A Catechism of the Steam Engine

MODES OF ESTIMATING THE POWER AND PERFORMANCE OF ENGINES AND BOILERS.

209. Q.--What do you understand by a horse power?

A.--An amount of mechanical force that will raise 33,000 lbs. one foot high in a minute. This standard was adopted by Mr. Watt, as the average force exerted by the strongest London horses; the object of his investigation being to enable him to determine the relation between the power of a certain size of engine and the power of a horse, so that when it was desired to supersede the use of horses by the erection of an engine, he might, from the number of horses employed, determine the size of engine that would be suitable for the work.

210. Q.--Then when we talk of an engine of 200 horse power, it is meant that the impelling efficacy is equal to that of 200 horses, each lifting 33,000 lbs. one foot high in a minute?

A.--No, not now; such was the case in Watt's engines, but the capacity of cylinder answerable to a horse power has been increased by most engineers since his time, and the pressure on the piston has been increased also, so that what is now called a 200 horse power engine exerts, almost in every case, a greater power than was exerted in Watt's time, and a horse power, in the popular sense of the term, has become a mere conventional unit for expressing a certain size of engine, without reference to the power exerted.

211. Q.--Then, each nominal horse power of a modern engine may raise much more than 33,000 lbs. one foot high in a minute?

A.--Yes; some raise 52,000 lbs., others 60,000 lbs., and others 66,000 lbs., one foot high in a minute by each nominal horse power. Some engines indeed work as high as five times above the nominal power, and therefore no comparison can be made between the performances of different engines, unless the power actually exerted be first discovered.

212. Q.--How is the power actually exerted by engines ascertained?

A.--By means of an instrument called the indicator, which is a miniature cylinder and piston attached to the cylinder cover of the main engine, and which indicates, by the pressure exerted on a spring, the amount of pressure or vacuum existing within the cylinder. From this pressure, expressed in pounds per square inch, deduct a pound and a half of pressure for friction, the loss of power in working the air pump, &c.; multiply the area of the piston in square inches by this residual pressure, and by the motion of the piston, in feet per minute, and divide by 33,000; the quotient is the actual number of horses power of the engine. The same result is attained by squaring the diameter of the cylinder, multiplying by the pressure per square inch, as shown by the indicator, less a pound and a half, and by the motion of the piston, in feet per minute, and dividing by 42,017.

213. Q. How is the nominal power of an engine ascertained?

A.--Since the nominal power is a mere conventional expression, it is clear that it must be determined by a merely conventional process. The nominal power of ordinary condensing engines may be ascertained by the following rule: multiply the square of the diameter of the cylinder in inches, by the velocity of the piston in feet per minute, and divide the product by 6,000; the quotient is the number of nominal horses power. In using this rule, however, it is necessary to adopt the speed of piston prescribed by Mr. Watt, which varies with the length of the stroke. The speed of piston with a 2 feet stroke is, according to his system, 160 per minute; with a 2 ft. 6 in. stroke, 170; 3 ft., 180; 3 ft. 6 in., 189; 4 ft., 200; 5 ft., 215; 6 ft., 228; 7 ft., 245; 8 ft., 256 ft.

214. Q.--Does not the speed of the piston increase with the length of the stroke?

A.--It does: the speed of the piston varies nearly as the cube root of the length of the stroke.

215. Q.--And may not therefore some multiple of the cube root of the length of the stroke be substituted for the velocity of the piston in determining the nominal power?

A.--The substitution is quite practicable, and will accomplish some simplification, as the speed of piston proper for the different lengths of stroke cannot always be remembered. The rule for the nominal power of condensing engines when thus arranged, will be as follows: multiply the square of the diameter of the cylinder in inches by the cube root of the stroke in feet, and divide the product by 47; the quotient is the number of nominal horses power of the engine, supposing it to be of the ordinary condensing description. This rule assumes the existence of a uniform effective pressure upon the piston of 7 lbs. per square inch; Mr. Watt estimated the effective pressure upon the piston of his 4 horse power engines at 6-8 lbs. per square inch, and the pressure increased slightly with the power, and became 6.94 lbs. per square inch in engines of 100 horse power; but it appears to be more convenient to take a uniform pressure of 7 lbs. for all powers. Small engines, indeed, are somewhat less effective in proportion than large ones, but the difference can be made up by slightly increasing the pressure in the boiler; and small boilers will bear such an increase without inconvenience.

216. Q.--How do you ascertain the power of high pressure engines?

A.--The actual power is readily ascertained by the indicator, by the same process by which the actual power of low pressure engines is ascertained. The friction of a locomotive engine when unloaded is found by experiment to be about 1 lb. per square inch on the surface of the pistons, and the additional friction caused by any additional resistance is estimated at about .14 of that resistance; but it will be a sufficiently near approximation to the power consumed by friction in high pressure engines, if we make a deduction of a pound and a half from the pressure on that account, as in the case of low pressure engines. High pressure engines, it is true, have no air pump to work; but the deduction of a pound and a half of pressure is relatively a much smaller one where the pressure is high, than where it does not much exceed the pressure of the atmosphere. The rule, therefore, for the actual horse power of a high pressure engine will stand thus: square the diameter of the cylinder in inches, multiply by the pressure of the steam in the cylinder per square inch less 1-1/2 lb., and by the speed of the piston in feet per minute, and divide by 42,017; the quotient is the actual horse power.

217. Q.--But how do you ascertain the nominal horse power of high pressure engines?

226. Q.--What is meant by the duty of a engine?

A.--The work done in relation to the fuel consumed.

227. Q.--And how is the duty ascertained?

A.--In ordinary mill or marine engines it can only be ascertained by the indicator, as the load upon such engines is variable, and cannot readily be determined; but in the case of engines pumping water, where the load is constant, the number of strokes performed by the engine will represent the work done, and the amount of work done by a given quantity of coal represents the duty. In Cornwall the duty of an engine is expressed by the number of millions of pounds raised one foot high by a bushel, or 94 lbs. of Welsh coal. A bushel of Newcastle coal will only weigh 84 Lbs.; and in comparing the duty of a Cornish engine with the performance of an engine in some locality where a different kind of coal is used, it is necessary to pay regard to such variations.

228. Q.--Can you tell the duty of an engine when you know its consumption of coal per horse power per hour?

A.--Yes, if the power given be the actual, and not the nominal, power. Divide 166.32 by the number of pounds of coal consumed per actual horse power per hour; the quotient is the duty in millions of pounds. If you already have the duty in millions of pounds, and wish to know the equivalent consumption in pounds per actual horse power per hour, divide 166.32 by the duty in millions of pounds; the quotient is the consumption per actual horse power per hour. The duty of a locomotive engine is expressed by the weight of coke it consumes in transporting a ton through the distance of one mile upon a railway; but this is a very imperfect method of representing the duty, as the tractive efficacy of a pound of coke becomes less as the speed of the locomotive becomes greater; and the law of variation is not accurately known.

229. Q.--What amount of power is generated in good engines of the ordinary kind by a given weight of coal?

A.--The duty of different kinds of engines varies very much, and there are also great differences in the performance of different engines of the same class. In ordinary rotative condensing engines of good construction, 10 lbs. of coal per nominal horse power per hour is a common consumption; but such engines exert nearly twice their nominal power, so that the consumption per actual horse power per hour may be taken at from 5 to 6 lbs. Engines working very expansively, however, attain an economy much superior to this. The average duty of the pumping engines in Cornwall is about 60,000,000 lbs. raised 1 ft. high by a bushel of Welsh coals, which weighs 94 lbs. This is equivalent to a consumption of 3.1 lbs. of coal per actual horse power per hour; but some engines reach a duty of above 100,000,000, or 1.74 lbs. of coal per actual horse power per hour. Locomotives consume from 8 to 10 lbs. of coke in evaporating a cubic foot of water, and the evaporation of a cubic foot of water per hour may be set down as representing an actual horse power in locomotives as well as in condensing engines, if expansion be not employed. When the locomotive is worked expansively, however, there is of course a less consumption of water and fuel per horse power, or per ton per mile, than when the full pressure is used throughout the stroke; and most locomotives now operate with as much expansion as can be conveniently given by the slide valves.

230. Q.--But is not the evaporative power of locomotives affected materially by the proportions of the boiler?

A.--Yes, but this may be said of all boilers; but in locomotive boilers, perhaps, the effect of any misproportion becomes more speedily manifest. A high temperature of the fire box is found to be conducive to economy of fuel; and this condition, in its turn, involves a small area of grate bars. The heating surface of locomotive boilers should be about 80 square feet for each square foot of grate bars, and upon each foot of grate bars about 1 cwt. of coke should be burnt in the hour.

231. Q.--Probably the heat is more rapidly absorbed when the temperature of the furnace is high?

A.--That seems to be the explanation. The rapidity with which a hot body imparts heat to a colder, varies as the square of the difference of temperature; so that if the temperature of the furnace be very high, the larger part of the heat passes into the water at the furnace, thereby leaving little to be transmitted by the tubes. If, on the contrary, the temperature of the furnace be low, a large part of the heat will pass into the tubes, and more tube surface will be required to absorb it. About 16 cubic feet of water should be evaporated by a locomotive boiler for each, square foot of fire grate, which, with the proportion of heating surface already mentioned, leaves 5 square feet of heating surface to evaporate a cubic foot of water in the hour. This is only about half the amount of surface usual in land and marine boilers per cubic foot evaporated, and its small amount is due altogether to the high temperature of the furnace, which, by the rapidity of transmission it causes, is tantamount to an additional amount of heating surface.

232. Q.--You have stated that the steam and vacuum gauges are generally glass tubes, up which mercury is forced by the steam or sucked by the vacuum?

A.--Vacuum gauges are very often of this construction, but steam gauges more frequently consist of a small iron tube, bent like the letter U, and into which mercury is poured. The one end of this tube communicates with the boiler, and the other end with the atmosphere; and when the pressure of the steam rises in the boiler, the mercury is forced down in the leg communicating with the boiler and rises in the other leg, and the difference of level in the legs denotes the pressure of the steam. In this gauge a rise of the mercury one inch in the one leg involves a difference of the level between the two legs of two inches, and an inch of rise is, therefore, equivalent to two inches of mercury, or a pound of pressure. A small float of wood is placed in the open leg to show the rise or fall of the mercury, and this leg is surmounted by a brass scale, graduated in inches, to the marks of which the float points.

233. Q.--What other kinds of steam and vacuum gauges are there?

A.--There are many other kinds; but probably Bourdon's gauges are now in more extended use than, any other, and their operation has been found to be satisfactory in practice. The principle of their action may be explained to be, that a thin elliptical metal tube, if bent into a ring, will seek to coil or uncoil itself if subjected to external or internal pressure, and to an extent proportional to the pressure applied. The end of the tube is sharpened into an index, and moves to an extent corresponding to the pressure applied to the tube; but in the more recent forms of this apparatus, a dial and a hand, like those of a clock, are employed, and the hand is moved round by a toothed sector connected to the tube, and which sector acts on a pinion attached to the hand. Mr. Shank, of Paisley, has lately introduced a form of steam gauge like a thermometer, with a flattened bulb; and the pressure of the steam, by compressing the bulb, causes the mercury to rise to a point proportional to the pressure applied.

234. Q.--You have already stated that the actual power of an engine is ascertained by an instrument called the indicator, which consists of a small cylinder with a piston moving against a spring, and compressing it to an extent answerable to the pressure of the steam. Will you explain further the structure and mode of using that instrument?

A.--The structure of the common form of indicator will be most readily apprehended by a reference to fig. 36, which is a McNaught's indicator. Upon a movable barrel A, a piece of paper is wound, the ends of which are secured by the slight brass clamps shown in the drawing. The barrel is supported by the bracket b, proceeding from the body of the indicator, and at the bottom of the barrel a watch spring is coiled with one end attached to the barrel and the other end to the bracket, so that when the barrel is drawn round by a string wound upon its lower end like a roller blind, the spring returns the barrel to its original position, when the string is relaxed. The string is attached to some suitable part of the engine, and at every stroke the string is drawn out, turning round the barrel, and the barrel is returned again by the spring on the return stroke.

235. Q--But in what way can these reciprocations of the barrel determine the power of the engine?

A.--They do not determine it of themselves, but are only part of the operation. In the inside of the cylinder c there is a small piston moving steam tight in a cylinder of which d is the piston rod, and e a spiral spring of steel, which the piston, when forced upwards by the steam or sucked downwards by the vacuum, either compresses or extends; f is a cock attached to the cylinder of the indicator, and which is screwed into the cylinder cover. It is obvious that, so soon as this cock is opened, the piston will be forced up when the space above the piston of the engine is opened to the boiler, and sucked down when that space is opened to the condenser--in each case to an extent proportionate to the pressure of the steam or the perfection of the vacuum, the top of the piston c being open to the atmosphere. A pencil, p, with a knife hinge, is inserted into the piston rod, at e, and the point of the pencil bears upon the surface of the paper wound upon the drum A. If the drum A did not revolve, this pencil would merely trace on the paper a vertical line; but as the drum A moves round and back again every stroke of the engine, and as the pencil moves up and down again every stroke of the engine, the combined movements trace upon the paper a species of rectangle, which is called an indicator diagram; and the nature of this diagram determines the nature of the engine's performance.

236. Q.--How does it do this?

A.--It is clear that if the pencil was moved up instantaneously to the top of its stroke, and was also moved down instantaneously to the bottom of its stroke, and if it remained without fluctuation while at the top and bottom, the figure described by the pencil would be a perfect rectangle, of which the vertical height would represent the total pressure of the steam and vacuum, and therefore the total pressure urging the piston of the engine. But in practice the pencil will neither rise nor fall instantaneously, nor will it remain at a uniform height throughout the stroke. If the steam be worked expansively the pressure will begin to fall so soon as the steam is cut off; and at the end of the stroke, when the steam comes to be discharged, the subsidence of pressure will not be instantaneous, but will occupy an appreciable time. It is clear, therefore, that in no engine can the diagram described by an indicator be a complete rectangle; but the more nearly it approaches to a rectangle, the larger will be the power produced at every stroke with any given pressure, and the area of the space included within the diagram will in every case accurately represent the power exerted by the engine during that stroke.

237. Q.--And how is this area ascertained?

A.--It may be ascertained in various ways; but the usual mode is to take the vertical height of the diagram at a number of equidistant points on a base line, and then to take the mean of these several heights as representative of the mean pressure actually urging the piston. Now if you have the pressure on the piston per square inch, and if you know the number of square inches in its area, and the velocity with which it moves in feet per minute, you have obviously the dynamical effort of the engine, or, in other words, its actual power.

238. Q.--How is the base line you have referred to obtained?

A.--In proceeding to take an indicator diagram, the first thing to be done is to allow the barrel to make two or three reciprocations with the pencil resting against it, before opening the cock attached to the cylinder. There will thus be traced a horizontal line, which is called the atmospheric line, and in condensing engines, a part of the diagram will be above and a part of it below this line; whereas, in high pressure engines the whole of the diagram will be above this line. Upon this line the vertical ordinates may be set off at equal distances, or upon any base line parallel to it; but the usual course is to erect the ordinates on the atmospheric line.

239. Q.--Will you give an example of an indicator diagram?

A.--Fig. 37 is an indicator diagram taken from a low pressure engine, and the waving line a b c, forming a sort of irregular parallelogram, is that which is described by the pencil. The atmospheric line is represented by the line o o. The scale at the side shows the pressure of the steam, which in this engine rose to about 9 lbs. per square inch, and the vacuum fell to 11 lbs. The steam begins to be cut off when, about one-fourth of the stroke has been performed, and the pressure consequently falls.

240. Q.--Is this species of indicator which you have just described applicable to locomotive engines?

A.--It is no doubt applicable under suitable conditions; but another species of indicator has been applied by Mr. Gooch to locomotive engines, which presents several features of superiority for such a purpose.

This indicator has its cylinder placed horizontally; and its piston compresses two elliptical springs; a slide valve is substituted for a cock, to open or close the communication with the engine. The top of the piston rod of this indicator is connected to the short arm of a smaller lever, to the longer arm of which the pencil is attached, and the pencil has thus a considerably larger amount of motion than the piston; but it moves in the arc of a circle instead of in a straight line. The pencil marks on a web of paper, which is unwound from one drum and wound on to another, so that a succession of diagrams are taken without the necessity of any intermediate manipulation.

241. Q.--These diagrams being taken with a pencil moving in an arc, will be of a distorted form?

A.--They will not be of the usual form, but they may be easily translated into the usual form. It is undoubtedly preferable that the indicator should act immediately in the production of the final form of diagram.

242. Q.--What other gauges or instruments are there for telling the state, or regulating the power of an engine?

A.--There is the counter for telling the number of strokes the engine makes, and the dynamometer for ascertaining the tractive power of steam vessels or locomotives; then there are the gauge cocks, and glass tubes, or floats, for telling the height of water in the boiler; and in pumping engines there is the cataract for regulating the speed of the engine.

243. Q.--Will you describe the mechanism of the counter?

A.--The counter consists of a train of wheel work, so contrived that by every stroke of the engine an index hand is moved forward a certain space, whereby the number of strokes made by the engine in any given time is accurately recorded. In most cases the motion is communicated by means of a detent,--attached to some reciprocating part of the engine,--to a ratchet wheel which gives motion to the other wheels in its slow revolution; but it is preferable to derive the motion from some revolving part of the engine by means of an endless screw, as where the ratchet is used the detent will sometimes fail to carry it round the proper distance. In the counter contrived by Mr. Adie, an endless screw works into the rim of two small wheels situated on the same axis, but one wheel having a tooth more than the other, whereby a differential motion is obtained; and the difference in the velocity of the two wheels, or their motion upon one another, expresses the number of strokes performed. The endless screw is attached to some revolving part of the engine, whereby a rotatory motion is imparted to it; and the wheels into which the screws work hang down from it like a pendulum, and are kept stationary by the action of gravity.

244. Q.--What is the nature of the dynamometer?

A.--The dynamometer employed for ascertaining the traction upon railways consists of two flat springs joined together at the ends by links, and the amount of separation of the springs at the centre indicates, by means of a suitable hand and dial, the force of traction. A cylinder of oil, with a small hole through its piston, is sometimes added to this instrument to prevent sudden fluctuations. In screw vessels the forward thrust of the screw is measured by a dynamometer constructed on the principle of a weighing machine, in which a small spring pressure at the index will balance a very great pressure where the thrust is employed; and in each case the variations of pressure are recorded by a pencil on a sheet of paper, carried forward by suitable mechanism, whereby the mean thrust is easily ascertained. The tractive force of paddle wheel steamers is ascertained by a dynamometer fixed on shore, to which the floating vessel is attached by a rope. Sometimes the power of an engine is ascertained by a friction break dynamometer applied to the shaft.

345. Q.--What will determine the amount of thrust shown by the dynamometer?

A.--In locomotives and in paddle steamers it will be determined by the force turning the wheels, and by the smallness of the diameter of the wheels; for with small wheels the thrust will be greater than with large wheels. In screw vessels the thrust will be determined by the force turning round the screw, and by the smallness of the screw's pitch; for with any given force of torsion a fine pitch of screw will give a greater thrust than a coarse pitch of screw, just as is the case when a screw works in a solid nut.

246. Q.--Will you explain the use of the glass gauges affixed to the boiler?

A.--The glass gauges are tubes affixed to the fronts of boilers, by the aid of which the height of the water within the boilers is readily ascertainable, for the water will stand at the same height in the tube as in the boiler, with which there is a communication maintained both at the top and bottom of the tube by suitable stopcocks. The cocks connecting the glass tube with the boiler should always be so constructed that the tube may be blown through with the steam, to clear it of any internal concretion that may impair its transparency; and the construction of the sockets in which the tube is inserted should be such, that, even when there is steam in the boiler, a broken tube may be replaced with facility.

247. Q.--What then are the gauge cocks?

A.--The gauge cocks are cocks penetrating the boiler at different heights, and which, when opened, tell whether it is water or steam that exists at the level at which they are respectively inserted. It is unsafe to trust to the glass gauges altogether as a means of ascertaining the water level, as sometimes they become choked, and it is necessary, therefore, to have gauge cocks in addition; but if the boiler be short of steam, and a partial vacuum be produced within it, the glass gauges become of essential service, as the gauge cocks will not operate in such a case, for though opened, instead of steam and water escaping from them, the air will rush into the boiler. It is expedient to carry a pipe from the lower end of the glass tube downward into the water of the boiler, and a pipe from the upper end upward into the steam in the boiler, so as to prevent the water from boiling down through the tube, as it might otherwise do, and prevent the level of the water from being ascertainable. The average level of water in the boiler should be above the centre of the tube; and the lowest of the gauge cocks should always run water, and the highest should always blow steam.

248. Q.--Is not a float sometimes employed to indicate the level of the water in the boiler?

A.--A float for telling the height of water in the boiler is employed only in the case of land boilers, and its action is like that of a buoy floating on the surface, which, by means of a light rod passing vertically through the boiler, shows at what height the water stands. The float is usually formed of stone or iron, and is so counterbalanced as to make its operation the same as if it were a buoy of timber; and it is generally put in connection with the feed valve, so that in proportion as the float rises, the supply of feed water is diminished. The feed water in land boilers is admitted from a small open cistern, situated at the top of an upright or stand pipe set upon the boiler, and in which there is a column of water sufficiently high to balance the pressure of the steam.

249. Q.--What is the cataract which is employed to regulate the speed of pumping engines?

A.--The cataract consists of a small pump-plunger b and barrel, set in a cistern of water, the barrel being furnished on the one side with a valve, c, opening inwards, through which the water obtains admission to the pump chamber from the cistern, and on the other by a plug, d, through which, if the plunger be forced down, the water must pass out of the pump chamber. The engine in the upward stroke of the piston, which is accomplished by the preponderance of weight at the pump end of the beam, raises up the plunger of the cataract by means of a small rod,--the water entering readily through the valve already referred to; and when the engine reaches the top of the stroke, it liberates the rod by which the plunger has been drawn up, and the plunger then descends by gravity, forcing out the water through the cock, the orifice of which has previously been adjusted, and the plunger in its descent opens the injection valve, which causes the engine to make a stroke.

250. Q.--Suppose the cock of the cataract be shut?

A.--If the cock of the cataract be shut, it is clear that the plunger cannot descend at all, and as in that case the injection valve cannot be opened, the engine must stand still; but if the cock be slightly opened, the plunger will descend slowly, the injection valve will slowly open, and the engine will make a gradual stroke as it obtains the water necessary for condensation. The extent to which the cock is open, therefore, will regulate the speed with which the engine works; so that, by the use of the cataract, the speed of the engine may be varied to suit the variations in the quantity of water requiring to be lifted from the mine. In some cases an air cylinder, and in other cases an oil cylinder, is employed instead of the apparatus just described; but the principle on which the whole of these contrivances operate is identical, and the only difference is in the detail.

251. Q.--You have now shown that the performance of an engine is determinable by the indicator; but how do you determine the power of the boiler?

A.--By the quantity of water it evaporates. There is, however, no very convenient instrument for determining the quantity of water supplied to a boiler, and the consequence is that this element is seldom ascertained.

PROPORTIONS OF BOILERS.

252. Q.--What are the considerations which must chiefly be attended to in settling the proportions of boilers?

A.--In the first place there must be sufficient grate surface to enable the quantity of coal requisite for the production of the steam to be conveniently burnt, taking into account the intensity of the draught; and in the next place there must be a sufficient flue surface readily to absorb the heat thus produced, so that there may be no needless waste of heat by the chimney. The flues, moreover, must have such an area, and the chimney must be of such dimensions, as will enable a suitable draught through the fire to be maintained; and finally the boiler must be made capable of containing such supplies of water and steam as will obviate inconvenient fluctuations in the water level, and abate the risk of water being carried over into the engine with the steam. With all these conditions the boiler must be as light and compact as possible, and must be so contrived as to be capable of being cleaned and repaired with facility.

253. Q.--Supposing, then, that you had to proportion a boiler, which should be capable of supplying steam sufficient to propel a steam vessel or railway train at a given speed, or to perform any other given work, how would you proceed?

A.--I would first ascertain the resistance which had to be overcome, and the velocity with which it was necessary to overcome it. I should then be in a position to know what pressure and volume of steam were required to overcome the resistance at the prescribed rate of motion; and, finally, I should allow a sufficient heating and fire grate surface in the boiler according to the kind of boiler it was, to furnish the requisite quantity of steam, or, in other words, to evaporate the requisite quantity of water.

254. Q.--will you state the amount of heating surface and grate surface necessary to evaporate a given quantity of water?

A.--The number of square feet of heating or flue surface, required to evaporate a cubic foot of water per hour, is about 70 square feet in Cornish boilers, 8 to 11 square feet in land and marine boilers, and 5 or 6 square feet in locomotive boilers. The number of square feet of heating surface per square foot of fire grate, is from 13 to 15 square feet in wagon boilers; about 40 square feet in Cornish boilers; and from 50 to 90 square feet in locomotive boilers. About 80 square feet in locomotives is a very good proportion.

255. Q.--What is the heating surface of boilers per horse power?

A.--About 9 square feet of flue and furnace surface per horse power is the usual proportion in wagon boilers, reckoning the total surface as effective surface, if the boilers be of a considerable size; but in the case of small boilers the proportion is larger. The total heating surface of a two horse power wagon boiler is, according to Boulton and Watt's proportions, 30 square feet, or 15 ft. per horse power; whereas, in the case of a 45 horse power boiler the total heating surface is 438 square feet, or 9.6 ft. per horse power. In marine boilers nearly the same proportions obtain. The original boilers of the Great Western steamer, by Messrs. Maudslay, were proportioned with about 10 square feet of flue and furnace surface per horse power, reckoning the total amount as effective; but in the boilers of the Retribution, by the same makers, but of larger size, a somewhat smaller proportion of heating surface was adopted. Boulton and Watt have found that in their marine flue boilers, 9 square feet of flue and furnace surface are requisite to boil off a cubic foot of water per hour, which is the proportion of heating surface that is allowed in their land boilers per horse power; but inasmuch as in most modern engines, and especially in marine engines, the nominal considerably exceeds the actual power, they allow 11 or 12 square feet of heating surface per nominal horse power in their marine boilers, and they reckon as effective heating surface the tops of the flues, and the whole of the sides of the flues, but hot the bottoms. For their land engines they still retain Mr. Watt's standard of power, which makes the actual and the nominal power identical; and an actual horse power is the equivalent of a cubic foot of water raised into steam every hour.

256. Q.--What is the proper proportion of fire grate per horse power?

A.--Boulton and Watt allow 0.64 of a square foot area of grate bars per nominal horse power in their marine boilers, and a good effect arises from this proportion; but sometimes so large an area of fire grate cannot be conveniently got, and the proportion of half a square foot per horse power, which is the proportion adopted in the original boiler of the Great Western, seems to answer very well in engines working with a moderate pressure, and with some expansion; and this proportion is now very widely adopted. With this allowance, there will be 22 to 24 square feet of heating surface per square foot of fire grate; and if the consumption of fuel be taken at 6 lbs. per nominal horse power per hour, there will be about 12 lbs. of coal consumed per hour on each square foot of grate. The furnaces should not be more than 6 ft. long, as, if much longer than this, it will be impossible to work them properly for any considerable length of time, as they will become choked with clinker at the back ends.

257. Q.--What quantity of fuel is usually consumed per hour on each square foot of fire grate?

A.--The quantity of fuel burned on each square foot of fire grate per hour, varies very much in different boilers; in wagon boilers it is from 10 to 13 lbs.; in Cornish boilers from 3-1/2 to 4 lbs.; and in locomotive boilers from 80 to 150 lbs.; but about 1 cwt. per hour is a good proportion in locomotives, as has been already explained.

258. Q.--In what manner are the proper sectional area and the proper capacity of the flue of a boiler determined?

A.--The proper collective area for the escape of the smoke and flame over the furnace bridges in marine boilers is 19 square inches per nominal horse power, according to Boulton and Watt's practice, and for the sectional area of the flue they allow 18 square inches per horse power. The sectional area of the flue in square inches is what is termed the calorimeter of the boiler, and the calorimeter divided by the length of the flue in feet is what is termed the vent. In marine flue boilers of good construction the vent varies between the limits of 20 and 25, according to the size of the boiler and other circumstances--the largest boilers having generally the largest vents; and the calorimeter divided by the vent will give the length of the flue in feet. The flues of all flue boilers diminish in their calorimeter as they approach the chimney, as the smoke contracts in its volume in proportion as it parts with its heat.

259. Q.--Is the method of determining the dimensions of a boiler flue, by a reference to its vent and calorimeter, the method generally pursued?

A.--It is Boulton and Watt's method; but some very satisfactory boilers have been made by allowing a proportion of 0.6 of a square foot of fire grate per nominal horse power, and making the sectional area of the flue at the largest part 1/7th of the area of fire grate, and at the smallest part, where it enters the chimney, 1/11th of the area of the fire grate. These proportions are retained whether the boiler is flue or tubular, and from 14 to 16 square feet of tube surface is allowed per nominal horse power.

260. Q.--Are the proportions of vent and calorimeter, taken by Boulton and Watt for marine flue boilers, applicable also to wagon and tubular boilers?

A.--No. In wagon and tubular boilers very different proportions prevail, yet the proportions of every kind of boiler are determinable on the same general principle. In wagon boilers the proportion of the perimeter of the flue which is effective as heating surface, is to the total perimeter as 1 to 3, or, in some cases as 1 to 2.5; and with any given area of flue, therefore, the length of the flue must be from 3 to 2.5 times greater than would be necessary if the total surface were effective, else the requisite quantity of heating surface will not be obtained. If, then, the vent be the calorimeter, divided by the length, and the length be made 3 or 2.5 times greater, the vent must become 3 or 2.5 times less; and in wagon boilers accordingly, the vent varies from 8 to 11 instead of from 21 to 25, as in the case of marine flue boilers. In tubular marine boilers the calorimeter is usually made only about half the amount allowed by Boulton and Watt for marine flue boilers, or, in other words, the collective sectional area of the tubes, for the transmission of the smoke, is from 8 to 9 square inches per nominal horse power. It is better, however, to make the sectional area larger than this, and to work the boiler with the damper sufficiently closed to prevent the smoke and flame from rushing exclusively through a few of the tubes.

261. Q.--What are the ordinary dimensions of the flue in wagon boilers?

A.--In Boulton and Watt's 45 horse wagon boiler the area of flue is 18 square inches per horse power, but the area per horse power increases very rapidly as the size of the boiler becomes less, and amounts to about 80 square inches per horse power in a boiler of 2 horse power. Some such increase is obviously inevitable, if a similar form of flue be retained in the larger and smaller powers, and at the same time the elongation of the flue in the same proportion as the increase of any other dimension is prevented; but in the smaller class of wagon boilers the consideration of facility of cleaning the flues is also operative in inducing a large proportion of sectional area. Boulton and Watt's 2 horse power wagon boiler has 30 square feet of surface, and the flue is 18 inches high above the level of the boiler bottom, by 9 inches wide; while their 12 horse wagon boiler has 118 square feet of heating surface, and the dimensions of the flue similarly measured are 36 inches by 13 inches. The width of the smaller flue, if similarly proportioned to the larger one, would be 6-1/2 inches, instead of 9 inches, and, by assuming this dimension, we should have the same proportion of sectional area per square foot of heating surface in both boilers. The length of flue in the 2 horse boiler is 19.5 ft., and in the 12 horse boiler 39 ft., so that the length and height of the flue are increased in the same proportion.

262. Q.--Will you give an example of the proportions of a flue, in the case of a marine boiler?

A.--The Nile steamer, with engines of 110 horse power by Boulton and Watt, is supplied with steam by two boilers, which are, therefore, of 55 horses power each. The height of the flue winding within the boiler is 60 inches, and its mean width 16-1/2 inches, making a sectional area or calorimeter of 990 square inches, or 18 square inches per horse power of the boiler. The length of the flue is 39 ft., making the vent 25, which is the vent proper for large boilers. In the Dee and Solway steamers, by Scott and Sinclair, the calorimeter is only 9.72 square inches per horse power; in the Eagle, by Caird, 11.9; in the Thames and Medway, by Maudslay, 11.34, and in a great number of other cases it does not rise above 12 square inches per horse power; but the engines of most of these vessels are intended to operate to a certain extent expansively, and the boilers are less powerful in evaporating efficacy on that account.

263. Q.--Then the chief difference in the proportions established by Boulton and Watt, and those followed by the other manufacturers you have mentioned is, that Boulton and Watt set a more powerful boiler to do the same work?

A.--That is the main difference. The proportion which one part of the boiler bears to another part is very similar in the cases cited, but the proportion of boiler relatively to the size of the engine varies very materially. Thus the calorimeter of each boiler of the Dee and Solway is 1296 square inches; of the Eagle, 1548 square inches; and of the Thames and Medway, 1134 square inches; and the length of flue is 57, 60, and 52 ft. in the boilers respectively, which makes the respective vents 22-1/2, 25, and 21. Taking then the boiler of the Eagle for comparison with the boiler of the Nile, as it has the same vent, it will be seen that the proportions of the two are almost identical, for 990 is to 1548 as 39 is to 60, nearly; but Messrs. Boulton and Watt would not have set a boiler like that of the Eagle to do so much work.

264. Q.--Then the evaporating power of the boiler varies as the sectional area of the flue?

A.--The evaporating power varies as the square root of the area of the flue, if the length of the flue remain the same; but it varies as the area simply, if the length of the flue be increased in the same proportion as its other dimensions. The evaporating power of a boiler is referable to the amount of its heating surface, and the amount of heating surface in any flue or tube is proportional to the product of the length of the tube and the square root of its sectional area, multiplied by a certain quantity that is constant for each particular form. But in similar tubes the length is proportional to the square root of the sectional area; therefore, in similar tubes, the amount of heating surface is proportional to the sectional area. On this area also depends the quantity of hot air passing through the flue, supposing the intensity of the draught to remain unaffected, and the quantity of hot air or smoke passing through the flue should vary in the same ratio as the quantity of surface.

265. Q.--A boiler, therefore, to exert four times the power, should have four times the extent of heating surface, and four times the sectional area of flue for the transmission of the smoke?

A.--Yes; and if the same form of flue is to be retained, it should be of twice the diameter and twice the length; or twice the height and width if rectangular, and twice the length. As then the diameter or square root of the area increases in the same ratio as the length, the square root of the area divided by the length ought to be a constant quantity in each type of boiler, in order that the same proportions of flue may be retained; and in wagon boilers without an internal flue, the height in inches of the flue encircling the boiler divided by the length of the flue in feet will be 1 very nearly. Instead of the square root of the area, the effective perimeter, or outline of that part of the cross section of the flue which is effective in generating steam, may be taken; and the effective perimeter divided by the length ought to be a constant quantity in similar forms of flues and with the same velocity of draught, whatever the size of the flue may be.

266. Q.--Will this proportion alter if the form of the flue be changed?

A.--It is clear, that with any given area of flue, to increase the perimeter by adopting a different shape is tantamount to a diminution of the length of the flue; and, if the perimeter be diminished, the length of the flue must at the same time be increased, else it will be impossible to obtain the necessary amount of heating surface. In Boulton and Watt's wagon boilers, the sectional area of the flue in square inches per square foot of heating surface is 5.4 in the two horse boiler; in the three horse it is 4.74; in the four horse, 4.35; six horse, 3.75; eight horse, 4.33; ten horse, 3.96; twelve horse, 3.63; eighteen horse, 3.17; thirty horse, 2.52; and in the forty-five horse boiler, 2.05 square inches. Taking the amount of heating surface in the 45 horse boiler at 9 square feet per horse power, we obtain 18 square inches of sectional area of flue per horse power, which is also Boulton and Watt's proportion of sectional area for marine boilers with internal flues.

267. Q.--If to increase the perimeter of a flue is virtually to diminish the length, then a tubular boiler where the perimeter is in effect greatly extended ought to have but a short length of tube?

A.--The flue of the Nile steamer if reduced to the cylindrical form would be 35-1/2 inches in diameter to have the same area; but it would then require to be made 47-3/4 feet long, to have the same amount of heating surface, excluding the bottom as non-effective. Supposing that with these proportions the heat is sufficiently extracted from the smoke, then every tube of a tubular boiler in which the same draught existed ought to have very nearly the same proportions.

268. Q.--But what are the best proportions of the parts of tubular boilers relatively with one another?

A.--The proper relative proportions of the parts of tubular boilers may easily be ascertained by a reference to the settled proportions of flue boilers; for the same general principles are operative in both cases. In the Nile steamer each boiler of 55 horse power has about 497 square feet of flue surface or 9 square feet per horse power, reckoning the total surface as effective. The area of the flue, which is rectangular is 990 square inches, therefore the area is equal to that of a tube 35-1/2 inches in diameter; and such a tube, to have a heating surface of 497 square feet, must be 53.4 feet or 640.8 inches in length. The length, therefore, of the tube, will be about 18 times its diameter, and with the same velocity of draught these proportions must obtain, whatever the absolute dimensions of the tube may be. With a calorimeter, therefore, of 18 square inches per horse power, the length of a tube 3 inches diameter must not exceed 4 feet 6 inches, since the heat will be sufficiently extracted from the smoke in this length, if the smoke only travels at the velocity due to a calorimeter of 18 square inches per horse power.

269. Q.--Is this, then, the maximum length of flue which can be used in tubular boilers with advantage?

A.--By no means. The tubes of tubular boilers are almost always more than 4 feet 6 inches long, but then the calorimeter is almost always less than 18 square inches per horse power--generally about two thirds of this. Indeed, tubular boilers with a large calorimeter are not found to be so satisfactory as where the calorimeter is small, partly from the propensity of the smoke in such cases to pass through a few of the tubes instead of the whole of them, and partly from the deposit of soot which takes place when the draught is sluggish. It is a very confusing practice, however, to speak of nominal horse power in connection with boilers, since that is a quantity quite indeterminate.

270. Q.--The main thing after all in boilers is their evaporative powers?

A.--The proportions of tubular boilers, as of all boilers, should obviously have reference to the evaporation required, whereas the demand upon the boiler for steam is very often reckoned contingent upon the nominal horse power of the engine; and as the nominal power of an engine is a conventional quantity by no means in uniform proportion to the actual quantity of steam consumed, perplexing complications as to the proper proportions of boilers have in consequence sprung up, to which most of the failures in that department of engineering may be imputed. It is highly expedient, therefore, in planning boilers for any particular engine, to consider exclusively the actual power required to be produced, and to apportion the capabilities of the boiler accordingly.

271. Q.--In other words you would recommend the inquiry to be restricted to the mode of evaporating a given number of cubic feet of water in the hour, instead of embracing the problem how an engine of a given nominal power was to be supplied with steam?

A.--I would first, as I have already stated, consider the actual power required to be produced, and then fix the amount of expansion to be adopted. If the engine had to work up to three times its nominal power, as is now common in marine engines, I should either increase correspondingly the quantity of evaporating surface in the boiler, or adopt such an amount of expansion as would increase threefold the efficacy of the steam, or combine in a modified manner both of these arrangements. Reckoning the evaporation of a cubic foot of water in the hour as equivalent to an actual horse power, and allowing a square yard or 9 square feet as the proper proportion of flue surface to evaporate a cubic foot of water in the hour, it is clear that I must either give 27 square feet of heating surface in the boiler to have a trebled power without expansion, or I must cut off the steam at one seventh of the stroke to obtain a three-fold power without increasing the quantity of heating surface. By cutting off the steam, however, at one third of the stroke, a heating surface of 13-1/2 square feet will give a threefold power, and it will usually be the most judicious course to carry the expansion as far as possible, and then to add the proportion of heating surface necessary to make good the deficiency still found to exist.

272. Q.--But is it certain that a cubic foot of water evaporated in the hour is equivalent to an actual horse power?

A.--An actual horse power as fixed by Watt is 33,000 lbs. raised one foot high in the minute; and in Watt's 40 horse power engine, with a 31-1/2 inch cylinder, 7 feet stroke, and making 17-1/2 strokes a minute, the effective pressure is 6.92 lbs. on the square inch clear of all deductions. Now, as a horse power is 33,000 lbs. raised one foot high, and as there are 6.92 lbs, on the square inch, it is clear that 33,000 divided by 6.92, on 4768 square inches with 6.92 lbs. on each if lifted 1 foot or 12 inches high, will also be equal to a horse power. But 4768 square inches multiplied by 12 inches in height is 57224.4 cubic inches, or 33.1 cubic feet, and this is the quantity of steam which must be expended per minute to produce an actual horse power.

273. Q.--But are 33 cubic feet of steam expended per minute equivalent to a cubic foot of water expended in the hour?

A..--Not precisely, but nearly so. A cubic foot of water produces 1669 cubic feet of steam of the atmospheric density of 15 lbs. per square inch, whereas a consumption of 33 cubic feet of steam in the minute is 1980 cubic feet in the hour. In Watt's engines about one tenth was reckoned as loss in filling the waste spaces at the top and bottom of the cylinder, making 1872 cubic feet as the quantity consumed per hour without this waste; and in modern engines the waste at the ends of the cylinder is inconsiderable.

274. Q.--What power was generated by a cubic foot of water in the case of the Albion Mill engines when working without expansion?

A.--In the Albion Mill engines when working without expansion, it was found that 1 lb. of water in the shape of steam raised 28,489 lbs. 1 foot high. A cubic foot of water, therefore, or 62-1/2 lbs., if consumed in the hour, would raise 1780562.5 lbs. one foot high in the hour, or would raise 29,676 lbs. one foot high in a minute; and if to this we add one tenth for waste at the ends of the cylinder, a waste which hardly exists in modern engines, we have 32,643 lbs. raised one foot high in the minute, or a horse power very nearly. In some cases the approximation appears still nearer. Thus, in a 40 horse engine working without expansion, Watt found that .674 feet of water were evaporated from the boiler per minute, which is just a cubic foot per horse power per hour; but it is not certain in this case that the nominal and actual power were precisely identical. It will be quite safe, however, to reckon an actual horse power as producible by the evaporation of a cubic foot of water in the hour in the case of engines working without expansion; and for boiling off this quantity in flue or wagon boilers, about 8 lbs. of coal will be required and 9 square feet of flue surface.

275. Q.--These proportions appear chiefly to refer to old boilers. I wish you to state what are the proportions of modern flue and tubular marine boilers.

A.--In modern marine boilers the area of fire grate is less than in Mr. Watt's original boilers, where it was one square foot to nine square feet of heating surface. The heat in the furnace is consequently more intense, and a somewhat less amount of surface suffices to evaporate a cubic foot of water. In Boulton and Watt's modern flue boilers they allow for the evaporation of a cubic foot of water 8 square feet of heating surface, 70 square inches of fire grate, 13 square inches sectional area of flues, 6 square inches sectional area of chimney, 14 square inches area over furnace bridges, ratio of area of flue to area of fire grate 1 to 5.4. To evaporate a cubic foot of water per hour in tubular boilers, the proportions are--heating surface 9 square feet, fire grate 70 square inches, sectional area of tubes 10 square inches, sectional area of back uptake 12 square inches, sectional area of front uptake 10 square inches, sectional area of chimney 7 square inches, ratio of diameter of tube to length of tube 1/28th to 1/30th, cubical content of boiler exclusive of steam chest 6.5 cubic feet, cubical content of steam chest 1.5 cubic feet.

276. Q.--These proportions do not apply to locomotive boilers?

A.--Not at all. In locomotive boilers the draught is maintained by the projection of the waste steam which escapes from the cylinders up the chimney, and the draught is much more powerful and the combustion much more rapid than in cases in which the combustion is maintained by the natural draught of a chimney, except indeed the chimney be of very unusual temperature and height. The proportions proper for locomotive boilers will be seen by the dimensions of a few locomotives of approved construction, which have been found to give satisfactory results in practice, and which are recorded in the following Table: