Or otherwise

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:—

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.

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.

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.

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.

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

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

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.

349. To find the traction due to a grade.

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,

or, algebraically,

the letters standing for the same quantities as above.

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

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

The tractive power of an engine is expressed by

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

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

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

(See tables 4 and 5.)

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

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

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

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

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

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.)

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

Also water consumption, or

(See table 9.)

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

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.)

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

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,

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,

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

and the whole area of water room,

the whole section of the barrel,

and the diameter of that area,

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.

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:—

and we shall have,

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

and we have

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).

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.

And the relative length of the several sections will be,

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).

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

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

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:—

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

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.

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:—

The value of r will be here

Whence the equation,

361. On the Baltimore and Ohio Railroad we have,

And as before,

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

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