heating-surface. Divide the square of the heating-surface in feet by the consumption of water in cubic feet per hour, and multiply by 00222. The product is the area of grate in square feet.1 The relations, just announced, between heating-surface, grate-area, and economical evaporative power, lead to the following important conclusions: 1st. That the economical evaporative power decreases directly as the area of grate is increased, even while the heating-surface remains the same; showing that the economic value of a given heating-surface is diminished by enlarging the grate; and inversely, that a reduction of the grate raises the value of the heating-surface. 2nd. That the economic evaporative power increases directly as the square of the heating-surface, when the grate remains the same; showing that every part of the heating-surface increases in economic value, in a compound ratio, by adding to its amount: such that, for example, doubling the heatingsurface would not only double, but quadruple the evaporative power, and would double the efficiency per square foot. 3rd. That the necessary heating-surface increases, only as the square root of the required economical evaporative power, when the grate remains constant; that is, for example, four times the evaporative power would require only twice the heating-surface. 4th. That the heating-surface, to supply the same evaporative power, must be increased as the square root of the grate-area; that is, an increase of grate reduces the efficiency of the surface, such that, for example, for four times the grate, twice the surface is necessary to evaporate the same quantity of water. : It is plain, then, that the heating-surface is economically weakened, by an extension of grate, and is strengthened by its reduction that, in short, the value of heating-surface increases rapidly with the ratio it bears to the grate, much more rapidly than the ratio itself. It follows that locomotive boilers, should be designed for the highest average rates of evaporation, The formulæ are regularly worked out, according to these Rules, in the "Treatise on Railway Machinery," by D. K. Clark, and the Rules are quoted from that work. per foot of grate, that may in good practice be adopted, consistently with the highest average rates of combustion at which coke can be properly burned; as, in this way, the smallest grate and the smallest amount of heating-surface will be arrived at, and consequently the smallest and lightest boiler, consistent with the required economical evaporative power. The grate cannot be too small, nor the surface too extensive, as respects economical evaporation; and the chief limit to the smallness of grate is that imposed by the physical qualifications of coke, as fuel, to resist the violence of strong draughts, at high rates of combustion, either in lifting it bodily off the grate, or in breaking it up into fragments. The practice of the carlier tube-boiler locomotive supplies some data on the point, as, with their imperfect proportions of boiler and engine, they were necessarily worked up to the highest rates of combustion. In these engines, 100 lbs. to 160 lbs. of coke per foot of grate per hour were consumed. Towards the latter limit, the coke, if of light and loose quality, was much shaken up and blown through the tubes. When it is sound, hard, and cohesive, coke will generally burn well at 150 lbs. to 160 lbs. per foot per hour, as is exemplified in the observations with the Sphynx,' class of engines, which are stated, by Mr. Peacock, to work satisfactorily even at such a high rate of combustion, and are not found materially to require more cleaning of tubes, or clearing of smokebox than is usual with other boilers. To cover all the necessities of practice, 150 lbs. of good sound coke may be fixed, as the ultimate maximum quantity which may be properly consumed, per foot of grate per hour; and to make allowance for inferior qualities, 112 lbs. or 1 cwt. of coke will be adopted for the average maximum consumption per foot of grate per hour; this determines the average maximum of economical evaporation to be 16 cubic feet of water per hour, allowing 9 lbs. of water per pound of coke. By the Rules, this rate of evaporation requires 85 feet of heating-surface per foot of grate; and therefore, in locomotive boilers, a total heating-surface equal to 85 times the grate-area is the smallest that should be adopted in practice. Table No. 2 contains a number of examples of the economical evaporative power of locomotive boilers, for given ratios of heating-surface. TABLE NO. 2.-ECONOMICAL EVAPORATIVE POWER of LOCOMOTIVE BOILERS, for giving ratios of Heating-Surfaces. Table No. 3 contains the whole economical evaporative power of boilers, with various amounts of grate-area and heating-surface. TABLE NO. 3.-Of RELATIVE GRATE-AREAS, HEATING-SURFACES, and EcoNOMICAL EVAPORATIVE POWERS of LOCOMOTIVE BOILERS; deduced from practice. Total Econo mical Evapo rative Power, in Cubic Feet of Water per Hour. Cub. Ft. 40 50 60 70 80 100 120 140 160 180 200 220 240 260 280 300 320 360 400 Total Heating-Surfaces, in Square Feet, due to the above Grate-Areas, and the annexed Evaporative Powers. 300 328 355 379 402 424 444 464 501 536 569 600 900 948 995 1039 1122 1199 1272 1341 1406 1468 1374 1469 1558 1642 1722 1799 1516 1610 1696 1778 1859 NOTE I.-Lower maximum rates of evaporation should be adopted for grates less than 8 feet, to meet the practical difficulties of working with very small grates, and are suggested as follows: The surfaces printed in pointed type are due to evaporations of from 2 feet as a minimum to 16 feet of water per foot of grate per hour, as the average maximum of evaporation. The heating surfaces are measured from the interior. It has been seen, that the efficiency of tube-surface may be neutralized by a deficiency of clearance between the tubes. The long boilers, such as, for example, the 'Sphynx,' with 142 tubes, work satisfactorily with inch of clearance; and also the Caledonian engines, with 158 tubes and inch of clearance. Fig. 2. SECTIONS OF BOILERS, TO ILLUSTRATE FREEDOM FOR CIRCULATION. These are well established data, and a mean of these gives, for 150 tubes, inch of clearance, or inch for every 30 tubes. As the necessity for clearance should vary in the ratio of the whole number of tubes, the following rule will yield satisfactory results for practice: RULE VI. To find the clearance between the tubes, suitable for economical evaporation, for a given number of tubes. Divide the number of tubes by 30. The quotient is the required clearance in eighths of an inch. Table No. 4 is drawn up by the Rule, showing the necessary clearance, in good practice, for given numbers of tubes. TABLE NO. 4.-Of the CLEARANCE between the TUBES suitable for ECONOMICAL EVAPORATION, at the rate of 9 lbs. Water per lb. of Coke. The lateral clearance between the upper rows of tubes and the barrel should be at least th of the diameter of barrel at each side. The diameter of the tubes is supposed to be about 2 inches. To find the relation of the diameter of a boiler-barrel and the number of tubes which can be received by it; let it be assumed as a practical standard, that the arrangement of tubes in the boiler is to be the same as in the Sphynx,' by Messrs. Sharp Brothers, and Co. In this boiler the tubes are suitably apart according to the Rule, and a free water-space is allowed between the tubes and the sides, and the bottom of the barrel. In cross section, they occupy a segment of the barrel, of which the versed sine is equal to about two-thirds of the diameter; they are ranged in horizontal rows, in each of which the tubes alternate with those immediately above and below, so that the lines joining the centres of contiguous tubes form equilateral triangles, of which there are two to each tube. In spacing out the tubes, therefore, supposing the whole area of the lower segment of the barrel to be fully occupied by them, their number is expressible by the number of times that the lower segment contains the quadrangular space set off for each tube. Let d the diameter of the barrel, = C = the clearance of the tubes, p = the pitch of the tubes, equal to d'+c, n = the number of tubes. Then the area of the tube-segment of the barrel, of which the depth is two-thirds of the diameter, is 55d; and the area of the four-sided space for each tube is the product of the pitch, by the vertical distance apart of two neighbouring rows of tubes, or 86 p3. Then, n = •55d = .62 2 But, of the total area of the tube-space, Sharp Brothers reserve one-sixth for clearance around the faggot of tubes; five-sixths of the above value of n, will therefore express the number of tubes available in good practice. Hence, finally |