ELEVATION OF THE EXTERIOR RAIL.
293. The motion of a train of cars around a curve is accompanied by a tangential force, depending in amount upon the velocity of the train and the radius of curvature. This force tends to throw the cars from the track; and is counteracted by elevating the exterior rail.
The centrifugal force of any body in motion in a curved line is shown by the formula
WV2
32R.
Where W is the weight in lbs.
V the velocity in feet per second.
R the radius of curvature,
and 32 the accelerating force of gravity.
The force tending to throw the car from the rail is not centrifugal but tangential, but it matters not whether the body is kept in position by tension upon the inside or by compression on the outside; the amount of the force is the same.
Fig. 148.
The horizontal projection of the centre of gravity of the car, when at rest, is at c, fig. 148, and when in motion the direction of the weight should be a b; and the inclination, c′ a′ b′, must be such that a b will be perpendicular to c′ a′; to effect which, c′ b′ should be to a′ b′ as the weight to the tangential force; or E being the elevation of the rail, g the gauge, W the weight, and c the tangential force; we have
E : g :: c : W,
or E = cg
W, and c being = WV2
32R;
finally E = (WV2
32R)g/W or V2g
32R = E.
Where W = weight of a car.
V = speed of train in feet per second.
g = gauge of road.
R = radius of curve.
E = elevation of outer rail in feet and decimals.
g and R are the only fixed quantities in the formula; and the average weight and speed of a car must be assumed.
Examination of the formula shows how important it is that all trains should run at such a velocity as to demand the same elevation of rail. The absolute elevation must be arranged to meet the requirement of the fastest trains; and other trains must conform, even at a disadvantage.
Note.—The subject of the mechanics of traversing railroad curves, is yet quite in the dark. The action of the train, as caused by its own momentum, is tangential; while the action of the engine tends to pull the cars against the inner rail, being opposed to the first motion. This might require a reduction of the elevation given by the formula when the engine is exerting a strong tractive power, but when running without steam the full elevation is needed, (see chapter III.)
Fig. 149.
In laying and maintaining the rails to the proper elevation, a clinometer attached to a rail gauge, as in fig. 149, answers a good end: the small arc being graduated according to the different elevations required by curves of different radii. Thus the index of the level being placed at 2°, when the rails are fitted to A and B, the elevation is correct for a 2° curve; or for a curve of 2,865 feet radius.
The difference in gauge of one foot makes a difference in the elevation of but 0.009 feet, or about ⅒ of an inch.
The following table is calculated for the average of the different gauges in use, thus,—
| 4.7 | ||
| 5.0 | ||
| 5.5 | ||
| 6.0 | ||
| 4)21.2 | ||
| Average gauge, | 5.3 | feet. |
| TABLE OF ELEVATION OF OUTER RAIL. | ||||||
| Radius of curve in feet, being | ELEVATION OF OUTER RAIL IN FEET AND DECIMALS, THE VELOCITY IN MILES PER HOUR BEING | |||||
|---|---|---|---|---|---|---|
| 10. | 15. | 20. | 25. | 30. | 40. | |
| 250 | .130 | |||||
| 500 | .070 | |||||
| 1,000 | .037 | .079 | ||||
| 2,000 | .018 | .040 | .074 | .111 | ||
| 3,000 | .013 | .026 | .048 | .074 | .106 | |
| 4,000 | .009 | .020 | .037 | .058 | .079 | .154 |
| 5,000 | .007 | .016 | .031 | .045 | .065 | .119 |
| 6,000 | .006 | .013 | .024 | .037 | .053 | .095 |
| 7,000 | .005 | .011 | .021 | .033 | .046 | .086 |
| 8,000 | .004 | .010 | .018 | .029 | .039 | .077 |
| 10,000 | .003 | .008 | .010 | .022 | .032 | .059 |
CHAPTER XIV.
EQUIPMENT.
PART I.
LOCOMOTIVES.
As the locomotive engine is the power by which railroads are worked, and as its proportions and dimensions are so intimately connected with the physical character of the road, it is thought proper to take space enough at this point to examine the general principles of its construction, and of its adaptation to the work required of it upon railroads.
Under the general principles, we recognize the production and consumption of steam, the disposition of weight upon the several pairs of wheels which shall secure the necessary adhesion, the application of the power generated in the boiler to the moving of the wheels, and that general arrangement of parts which shall render the use of power economical.
BIRTH AND GROWTH OF THE LOCOMOTIVE.
294. The first idea of the application of steam to locomotion, is due to the unfortunate Solomon de Caus, of Normandy (France), who was confined in a madhouse for insisting that steam could be made to move wheeled carriages.
295. In the year 1784, William Murdoch, the friend and assistant of James Watt, built a non-condensing steam locomotive engine, on a scale of about one inch per foot, having
| Cylinders, | ¾ × 2 inches, | |
| Wheels, | 9½ inches, | |
| and | Weight, | 10 lbs. |
This little engine, however, accomplished the speed of ten miles per hour.
296. In 1802, Richard Trevethick patented the application of the non-condensing steam-engine to the propelling of carriages on railroads; his engine was fitted with one horizontal cylinder, which applied its power to the wheels by means of spur gear.
297. In 1825, the truck was first applied, to relieve the driving wheels of a part of the weight, and to enable the engine to pass freely around curves.
298. In 1827, Timothy Hackworth applied the blast pipe, for the purpose of draft. He applied, also, spring balances to the safety-valves, and used the waste steam to heat the feed water. This engine drew one hundred tons, at five miles per hour, and forty-five tons on a fifty feet grade.
299. In 1828, M. Seguin (France) introduced the multitubular boiler.
300. In 1829, the directors of the Liverpool and Manchester Railroad offered a premium for the best locomotive, which should draw three times its own weight, at ten miles miles per hour. The “Rocket,” by Robert Stephenson, of Newcastle on Tyne, was the successful competitor, and drew the load required, seventy miles, at an average speed of 13.8 miles per hour; its maximum velocity was twenty-nine miles per hour; it evaporated 5.4 lbs. of water per pound of coke, and 18.24 cubic feet per hour of water.
301. From 1830 to 1840, the changes that were made were rather those of dimension, proportion, and arrangement, than of essential elements of steam producing.
302. In 1840, several truck frame engines were sent to England from the Norris Works of Philadelphia. These locomotives would draw a load of one hundred and twenty tons over a sixteen feet grade, at the rate of twenty miles per hour.
303. In 1845, the Great Western Railroad, of England, was supplied with an engine of twenty-two tons weight, having cylinders 15¾ × 18, wheels 7 feet, heating surface 829 square feet. This locomotive carried seventy-six and one half tons at a velocity of fifty-nine miles per hour. The consumption of coke was 35.3 lbs. per mile, and of water, 201.5 cubic feet per hour.
THE ENGLISH LOCOMOTIVE OF 1850.
304. The “ne plus ultra” for the seven feet gauge (Great Western Railway) by Gooch, has inside cylinders 18 × 24 inches, one pair of eight feet driving wheels, grate area twenty-one square feet. Fire-box surface, one hundred and fifty-three feet. Three hundred and five two inch tubes, giving 1,799 feet of surface. Total heating surface, 1,952 square feet. Weight of engine, empty, thirty-one tons; of tender, eight and one half tons; whole weight with wood and water, fifty tons. Evaporating power, three hundred cubic feet of water per hour. This engine can draw two hundred and thirty-six tons, at forty miles per hour.
The maximum for the London and North-western Railroad, four feet, eight and one half inches gauge (Crampton’s patent), has cylinders 18 × 24 inches; wheels, eight feet; two hundred two and three sixteenths inch (outside diameter) tubes; grate, twenty-one and one half square feet; fire surface, one hundred and fifty-four feet; tube surface, 2,136 feet; whole heating surface, 2,290 square feet; weight, loaded, thirty-five tons; twelve tons upon driving wheels; tender, twenty-one tons, loaded; whole weight, fifty-six tons.
THE AMERICAN LOCOMOTIVE OF 1855.
305. The engine “Charles Ellet, Jr.,” drew on the 9th of August, 1854, forty tons, over a grade of two hundred and seventy-five feet per mile, and over grades of two hundred and thirty-eight feet, upon curves of three hundred feet radius. This engine has wheels four and one half feet in diameter coupled seven feet apart; cylinders 14 × 26 inches; and weighs, including wood and water, 53,058 lbs. This is a tank locomotive, the tender is dispensed with, and in its room a tank containing one hundred cubic feet of water, and one cord of wood is used. This engine was built by Richard Norris and Son.
An engine built by the Cuyahoga Steam Furnace Co. of Cleveland, Ohio, performed the following feat.
An ordinary passenger train was carried one hundred and one miles, over a total ascent of 1,255 feet of grades, making twenty stops, at an average speed of twenty-five miles per hour, with a consumption of only ninety cubic feet of wood.
The same engine drew an average load of three and one third cars four hundred and thirty miles, making seventy-five stops, surmounting a total ascent of 5,439 feet, averaging twenty-five miles per hour, with one tender full of wood only.
In the months of July and August, 1856, two engines upon the Pacific Railroad (Missouri), one by R. K. and G., and one by Palm & Robertson, ran each one hundred and twenty-five miles, with three passenger and one baggage cars, using only one cord of wood.
Note.—For an interesting example of what can be done by the American locomotive, and an illustration of engineering peculiarly American, the reader is referred to a description of the “Mountain top track” at the Rock-fish Gap crossing of the Blue Ridge (Va.), by the Virginia Central Railroad, given by the engineer under whose direction the work was proposed and executed (Charles Ellet, Esq.), from which is extracted the following:—
“The eastern slope is 12,500 feet long, and rises 610 feet; the average grade being 2574
10 feet, and the maximum 29568
100 feet per mile. The least radius of curvature 234 feet; upon which curve the grade is 2376
10 feet per mile. The western slope is 10,650 feet long, and falls 450 feet; the average grade being 223⅒, and the range 27984
100 feet per mile.
“The engines, which have taken loads ranging from twenty-five to fifty tons up one slope at seven and one half miles per hour, and down the opposite one at six miles per hour, making four trips of eight miles per day for three years, were designed and built by M. W. Baldwin & Co., Philadelphia, and have three pair of forty-two inch wheels all coupled, the flange base being 9′ 4″, cylinders 16½ × 20 inches, weigh, with wood and water, 55,000 lbs., or twenty-seven and one half tons. They run without a tender, the engine carrying its own feed; thus gaining the double advantage of increasing the adhesion of the engine, and avoiding the resistance of a tender.”
GENERAL DESCRIPTION.
306. The locomotive is a non-condensing, high pressure engine, working at a greater or less degree of expansion, according to the labor to be performed, and placed upon wheels which are so connected with the piston, that any motion of the latter is communicated to the former, by which the whole is moved.
The power exerted in the cylinder and referred to the circumference of the driving wheel, is called traction; its amount depends upon the cylinder diameter and steam pressure, upon the diameter of wheel and stroke, this latter being the distance between the wheel centre and point of application of power.
The means by which the “traction” is rendered available for moving the engine and its load, is the resistance which the wheel offers to slipping on the rail, or its bite, and is called adhesion; it is directly as the weight applied to the wheels, but depends also upon the state of the rails. It varies from nothing, when there is ice on the rail, to one fifth of the weight upon the driving wheels when the rail is clean and dry, and in some cases has reached as high as nearly one third. It should be enough to resist the maximum force of traction, that is, the wheel should not slip when the engine is doing its greatest work.
Steam producing, Traction, and Adhesion, are the three elements which determine the ability of an engine to perform work. The proportions and dimensions of the machine depend upon the duty required of it; sufficient adhesion for a required effect should be obtained rather by a proper distribution, than by increase of weight.
Fig. 150 shows the relative position of parts in the locomotive engine as at present constructed in America.
| 1 2, | Grate upon which the fuel is placed. |
| 1 2 3 4, | Interior fire-box. |
| 5 6, | Exterior fire-box. |
| 7 7 8 8, | Shell of the boiler. |
| 9 9, | Boiler flues. |
| 10 11 12 13, | Exhaust chamber, or smoke box. |
| 14, | Steam dome, entrance to steam pipe. |
| 15, | Steam pipe. |
| 16, | Piston. |
| 18, | Piston rod. |
| 19, | Connecting rod. |
| 20, | Crank. |
| 21, | Driving wheel. |
| 22, | Blast pipe. |
| 23, | Chimney. |
| 27 28, | Leading wheels, supporting the front end of the engine, turning on a swivel, 29. |
| 30, | “Blow off” safety-valve. |
Fig. 150.
307. The operation of generating and applying steam for the production of motion is as follows:—
The boiler and the space between the two fire-boxes being filled with water, (high enough at least to cover the flues and the top of the inner box,) fire is applied to the fuel placed upon the grate; the heat which fills the fire-box and tubes, is communicated to the water and converts the same to steam; which entering the mouth of the pipe, 15, flows to the cylinder, where it forces the piston to the end of the stroke. This motion is transferred through the connecting rods and cranks to the wheels, which revolving, move the engine upon the rails. At the same time the eccentrics, placed upon the driving axle, give a motion to the valve gear, and thence to the valves, by which the admission of steam is stopped at the first end of the cylinder, and commenced at the other. The volume of steam which entered during the first half stroke is forced out of the cylinder by the returning piston, up the blast pipe, and out at the chimney, where a vacuum is produced, which can be supplied with air only from the chamber 10 11 12 13; after a few strokes the air is exhausted from the chamber, which can be refilled only by the external air drawn through the fuel, furnace, and tubes. The more complete this vacuum, the stronger the current of air drawn through the fire, which (current) is the draft. The admission of fresh air is regulated by a damper placed at 2. The fuel is placed upon the grate by means of a door in the rear of the fire-box. The necessary height of water is maintained in the boiler by pumps worked by the engine, in such a manner as to secure at all times the proper supply. The proportions and dimensions of the boiler, the engine, and the carriage, with the rules for obtaining the same will be considered shortly.
DUTIES EXPECTED OF LOCOMOTIVE ENGINES.
308. The work required of any engine depends upon the nature and amount of traffic, and upon the physical character of the road.
The nature of the traffic, whether bulky or compact, and whether requiring quick or slow transport, determines somewhat the number and size of the trains, and consequently the number and power of the engines.
A road with steep grades and sharp curves, with the same amount of traffic, will need stronger engines than a road with easy grades and large curves.
The amount of motive power and cost of working it, depends in a great degree upon the disposition of grades as regards the direction of the traffic movement. The most economically worked road will be either a level one, or one where the bulk of the traffic is moved down hill.
The mineral, commercial, or agricultural nature of the country, determines the direction of the traffic, and the physical nature, the arrangement of the grades.
The different kinds of labor required of locomotives, necessitate the employment of engines of different proportions; and the different classes of railways, require engines possessing different amounts of power.
309. The classification of locomotives should be determined according to the following relations.
Department depends upon commercial duty.
Division depends upon character of road.
Order depends upon weight of trains.
Class depends upon speed of trains.
Note.—The general classification is given at the end of this chapter.
High rates of speed are generally combined with light loads, and heavy trains are required to move at the lower velocities.
Great speeds require the rapid production and consumption of a large bulk of steam of but little density; large wheels and short stroke, that the ratio of velocities of piston and wheel may be as great as possible.
Heavy trains consume less steam by bulk, per mile, but of a much greater density, and combine a long stroke with a small wheel, by which great leverage is obtained.
In general, engines for winter use should be heavier than those for summer, upon the same ground, as natural causes are more liable to resist adhesion in the winter.
The locomotive engine may be so proportioned as to run at any speed from ten to sixty miles per hour, over grades from ten to two hundred feet per mile, and to carry loads from two hundred to two thousand tons.
The rules by which the necessary dimensions to perform any required duty are fixed, depend upon the very simplest mechanical laws.
Note.—The formulæ expressing the most proper relations to exist between the several steam-producing and steam-consuming parts are more reliable than the assertions of any machinist in America, and though taken from books, are the result of the experience of the most able and practical men for twenty years. Operatives are too apt to despise book knowledge, forgetting that the very knowledge so despised is the result of more practice than a lifetime can afford them. Railroad managers are too apt to receive as indisputable, the opinions of men who are practical, simply because they understand nothing of principle.
Since the work of D. K. Clark (England) has appeared, any dimension from the beginning to the end of a locomotive may be fixed, to the eighth of an inch, with absolute correctness, and there is no excuse for departing from the proper proportions. It does not follow that because a locomotive does actually start off and draw the train, that it is properly made. A race-horse can draw a plough, and a yoke of oxen a “trotting buggy,” but this is by no means the correct adaptation of power.
310. The elements which govern the requirements of power are
The maximum grades.
The weight of the train.
The required speed.
And the elements which govern our ability to produce the power needed,
The grate area.
The heating surface.
The cylinder diameter.
The steam pressure.
The stroke.
The diameter of wheels.
The weight upon driving wheels.
MECHANICAL AND PHYSICAL PRINCIPLES GOVERNING THE CONSTRUCTION OF THE LOCOMOTIVE ENGINE.
RESISTANCE TO THE MOTION OF RAILROAD TRAINS.
311. The exact resistance to the motion of a railroad train cannot be determined, as some of the elements are so variable; for example, the state of the weather. An approximate estimate, near enough for practice, is easily obtained. To arrive at correct data the observations must be made upon trains working under the same conditions that they are subject to in practice.
The whole resistance is made up of several partial resistances, some of which are constant at all speeds, and some of which increase with the velocity.
The engine and tender resistance is composed of the friction of pistons, cross heads, slide valves, cranks, eccentrics, pumps, the back pressure of the blast, and various erratic movements, rolling, twisting, and pitching together with both wheel and axle friction, which is common to the engine and tender.
The atmospheric resistance is not due to the direct action of the air upon the front and sides of the train entirely, but chiefly to the exhausting action in the rear. The train has, as it were, to pull along a large column of air like the water in the wake of a ship; form or amount of frontage has little or no effect. The resistance depends upon the bulk of the train and its velocity. A train with the same frontage offers more resistance as its bulk increases.
Oscillatory resistance is caused by irregularities in the surface of the rails, and increases with the velocity, and also with increase of height of the centre of gravity of the car or engine.
Frictional resistance may be divided into wheel and axle friction. That of the axle is composed of two parts, the direct vertical friction on the journal, and the side friction on the collar, consequent upon lateral motion. The vertical friction is independent of the surface pressed or of velocity, but is directly proportional to the pressure, and the same remark applies to that of the collars. As the diameter of wheel increases, the oscillation is increased, the centre of gravity being raised. The direct cause of the vertical friction is the weight of the car or engine, and of the lateral irregularities in the surface of the rails, which cause the car to sway from side to side. Wheel friction which acts between the periphery of the wheel and the surface of the rail increases with the load, and decreases as the wheel diameter augments.
For the total resistance to the motion of a railroad train, D. K. Clark gives the following formula:—
V2
171 + 8 = R,
Where R is the resistance in lbs. per ton,
and V the velocity in miles per hour.
From this expression we form the following table:—
| Velocity in miles per hour. | Resistance in lbs. per ton. |
| 10 | 8.585 |
| 12 | 8.842 |
| 15 | 9.315 |
| 20 | 10.339 |
| 25 | 11.655 |
| 30 | 13.263 |
| 40 | 17.356 |
| 50 | 22.620 |
| 60 | 29.052 |
| 100 | 66.480 |
From a great number of experiments made by Mr. Clark, the relative resistance to the motion of inside and outside connected engines is as follows:—
| Inside connections | 17 |
| Outside connections | 14 |
The effect of curves, bad state of the road, and adverse winds, amounts (according to the same author) to the following percentages:—
| Bad state of the road | 40 |
| Curves | 20 |
| Strong head and side winds | 20 |
| In all | 80 |
The resistance due to grades depends entirely upon the rate of incline, and is quite independent of all other considerations. The relative effect of grades decreases with the absolute increase of resistance on a level. Thus common roads admit of steeper grades than do railroads, because the level resistance is much more upon the former than on the latter.
The exact determination of the resistance due to any grade depends upon the very simple mechanical principle, regulating motion upon the inclined plane. For each foot rise of grade per mile, the resistance per ton is
2240 × 1
5280.
Thus the resistance to one ton upon a forty feet grade is
2240 × 40
5280 or 17 lbs.
And if we are moving at thirty miles per hour the sum of all other resistances is, by the formula, or the table at the end of Chapter XIV., part I., 13.3 lbs. per ton; whence the whole resistance to the motion of one ton, at thirty miles per hour, upon a forty feet grade, is
17 + 13.3 or 30.3 lbs.
and one hundred tons would be one hundred times as much. Table 1, at the end of Chapter XIV., part I., gives the whole resistance to the motion of trains of from fifty to one thousand tons, moving at speeds varying from ten to one hundred miles per hour, and table 2 gives the resistance upon grades from ten to one hundred feet per mile.
TRACTION AND ADHESION.
312. The whole steam pressure upon both pistons, referred by means of the crank, connecting, and piston rods, and wheel, to the rail, is called “traction.” It is the drawing power of the engine. Its amount depends upon the diameter of cylinder, steam pressure, stroke, and diameter of wheel.
By increasing the steam pressure, we increase the power. By increasing the cylinder diameter, we increase the power. By increasing the stroke, we increase the power. By decreasing the wheel diameter, we increase the power. And by adjusting the dimensions of the above parts, we may give any desired amount of power to the engine.
The formula expressing the tractive power of an engine, of any dimensions, is
(2A) P × 2S
C.
Where A = the area of one piston.
P = the steam pressure in cylinder per square inch,
S = the stroke in inches.
C = the circumference of the wheel in inches.
The formula is expressed verbally as follows: Double the stroke and multiply it by the total steam pressure on both pistons; divide the product by the circumference of the driving-wheel in inches.
ADHESION.
313. As observed on page [307], the adhesion or the bite of the wheels upon the rail is, as an average, from one fifth to one sixth of the weight; one fifth when the rail is in a good state, and less when wet or greasy; we cannot depend upon more than one sixth in practice. Therefore, if the tractive power of an engine is 3,000 lbs. we must, to make it available, place 3,000 × 6 or 18,000 lbs. upon those wheels which are connected with the machinery, (driving wheels).
FUEL.
314. The fuels employed in the locomotive engine for the evaporation of water are wood, coal, and coke. In England the latter is used exclusively. In America the first has, on account of its cheapness, been quite generally adopted; but of late railroad companies have been turning their attention to coal and coke.
The immense beds of coal distributed throughout the United States will furnish fuel to railroad companies almost without limit. Its position as well as its amount will render its adoption practicable in nearly all of the States. Ohio alone contains more coal than all of Great Britain. The following table is from the iron manufacture of Frederick Overman.
| Name of State. | Area of Coal-fields. | |
|---|---|---|
| Georgia | 150 | square miles. |
| Maryland | 550 | square miles. |
| Alabama | 3,400 | square miles. |
| Tennessee | 4,300 | square miles. |
| Michigan | 5,000 | square miles. |
| Missouri | 6,000 | square miles. |
| Indiana | 7,700 | square miles. |
| Ohio | 11,900 | square miles. |
| Kentucky | 13,500 | square miles. |
| Pennsylvania | 15,437 | square miles. |
| Virginia | 21,195 | square miles. |
| Illinois | 44,000 | square miles. |
| In all | 133,132 | square miles. |
315. The following table (also from the works of Overman) gives the nature and evaporative power of the different American coals.
| Name of Coal. | State where found. | Percentage of carbon. | Steam of 212° evaporated per lb. | Quantity of heat by volume. | Percentage of coke by weight. |
|---|---|---|---|---|---|
| Anthracite. | |||||
| Beaver Meadow, | Pa. | 88.9 | 10.4 | 94 | |
| Forest Improvement, | Pa. | 90.7 | 10.8 | 94 | |
| Lehigh, | Pa. | 89.1 | 9.6 | 94 | |
| Lackawanna, | Pa. | 87.7 | 10.7 | 94 | |
| Coke. | |||||
| Midlothian, | Va. | 10.3 | 92 | .66 | |
| Cumberland, | Md. | 10.3 | 92 | .75 | |
| Bituminous. | |||||
| Maryland, | Md. | 73.5 | 11.2 | 85 | |
| Cumberland, | Md. | 74.3 | 11.0 | 85 | |
| Blossburg, | Pa. | 73.4 | 10.9 | 85 | .83 |
| Karthans, | Pa. | 73.8 | 9.8 | 85 | .88 |
| Cambria County, | Pa. | 69.4 | 10.2 | 85 | |
| Clover Hill, | Va. | 56.8 | 8.5 | 85 | .68 |
| Tippecanoe, | Va. | 64.6 | 8.5 | 85 | |
| Pittsburgh, | Pa. | 55.0 | 8.9 | 85 | .68 |
| Missouri, | Mo. | .57 |
316. The employment of the several varieties of wood depends more upon the commercial than the chemical character. The following table shows the specific gravity, the nature and the evaporative value of the different species.
| Species. | Specific gravity green. | Specific gravity air dried. | Specific gravity kiln dried. | Degrees of heat which may be generated. | Percentage of Charcoal. | Quantity of heat as to volume. | Weight of one cord in lbs. | Relative value as fuel. | Species. |
|---|---|---|---|---|---|---|---|---|---|
| Hickory, | 3000 | 44.69 | 25 | 4469 | 1.00 | Hickory. | |||
| White Oak, | 1.07 | 0.71 | 0.66 | 3000 | 21.62 | 25 | 3821 | 0.81 | White Oak. |
| Black Oak, | 3000 | 23.80 | 25 | 3254 | 0.71 | Black Oak. | |||
| Red Oak, | 1.05 | 0.68 | 0.66 | 3000 | 22.43 | 25 | 3254 | 0.69 | Red Oak. |
| Beech, | 0.98 | 0.59 | 0.58 | 3000 | 32.36 | 25 | 3236 | 0.65 | Beech. |
| Birch, | 0.90 | 0.63 | 0.57 | 3000 | 25 | Birch. | |||
| Maple, | 0.90 | 0.64 | 0.61 | 3000 | 27.00 | 25 | 2700 | 0.57 | Maple. |
| Yellow Pine, | 2800 | 24.63 | 23 | 2463 | 0.54 | Yellow Pine. | |||
| Chestnut, | 3000 | 25.25 | 25 | 2333 | 0.52 | Chestnut. | |||
| Pitch Pine, | 2800 | 19.04 | 23 | 1904 | 0.43 | Pitch Pine. | |||
| White Pine, | 0.87 | 0.47 | 0.38 | 2800 | 18.68 | 23 | 1868 | 0.42 | White Pine. |
| Species. | Specific gravity green. | Specific gravity air dried. | Specific gravity kiln dried. | Degrees of heat which may be generated. | Percentage of Charcoal. | Quantity of heat as to volume. | Weight of one cord in lbs. | Relative value as fuel. | Species. |
Of the relative value of wood and coal, we have the following results of experience.
In the engines of the Baltimore and Ohio Railway 2.55 lbs. of pine wood were found equal to one pound of Cumberland coal.
On the Reading Railroad (Pennsylvania), three pounds of pine wood equal to one pound of Anthracite coal.
Mr. Haswell estimates the best varieties of wood fuel to contain twenty per cent. of carbon.
Walter R. Johnson found that one pound of wood, upon an average, evaporated two and one half pounds of water.
The average percentage of coke from American bituminous coal from the above table is seventy-three per cent., and the average percentage of carbon, sixty-seven and one half per cent.
317. The following table shows the relative properties of good coke, coal, and wood.
| Name of fuel. | Weight per cubic foot, in lbs. | Degrees of heat generated. | Percentage of carbon, in the fuel. | Economic bulk, or cubic feet required to stow one ton. | Economic, or stowage weight per cubic foot. | Cubic feet of air to evaporate one lb. of water. | Equivalent economic bulk, to evaporate the same weight of water. | Weight of water evaporated per lb.of fuel in ordinary practice. | Relative value as fuel, disregarding the actual cost. |
|---|---|---|---|---|---|---|---|---|---|
| Coke. | 63 | 4300 | 95 | 80 | 28 | 22.4 | 13 | 8½ | 100 |
| Coal. | 80 | 4000 | 88 | 44 | 51 | 32.0 | 10 | 6 | 71 |
| Wood. | 30 | 2800 | 20 | 107 | 21 | 16.0 | 60 | 2½ | 29 |
The power of fuel depends upon the amount of carbon in it.
Pure coke is solid carbon.
Hence its superior value as a heat generator.
OF THE PROCESS OF COKING.
318. Anthracite coal is used for locomotive fuel in its natural state. It is employed chiefly upon those roads on the eastern slope of the Alleghanies. The bituminous coal lies in the Mississippi valley, and may be found anywhere between the summits of the Alleghanies and the Rocky Mountains. This, in its natural state, contains so much pitchy matter as to render it unfit for locomotive purposes. Upon being heated, it melts, runs into a mass, and clogs the grate; requiring frequent poking and a strong draft. But when the bitumen is burnt off by slow and careful baking, (as described below,) no fuel equals it.
Just as carbonized wood is charcoal, so carbonized coal is coke. Coke is bituminous coal deprived of its bitumen, the raw coal being baked in ovens having vents so regulated as to admit air enough to char, without consuming the coal. The ovens being closed at the proper time, the fire is gradually extinguished, and the coke, compacted into large masses, requiring to be broken up before taken out. Coal may be coked by piling loosely in heaps, covering with earth, and firing through openings, which, after forty or fifty hours, are closed. In preparing coke, however, in the large quantities required for railroads, and that it may be of the very best quality, a good deal of care must be taken.
Probably in no place more or better coke is made, or the operation more skilfully carried on, than at the Camden-town station of the London and North-western Railroad, (England).
The company have built eighteen ovens, in two rows, all discharging their volatile gases into a horizontal flue terminating in a chimney one hundred and fifteen feet high; having an internal diameter of eleven feet, and being three feet thick, (making the external diameter seventeen feet). The ovens are elliptical, 11 × 12 feet inside, with walls three feet thick. The height is ten feet, the first three feet from the ground being solid, and furnished with a fire brick floor, on which the coal is placed. Each oven communicates with the flue by an opening in the top two and one half feet by twenty-one inches; which opening is closed by an iron damper, to regulate the draft. The openings for the doors are three and one half feet square outside, and two and three fourths inside, being closed with iron doors four and one half by five feet, lined with fire brick, and balanced in opening by counterweights. (The object of the chimney and horizontal flue is to carry the smoke and unburned gases so far up that they shall not be a nuisance. In America we might allow the smoke of each oven to escape through a low chimney of its own, (ten or twelve feet high,) and save the cost of a large stack; like the coking ovens in our foundries).
The operation of coking is carried on as follows:—Each alternate oven is charged between eight and ten A. M. every day, with three and one half tons of good coals. A whisp of straw is then thrown in, which takes fire from radiation from the top, and inflames the smoke then arising from the surface, by the reaction of the hot sides and bottom upon the body of the fuel. In this way the smoke is consumed at the very point of the process, where it would otherwise be the most abundant. The coking process is a complete combustion of the volatile principles of the coal. The mass of coal being first kindled at the surface, where it is supplied with an abundance of oxygen, because the doors in front and vents in the rear are open, no more smoke goes from the chimney than from that of a common kitchen fire. The gas generated from the slightly heated coal cannot escape destruction in passing up to the bright flame of the oven. Any deficiency in oxygen for consuming the smoke is supplied by the air entering the grooves of the dampers.
As the coking process advances most slowly from the top to the bottom, only one layer is consumed at a time; while the surface is covered with red-hot cinders, ready to consume any particles of carburetted or sulphuretted hydrogen gases which may escape from below. The greatest mass cannot emit more gases than the smallest heap.
The coke being perfectly freed from all smoky and volatile matters, by a calcination of forty hours, is cooled down to a moderate ignition by sliding in the dampers and opening the doors, which had been partly closed during the latter part of the operation.
The coal is now converted into a clean, crystalline, porous, columnar mass, of a steel-gray color, and so hard as to cut glass. This is broken up and taken out—coke. It is sometimes extinguished by a watering-pot. This is wrong, it ought not to be wet, and even more, ought to be immediately shut up in fire-proof boxes and bins. Even left to itself in the air, it absorbs moisture rapidly, which must be burned off in the boiler; it should by all means be kept in a dry place. Mr. Woods (England) observes, that coke may absorb as much as eight per cent. of water in going from the oven to the storehouse. The amount of absorption depends upon the nature of the coke. D. K. Clark records the following, the coke being immersed in water.
No. 1. Close-grained and good, absorbed 14.5 per cent. of water.
No. 2. Porous and ordinary, absorbed 21 per cent.
No. 3. Very close-grained and good, 9 per cent.
The time of coking may be stated generally as fifty hours, though it is somewhat improved by being allowed forty hours more; this gives time for a better consolidation, and gives a firmer, brighter, and more crystalline mass.
Mr. Gooch, of the Great Western (England) Railroad, experimented upon the time of coking with the following results.
| In oven. | Yield per ton of coal. | Water evaporated per lb. of coke. | Result. |
|---|---|---|---|
| 48 hours | 12.71 cwt. | 7.1 lbs. | 902. |
| 72 hours | 12.00 cwt. | 7.7 lbs. | 924. |
Thus, though the yield per ton is decreased by a greater time, the value of the coke per pound is augmented, and the increase overbalances the decrease.
Firstrate coal gives from seventy-five to eighty per cent. by weight, of compact glistening coke, weighing about 14 cwt. per chaldron, (thirty-six bushels). The bulk is increased from ten to fifty per cent.
In breaking out the coke from the ovens, a great deal is unavoidably reduced too fine for use in the locomotive furnace under a strong draft; such may, however, be used in firing up, in standing still, and at the stations.
In taking the coke from the ovens it should be separated into the three following classes.
| Large coke. | Cubes of 9 inches to the side. |
| Medium coke. | Cubes of 6 inches to the side. |
| Small coke. | Cubes of 3 inches to the side. |
Pittsburgh coal carefully coked for forty-eight hours, gives seventy-five per cent., by weight, and one hundred twenty-five per cent. by bulk, of firstrate, firm, bright, clean coke.
The best test for coke is to place it in water. Water, weighing sixty-two and one half pounds per cubic foot, should not float good coke, which ought to weigh sixty-three pounds per cubic foot, therefore if the coke floats it is too light.
Much of the bituminous coal in the Mississippi valley does not coke, but burns up. A large part cokes moderately well, but not so well as the Pittsburgh coal. In estimating for a comparison of fuels, the particular coal of any location must be tested.
OF THE COMPARATIVE VALUE OF WOOD, COAL, AND COKE.
This question divides itself into two parts,
The relative cost of the different fuels,
and The relative power to produce heat.
319. It does not follow that because coke in England, anthracite in Pennsylvania, or wood in New England, is the most economical fuel, that either of the above will be so in Ohio, Indiana, or Illinois, or because wood is the cheapest in some parts of a State, that it is so throughout, or even that one fuel should be applied to the whole length of a single road.
The heat used to evaporate water in the locomotive boiler is developed by combustion; combustion is produced by chemically combining the oxygen of the air with the carbon of the fuel; whence, that material containing in a given cost the largest amount of carbon will produce heat the most economically.
From the table on page [320], we see that, by bulk, thirteen of coke are equal to sixty of wood; that one pound of coke evaporates eight and one half pounds of water; that one pound of wood will evaporate two and one half pounds of water. Tables of specific gravity give as an average weight per cubic foot of hard wood, thirty pounds. A cord of wood, by very careful measurement, contains one hundred cubic feet solid, or one hundred twenty-eight feet as piled, taking the average size of wood; whence a cord will weigh three thousand pounds. And we have as the relative evaporative efficiency of a cord of wood and a ton of coke,
| 2240 × 8½ = | 19040, |
| 3000 × 2½ = | 7500. |
Now if the cost of a cord of wood is to the price of a ton of coke as 7,500 to 19,040, it is immaterial which we use.
As an example of the use of the above proportion, when the absolute cost of wood, coal, coke, and labor are known, take the following.
If wood, cut and ready for burning, costs $3.00 per cord, how much may be given for a ton of coke?
As 7,500 is to 19,040, so is 300 to 762, or $7.62.
From the same proportion we form the following table.
| Cost per cord of wood ready for burning. | Price that may be paid per ton for coke. |
|---|---|
| (Cents.) | (Cents.) |
| 200 | 508 |
| 225 | 571 |
| 250 | 635 |
| 275 | 698 |
| 300 | 762 |
| 325 | 825 |
| 350 | 877 |
| 375 | 952 |
| 400 | 1016 |
| 425 | 1079 |
| 450 | 1143 |
| 475 | 1206 |
| 500 | 1270 |
In the comparison above, the maximum evaporative power of wood has been used, 2½ lbs., and the ordinary power of coke, 8½ lbs. of water per pound of fuel.
320. In making coke in large quantities, the ovens should be at the mines, as we thus save transporting the extra weight of coal over coke.
The cost of making coke, exclusive of the cost of the coal, is approximately as follows:—
| 10 ovens capable of making annually 5,000 tons of coke, | $5,000 |
| Sheds, and apparatus to correspond, | 3,000 |
| In all, | 8,000 |
| Annual interest at 6 per cent., | 480 | |
| Annual cost of attendance, 2 men, | 1,000 | |
| The sum of which is, | $1,480 | |
| And the cost per ton, | 0.296 10 | |
or in round numbers, thirty cents per ton; and if coal is $1.50 per ton, adding twenty-five per cent. we have $1.87 as the cost of coal that will make one ton of coke, to which add the cost of making per ton, thirty cents, and we have as the whole cost of one ton of coke $2.17; and from the rule on page [327] we see that wood must not cost over $0.85 per cord to be as economical as coke at $2.17; of course inferior qualities of coal will give less good coke and change the comparison.
COMBUSTION.
321. The combustible element in all fuels is carbon; the heat necessary for steam producing, is obtained by combining the carbon of the fuel with the oxygen of the air, forming carbonic acid gas.
Carbonic acid gas consists of
| Oxygen | 16 | Parts by weight. |
| Carbon | 6 |
Atmospheric air consists of
| Oxygen | 8 | Parts by weight. |
| Nitrogen | 28 |
Whence, for the combustion of one pound of carbon, we require
| Carbon | 1.00 |
| Oxygen | 2.66 |
But to obtain 2.66 of oxygen from the atmospheric air, we also use nitrogen in the proportion of 28 nitrogen to 8 oxygen; whence, for converting one pound of carbon to carbonic acid, we require
| Oxygen | 2.66 | |
| Nitrogen | 9.31 | |
| Or | 11.97 | lbs. of atmospheric air. |
From careful observations on the gases passing through the chimneys of well-constructed boilers, oxygen is found free, varying in amount from one quarter to one half of the quantity necessary for combustion; this is owing to the mechanical obstructions to the perfect conversion of the air arising from leakage through the fuel.
More than the above 11.97 lbs. of air should, therefore, be applied to the fire for each pound of carbon consumed. Twenty-five per cent. is found by experience to be a sufficient surplus allowance to convert the carbon.
| Whence, to | 11.97 | |
| add | 3.03 | |
| and we have | 15.00 | lbs. of atmospheric air per lb. of carbon. |
Air weighs .075 lbs. per cubic foot, whence 15
.075 or 200 cubic feet of air are necessary for the proper combustion of one lb. of pure carbon.
Knowing the necessary amount of air for one lb. of carbon, and also the percentage of carbon in the different kinds of fuel, it becomes a simple arithmetical operation to fix the bulk of air required for any species of coal, coke, or wood. The result of such a calculation is shown in the seventh column of the table on page [320].
“There are two causes why all the heat which fuel may furnish is not obtained. First, that the inflammable gases evolved by the heat are not all consumed from want of a sufficient supply of oxygen, the air drawn through the fire being only sufficient to decompose more fuel than when decomposed it could burn, or supply with oxygen. The thick smoke that escapes from a chimney when fresh fuel is thrown on a hot fire, is unconsumed gas; decomposed from the fuel, but without oxygen enough to burn—although there may have been a sufficient supply of heat. From this cause it is, perhaps, that flame is seen coming from the top of a steamboat chimney which appears to be continuous from the furnace; but which, in fact, is ignited by contact with the air, having retained sufficient heat for that purpose.
“All smoke-consuming furnaces are simply means of admitting fresh air to the unconsumed gases above the fire, which, in a common chimney, will effect the object, as so large a mass of smoke retains the necessary amount of heat. This only prevents the nuisance of smoke. To render the gases thus reheated useful in evaporating water, this supply of oxygen must be added while the gases are yet in the flues.” This might seem difficult. Mr. McConnell (England) divides the flues of his locomotives into two parts, connecting the front ends of the first part and the back ends of the second part by a space of twelve or fifteen inches, (called by him a ‘combustion chamber,’) into which he admits any required amount of fresh air. (See appendix E.)
“A second cause why the full value of the fuel produced is not obtained is, that so much is abstracted from the gases in passing through long tubes, that there is not enough left to continue combustion, although the inflammable gas is still there. That a tube or any substance in the way of the hot gases does absorb the heat enough to prevent the burning of the gas, is proved by the action of Davy’s Safety Lamp; this is a common light surrounded by a wire gauze, which so absorbs the heat from the flame as to extinguish the latter at the wire; by applying fire above the gauze, the gas is again kindled, showing plainly that want of heat above had quenched the flame.” See Stöckhardt’s Chemistry; translation by C. H. Peirce, M. D., Cambridge, Mass., 1852, page 105.
We require, then, in every boiler, first, to have a sufficient supply of oxygen to decompose the fuel; next, a quantity above the fire to consume the produced gases; third, such an arrangement of communicating surface that so much heat shall not be abstracted from the gases as to deaden their combustion, until just as they are discharged, at which period they ought to be consumed. (See appendix E.)
GENERATION OF STEAM.
322. The means of producing the power is of course of the first importance.
The heat generated in the fire-box is conducted through the tubes to the exhaust chamber; during which passage it is imparted to the metal, and from thence absorbed by the adjacent water, which being thereby made lighter, rises to the surface and gives place to a new supply. The duty of the furnace is to generate, and of the tubes to communicate, heat.
The power of a plain surface to generate steam, depends upon its position and on the ability of the material to transmit heat An experiment recorded in Clark’s Railway Machinery, gave the following results: A cubic metallic box submerged in water and heated from within, generated steam from its upper surface more than twice as fast as from the sides when vertical, while the bottom yielded none at all. By slightly inclining the box the elevated side produced steam much faster, while the depressed one parted so badly with it as to cause overheating of the metal.
Acting upon this result, most builders of engines of the present day give an inclination of from one inch to one quarter of an inch per foot to the sides of the inner fire-box. That the heat should be applied in the most effectual manner to the water, the latter should circulate freely around the hot metal, carrying off the heat as soon as it reaches the surface. As the heat is applied to the inside of the furnace and tubes, it must, therefore, be the inside dimensions which determine the amount of heating surface.
Note.—If we multiply the interior surface of a tube by the intensity of heat applied, and divide the product by the exterior surface, we shall have the intensity at the outside. We also apply more heat to the outside of a tube, which, passing to the inner surface, augments in intensity per unit of area.
The area of the inner fire-box is not all available for heating, but requires to be reduced as follows:—
For the fire-door.
For the ferrule area.
For the top stays.
For the side stay bolts.
The area is, therefore,
Sides, twice length by height, less stay bolts.
Back, height by width, less fire-door.
Front, height by width, less ferrule area.
Top, length by width, less top stays.
TUBES.
323. The tubes or flues, varying in number from one hundred to three hundred, in diameter from one and a half to three inches, and in length from eight to sixteen feet, furnish the real communicating surface. The amount of heating surface thus obtained for any length, number, and diameter, is given in table 10, Chapter XIV., Part I. The surface of a single tube is found by the formula
Ld3.1416
144.
Where L = the length,
and d = the diameter, both in inches.
The efficiency of circular tubes is a matter not yet fully understood. They certainly give a large amount of surface in a small boiler. Pambour considered the value of tube area per unit of surface, in terms of the furnace area, as one third only; that is, three square feet of tube surface as equal to one foot of furnace area, in power of generating steam. D. K. Clark makes no distinction between the two surfaces, but observes “there is reason to believe that in the upper semicircular part of each tube the efficiency principally resides. The winding progressive motion, observable in tubes of considerable diameter, confirms this conclusion, as it is with much probability due to the cooling of the upper portion of the gases of combustion, which, as they cool also, become heavier and descend laterally, to make room for the hotter smoke next the bottom of the flue; the general result of which is the spiral motion of the current in its progress onwards.” Certainly the upper half of the tube would part much easier with the steam than the under one, even supposing the applied heat to be the same.
At page 340 of “Overman’s Mechanics,” is the following: “The application of heat to a concave surface is wrong in principle. The heat in gases is conducted to other bodies, and among themselves by convection only. This quality of gases causes the convex form of a vessel to be the most profitable in absorbing the heat of ascending gases, because the motion of the gas causes a constant change of particles on the convex body. On a concave surface exposed to the influence of moving gases, but little effect is produced; because the particles of gas in the concavity are at rest. A plane surface is for the same reason an imperfect form for absorbing heat; it must be exposed at an angle of 45° to obtain the best effect of the heating gases. In all cases if we wish to obtain the best effect from the fuel, we should expose a convex surface to the current of hot air. The direction of the motion of the hot gases decides the position of the metal which is to absorb the heat; if the current is horizontal the pipes must be vertical. Gases do not convey heat by radiation. Tubes and other vessels containing water must be so placed that the hot gases play around the outside.
“If we lead a current of hot air around a cylinder we shall observe that a particle of air plays but a short time upon its surface, when it gives way to another; the particles play almost around the cylinder, and a concentration or increase of density behind the pipe is the result. The relative position of pipes in the range is not indifferent, and the distance of one from the other must be related to their diameter.”
The conducting power of the metal composing the fire-box and tubes, is one condition which limits the rate of evaporation, when the heat is abundant on the one side and circulation free on the other, as the water certainly carries off the heat as fast as it arrives at the outer surface.
All the heat should be extracted if possible from the gases before they enter the smoke box. We should so arrange the flues, that without so much contracting the passage for the exit of the gases as to need too strong a blast, yet to confine the gases until their full value is extracted.
Several attempts have been made to apply the ideas of Clark and Overman, but as yet they have been very indirect and have met with only moderate success. (See Appendix, E.)
EVAPORATION, PRESSURE, TEMPERATURE, AND DENSITY.
324. The character of work to be done determines the nature of the steam to be used.
The quantity of work to be done shows the amount of steam to be produced.
The amount and character of the steam required, fixes the dimensions and proportions of the boiler.
A cubic foot of water, at a temperature of 62°, weighs 62.321 lbs.
A cubic foot of steam, generated at 212° Fahrenheit, under the atmospheric pressure (14.7 lbs. per square inch) weighs .03666 lbs.
Whence one cubic foot of water boiled at 212°, makes 1,700 cubic feet of steam.
The total heat of saturated steam (steam produced in contact with the water), consists of two parts at all temperatures; the latent and the sensible. The sensible heat is that shown by the thermometer, and varies with the pressure. The latent heat absorbed during the generation of steam, amounts to three fourths of the whole. As the temperature at which the steam is produced increases, the bulk produced from a given unit of water decreases, but the pressure and the total heat increase. (See C. R. M. p. 59, 61, Regnault’s experiments.)
Table 8, Chapter XIV., Part I., gives the properties of saturated steam, produced under pressures varying from fifty to one hundred and fifty pounds per square inch.
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 Colburn.[[6]] | Norris.[[7]] | D. K. Clark.[[8]] | D. K. 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. |
[6]. Colburn on the Locomotive Engine.
[7]. Norris’s Handbook for Locomotive Engineers and Machinists.
[8]. D. K. Clark’s Railway Machinery, calculated for coke.
[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.
[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.
Fig. 151.
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.
Fig. 152.
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.
Fig. 153.
If the traction bar (draw link) is above the wheel centres, it will tend to lift the rear of the engine from the rails.
Fig. 154.
The general form of engines used in America are shown in figs. 151, 152, 153, 154, and 155.
Fig. 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
V2
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.
6T,
where T is the whole tractive power. (Table 3.)
Nos. 4 and 5.
The tractive power of an engine is expressed by
T = (2A)P × 2S
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 (2A)2S. | (A.) |
| The stroke, or S = CT (2A)(2P). | (B.) |
| The piston area, or A = TC 4SP. | (C.) |
| The wheel circumference, or C = 2A × P × 2S 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.
D2 × .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.
N5280
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
Ldπ,
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)2n],
and the diameter of that area,
D = √([(d + c)2n]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
3R+R
3)L = (4R
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 traction of | 11,500 lbs. |
| 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 require | 2 engines, |
| 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.
| Division. | Length. | Miles run by an engine not adapted. | Miles run by an engine adapted. | Difference. | |
|---|---|---|---|---|---|
| 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 per hour, | 1,550 | lbs. |
| 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.
| Number of division. | Maximum grades. | Designation of parts. | Order 1 50 tons. | Order 2 100 tons. | Order 3 250 tons. | Order 4 500 tons. | Order 5 750 tons. | Order 6 1,000 tons. |
|---|---|---|---|---|---|---|---|---|
| 1 | Level. | Grate area. Tube 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.
| Classification. | Order 1 50 tons. | Order 2 100 tons. | Order 3 150 tons. | Order 4 200 tons. | Designation of parts. | |
|---|---|---|---|---|---|---|
| Division 1 Level. | 25 miles per hour. | Grate area. Tube surface. Cylinders. Wheels. Weight. | ||||
| Division 2 20′ grades. | 25 miles per hour. | |||||
| Division 3 40′ grades. | 25 miles per hour. | |||||
| Division 4 60′ grades. | 25 miles per hour. | |||||
| Division 5 80′ grades. | 25 miles per hour. | |||||
| Division 6 100′ grades. | 25 miles per hour. | |||||
The engines in the Northern States require more power in winter than in summer.
To the above classification might be added, an engine for “making up trains,” and similar station work; such an engine should be able to start easily the extreme weights of trains, from fifty to one thousand tons, and should be fitted with a power of varying its adhesion.
FORMULA.
W × [V2
171 + 8] = R.
Example.
The speed being thirty miles per hour, and load 250 tons.
R will be [(30 × 30)
171 + 8] × 250 = 3315 lbs.
366. Table 1. Showing the required traction on a level for loads from fifty to one thousand tons, and for velocities from ten to one hundred miles per hour.
| Velocity. | 50 Tons. | 75 Tons. | 100 Tons. | 250 Tons. | 500 Tons. | 750 Tons. | 1000 Tons. |
|---|---|---|---|---|---|---|---|
| 10 | 429 | 643 | 858 | 2146 | 4292 | 6435 | 8585 |
| 12 | 442 | 663 | 884 | 2210 | 4421 | 6630 | 8842 |
| 15 | 465 | 698 | 931 | 2328 | 4657 | 6982 | 9315 |
| 20 | 517 | 773 | 1034 | 2585 | 5170 | 7735 | |
| 25 | 582 | 874 | 1165 | 2912 | 5825 | ||
| 30 | 663 | 994 | 1326 | 3315 | 6630 | ||
| 40 | 868 | 1302 | 1736 | 4340 | |||
| 50 | 1131 | 1696 | 2262 | 5655 | |||
| 60 | 1452 | 2180 | 2905 | ||||
| 100 | 3324 | 4986 | 6648 |
FORMULA.
WR
L.
Example.
The tractive power to overcome the resistance of 750 tons upon a sixty feet grade is
750 × 60
5280 = 19050.
367. Table 2. Showing the tractive power necessary to overcome grades from ten to one hundred feet per mile with loads from one to one thousand tons.
| Grade. | 1 Ton. | 50 Tons. | 75 Tons. | 100 Tons. | 250 Tons. | 500 Tons. | 750 Tons. | 1000 Tons. | Grade. |
|---|---|---|---|---|---|---|---|---|---|
| 10 | 4 | 212 | 318 | 424 | 1061 | 2121 | 3181 | 4240 | 10 |
| 20 | 8 | 424 | 636 | 848 | 2122 | 4242 | 6362 | 8480 | 20 |
| 30 | 13 | 636 | 955 | 1273 | 3170 | 6363 | 9545 | 12730 | 30 |
| 40 | 16 | 848 | 1272 | 1696 | 4244 | 8484 | 12724 | 16960 | 40 |
| 50 | 20 | 1060 | 1590 | 2120 | 5305 | 10605 | 15905 | 21200 | 50 |
| 60 | 26 | 1272 | 1910 | 2546 | 6340 | 12726 | 19050 | 25460 | 60 |
| 70 | 30 | 1500 | 2240 | 3000 | 7500 | 15000 | 22400 | 30000 | 70 |
| 80 | 33 | 1697 | 2545 | 3393 | 8489 | 16969 | 25459 | 33950 | 80 |
| 100 | 40 | 2120 | 3180 | 4240 | 10610 | 21210 | 31810 | 42400 | 100 |
| Grade. | 1 Ton. | 50 Tons. | 75 Tons. | 100 Tons. | 250 Tons. | 500 Tons. | 750 Tons. | 1000 Tons. | Grade. |
FORMULA.
6T.
Example.
Required traction 5,000 lbs.; upon driving axles the weight is 5000 × 6 = 30,000 lbs.
368. Table 3. Giving the weight which should be placed upon the driving axles to secure any amount of adhesion; the latter being one sixth of the weight.
| Required traction. | Weight in pounds. | Weight in tons. |
|---|---|---|
| 500 | 3000 | 1.34 |
| 1000 | 6000 | 2.69 |
| 2000 | 12000 | 5.36 |
| 3000 | 18000 | 8.04 |
| 4000 | 24000 | 10.80 |
| 5000 | 30000 | 13.40 |
| 6000 | 36000 | 16.07 |
| 7000 | 42000 | 18.75 |
| 8000 | 48000 | 21.43 |
| 9000 | 54000 | 24.11 |
| 10000 | 60000 | 26.80 |
| 12000 | 72000 | 32.14 |
| 14000 | 84000 | 37.50 |
| 16000 | 96000 | 42.86 |
| 18000 | 108000 | 48.22 |
| 20000 | 120000 | 53.60 |
FORMULA.
2S
c.
Where S = stroke.
c = circumference of wheel, (both in inches.)
Example.
Let stroke be twenty inches, and diameter of wheel five feet, the ratio will be
40
188.4 = 0.2122.
369. Table of decimals, which, multiplied by the total piston pressures (table 5) will give the traction in pounds, or ratio between double stroke and wheel circumference. Table 4.
| Wheel. | STROKE IN INCHES. | Wheel. | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 18 | 20 | 22 | 24 | 26 | 28 | 30 | 32 | 34 | 36 | ||
| 3½ | 2728 | 3031 | 3334 | 3638 | 3½ | ||||||
| 3¾ | 2553 | 2837 | 3120 | 3404 | 3688 | 3¾ | |||||
| 4 | 2386 | 2652 | 2918 | 3182 | 3444 | 3708 | 4 | ||||
| 4¼ | 2250 | 2500 | 2750 | 3000 | 3250 | 3500 | 3750 | 4¼ | |||
| 4½ | 2151 | 2390 | 2593 | 2830 | 3071 | 3294 | 3529 | 3764 | 4½ | ||
| 4¾ | 2012 | 2235 | 2459 | 2682 | 2905 | 3129 | 3352 | 3575 | 3800 | 4¾ | |
| 5 | 1910 | 2122 | 2334 | 2546 | 2766 | 2979 | 3192 | 3405 | 3617 | 3830 | 5 |
| 5½ | 1736 | 1929 | 2122 | 2315 | 2500 | 2692 | 2885 | 3077 | 3273 | 3473 | 5½ |
| 6 | 1591 | 1768 | 1945 | 2122 | 2321 | 2500 | 2678 | 2857 | 3036 | 3215 | 6 |
| 6½ | 1468 | 1632 | 1796 | 1958 | 2131 | 2295 | 2459 | 2623 | 2790 | 2951 | 6½ |
| 7 | 1364 | 1516 | 1667 | 1819 | 1970 | 2121 | 2273 | 2424 | 2576 | 2727 | 7 |
| 7½ | 1272 | 1414 | 1556 | 1691 | 1831 | 1972 | 2114 | 2254 | 2394 | 2535 | 7½ |
| 8 | 1194 | 1326 | 1417 | 1592 | 1688 | 1818 | 1948 | 2078 | 2208 | 2337 | 8 |
| Wheel. | 18 | 20 | 22 | 24 | 26 | 28 | 30 | 32 | 34 | 36 | Wheel. |
| STROKE IN INCHES. | |||||||||||
FORMULA.
2(d2 .7854 × p) = P.
Where d = diameter.
p = pressure per inch.
Example.
The whole pressure at one hundred pounds per inch on two sixteen inch pistons will be
2[16 × 16 × 0.7854 × 100] = 40212.
370. Table 5. Total pressures upon pistons from ten to twenty-four inches in diameter, and for steam pressures from fifty to one hundred and fifty pounds per square inch.
| Diam. of cyl’r. | Area of one Piston. | WHOLE PISTON PRESSURE ON BOTH PISTONS, AT A PER INCH PRESSURE OF | Diam. of cyl’r. | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | 130 | 140 | 150 | |||
| 10 | 78.5 | 7950 | 9420 | 10990 | 12560 | 14130 | 15700 | 17270 | 18840 | 20410 | 21980 | 23550 | 10 |
| 11 | 95.0 | 9500 | 11400 | 13300 | 15200 | 17100 | 19000 | 20900 | 22800 | 24700 | 26600 | 28500 | 11 |
| 12 | 113.1 | 11310 | 13572 | 15834 | 18096 | 20358 | 22620 | 24882 | 27144 | 29406 | 31768 | 33930 | 12 |
| 13 | 132.7 | 13270 | 15924 | 18564 | 21232 | 23906 | 26540 | 29194 | 31848 | 34502 | 37156 | 39810 | 13 |
| 14 | 153.9 | 15390 | 18468 | 21546 | 24624 | 27702 | 30780 | 33858 | 36756 | 40014 | 43092 | 46170 | 14 |
| 15 | 176.7 | 17670 | 21204 | 24738 | 28272 | 31806 | 35340 | 38874 | 42408 | 55942 | 49476 | 53010 | 15 |
| 16 | 201.1 | 20110 | 24132 | 28154 | 32176 | 36198 | 40220 | 44242 | 48264 | 52062 | 56308 | 60330 | 16 |
| 17 | 227.0 | 22700 | 27240 | 31780 | 36320 | 40860 | 45400 | 49940 | 54480 | 59020 | 63560 | 68100 | 17 |
| 18 | 254.5 | 25450 | 30540 | 35630 | 40720 | 45810 | 50900 | 55990 | 61080 | 66170 | 71260 | 76350 | 18 |
| 19 | 283.5 | 28350 | 34020 | 39690 | 45360 | 51030 | 56700 | 62370 | 68040 | 73710 | 79380 | 85050 | 19 |
| 20 | 314.2 | 31420 | 37704 | 43988 | 50272 | 56556 | 62840 | 69124 | 75408 | 81692 | 87976 | 95260 | 20 |
| 21 | 346.4 | 34640 | 41568 | 48496 | 55424 | 62352 | 69380 | 76208 | 83136 | 90064 | 96992 | 103920 | 21 |
| 22 | 380.1 | 38010 | 45612 | 53214 | 60816 | 68418 | 77020 | 83622 | 91224 | 98826 | 106428 | 114030 | 22 |
| 23 | 415.5 | 41550 | 49860 | 58170 | 66480 | 74790 | 83100 | 91410 | 99720 | 108030 | 116340 | 124650 | 23 |
| 24 | 452.4 | 45240 | 54288 | 63336 | 72384 | 81432 | 90480 | 99528 | 108576 | 117626 | 126672 | 135720 | 24 |
FORMULA.
N = 5280
c × 4.
Where N = the number.
c = wheel circumference.
Example.
Speed twenty-five miles per hour, wheels four and a half feet, the number of cylinders per hour is
25 × 5280
4 × 3.1416 × 4 = 37348
371. Table 6. Showing the hourly consumption of steam in terms of the capacity of one cylinder, with wheels from three and a half to eight feet, and speeds from ten to sixty miles per hour.
| Wheel. | Wheel in inches. | Revolutions per mile. | NUMBER OF CYLINDERS PER HOUR AT A VELOCITY OF | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 10 | 12 | 15 | 20 | 25 | 30 | 40 | 50 | 60 | |||
| 3½ | 42 | 480 | 19200 | 23040 | |||||||
| 3¾ | 45 | 449 | 17960 | 21552 | 26940 | ||||||
| 4 | 48 | 421 | 16840 | 20208 | 25260 | 33681 | |||||
| 4¼ | 51 | 397 | 15880 | 19056 | 23820 | 31760 | 39700 | ||||
| 4½ | 54 | 373 | 14920 | 17904 | 22380 | 29840 | 37300 | ||||
| 4¾ | 57 | 361 | 14440 | 17328 | 21660 | 28880 | 36100 | ||||
| 5 | 60 | 336 | 20160 | 26880 | 33600 | ||||||
| 5½ | 66 | 306 | 18360 | 24480 | 30600 | 36720 | |||||
| 6 | 72 | 281 | 22480 | 28100 | 33720 | 44960 | |||||
| 6½ | 78 | 259 | 20720 | 25900 | 31080 | 41440 | 51800 | 62160 | |||
| 7 | 84 | 240 | 19200 | 24000 | 28800 | 38400 | 48000 | 57600 | |||
| 7⅛ | 90 | 224 | 22400 | 26880 | 35840 | 44800 | 53760 | ||||
| 8 | 96 | 211 | 21109 | 25320 | 33760 | 42200 | 50640 | ||||
FORMULA.
D2 × .7854 × Stroke
1728 = C.
Example.
Cubic content of a cylinder 15 × 24 is
15 × 15 × 0.7854 × 24
1728 = 2.44 cubic feet.
372. Table 7. Capacity of cylinders in cubic feet of from ten to twenty-four inches in diameter, and from eighteen to thirty-six inches stroke.
| Diam. of cyl’r. | CAPACITY OF CYLINDERS IN CUBIC FEET, STROKE BEING | Diam. of cyl’r. | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 18 | 20 | 22 | 24 | 26 | 28 | 30 | 32 | 34 | 36 | ||
| 10 | 082 | 091 | 100 | 109 | 118 | 127 | 136 | 145 | 10 | ||
| 11 | 093 | 104 | 115 | 126 | 137 | 148 | 159 | 170 | 181 | 11 | |
| 12 | 118 | 131 | 144 | 157 | 170 | 183 | 196 | 209 | 222 | 235 | 12 |
| 13 | 133 | 149 | 165 | 181 | 197 | 213 | 229 | 245 | 261 | 277 | 13 |
| 14 | 160 | 178 | 196 | 214 | 232 | 250 | 268 | 286 | 304 | 322 | 14 |
| 15 | 184 | 204 | 224 | 244 | 264 | 284 | 304 | 324 | 344 | 364 | 15 |
| 16 | 208 | 232 | 255 | 278 | 301 | 324 | 347 | 370 | 393 | 416 | 16 |
| 17 | 235 | 263 | 289 | 315 | 341 | 367 | 393 | 419 | 445 | 471 | 17 |
| 18 | 263 | 294 | 323 | 352 | 381 | 410 | 439 | 468 | 497 | 526 | 18 |
| 19 | 361 | 394 | 427 | 460 | 493 | 526 | 559 | 592 | 19 | ||
| 20 | 400 | 437 | 474 | 511 | 548 | 585 | 622 | 659 | 20 | ||
| 21 | 481 | 521 | 561 | 601 | 641 | 681 | 721 | 21 | |||
| 22 | 528 | 572 | 616 | 660 | 704 | 748 | 792 | 22 | |||
| 23 | 625 | 674 | 723 | 772 | 821 | 876 | 23 | ||||
| 24 | 681 | 733 | 785 | 837 | 889 | 941 | 24 | ||||
373. Table 8. Giving the volume, pressure, temperature, and density of steam.
| Steam pressure. | Relative volume or cubic feet of steam, water being 1. | Temperature. | Total heat. | Weight of a cubic foot. | Steam pressure. |
|---|---|---|---|---|---|
| 50 | 552 | 281 | 1200 | 1129 | 50 |
| 60 | 467 | 293 | 1203 | 1335 | 60 |
| 65 | 434 | 298 | 1205 | 1436 | 65 |
| 70 | 406 | 303 | 1206 | 1535 | 70 |
| 75 | 381 | 307 | 1208 | 1636 | 75 |
| 80 | 359 | 312 | 1209 | 1736 | 80 |
| 90 | 323 | 320 | 1212 | 1929 | 90 |
| 100 | 293 | 328 | 1214 | 2127 | 100 |
| 110 | 269 | 335 | 1216 | 2317 | 110 |
| 120 | 249 | 341 | 1218 | 2505 | 120 |
| 130 | 231 | 347 | 1220 | 2698 | 130 |
| 140 | 216 | 353 | 1221 | 2885 | 140 |
| 150 | 203 | 358 | 1223 | 3070 | 150 |
FORMULA.
S =√ac × 21.2.
Where S = surface.
a = grate area.
c = cubic feet of water per hour.
Example.
Grate area sixteen square feet, cubic feet of water per hour two hundred, surface is
√16 × 200 × 21.2 = 1199.92.
374. Table 9. Showing the necessary amount of grate area and heating surface for an hourly consumption of water.
| Cubic ft. of water evap’d per hour. | GRATE AREAS IN SQUARE FEET. | |||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | |
| HEATING SURFACE CORRESPONDING TO ABOVE GRATE AREAS AND TO SIDE COLUMN. | ||||||||||||||||||||||||
| 100 | 561 | 599 | 636 | 670 | 703 | 734 | 764 | 793 | 821 | 848 | 874 | 900 | 924 | 948 | 972 | 995 | 1017 | 1039 | 1060 | 1081 | 1102 | 1122 | 1142 | 1161 |
| 110 | 588 | 628 | 667 | 702 | 737 | 770 | 802 | 831 | 861 | 888 | 916 | 943 | 969 | 994 | 1018 | 1042 | 1066 | 1089 | 1111 | 1133 | 1155 | 1176 | 1197 | 1217 |
| 120 | 614 | 657 | 697 | 734 | 770 | 805 | 837 | 869 | 900 | 927 | 957 | 985 | 1013 | 1039 | 1064 | 1089 | 1114 | 1138 | 1162 | 1184 | 1207 | 1229 | 1251 | 1272 |
| 130 | 639 | 683 | 725 | 764 | 801 | 837 | 871 | 904 | 936 | 965 | 996 | 1025 | 1053 | 1081 | 1107 | 1133 | 1159 | 1184 | 1208 | 1232 | 1255 | 1278 | 1300 | 1323 |
| 140 | 663 | 709 | 752 | 793 | 831 | 869 | 904 | 938 | 972 | 1003 | 1034 | 1064 | 1093 | 1122 | 1150 | 1177 | 1203 | 1229 | 1254 | 1279 | 1303 | 1327 | 1351 | 1374 |
| 150 | 686 | 734 | 779 | 821 | 860 | 900 | 935 | 971 | 1006 | 1038 | 1070 | 1101 | 1131 | 1161 | 1190 | 1218 | 1245 | 1272 | 1298 | 1323 | 1350 | 1373 | 1398 | 1422 |
| 160 | 758 | 805 | 848 | 889 | 927 | 966 | 1004 | 1039 | 1073 | 1106 | 1138 | 1169 | 1199 | 1229 | 1258 | 1286 | 1314 | 1341 | 1367 | 1393 | 1419 | 1444 | 1469 | |
| 170 | 782 | 829 | 874 | 916 | 957 | 996 | 1034 | 1071 | 1106 | 1140 | 1173 | 1205 | 1236 | 1266 | 1296 | 1325 | 1354 | 1382 | 1409 | 1436 | 1462 | 1488 | 1514 | |
| 180 | 805 | 853 | 900 | 943 | 985 | 1025 | 1064 | 1102 | 1138 | 1173 | 1207 | 1240 | 1272 | 1303 | 1334 | 1364 | 1393 | 1422 | 1450 | 1478 | 1505 | 1532 | 1558 | |
| 190 | 877 | 924 | 969 | 1013 | 1053 | 1093 | 1132 | 1169 | 1205 | 1240 | 1274 | 1307 | 1339 | 1370 | 1401 | 1431 | 1461 | 1490 | 1518 | 1546 | 1573 | 1600 | ||
| 200 | 900 | 948 | 995 | 1039 | 1081 | 1122 | 1161 | 1199 | 1236 | 1272 | 1307 | 1341 | 1374 | 1406 | 1437 | 1468 | 1499 | 1529 | 1558 | 1586 | 1614 | 1642 | ||
| 210 | 928 | 974 | 1019 | 1064 | 1107 | 1149 | 1189 | 1229 | 1264 | 1298 | 1336 | 1374 | 1408 | 1441 | 1473 | 1505 | 1536 | 1566 | 1596 | 1625 | 1654 | 1683 | ||
| 220 | 1000 | 1042 | 1089 | 1133 | 1176 | 1217 | 1258 | 1291 | 1324 | 1365 | 1406 | 1441 | 1475 | 1508 | 1541 | 1572 | 1603 | 1634 | 1664 | 1693 | 1722 | |||
| 230 | 1019 | 1067 | 1114 | 1159 | 1203 | 1245 | 1286 | 1323 | 1359 | 1398 | 1437 | 1473 | 1508 | 1542 | 1575 | 1607 | 1639 | 1663 | 1701 | 1724 | 1761 | |||
| 240 | 1091 | 1138 | 1184 | 1229 | 1272 | 1314 | 1354 | 1393 | 1431 | 1468 | 1505 | 1541 | 1575 | 1609 | 1642 | 1675 | 1692 | 1738 | 1754 | 1799 | ||||
| 250 | 1111 | 1162 | 1208 | 1254 | 1298 | 1341 | 1380 | 1422 | 1458 | 1499 | 1533 | 1572 | 1606 | 1642 | 1675 | 1709 | 1733 | 1774 | 1797 | 1836 | ||||
| 260 | 1184 | 1232 | 1278 | 1323 | 1367 | 1406 | 1450 | 1484 | 1529 | 1560 | 1603 | 1636 | 1675 | 1708 | 1743 | 1774 | 1809 | 1840 | 1872 | |||||
| 270 | 1207 | 1256 | 1303 | 1349 | 1401 | 1433 | 1478 | 1515 | 1557 | 1592 | 1634 | 1668 | 1692 | 1741 | 1776 | 1808 | 1843 | 1875 | 1908 | |||||
| 280 | 1279 | 1327 | 1374 | 1435 | 1460 | 1505 | 1546 | 1586 | 1624 | 1664 | 1700 | 1738 | 1774 | 1809 | 1842 | 1877 | 1910 | 1943 | ||||||
| 290 | 1302 | 1351 | 1400 | 1452 | 1486 | 1532 | 1573 | 1614 | 1653 | 1693 | 1729 | 1754 | 1804 | 1841 | 1873 | 1910 | 1939 | 1977 | ||||||
| 300 | 1374 | 1425 | 1469 | 1512 | 1558 | 1600 | 1642 | 1682 | 1722 | 1758 | 1799 | 1834 | 1872 | 1904 | 1943 | 1968 | 2011 | |||||||
| 320 | 1469 | 1516 | 1564 | 1610 | 1654 | 1696 | 1738 | 1778 | 1816 | 1859 | 1894 | 1932 | 1970 | 2008 | 2024 | 2078 | ||||||||
| 340 | 1564 | 1612 | 1658 | 1704 | 1748 | 1792 | 1833 | 1872 | 1915 | 1954 | 1993 | 2032 | 2069 | 2096 | 2141 | |||||||||
| 360 | 1658 | 1706 | 1754 | 1800 | 1844 | 1886 | 1928 | 1971 | 2012 | 2050 | 2090 | 2128 | 2166 | 2204 | ||||||||||
| 380 | 1753 | 1802 | 1848 | 1894 | 1938 | 1982 | 2025 | 2066 | 2107 | 2148 | 2187 | 2226 | 2264 | |||||||||||
| 400 | 1800 | 1848 | 1900 | 1944 | 1990 | 2034 | 2077 | 2120 | 2162 | 2204 | 2244 | 2284 | 2322 | |||||||||||
| 425 | 1950 | 2014 | 2056 | 2077 | 2142 | 2187 | 2226 | 2268 | 2317 | 2353 | 2396 | |||||||||||||
| 450 | 2014 | 2056 | 2120 | 2150 | 2190 | 2200 | 2300 | 2332 | 2374 | 2417 | 2459 | |||||||||||||
| 475 | 2175 | 2210 | 2268 | 2310 | 2353 | 2416 | 2445 | 2480 | 2523 | |||||||||||||||
| 500 | 2332 | 2370 | 2412 | 2459 | 2523 | 2565 | 2608 | |||||||||||||||||
FORMULA.
N = S
Ldπ or S
Ld3.1416.
Where S = whole surface,
Where L = length,
Where d = diameter, in feet,
Where π = 3.1416,
Where N = the number.
Example.
Diameter two inches, surface 1466, length fourteen feet, we have,
N = 1466
14 × 0.167 × 3.1416 = 200.
375. Table 10. Giving the number and dimensions of tubes to obtain any given amount of surface.
| L’gth. | Diam. 1½ | Diam. 1¾ | Diam. 1⅞ | Diam. 2 | Diam. 2⅛ | Diam. 2¼ | Diam. 2⅜ | Diam. 2½ | L’gth. |
|---|---|---|---|---|---|---|---|---|---|
| 8 | 314 | 336 | 397 | 419 | 445 | 471 | 504 | 523 | 8 |
| 8½ | 334 | 389 | 422 | 445 | 473 | 500 | 535 | 556 | 8½ |
| 9 | 352 | 411 | 447 | 471 | 507 | 530 | 566 | 588 | 9 |
| 9½ | 372 | 435 | 471 | 497 | 523 | 559 | 597 | 621 | 9½ |
| 10 | 392 | 457 | 496 | 524 | 556 | 589 | 628 | 655 | 10 |
| 10½ | 411 | 480 | 521 | 549 | 584 | 618 | 659 | 687 | 10½ |
| 11 | 431 | 503 | 545 | 576 | 612 | 647 | 690 | 720 | 11 |
| 11½ | 451 | 526 | 570 | 602 | 640 | 677 | 721 | 753 | 11½ |
| 12 | 471 | 549 | 595 | 628 | 667 | 705 | 752 | 786 | 12 |
| 12½ | 490 | 572 | 620 | 654 | 695 | 735 | 783 | 818 | 12½ |
| 13 | 510 | 595 | 645 | 681 | 723 | 764 | 814 | 851 | 13 |
| 13½ | 530 | 617 | 669 | 707 | 750 | 793 | 845 | 884 | 13½ |
| 14 | 549 | 640 | 695 | 733 | 778 | 823 | 876 | 916 | 14 |
| 14½ | 569 | 663 | 719 | 759 | 806 | 852 | 907 | 949 | 14½ |
| 15 | 589 | 686 | 744 | 785 | 834 | 882 | 938 | 982 | 15 |
| 15½ | 608 | 708 | 769 | 811 | 861 | 911 | 969 | 1015 | 15½ |
| 16 | 628 | 731 | 794 | 837 | 889 | 941 | 1000 | 1048 | 16 |
| 16½ | 648 | 754 | 819 | 863 | 917 | 971 | 1031 | 1081 | 16½ |
| 17 | 668 | 777 | 843 | 889 | 945 | 1000 | 1062 | 1114 | 17 |
FORMULA.
13.5√a – 28,
where a is the percentage of admission.
Example.
What is the mean pressure, with an initial pressure of one hundred pounds, and sixty per cent. admission.
13.5√60 – 28 = (13.5 × 7.7) – 28 = 76
100 of 100, or 76 lbs.
376. Table 11. Showing the mean cylinder steam pressure for any percentage of admission, the initial pressure being from 50 to 150 lbs. per inch.
| Initial pressure in pounds. | MEAN CYLINDER PRESSURE, ADMISSION BEING IN HUNDREDTHS OF THE STROKE. | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 | |
| 50 | 7 | 12 | 16 | 20 | 23 | 26 | 28 | 31 | 33 | 36 | 38 | 40 | 42 | 44 |
| 60 | 9 | 14 | 19 | 24 | 28 | 31 | 34 | 37 | 40 | 43 | 46 | 49 | 51 | 53 |
| 70 | 10 | 17 | 22 | 28 | 33 | 36 | 40 | 43 | 47 | 50 | 54 | 57 | 59 | 62 |
| 80 | 12 | 19 | 26 | 32 | 38 | 42 | 41 | 49 | 54 | 58 | 62 | 65 | 68 | 71 |
| 90 | 13 | 22 | 29 | 36 | 42 | 47 | 51 | 54 | 60 | 65 | 69 | 73 | 76 | 80 |
| 100 | 15 | 24 | 32 | 40 | 47 | 52 | 57 | 62 | 67 | 72 | 77 | 81 | 85 | 89 |
| 110 | 16 | 26 | 35 | 44 | 52 | 57 | 63 | 68 | 74 | 79 | 85 | 89 | 93 | 98 |
| 120 | 18 | 29 | 38 | 48 | 56 | 62 | 68 | 74 | 80 | 86 | 91 | 97 | 102 | 107 |
| 130 | 19 | 31 | 42 | 52 | 61 | 68 | 74 | 81 | 87 | 94 | 99 | 105 | 110 | 116 |
| 145 | 21 | 34 | 45 | 56 | 65 | 73 | 80 | 87 | 94 | 101 | 107 | 113 | 119 | 125 |
| 160 | 22 | 36 | 48 | 60 | 70 | 78 | 85 | 93 | 100 | 108 | 114 | 121 | 127 | 134 |
PART II.
CARS.
WHEELS AND AXLES.
377. Of the mechanical details of car building it is not necessary here to speak; but of those matters which fit a car for special duty, and depend upon particular characteristics of any road, such as the gauge, something must be said.
The trend of the wheel tire, as remarked in Chapter XIII., is not turned cylindrical, but conical. A perfectly straight road would of course require no cone upon the wheels; the object of the latter being to vary the wheel diameter when upon curves. The general practice is to give a certain standard cone to all wheels, for all gauges. This is quite wrong, as will be seen by the following formula, which is from “Pambour on the Locomotive Engine.”
Fig. 156.
Let m m′, fig. 156, represent the outer rail, and n n′ the inner one. The circumferences upon the same axles must evidently vary as the length of these curves, which are included between the same radii.
Let D, be the diameter of the first wheel, and d, that of the second; and we shall have,
mm′
nn′ = (πD)/(πd),
or otherwise
mm′ = 3.1416 D,
and
nn′ = 3.1416 d.
We have also,
mm′
nn′ = mo
no.
Expressing the radius of curvature by r, and the half gauge by e, the above proportion may be expressed by
mm′
nn′ = r + e
r – e,
and also
D
d = r + e
r – e,
and finally
D – d = 2eD
r + e.
This equation shows the difference in diameters that ought to exist between the inner and outer wheels, that the required effect, (no dragging of the outer and no slipping of the inner wheel,) is produced.
| Example. | |
| Let the radius of curvature be | 1,000 feet. |
| The gauge of the road, | 6 feet. |
| The wheel diameter, | 4 feet. |
And the formula becomes
2ed
r + e = 24
1003 = .024 feet,
or .288 inch on both wheels, or 0.144 inch for each wheel; which for four inches breadth, gives a curve of 1
28 of the width, or decimally, 0.144, and vulgarly, ⅐ of an inch. For a three feet wheel, the rule gives a cone of 0.11 inch.
Note.—Messrs Bush and Lobdel cone their wheels 0.08 inches in a four inch tire; or ¼ inch per foot. The formula above for a three feet wheel, and 4′ 8½″ gauge, gives a curve of 0.09 inches.
The wheel most used upon American roads is made of cast-iron, in one piece, and consists either of two side plates, connected by a hub and rim, or of a central plate ribbed on the sides. Messrs Whitney and Son, (Philadelphia,) pass all their wheels through an annealing process, which renders them much less liable to fracture from shocks and from cold than when the wheel is allowed to cool at once, when hot from the foundery.
The wheels used upon English roads are made with a wrought iron rim and spokes, with a cast hub, the tire being, put on separately. Such wheels are less liable to fracture, but cost more than the American wheel.
378. A very frequent cause of accident upon railroads, is the breakage of axles. Experiments made at Wolverhampton, (England,) upon differently formed axles, show very plainly that it is quite wrong to reduce the diameter of the axle at the middle. That if any variation exists it should be in making the middle the largest. That the effect of a shoulder behind the wheel was to decrease very much the strength. Probably the strongest and most economical railroad axle, would be a wrought iron tube. Certainly a hollow axle is much stronger in resisting tension than a solid one containing the same amount of material.
Note 1.—Thomas Thorneycroft, of Wolverhampton, England, an educated man, and a manufacturer of railway axles, observes:—That the various forms of axles, as generally made, possess within themselves the elements of destruction. That there are certain fixed principles to be observed in proportioning axles, and that just as such principles are departed from, just so much is liability to failure increased.
He says:—It is doubtful whether the wheel is the support and the journal the loaded part, or the reverse. If the latter is the case, then the cone of the wheels causes a lateral strain, tending to bend the axle; and should that bending extend no further than one half of the elastic limit, if long continued, fracture must result; and should the elastic limit be exceeded, the plane of the wheel will be removed from that in which it ought to revolve.
The object of the first experiment was to determine the effect of the form of the longitudinal section of the axle upon its elastic limit.
By reducing the diameter of the axle from 45
16 inches at centre, to 3¾ inches; the limit of elasticity was reduced from .343 to .232 inches; and the load, to produce that elasticity, from fourteen to seven tons.
Experiment second was to ascertain the effect of a reduction of diameter at the centre, upon the ability to resist sudden shocks. One half of the axle was made 4½ inches in diameter from middle to end, and the other half was reduced from 4½ to four inches at centre. The wheel being fixed, and a ram allowed to fall upon the journal, when the following result was obtained. Under forty-six blows, the unreduced end was bent to an angle of eighteen degrees. Under sixteen blows, the reduced end was bent to twenty-two degrees.
Experiment third was to ascertain the effect of a shoulder behind the wheel, one end being turned with a shoulder of one eighth of an inch, as a stop to the wheel, the other end turned plain. Tested by hydraulic pressure, the shouldered end broke with sixty tons, the plain end with eighty-four tons.
The object of the fourth experiment was to find the influence of the position of the wheel, as regards the end of the journal. An axle was fastened into a cast-iron frame, in a line with the neck of the journal, when the latter was broke with seven blows of a ram falling ten feet. The other end was keyed into the frame, with the neck of the journal projecting 1½ inch, and broke at the twenty-fourth blow of the same ram, falling ten feet.
The results of the trials are thus summed up by the experimenter:—That axles should never be smaller at the centre than at the ends, but on the contrary, that if a difference in size is made, the centre should be the largest.
The best authorities on the strength of materials, give the hollow tube as three times stronger in resisting twisting, than the solid bar possessing the same weight. Thus an axle with an external diameter of five inches, and an internal diameter of 3¾ inches, is three times as strong as a solid axle of 3¾ inches diameter.
Note 2.—The following experiments were prepared by M. Bourville, and executed by the Austrian government. The apparatus consisted of a bent axle, which was firmly fixed up to the elbow in timber, and which was subjected to torsion by means of a cog-wheel connected with the end of the horizontal part. At each turn the angle of torsion was twenty-four degrees. A shock was produced each time that the bar left one tooth to be raised by the next. An index adapted to the apparatus, indicated the number of revolutions and shocks. Seven axles, submitted to this trial, presented the following results:—
1st. The movement lasted one hour; 10,800 revolutions and 32,400 shocks were produced. The axle, two and six tenths inches in diameter, was taken from the machine and broken by an hydraulic press. No change in the texture of the iron was visible.
2d. A new axle, having been tried four hours, sustained 129,000 torsions, and was afterwards broken by means of an hydraulic press. No alteration of the iron could be discovered, by the naked eye, on the surface of rupture; but tried with a microscope, the fibres appeared without adhesion, like a bundle of needles.
3d. A third axle was subjected, during twelve hours, to 388,000 torsions, and broken in two. A change in its texture, and an increased size in the grain of the iron, was observed by the naked eye.
4th. After one hundred and twenty hours, and 3,888,000 torsions, the axle was broken in many places; a considerable change in its texture was apparent, which was more striking towards the centre; the size of the grains diminished towards the extremities.
5th. An axle, submitted to 23,328,000 torsions during seven hundred and twenty hours, was completely changed in its texture; the fracture in the middle was crystalline, but not very scaly.
6th. After ten months, during which the axle was submitted to 78,732,000 torsions and shocks, fracture, produced by an hydraulic press, showed clearly an absolute transformation of the structure of the iron; the surface of rupture was scaly like pewter.
7th. Finally, as a last trial, an axle submitted to 128,304,000 torsions, presented a surface of rupture like that in the preceding experiment. The crystals were perfectly well defined, the iron having lost every appearance of wrought iron.
CLASSIFICATION OF CARS.
379. Railroad cars come under three general heads,
Those for passenger transport,
Those for freight traffic,
Those for repairs of the road.
380. The American passenger car consists of a body about fifty feet long, ten feet wide, and seven feet high, containing seats for about sixty passengers, being cushioned, warmed, lighted, and ventilated. Except for emigrants, second and third class cars are but little used in America.
House, box, or covered freight cars, differ from the “flat,” or platform car, only in having a simple rectangular house, about six feet high and nine feet wide, built upon the floor. This is used for the protection of such freight as will not bear exposure; as furniture, books, dry goods, hardware, and small machinery. Carriages, boxes, bales, masts, lumber, and fuel are carried by platform cars. Bulky machinery, and first and second class freight too large for the box cars, should be protected by tarpaulins.
381. The general arrangement of wheels, springs, and brakes, is the same for the several classes of cars, the chief difference being in the ease of springs. Each car rests upon two “trucks,” consisting of four, six, or eight wheels, so connected by levers and springs, as best to absorb shocks, and connected with the body by a pin only, by which the passage of curves is made quite easy.
Cars used for the movement of earth are so arranged as to allow the body to be tipped up, that the contents may be quickly “dumped,” either at the sides, ends, or middle, as desired.
382. Upon some roads, a continuous draw bar is passed under the whole train, the several cars being attached to it, and to each other by safety chains only. By adopting this, and at the same time by springing the buffer beams tight upon each other, the whole train becomes one piece; and the jerks at stopping and at starting are in a great measure avoided.
As lightness combined with strength is a desideratum in all cases, it will be found best to truss the longitudinal frame pieces of the car with rods, rather than to use large and heavy beams, as done by many builders.
RETARDING OF TRAINS.
383. As regards the mode of retarding trains of cars, the practice of applying blocks to the wheels is justly considered by many as quite wrong. The brake should be applied to the rail and not to the wheel. Blocks drawn against the wheel are supplied with friction by means of levers worked by a brakeman, who can at pleasure cause the wheels to slide upon the rail. A shoe, sliding upon the rail, may be supplied with friction from the whole weight of the car.
The retarding force should be applied at once to every car alike; if too much in front, the rear cars are driven against those in advance; if too much behind, the train is liable to break.
The proper place for the brakeman is upon the top of the train, where all signals may be quickly seen.