by means of a Wanner optical pyrometer. All observations were made looking into the combustion chamber, about 2 feet from the rear end, 1 foot below the tile roof. When looking at flame, as was generally the case, the indications were perhaps well within 200° F. of the right value, generally perhaps within 100° F., although this is merely an estimate based on circumstantial evidence. In the absence of flame, light was received from the opposite wall, which was plainly cooler than the gases, as was evident on comparing it by eye with the tile roof near by; and even this latter was cooler than the gases which heated it, because heat was constantly passing upward through the tile into the water tubes. How much too low such readings are is only a guess-perhaps 100° to 200° F. In general, the tests on coals high in "fixed carbon" have combustion-chamber temperatures too low. Item 28: Total weight of ash and refuse. Refuse was taken to mean everything which fell through the grate plus the ash and clinker pulled out of the furnace during cleaning of fire. It is noteworthy that the weight of earthy matter in the refuse from a test is usually 15 or 20 per cent short of the amount that the chemical analysis indicates; the difference undoubtedly goes over into the combustion chamber and up the stack. Item 32: Fixed carbon of proximate analysis. Item 33: Volatile matter of proximate analysis. The preceding two items are based on arbitrary methods of driving off the so-called "volatile matter" and weighing the remainder to get ash and fixed carbon. By varying the standard of conditions under which the distillation is effected very different results can be obtained, and thus it may be seen that care should be exercised in deducing results of practical trials from the purely arbitrary results obtained from proximate analyses of dry or moist coal. A greater number of ultimate analyses should customarily be made, inasmuch as they furnish absolute data. Coal molecules are probably complex, and although little is known on the subject it is likely that the products and even the amounts of products of destructive distillation vary widely with the method followed, as to temperature, rapidity of heating, etc. Item 34: Percentage of moisture in coal. This item is uncertain at best. It is probable that on warm, dry, and windy days the coal lost some moisture while being quartered on the floor of the boiler room, so that the coal fired was really lower in heating value than the chemical analysis indicates.. Items 37, 38, 39, 40, 41, and 42: Ultimate analysis of dry coal. Furnished by the chemical division. Items 50 and 51: Furnished by the chemical division. These items were used in test calculations in preference to items 52 and 53. Items 54 and 56: These items are untrustworthy in these tests; concordant results were never obtained. All the investigational work done on the matter pointed to the possibility that eddies vitiated the readings, because the vertical section of pipe in which the sampling nipples were placed was only 2 feet long. These items are probably not reliable within 50 per cent of the values given. Item 77: Percentage of smoke. Dense black (so estimated) taken as 100 per cent. Item 81: Average thickness of fire. Only approximate, because of difficulties of measurement when flame is present. It also varies with the personal equation of the observer. Items 84, 85, 86, 87, and 88: These items are somewhat in error, owing to air dilution. Heat balance: Items 2 and 3, very nearly correct; item 4, usually doubtful, owing to inaccurate flue-gas temperatures; item 5, only approximate; item 6, doubtful— results of our tests show that the unaccounted-for loss and the flue-gas loss up the stack take and give reciprocally. (See fig. 35, p. 63.) The chart shown in fig. 68 indicates that in general terms the unaccounted-for heat increases in percentage with the loss due to CO. FIG. 68.-Relation of unaccounted-for loss to CO loss (tests grouped on basis of per cent of CO loss). COMPUTATIONS OF A STEAMING TEST. The data necessary for complete results of a steaming test come from three sources: (1) The boiler room, (2) the chemical laboratory, and (3) the United States Weather Bureau. After a coal has been tested, from ten days to two weeks are required for the chemical work to be completed before definite results are known. The state of weather, the barometric pressure, and the relative humidity for the day of the test are obtained from the Weather Bureau. The computed results given in this report have been calculated according to the methods indicated in the A. S. M. E. code for making boiler trials. However, it has been thought advisable to explain how several of the items were obtained or determined, and in doing this, for brevity, code numbers will be used. Item 23: See explanation under "Average diameter of coal,” p. 45. Item 27=item 25X(100-item 34). Item 28=total ash and refuse from test. This includes the coal which falls through the grate. |