Chapter XXIII: Part I: Locomotives (2)

The steam produced over water is called saturated, and an application of heat to an isolated volume of this steam, raises both the temperature and pressure, the volume and density remaining the same. The saturation is then no more, and the steam is surcharged. If the heat be withdrawn, pressure and density fall, and a precipitation of water takes place. The priming of steam in a cylinder is an illustration of this. D. K. Clark, in Railway Machinery, urges the necessity of thoroughly drying the steam before applying it to the pistons in this manner, he says, ten per cent. may be gained at low velocities, and in some cases forty per cent. at high speeds.

MOTION OF STEAM IN PIPES.

325. Steam may flow from any vessel into a vacuum, into the open air, or into steam of a less density. The velocity of efflux of steam is the same as that of a stream of water flowing under a pressure equal to that of the steam. Steam flowing into the atmosphere of course has 14.7 lbs. per inch resistance to meet, which is equivalent to a reduction of 14.7 lbs. of its pressure. The following numbers show the velocity of efflux of steam into the open air under different pressures.

Pressure. Velocity, in feet per second.
50 1791
60 1838
70 1877
80 1919
90 1936
100 1957
110 1972
120 1990
130 2004

LOSS OF PRESSURE CAUSED BY THE MOTION OF STEAM.

326. The loss of power suffered by the steam during its motion from the boiler to the cylinder is caused by condensation in passing through cold pipes, and by friction and sharp bends. The total fall that may be caused by a combination of circumstances is from ten to fifteen per cent. at low velocities, and from fifty to sixty per cent. at high speeds. The fall of pressure decreases as the square of the velocity of motion, that is, the fall at a velocity of 1,600 feet per second is four times as great as the fall at a velocity of eight hundred feet. By well protecting the steam pipes and cylinders, and by drying, it may be worked at nearly its initial pressure.

APPLICATION OF STEAM.

327. The steam being generated in the boiler, and conveyed to the cylinders, is admitted alternately to the opposite sides of the piston, by which its reciprocations are produced. The first valve applied to regulating the admission of steam to the cylinder was so arranged that the steam was admitted during the whole stroke; at the end of which, ingress stopped and egress commenced at the first end, and ingress commenced at the second end simultaneously; this caused an unnecessary resistance to the return movement, by preventing the quick escape of the first cylinder-full, which had to be _pushed_ out, instead of _flowing_ out. The continuance of the full pressure upon the piston also, until the end of the stroke, caused a dangerous momentum to be given to the reciprocating machinery.

These evils are obviated by causing the exhaust passage to open, and the entering port to close a little _before_ the end of the stroke. This is effected by moving the valve bodily forward.

Now it is well ascertained, that with very free steam entrances, if we allow the cylinder to be only partially filled, and then cause the steam to expand itself, more work is accomplished with a given bulk than when the cylinder is completely filled. That the steam may have time thus to expand itself, the return of the piston must not take place until after the suppression (the stopping of admission).

328. There are four positions of the valve during each half stroke, and three distinct actions of steam in the same period, which are as follows:—

Position of valve. Action of steam.

Admission (A).
Entrance.
Suppression.
Expansion.
Release.
Compression.
Admission (B).

The longer the time between suppression and release, of course the more complete will be the expansion. The entire force of the steam should not (even if possible) be extracted, as a certain force is necessary to produce a blast.

The time of expansion is regulated by the proportions of the valve cover; which may be so adjusted as to fix suppression or release at any desired part of the stroke.

By the above means any rate of expansion may be established, but when once fixed will remain the same, the valve being invariably connected with the eccentric, and thus partaking of its motion.

329. The great step which has been taken in locomotive construction since 1840 is the invention of the “link motion,” by Williams, which, perfected by Howe, admits of varying the travel of the valve, and thus using the steam under any desired rate of expansion. By this arrangement, the power of regulating the force applied to the piston, according to the work to be done, is placed in the engineer’s hands, to be used at any time under whatever conditions the engine may be working.

By this arrangement, two eccentrics to each cylinder are required, (and in some dispositions of the link, only one). Fig. 150 shows the general plan of varying the expansion. A fixed relation evidently exists between the points A and B, two distinct motions are communicated by the eccentrics C and D through the rods E and F, to the two ends G H, of the curved link L; the eccentrics are so adjusted upon the driving axle as to cause the two ends of the link to move in opposite directions, whence at some point midway there is no motion; the link is movable (vertically) upon the suspended point L, so that by bringing L to one end or the other, the motion given to the rod _m_ partakes of the motion of that eccentric which is nearest to it. Thus the movement of the valve may be checked, or even reversed in a second, while the engine is in motion, and that without sudden shocks.

The link is moved by the levers _n n′ n″_ terminating in the bar O, placed at the foot board of the engine in reach of the engineer. Applied to this is an iron sector _h h′ h″_ made fast to the frame of the engine. Now when the point L is in such a part of the link as to place the valve in a position admitting steam for any fraction of the stroke, let the point at which the bar O stands upon the sector be marked for that admission; and so also for any number of different degrees of expansion. It is plain that the engineer may thus, by fixing the lever O, use any percentage of admission that is required; and may always know just what duty the engine is doing. Five minutes’ examination of the reversing gear upon an engine will render the operation plain.

330. If we cut the steam off at half stroke and then allow it to expand, of course the mean pressure during the whole stroke is less than that at entering. The effective mean pressure obtained by any degree of expansion is shown by the following formula, deduced from a mean of forty-nine experiments with the Great Britain locomotive, (Great Western Railroad, England,) having cylinders 18 × 24.

13.5(√(_a_) – 28) = mean pressure

where _a_ is the percentage of admission.

From this formula, table 11 is made.

331. Mr. Clark deduces as general results, from a very extensive and carefully conducted system of experiments, the following.

That the maximum useful admission is seventy-five per cent.

The minimum useful admission is ten per cent.

The greatest possible gain by working expansively is one hundred per cent., which is effected by an admission of ten per cent.

The best admission for engines having ports 1/14 of the area of the piston, and blast area from 1/13 to 1/16 of piston, at high speeds (from thirty to sixty miles per hour) and with considerable loads, is from sixty to sixty-six per cent. With a wider port and blast area, the best admission is seventy-five per cent.

The resistance due to the back pressure of the blast, varies as the speed squared, and inversely as the square of the area of blast orifice.

332. From the experiments made by Daniel Gooch, with the engine “Great Britain,” the following results appear.

The loss of fuel at seventy-five per cent. admission, the blast orifice being from ⅒ to 1/11 of piston at sixty miles per hour, is from ⅓ to ⅒; at thirty or forty per cent. admission, the loss is from ⅛ to 1/50; and at thirty miles per hour, (seventy-five per cent. admission,) from 1/11 to 1/40.

The resistance from steam compressed in the cylinder, increases with the speed, and also with the degree of expansion; it varies from eight per cent. in full gear, (seventy-five per cent.,) to twenty-eight per cent. at an admission of forty per cent.

At the highest velocities, the whole resistance from back pressure is nearly the same for all expansions; for compression increases as blast pressure decreases.

The above deductions hold good for speeds under forty miles per hour, with steam ports at least 1/14, and blast orifice from 1/12 to 1/15 of the piston area.

OF BOILER PROPORTIONS.

333. The dimensions of American locomotives seem to depend more upon the shop whence they come, than upon any special duty required of them. It is not surprising that the utmost economy is seldom attained when a railroad president orders a lot of locomotives, from the cheapest builder, to suit his own ideas of an engine; or when engines are ordered by a superintendent of machinery who does not know the difference between a sixty foot grade and a level. It is the affair of the company’s agent and not of the machinist to know just what a railroad needs. It is a common, and most absurd practice, for a man who is completely ignorant of machinery to order five or ten engines, without the least regard to the character of the road or of the traffic.

334. The particular characteristics of each class of engines is entirely a matter of figures. There is no reason why a general table should not be formed embracing all divisions, orders, and classes of locomotives, in which the requirements and general dimensions corresponding thereto should be laid down for machine shop reference. Such a table would at once establish a mutual understanding between railroad companies and builders. Such a general classification is shown hereafter. The dimensions of engines are not given, as it was thought best to let each person fill it up according to his own ideas. By so doing some valuable general proportions may be arrived at.

335. Thus far experience has been the only guide to proportion (in America at least). Practice, in many things, is the only correct path to the right results, but locomotives are too expensive for philosophical apparatus; correct experiments upon imperfect machines will lead to the means of avoiding errors. The following is the _modus operandi_ of D. K. Clark in his “Railway Machinery.”

A number of engines of different proportions are chosen, and observations made upon the amounts of fuel and water consumed upon the work done, and under what conditions. These results are so tabulated as to show the effect in difference of construction upon the performance of the engine, whence the proportioning of parts becomes a simple arithmetical operation. The reduction of experiments to tables, and the deduction from tables of formulæ, is a simple operation compared with the skill and care required in observing the operation of a machine, subject to so many disturbances as a locomotive engine in rapid motion. None have had a better opportunity of observing, have conducted experiments with more care, or have obtained results which show fewer discrepancies than the English engineers Clark and Gooch, and the French and German observers Le Chatlier and Nollau.

336. Three essential parts of the locomotive are the _grate area_, _heating surface_, and _cylinders_. No two writers upon this subject arrive at the same dimensions to perform the same work. They not only differ, but differ widely. They cannot all be right; all but one, or all must be wrong. American builders have fixed the dimensions of their engines by observing the performance of constructed machines, not by rules deduced from any systematic experiments, but upon a system of remedying visible errors. If a chimney diameter of ten inches is found too small and twenty too large, fifteen has been assumed as about right.

337. As an example of the difference in the results obtained by different authors, take the following:—

An engine to do the same work must have, according to

Zerah Norris.[7] D. K. D. K.
Colburn.[6] Clark.[8] Clark.[9]
18 × 22 18 × 22 18 × 22 18 × 22 Cylinders.
5 5 5 5 Wheels.
13.00 13.86 14.00 19.60 Grate area.
1114 812 1327 1327 Heating surface.
250 324 134 134 Area of chimney.
4 23 28 28 Area of blast.
59 73 —— —— Steam room.
100 73 —— —— Water room.

Footnote 6:

Colburn on the Locomotive Engine.

Footnote 7:

Norris’s Handbook for Locomotive Engineers and Machinists.

Footnote 8:

D. K. Clark’s Railway Machinery, calculated for coke.

Footnote 9:

D. K. Clark’s Railway Machinery, calculated for wood.

From these figures, the work done being the same, Mr. Clark gives forty per cent, more grate area than either Colburn or Norris, an easier blast, and greater heating surface. Norris makes the steam and water room equal, while Colburn makes the latter almost double the former. It is to be observed that Colburn gives only rules adopted by different builders, not vouching for their correctness, while Norris lays down his rules as fixed and right. The engines used by the English experimenters in their observations, vary in dimension between the following wide limits, whence the universal application of their results.

Grate area 9 to 24 square feet.
Fire surface 50 to 100 square feet.
Tube surface 400 to 1,000 square feet.
Whole surface 450 to 1,100 square feet.
Blast orifice 10 to 20 sq. inches, area.
Speed of engine 12 to 20 miles per hour.

338. The result of some sixty experiments upon forty-five different engines (detailed in Clark’s Railway Machinery, page 156), gives the following formula, expressing the relations which ought to exist between grate area, heating surface, and consumption of water; that evaporation may be carried on in the most economical manner.

_S_ = √(_ac_) × 21.2 = surface.

Where _S_ is the heating surface in square feet.
_a_ is the grate area in square feet.
_c_ is the hourly consumption of water in cubic feet.

From which we deduce the value of _a_ or _c_ thus,

_a_ = ((_S_/21.2)^2)/_c_ = grate area;

and _c_ = ((_S_/21.2)^2)/_a_ = hourly water consumption.

The maximum evaporation which should be carried on per square foot of grate is found, by Mr. Clark, to be sixteen cubic feet per hour. Thus, if we wish to evaporate 160 cubic feet of water per hour, we must have a grate area of at least 160/16 or ten square feet.

339. The above formula for the grate area gives the dimension for a coke-burning furnace. Locomotives burning wood or coal require a modification of the above, as follows:—

To produce a given amount of heat, a certain amount of carbon must be burnt. As wood contains much less carbon than coke, a correspondingly larger bulk must be burnt, and a larger grate is necessary; not, however, larger in proportion to the larger bulk of fuel, as we may have a deeper wood than coke fire. The relative depth of fire being as the stowage bulk, and the actual depth of a coke fire being 1.9 feet, that of a wood fire will be 2.5 feet.

Now let _A_ be the number of lbs. of coke per foot of water evaporated.

_B_ the number of lbs. of coal per foot of water evaporated.

_C_ the number of lbs. of wood per foot of water evaporated.

Call _d_ the depth at which if is the most economical to burn coke; _d′_ the same depth for coal, and the depth for wood _d″_. Then will the area of a coke grate be

_A_/_d_;

Of a coal grate

_B_/_d′_;

And of a wood grate

_C_/_d″_.

To be able to fix the proper grate area for any fuel, we must know its evaporative power, and a depth of a layer in the furnace. Knowing the absolute value for coke, it remains only to obtain the relative value for any other. Thus far we have disregarded the difference in _time_ of burning wood and coke. To produce a given amount of heat, we burn a certain chemical value of fuel; a much larger bulk of wood than of coke is needed. If we burn wood and coke _at the same depth_ and _in the same time_, the grate areas would be proportional to the bulks of fuel to produce the same heat; but, _first_, we burn fuel in a depth proportioned to the economic stowage bulk, or as 2.5 to 1.9, which decreases the wood area; and, _second_, a layer of coke 1.9 feet deep burns in one hour, while a layer of wood 24 feet deep burns in fifteen minutes; whence 60 m. divided by 15 m. = 4 layers of 2½ feet deep each, or in all ten feet, which into the bulk (equal to a mass of coke 1 foot square × 1.9 high) or 1 foot square by 14 high, gives 14 ÷ 10 = 1.4; or, finally, the area of the wood grate should be 1.4 times that of a grate to burn coke.

OF THE SIZE AND USE OF THE SMOKE BOX.

340. The smoke box is the general termination of the flues, and the place where the vacuum is produced, which causes the draft. The size of the boiler being the same, the vacuum varies directly as the blast pressure. The power of the blast is of course affected by the capacity of the smoke box. Mr. Clark fixes the capacity of the exhaust chamber at three cubic feet per square foot of grate. The vacuum in the furnace varies from one to two thirds of that in the smoke box. The less the resistance to the hot gases experienced in the flues, the less may be the vacuum. Upon the vacuum depends the amount of air drawn through the grate; upon the bulk of air drawn through the grate depends the combustion; upon the combustion the evaporation. Whence the evaporation _cet. par._ depends the vacuum in the smoke box.

The velocity of any fluid depends upon the power applied to it, (being as the square root,) the pressure applied to the gases in the furnace of a locomotive is the vacuum in the smoke box; thus the combustion or rate of evaporation is as the square root of this vacuum. To double the evaporation it is necessary to quadruple the vacuum.

BLAST PIPE.

341. The blast pipe conducts the waste steam from the cylinder, which drives the air from the chimney and produces the vacuum in the smoke box; its form should permit the freest escape of the steam from the cylinder. The blast pipe area should nowhere be smaller than the exit port, except at the contraction at the top. “Too much care,” says Mr. Clark, “cannot be taken to adjust the blast pipe concentrically with the chimney; one half inch has been known to spoil the draft of a locomotive.” “The area of orifice is the most critical and most important item in the composition of the locomotive.”

For the form, dimensions, and influence of this important member, the reader is referred to Clark’s Railway Machinery.

As the grate area increases, the blast may decrease. The greater the flue area the easier may be the blast; decrease of smoke box capacity and of chimney diameter, both allow a milder blast.

342. The following proportions are collected from the work of Mr. Clark. The order in which the different parts of the engine stand in importance with relation to the blast, is shown in column 1. The figures show the ratios (the best) which may be had under the most favorable circumstances.

Grate area 1
Ferrule area (area of section of tubes at back flue sheet) ⅕
Tube, sectional area ¼
Capacity of smoke box, cubic feet 3
Chimney, height four diameters, area of section 1/15
Blast orifice 1/75

The vacuum in the smoke box is somewhat regulated by a damper placed in front of the ash pan, by a valve in the chimney, or by a Venetian blind covering the front ends of the tubes.

TUBE SECTION AND LENGTH.

343. The section of the tubes (crosswise) is the space through which the hot gases pass off. By increasing the length or decreasing the diameter, we of course require a stronger blast.

That the steam may escape as soon as generated, there must be a certain clearance between the tubes, which Mr. Clark fixes as follows:—

Divide the number of tubes by thirty and the result is the clearance in eighths of an inch; or algebraically

_C_ = ((_N_/30))/8 = clearance in inches;

Or otherwise

_C_ = _N_/240 = clearance in inches.

PROPORTIONS OF CYLINDERS AND WHEELS.

344. The above proportions depend entirely upon the nature and amount of work to be done, and upon the character of the road. Small wheels and long stroke are to be applied to heavy trains and steep grades. Short stroke and large wheels to fast trains and level roads.

There are some advantages in a long cylinder, even with a constant ratio between the stroke and wheel diameter. The steam has more time to expand; the action of the machinery is slower, and the erratic movements of the engine caused by the movement of the reciprocating machinery are lessened, at the same time the centre of gravity is raised and oscillation increased.

OF THE CARRIAGE.

345. The arrangement of the wheels, axles, springs, and draw-link, and the distribution of the weight of the engine upon its several bearings so as to provide the necessary adhesion, and to run steadily upon the rails, is a matter well worthy of more attention than is commonly given to it.

The frame is the base of the engine, to which every thing should be attached. The cylinders and the wheel both being attached to it, it of course becomes the counterpart to the piston and connecting rod; the former holding the cylinder and wheel together, while the latter pushes them apart. The frame _should_ form a rigid connection between the piston and the wheel; and its strength must be able to resist the whole power of the engine, applied alternately as compression and as extension.

The wheels of a locomotive answer three several purposes, and are classed as follows:—

Leading wheels.
Driving wheels.
Trailing wheels.

The duty of the driving wheels is to transfer the power of the engine to the rails, by which the motion is produced. That of the leading wheels, to guide the engine; and that of the trailing wheels, to support the after end of the engine.

The weight upon the driving wheels must be enough for sufficient adhesion. That upon the leading wheels, sufficient to guide the engine upon curves, (decreasing as their distance from the centre of gravity becomes greater, and increasing with the speed.)

The centre of gravity of an engine is generally at a distance of from one quarter to one sixth of the length of the barrel from the furnace horizontally and forwards, and in the lower part of the barrel, vertically.

The weight upon any one pair of wheels is as their distance from the centre of gravity; by changing their position we change the applied weight.

The flange base[10] must increase as the engine becomes heavier, when applied to fast trains, as more leverage is necessary to keep it on the rails. Heavy freight engines with four or five pairs of wheels, and no truck, wear the rails and strain themselves very much. We should make the wheels of such very small and near together, in order to contract the flange base.

Footnote 10:

_Wheel base_,—Horizontal length between centres of extreme wheels.
_Flange base_,—Horizontal length between centres of extreme fixed
flanged wheels.

DISTRIBUTION OF WEIGHT.

346. Suppose the whole load upon the wheels is 60,000 lbs. If the centre of gravity is half-way between the wheels (there being two pairs), each will support 30,000 lbs. If the centre of gravity is twice as near to one axle as to the other, the furthest one will support 20,000 lbs., and the nearest one 60,000–20,000, or 40,000 lbs.

Suppose the engine has six points of support, or three points in the side elevation, (the ordinary four driving wheels and a truck engine). Let the centre of gravity be one foot behind the middle axle and the distances between the wheel centres eight feet.

The weight upon the middle axle being _H_, that upon the hind axle is _H_/7, because that axle is seven times more distant from the centre of gravity than the middle one, and for the same reason the weight upon the front axle is _H_/9.

Now _H_ + _H_/7 + _H_/9 = 60,000 lbs.

Whence _H_ = 47,976 lbs.

Also, _H_/7 = 6,853 lbs.

And _H_/9 = 5,331 lbs.

And the same laws (see article Lever, in any work on Mechanics) apply to any arrangement of wheels and to any position of centre of gravity.

Springs are employed to absorb the shocks received by the wheels from irregularities in the surface of the rails. They must be equally stiff on both sides of the engine, or lateral rocking will be generated.

When, as is generally the case, the springs are connected by compensating levers, their stiffness being as the load upon them, the arms of the connecting lever must be inversely proportional to the applied weights. The shock received by one wheel is by the lever communicated to the whole four, (or even more when there are such). The truck springs of some builders are also connected by an equalizing lever.

According to Mr. Clark, not more than twelve tons should ever be placed upon one axle; whence engines requiring a tractive power of twelve tons and less may be of the form shown in fig. 151. Between twelve and twenty-four tons, of the form fig. 152; and over the forms figs. 153, 154, and 155.

The weight upon the leading wheels of fast passenger engines should be as much as one fifth of the whole weight. Upon freight engines it need not be more than one sixth.

The line of traction of a locomotive ought to be as near as possible at the same vertical height as the driving wheel centres. If much below this the load will tend to lift the engine off from the leading wheels, upon the drivers as a fulcrum, thus increasing the adhesion and lessening the leading power.

If the traction bar (draw link) is above the wheel centres, it will tend to lift the rear of the engine from the rails.

The general form of engines used in America are shown in figs. 151, 152, 153, 154, and 155.

Fig. 151 is the express passenger locomotive.

Fig. 152 is the ordinary passenger, mail, and mixed engine.

Fig. 153 is the heavy freight engine.

We have, also, engines with three, four, and five pairs of small wheels without a truck, for heavy grades and large amounts of work.

OF ERRATIC MOVEMENTS.

347. The erratic movements of a locomotive in motion are due to three separate causes.

To the motion of the machinery.
To the arrangement of the frame and wheels.
To the state of the surface of the rails.

Those caused by the motion of the machinery are as follows: _Longitudinal fore and aft movement_, generated by the reciprocations of the piston rod, cross head, connecting rod, and crank; and depending in amount upon the weights of the moving parts, steam pressure, and velocity of motion. _Pitching_ of the engine, arising from the oblique action of the cross heads upon the guides, which tends to lift the front end of the engine from the rails; and depends in amount upon the ratio between the stroke and length of connecting rod. _Rocking_ laterally, arising from the difference of time of action of the cross heads; one acting with its greatest vertical power, when the opposite one acts with none. _Vibration in plan_ about the centre of gravity of engine, produced by the pressure between the piston and crank pin, and by the momentum of the reciprocating machinery. This last, combined with lateral rocking, produces _sinuous_ or _spiral_ motion.

The amounts of these several irregularities depend considerably upon the arrangement of carriage; that is, upon the position of wheels; being less as the base included by the bearing points is greater.

The influence of the state of the rails is shown by the vertical and lateral shocks arising from the rail joints and from bad adjustment, both horizontally and vertically.

The amounts of these irregularities increase very rapidly with the speed. Le Chatelier’s experiments make them increase nearly as the square of the velocity.

Longitudinal fore and aft motion is nearly balanced by applying a counterweight to the wheel, opposite the point to which the connecting rod is attached. The remedy for pitching consists in placing the guide bars under the heaviest part of the engine; by which, a great weight is opposed to the vertical action of the cross heads. Crampton’s engine is quite free from this disturbance, as the guide bars are almost directly under the centre of gravity.

The only counteracting effort (remedy it is not) for sinuous motion yet applied, is extension of wheel and flange base, thus giving the guiding wheels more control over the mass of the engine.

The remedy, however, which applies at once to all of the erratic movements, is reduction of speed, as when we divide the velocity by two we decrease the disturbances nearly fourfold.

REVIEW OF THE FORMULÆ AND FORMATION OF THE TABLES.

No. 1.

348. Given the weight and velocity of a train, to find the necessary traction on a level.

_Formula._

_W_ × _R_,

_W_ being the weight of the train in tons, and _R_ the resistance in lbs. per ton; found by the formula

(_V^2_)/171 + 8 = _R_.

By this formula is formed table 1, giving the traction required to move trains of from fifty to one thousand tons weight, at speeds from ten to one hundred miles per hour.

No. 2.

349. To find the traction due to a grade.

_Formula._

_W_ × _R_/_L_,

where _W_ is the weight of the train in tons, _R_ the rise, and _L_ the length of the incline. By this rule is formed table 2, giving the necessary traction to overcome grades from ten to one hundred feet per mile, with loads from one to one thousand tons.

To obtain the whole traction required, add the amounts taken from tables 1 and 2; thus the traction necessary to draw five hundred tons at twenty miles per hour over fifty feet grades is,

By table 1, 5,170 lbs.
By table 2, 10,605 lbs.
——————
In all, 15,775 lbs.

or, algebraically,

(_W_ × _R_) + (_WR_/_L_) = _T_,

the letters standing for the same quantities as above.

No. 3.

350. To find the weight to place on the driving wheels.

_Formula._

6_T_,

where _T_ is the whole tractive power. (Table 3.)

Nos. 4 and 5.

The tractive power of an engine is expressed by

_T_ = ((2_A_)_P_ × 2_S_)/_C_,

Where _T_ is the tractive power.
_P_, steam pressure in lbs. per square inch.
_S_, stroke in inches.
_C_, circumference of wheel in inches.
_A_, area of one piston in inches.

From this formula we get the values of the several factors as follows:—

The steam pressure, or _P_ = (_TC_)/((2_A_)2_S_). (A.)

The stroke, or _S_ = (_CT_)/((2_A_)(2_P_)). (B.)

The piston area, or _A_ = (_TC_)/(4_SP_). (C.)

The wheel circumference, or _C_ = (2_A_ × _P_ × 2_S_)/_T_. (D.)

And from (C) we get the diameter of piston by the following:—

_d_ = √(area/.7854).

And in like manner from (D) the diameter of wheel by

_d_ = _c_/3.1416.

(See tables 4 and 5.)

No. 7.

351. To find the capacity of cylinders of any dimension.

_Formula._

(_D^2_ × .7854 × Stroke)/1728.

This gives the capacity in cubic feet. The dimensions above (see D and S) being in inches. (Table 7.)

No. 6.

352. To find the hourly steam consumption in terms of the capacity of one cylinder, (that is, the number of cylinderfuls per hour).

_Formula._

_N_(5280/_c_) × 4,

where _N_ is the number of miles per hour, _c_ the wheel circumference. (Table 6.)

No. 8.

353. Knowing the hourly consumption of steam, to reduce it to water.

_Formula._

_B_/_N_,

_B_ being the bulk of steam in cubic feet, and _N_ the relative volume of steam and water. (The values of _N_ are given in table 8.)

No. 9.

354. Knowing the hourly water consumption, to find the grate area and heating surface.

First, (Cubic feet of water per hour)/16 = grate area in square ft.

Second, _S_ = √(_ac_) × 21.2 = heating surface,

where _a_ is the grate area, and _c_ the hourly consumption of water in cubic feet.

From the same formula,

Grate area, or

_a_ = ((_S_/21.2)^2)/_c_

Also water consumption, or

_c_ = ((_S_/21.2)^2)/_a_

(See table 9.)

No. 10.

355. To find the necessary number of tubes to give any amount of heating surface.

_Formula._

_N_ = _S_/(_Ld_π),

when _N_ is the number, _S_ the required surface, _L_ the length, _d_ the diameter, both in feet, and π = 3.1416. (See Table 10.)

No. 11.

356. To find the mean cylinder pressure for any percentage of admission.

_Formula._

13.5√(_a_) – 28,

where _a_ is the percentage of admission. (See Table 11.)

As to the internal arrangement of the barrel of the boiler, we must of course have the length of tubes the same as that of the barrel, (that is, in the general plan of boiler, some makers have moved the back flue plate ahead). The length of tubes will of course be the same as the distance between the tube sheets. The number is governed by their diameter and by the proper clearance, which is found by the formula,

(_N_/|30|)/8 in eighths of inches, or _N_/240 inches.

The upper fifteen to eighteen inches of the barrel must be left for steam room.

OF THE DIAMETER OF BARREL.

357. To find the diameter of a barrel to contain a given number of tubes,

Represent the inside diameter of boiler by _D_,
Diameter of one tube _d_,
Clearance between tubes _c_,
Number of tubes _n_,
Sectional area of boiler, in inches _A_,
Water section, in inches _B_,

we shall have as the area of water room per tube,

(_d_ + _c_)^2,

and the whole area of water room,

(_d_ + _c_)^2 × _n_,

the whole section of the barrel,

_A_/_B_[(_d_ + _c_)^2_n_],

and the diameter of that area,

_D_ = √(([(_d_ + _c_)^2_n_]_A_/_B_)/.7854)

which is the boiler diameter in inches, to which add _D_/16 on each side, or in all _D_/8 as the room to be left between the sides of the boiler and first tube.

The _diameter_ finds its maximum limit in the gauge less the two half breadths of tire, and two or three inches allowance for attachment to the frame and other mechanical incidentals. The _length_ must be enough to carry the leading wheels a sufficient distance from the centre of gravity of the engine.

ADAPTATION OF THE LOCOMOTIVE ENGINE TO THE MOVEMENT OF RAILWAY TRAINS.

358. First, as regards the nature of the traffic.

There are certain necessary causes of a bad application of power upon railroads; for example, when the trains are very much heavier in one direction than in the other, as we are obliged to use the same engine both ways, because when it arrives at one end of the road it must go back to start again. Where the traffic requires to be worked chiefly up hill, we use an engine much heavier to _ascend with the load_ than is necessary to _descend without a load_. Different objects of transport require different speeds. Perishable freight, such as ice, beef, pork, cattle, &c., requires to be moved in much less time than grain, lumber, flour, coal, and manufactured articles. As a general thing, the difference between the characters of freight engines, as regards the nature of the traffic, can be adapted only with a view to amount, disregarding the nature.

With passenger traffic, however, there is a great variety of speeds made use of, and consequently may be a greater difference in the proportions of engines depending entirely upon the nature of the traffic.

ADAPTATION AS REGARDS THE PHYSICAL CHARACTER OF THE ROAD.

The best adaptation of locomotive power to any system of grades, would be that which should render the mileage a minimum; and this will be done, as nearly as possible, by applying engines, the strength of which shall be proportional to the resistance to be overcome. The best mode of comparing different adaptations of power is by reducing the grades to a level; or by equating for grades by means of the capacity of motive power.

This is done as follows:—

The length of an incline being _L_, The resistance on a level being _R_, The ratio of the resistance due to the grade to the resistance on a level by _r_, The equivalent horizontal length by _L′_,

and we shall have,

(_R_ + _r_)_L_ = _L′_.

_Example._—Let the length of a grade be seventy-five miles; the value of

_r_ = _R_/3;

and we have

(3/3_R_+_R_/3)_L_ = ((4_R_)/3)75 = 100 miles.

Let us now compare the mileage of some of the large roads of America, as given by a good, and also by a bad adaptation of power.

The Massachusetts Western Railroad may be divided into the four sections below (including the Boston and Worcester road).

Length miles. Maximum grade.
Boston to Worcester, 44 30
Worcester to Springfield, 54½ 50
Springfield to Pittsfield, 52 83
Pittsfield to Albany, 49½ 45

Assume the speed of freight trains as fifteen miles per hour, the resistance on a level will be 9.3 lbs., or for simplicity call it ten pounds per ton.

The resistance due to a 30 feet grade is 13 lbs. per ton.
The resistance due to a 50 feet grade is 21 lbs. per ton.
The resistance due to a 83 feet grade is 35 lbs. per ton.
The resistance due to a 45 feet grade is 19 lbs. per ton.
And the value of _r_ for a 30 feet grade is 13/10 lbs. per ton.
And the value of _r_ for a 50 feet grade is 21/10 lbs. per ton.
And the value of _r_ for a 83 feet grade is 35/10 lbs. per ton.
And the value of _r_ for a 45 feet grade is 19/10 lbs. per ton.

And the relative length of the several sections will be,

Boston to Worcester, 10/10 + 13/10 = 23/10 of 44 = 101
Worcester to Springfield, 31/10 of 54½ = 169
Springfield to Pittsfield, 45/10 of 52 = 234
Pittsfield to Albany, 29/10 of 49½ = 144
——— ———
And the sums, 200 648

the equated distance being 3¼ times the actual length. This length assumes the resistance of the several sections to be for their whole length that given by their maximum grade. This might seem erroneous; but its correctness will be seen when it is remembered that the greatest load that can be taken over any section is limited by its maximum grade.

Now suppose that the engine employed is of the following dimensions (as it is very nearly).

Cylinders 16 × 20 inches,
Wheels 54 inches.

Assume the cylinder pressure 110 lbs., and the tractive power of the engine is 5,287 lbs.

A load of 500 tons, upon a 30 feet grade, requires a 11,500 lbs.
traction of

Upon a 50 feet grade, 15,500 lbs.

Upon an 83 feet grade, 22,500 lbs.

Upon a 45 feet grade, 14,500 lbs.

To move the above load from Boston to Worcester we should 2 engines,
require

From Worcester to Springfield, 3 engines,

From Springfield to Pittsfield, 5 engines,

From Pittsfield to Albany, 3 engines,

And the products of the number of engines by the lengths of the corresponding divisions, are

Boston to Worcester, 44 × 2 = 88
Worcester to Springfield, 54½ × 3 = 163½
Springfield to Pittsfield, 52 × 5 = 260
Pittsfield to Albany, 49½ × 3 = 148½
————
660

Suppose that by making the engines on the several sections strong in proportion to the resistance of those sections, one engine is capable of taking the whole load over all of the grades. The mileage becomes as follows:—

Boston to Worcester, 44 × 1 = 44
Worcester to Springfield, 54½ × 1 = 54½
Springfield to Pittsfield, 52 × 1 = 52
Pittsfield to Albany, 49½ × 1 = 49½
———
200 miles.

The mileage before was 660 miles,
And the saving therefore 400 miles.

or about 70 per cent. of the first mileage.

359. From a recent report of the New York and Erie Railroad it appears that the same power will draw

28 tons on the Western division,
80 tons on the Susquehanna division,
85 tons on the Delaware division,
and 20 tons on the Eastern division,

neglecting the assistance required from Susquehanna to Deposite. In the following table are given the actual lengths of the several divisions, and the sum of the products of three lengths both by the relative and a uniform resistance on each.

Miles run Miles run by
Division. Length. by an an engine Difference.
engine not adapted.
adapted.
Western, 128 128 × 3.04 128 × 1.0 261.12
Susquehanna, 139 139 × 1.06 139 × 1.0 8.35
Delaware, 104 104 × 1.00 104 × 1.0 0.00
Eastern, 88 88 × 4.25 88 × 1.0 286.00
——————
Sum of differences, 555.47 miles,

that is, the miles run by engines adapted to the work on the several divisions will be 555.47 less than the miles run by engines not adapted. (See Appendix F.)

PENNSYLVANIA CENTRAL RAILROAD.

360. The physical character of this road is as follows:—

Length. Max. grades.
Philadelphia to Harrisburg, 106 45
Harrisburg to Altoona, 131 21
Altoona to Johnstown, 48½ 92
Johnstown to Pittsburgh, 78½ 53

The value of _r_ will be here

45 feet grades, 19/10
21 feet grades, 9/10
92 feet grades, 39/10
53 feet grades, 25/10

Whence the equation,

106 × (10/10 + 19/10) = 307
131 × (10/10 + 9/10) = 249
42½ × (10/10 + 39/10) = 208
78½ × (10/10 + 25/10) = 275
——— ———
Sum, 358 Sum, 1039
and 1039 – 358 = 681.

361. On the Baltimore and Ohio Railroad we have,

Miles. Max. grade.
Baltimore to Harper’s Ferry, 80 82
Harper’s Ferry to Cumberland, 98 40
Cumberland to Raccoon, 88.2 116
Raccoon to 148⅔ miles, 60.5 40
148⅔ miles to Wheeling, 51.3 80

And as before,

80 × (10/10 + 35/10) = 360
98 × (10/10 + 17/10) = 265
88.2 × (10/10 + 49/10) = 520
60.5 × (10/10 + 17/10) = 163
51.3 × (10/10 + 35/10) = 231
Sum of Col. 1 = 378, Sum of Col. 3 = 1539; difference 1161.

Thus by the most correct adaptation of power, upon the above-named railroads, the following percentages of mileage may be saved.

Massachusetts Western, 70
New York and Erie, 55½
Pennsylvania Central, 68
Baltimore and Ohio, 75

Of these roads the Baltimore and Ohio is that which has actually the best adaptation; and the Western road of Massachusetts that which has the worst.

362. To determine the actual dimensions of the engines which should be used upon any road, from the tables, proceed as follows:—Let the load be one hundred tons, the maximum grade thirty feet per mile, and speed twenty-five miles per hour.

Referring to the tables in succession we have,

By table 1, Traction for 100 tons, on a level, at 25 miles 1,550 lbs.
per hour,

By table 2, Traction for 100 tons, on a 30 feet grade, 1,273 lbs.

—————

Whole traction required, 2,823 lbs.

By the formula, table 3, the weight upon the drivers must be

2823 × 6 = 16938 lbs., or 8 tons.

By table 4, with a wheel five feet in diameter, and a stroke of twenty inches, we have the decimal .2122.

By table 5, the mean cylinder pressure being sixty pounds per inch, and piston twelve inches in diameter, we have as the total pressure

On both pistons, 13,572 lbs.
And finally, 13572 × .2122 = 2,880 lbs.
The requirement being 2,823 lbs.

By table 6, we see that five feet wheels at twenty-five miles per hour, use 33,600 cylinders of steam per hour.

By table 7, the capacity of a cylinder 12 × 20 is 1.31 cubic feet; also 33600 × 1.31 = 44016 cubic feet of steam per hour.

Assuming the mean cylinder pressure at sixty pounds, and the entering pressure at eighty pounds, also the loss in passing from the boiler at twenty pounds, we must generate the steam at one hundred pounds per square inch.

By table 8, we see that when steam is produced under one hundred pounds pressure per inch, each cubic foot of water makes 293 cubic feet of steam; whence

44016/293 = 150,

is the number of cubic feet of water to be evaporated per hour. At sixteen cubic feet of water per hour per square foot of grate, we thus require

15.0/16 or 9.4 feet, nearly;

and by table 9, we find the heating surface necessary to evaporate 150 cubic feet of water per hour, with nine square feet of grate surface, to be 779 square feet; and by the formula, with 9.4 square feet, we have,

_S_ = √(9.4 × 150) × 21.2 = 797 square feet,

the fuel being coke; for wood, multiply the grate area (as mentioned before) by 1.4 and the grate area will be 1.4 × 9.4 = 13.16. The tube surface of course remains the same, as, when the necessary amount of heat is developed, the same surface only is enough to apply it to the water.

To obtain 779 square feet of heating surface, we see, by table 10, that it is given by

100 tubes 17 feet long and 1¾ inch diameter,
or 100 tubes 16 feet long and 1⅞ inch diameter,
or 100 tubes 15 feet long and 2 inch diameter,
or 100 tubes 14 feet long and 2⅛ inch diameter,
or 100 tubes 12½ feet long and 2⅜ inch diameter,
or 100 tubes 12 feet long and 2½ inch diameter,

or by consulting the table, and having given the number and length, the number and diameter, or the length and diameter, we may easily find the third factor of the surface. Thus the length being eleven feet, and diameter two inches, 779 feet is obtained by

779/(11 × 3.1416 × 167) = 135 tubes.

To obtain the diameter of barrel to contain 135 two inch tubes, we use the formula

D = √((_A_/_B_[_n_(_d_+_c_)^2])/(.7854)).

We have already found _d_ = 2 inches, _n_ = 135, whence _c_ will be by formula,

_c_ = _N_/240 = 0.54,

and

_d_ + _c_ = 2.54,

also,

(_d_ + _c_)^2 = 6.45,

and

135 × 6.45 = 871+;

and allowing three fourths of the boiler cross section to be filled with tubes, we have,

4/3 of 871 = 1161;

also,

1161/.7854 = 1478,

the square root of which is 38.5 nearly, to which add 38.5/8 or 4.8 inches, (see page 359), and we have

38.5 + 4.8 = 43.3 inches,

as the inside diameter of boiler, whence the following locomotive to meet the requirement as stated.

Weight upon driving wheels, 16,938 lbs.,
Cylinders, 12 × 12 inches,
Wheels, 5 feet,
Tubes, 135—11 feet × 2 inches,
Grate, 13.16 square feet,
Barrel, (inside diameter,) 43.3 inches,

and under the most favorable circumstances, the chimney may be 40 inches high, 12.7 inches in diameter; the blast orifice 5.8 inches in diameter; and the capacity of smoke box 39½ cubic feet.

363. We may vary the tractive power of an engine by using the steam at a greater or less degree of expansion, but the adhesion remains the same. If an engine was built able to work a road partly level, and partly on steep grades, varying the power simply by varying the expansion, it would be unnecessarily heavy for the easy parts of the road. The expansive principle may be advantageously employed in adjusting the power to the difference of resistance on any one division of a road, and also to the varying load which each day’s traffic will present.

Suppose we would move a load of two hundred tons over the road below; and suppose, also, that we require the cylinder pressures set opposite the several divisions.

10 miles, level, 60 lbs.,
10 miles, 10 feet per mile, 80 lbs.,
10 miles, 20 feet per mile, 100 lbs.,
10 miles, 30 feet per mile, 120 lbs.

The boiler pressure being 150 lbs., and the pressure at entering the cylinder 145 lbs.,

An admission of 71 per cent. gives a mean pressure of 120 lbs.,
An admission of 55 per cent. gives a mean pressure of 100 lbs.,
An admission of 40 per cent. gives a mean pressure of 80 lbs.,
An admission of 28 per cent. gives a mean pressure of 60 lbs.,

And if the 1st notch of the sector admits, 75 per cent,
And if the 2d notch of the sector admits, 70 per cent,
And if the 3d notch of the sector admits, 65 per cent,
And if the 4th notch of the sector admits, 60 per cent,
And if the 5th notch of the sector admits, 55 per cent,
And if the 6th notch of the sector admits, 50 per cent,
And if the 7th notch of the sector admits, 45 per cent,
And if the 8th notch of the sector admits, 40 per cent,
And if the 9th notch of the sector admits, 35 per cent,
And if the 10th notch of the sector admits, 30 per cent.

We should work the engine as follows:—

From 0 to 10 miles, use the 10th notch,
From 10 to 20 miles, use the 8th notch,
From 20 to 30 miles, use the 5th notch,
From 30 to 40 miles, use the 2d notch,

APPLICATION OF LOCOMOTIVE ENGINES TO RAILROADS.

364. _Department 1. Freight._

GENERAL CLASSIFICATION.

┌─────────┬─────────┬───────────┬─────┬─────┬─────┬─────┬─────┬─────┐ │ │ │ │Order│Order│Order│Order│Order│Order│ │Number of│ Maximum │Designation│ 1 │ 2 │ 3 │ 4 │ 5 │ 6 │ │division.│ grades. │ of parts. │ 50 │ 100 │ 250 │ 500 │ 750 │1,000│ │ │ │ │tons.│tons.│tons.│tons.│tons.│tons.│ ├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤ │ │ │Grate area.│ │ │ │ │ │ │ │ │ │ Tube │ │ │ │ │ │ │ │ 1 │ Level. │ surface. │ │ │ │ │ │ │ │ │ │Cylinders. │ │ │ │ │ │ │ │ │ │ Wheels. │ │ │ │ │ │ │ │ │ │ Weight. │ │ │ │ │ │ │ ├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤ │ 2 │ 10 feet │ │ │ │ │ │ │ │ │ │per mile.│ │ │ │ │ │ │ │ ├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤ │ 3 │ 20 feet │ │ │ │ │ │ │ │ │ │per mile.│ │ │ │ │ │ │ │ ├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤ │ 4 │ 40 feet │ │ │ │ │ │ │ │ │ │per mile.│ │ │ │ │ │ │ │ ├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤ │ 5 │ 60 feet │ │ │ │ │ │ │ │ │ │per mile.│ │ │ │ │ │ │ │ ├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤ │ 6 │ 80 feet │ │ │ │ │ │ │ │ │ │per mile.│ │ │ │ │ │ │ │ ├─────────┼─────────┼───────────┼─────┼─────┼─────┼─────┼─────┼─────┤ │ 7 │100 feet │ │ │ │ │ │ │ │ │ │per mile.│ │ │ │ │ │ │ │ └─────────┴─────────┴───────────┴─────┴─────┴─────┴─────┴─────┴─────┘

The speed is assumed from twelve to fifteen miles per hour. The mean cylinder pressure is assumed at sixty lbs. per square inch; the initial pressure at ninety pounds, and the boiler pressure at 120 lbs. per square inch. The grate areas are designed for coke; for wood multiply the same by 1.4.

365. _Department 2. Passenger._