PART XXI.

PROPORTIONS OF LOCOMOTIVES.

QUESTION 412. _In proportioning a locomotive to any given kind of work, what are the first facts which should be known?_

_Answer._ We should first know the weight of the train which the locomotive must draw; second, the speed at which it must run; and third, the steepest grades and the shortest curves of the road on which it must work. From these data the resistance of the train which the locomotive must overcome can be at least approximately determined.

QUESTION 413. _When the greatest resistance of the train is known, what is the next thing to be determined?_

_Answer._ As was stated in answer to Question 66, if the wheels revolve and their adhesion is greater than the resistance opposed to the movement of the locomotive, the latter will overcome the resistance; but if the latter is greater than the friction, the wheels will slip. It therefore follows that the adhesion must be somewhat greater than the resistance. As the adhesion is equal to about one-fifth[100] of the adhesive weight or pressure of the driving-wheels on the rails, obviously this weight should be five times the resistance. Thus, if we have a train weighing 400 tons which we want to take up a grade of 40 feet per mile at a speed of 20 miles per hour, its resistance, calculated from the table given in the previous part, would be 9,360 lbs. Therefore, 9,360 × 5 = 46,800 lbs. = the required adhesive weight.

[100] See answer to Question 309.

QUESTION 414. _What considerations determine the manner of distributing this weight on the wheels?_

_Answer._ It is found by experience that if too much weight is placed upon one wheel, the material of which the rails are made is partly crushed and injured, and they then wear out much more rapidly than they would if the weight was distributed on more wheels, and thus a smaller amount of weight rested on each point of contact with the rails. The amount of weight which can be carried on a single wheel depends upon the material of which the rails are made, and to some extent on their form and size, or as the latter is usually expressed, on their weight per yard.

QUESTION 415. _When the adhesive weight and the number of driving-wheels are known, how is the size of the latter and of the cylinders determined?_

_Answer._ The size of the wheels will to a certain extent depend upon the speed, because the larger the wheels, the further will the locomotive move in one revolution; but no exact rule can be given for their size. At present there is still a great diversity of opinion among engineers regarding the best sizes of wheels and cylinders for any given service. Probably the safest plan will be to consult the best practice, and in the absence of any better reasons be guided for the present by that. In this country the most common size of locomotives used is that which we have selected for our illustrations, that is, what are called five-feet wheels, and cylinders of 16 inches diameter and 24 inches stroke. More engines of these dimensions are used than of any other. For freight service the wheels are sometimes made of smaller and for passenger trains of larger diameter; but locomotives with driving-wheels and cylinders of the dimensions given are used for both passenger and freight service. It should be stated here that what are called five-feet wheels are usually about 1¹⁄₂ in. larger in diameter than five feet. This arose from the fact that the tires which are now used are made thicker than they were on the first engines, and the practice thus established has been continued. We will therefore take the diameter of what is called a five-feet wheel at what it really is, 61¹⁄₂ in. Such locomotives also have about 40,000 lbs. of adhesive weight. Now, the circumference of such wheels is 193.2 in., and therefore in one revolution of the wheels, if they do not slip, the locomotive will move that distance on the rails. At the same time each piston will sweep through the cylinder twice, and therefore in one revolution 4 times one cylinder full of steam is used. Now a cylinder of 16 in. diameter and 24 in. stroke contains or will hold 4,825¹⁄₂ cubic inches, so that in one revolution of the wheels 4,825¹⁄₂ × 4 = 19,302 cubic inches of steam are used. As has been stated, in one revolution of the wheels, if they do not slip, the locomotive will move 193.2 in. If, now, we divide 19,302 by 193.2 it will give us the amount of steam used to move the locomotive and train one inch. Now, 19,302 ÷ 193.2 = 99.9, which, for the sake of even figures we will call 100. We thus see that a locomotive with 40,000 pounds or 20 tons (of 2,000 lbs.) of adhesive weight requires 100 cubic inches of cylinder capacity[101] to move it one inch. Now, if a locomotive had only half as much weight on the driving-wheels, it could pull only half as much load, and would therefore use only half as much steam, and consequently need only half the cylinder capacity of the other locomotive. If there was three-quarters or a third as much adhesive weight, the cylinder capacity should also be three-quarters or a third. We thus see that the cylinder capacity should be proportioned to the total adhesive weight. Now as 100 cubic inches of cylinder capacity are needed to move an engine with 20 tons adhesive weight one inch, if we divide 100 by 20 we will get the cylinder capacity needed for each ton. That is, 100 ÷ 20 = 5 CUBIC IN. CYLINDER CAPACITY PER TON (of 2,000 lbs.) OF ADHESIVE WEIGHT IS NEEDED TO MOVE ANY LOCOMOTIVE ONE INCH. This quantity we have named the _modulus of propulsion_.

[101] The cylinder capacity is the space swept through by the two pistons. In the above illustrations what is meant is, that the average space in the cylinder swept through by the piston is 100 cubic inches for each inch that the locomotive advances.

Supposing now that it is required to calculate the cylinder capacity for a locomotive with 15 tons adhesive weight, and wheels 4¹⁄₂ feet or 54 in. in diameter. We will first multiply 15 by the modulus of propulsion, 15 × 5 = 75 = the number of cubic inches of cylinder capacity required to move such a locomotive one inch. Multiplying the length of the circumference of the wheels, which in this case is 169.6 in. by 75, will give us the total cylinder capacity for one revolution. That is 169.6 × 75 = 12,720 cubic inches of cylinder capacity, or the space which should be swept through by the two pistons. Dividing this by 4 will give us the cubical contents in inches of one of the cylinders. Thus, 12,720 ÷ 4 = 3,180 cubic inches = the capacity of one cylinder. Now as the capacity of a cylinder is calculated by multiplying the area of the piston by the length of the stroke, if we have the one we can easily determine the other. Thus, supposing it was intended to make the stroke of the pistons 22 in., dividing 3,180 by 22 will give us the area of the piston. Thus, 3,180 ÷ 22 = 144.5 square inches. Now by the well-known rule in mensuration, if we DIVIDE THE AREA OF A CIRCLE BY 0.7854, THE SQUARE ROOT OF THE QUOTIENT WILL BE THE DIAMETER OF THE CIRCLE. Thus, 144.5 ÷ 0.7854 = 183.9. The square root of 183.9 is 13¹⁄₂ nearly, which should be the diameter of the cylinder. Instead of calculating the diameter of the circle, a more convenient way is to refer the area to a table of areas, and from it find the diameter. Of course if we have the diameter of the piston and want to get the stroke, we DIVIDE THE CUBICAL CONTENTS OF THE CYLINDER BY THE AREA OF THE PISTON. Thus, in the present illustration, if it was intended to have the piston 13¹⁄₂ in. diameter, we would have divided 3,180 by the area of a piston 13¹⁄₂ in. diameter, which is 143.1, so that we would have 3,180 ÷ 143.1 = 22 nearly, = inches of stroke of piston.

From the above considerations we can deduce the following RULE FOR CALCULATING THE CAPACITY OF THE CYLINDERS WHEN THE ADHESIVE WEIGHT IS KNOWN:

MULTIPLY THE TOTAL WEIGHT ON THE DRIVING-WHEELS IN TONS (of 2,000 lbs.) BY 5, AND THEN BY THE CIRCUMFERENCE OF THE WHEELS IN INCHES, AND DIVIDE BY 4. THE QUOTIENT WILL BE THE CUBICAL CONTENTS IN INCHES OF EACH CYLINDER. From this, if either the diameter or stroke is given the other can easily be found, as has been explained.

It should be remarked here that it is unimportant, so far as the power of the locomotive is concerned, whether the cylinders have a large diameter and a short stroke or a small diameter and a long stroke, provided the cubical contents are the same. Thus cylinders 17¹⁄₂ in. in diameter and with 20 in. stroke would have almost exactly the same capacity and the same power would be exerted with them as with cylinders 16 × 24 in.; the only difference would be that with the cylinder of the largest diameter the pressure on the piston and consequently on the crank-pin journal and the strain on the parts would be greater than with the smaller cylinder. The difference in pressure would, however, be exactly compensated by the loss or gain in the leverage exerted through the driving-wheels on the rails.

QUESTION 416. _What circumstances should determine the size of locomotive boilers?_

_Answer._ They should be proportioned to the amount of adhesive weight, and to the speed at which the locomotive is intended to work. Thus, a locomotive with a great deal of weight on the driving-wheels could pull a heavier load and would, by the above rule for proportioning the cylinders, have a greater cylinder capacity than one with little adhesive weight, and would therefore consume more steam, and therefore should have a larger boiler. It is also obvious that if a locomotive like that shown in plates I and II should have a boiler just large enough to furnish steam when running at the rate of 20 miles an hour, it would be too small if the locomotive ran 40 miles an hour, the train resistance being the same in both cases. Driving-wheels 5 feet in diameter would at 20 miles per hour make 112 revolutions per minute, and would therefore consume 448 cylinders full of steam. At 40 miles per hour double the number of revolutions would be made, and consequently twice the quantity of steam would be used, and therefore the boiler should have twice the steam-producing capacity. If, therefore, we know the size of a boiler required for a given amount of adhesive weight and a given speed, we can easily calculate the boiler capacity for any other weight and speed.

QUESTION 417. _How can we determine the boiler capacity needed for an engine with a given amount of adhesive weight and for a given speed?_

_Answer_. This must be determined empirically, that is from experience.

QUESTION 418. _On what does the steam-generating capacity of a boiler depend?_

_Answer_. First, upon the size of its grate and fire-box, because more fuel can be burned in a large fire-place than in a small one; second, on the amount of heating surface to which the products of combustion are exposed, and third, on the draft produced by the blast or exhaust steam. Of course the amount of steam generated is also dependent upon a great variety of other circumstances, such as the nature of the combustion, the firing, the arrangement of the fire-box, grates, etc., and the condition of the heating surfaces; but these have nothing to do with the proportions or size of the boiler.

QUESTION 419. _What are the proportions of boilers used in locomotives like that which has been illustrated in these articles and represented in Plates I and II?_

_Answer_. The area of the grate is about 2,100 square inches and the total heating surface about 800 square feet, and the water capacity about 5,000 lbs., and the total weight of the boiler, including all the boiler attachments and appliances for promoting combustion, about 30,000 lbs.

QUESTION 420. _At what speed are such engines usually run?_

_Answer_. The speed varies so much under different circumstances, that it is impossible to give even approximately the average speed of such engines.

QUESTION 421. _How then can we determine the proper proportions of a boiler for a locomotive intended for any given service?_

_Answer_. As stated before, this can only be done empirically. The safest method is to select a locomotive which is doing the best service, and learn the average speed at which it runs, the size of its grate and the amount of its heating surface, and its adhesive weight. NOW MULTIPLY THE ABOVE SPEED IN MILES PER HOUR BY THE ADHESIVE WEIGHT OF THE LOCOMOTIVE IN TONS (of 2,000 lbs.) AND DIVIDE THE PRODUCT INTO THE AREA OF THE GRATE IN SQUARE INCHES. THEN MULTIPLY THE ADHESIVE WEIGHT OF THE LOCOMOTIVE FOR WHICH THE BOILER IS TO BE PROVIDED BY ITS SPEED, IN MILES PER HOUR, AND BY THE QUOTIENT OBTAINED ABOVE: THE PRODUCT WILL BE THE AREA OF THE GRATE IN SQUARE INCHES FOR THE NEW ENGINE. To illustrate this, suppose an engine of the dimensions given to run at an average speed of 20 miles per hour. Now, multiplying that speed by the number of tons of adhesive weight and dividing the product into the area of the grate, we have 20 × 20 = 400 and 2100 ÷ 400 = 5.25. We now want to determine the size of a grate for the boiler of a locomotive with 30 tons adhesive weight and to run at a speed of 15 miles per hour. We therefore multiply 15 by 30 and the product by the above quotient, or 15 × 30 × 5.25 = 2,362.5 = square inches of grate surface for the boiler. The required heating surface can be obtained in a similar way, by substituting it instead of the grate surface in the calculations.

QUESTION 422. _How is the size of locomotive boilers usually limited?_

_Answer_. By the weight of the locomotive and to some extent by the distance between the rails. It will be found often that it is impossible to make the boiler of the size indicated by a calculation similar to the above without at the same time making the weight of the locomotive and the adhesive weight greater than was assumed. The result of such a calculation indicates, therefore, that too large a proportion of the weight of the locomotive is on the driving-wheels for the speed at which it is intended to work, and that either they should bear less weight or the speed be reduced.

QUESTION 423. _In what respects is the operation of locomotive boilers different from that of nearly all other steam boilers?_

_Answer_. The amount of steam generated in proportion to the amount of heating surface is much greater in locomotive boilers than in any other kind. To produce combustion which will be sufficiently active to generate the requisite quantity of steam, the fire must be stimulated by the blast created by the exhaust steam to a degree unknown in other kinds of boilers. So rapid is the movement of the products of combustion that a smaller proportion of the heat is imparted to the water contained in the boiler, and consequently a less amount of water is evaporated in proportion to any given amount of fuel than in boilers in which combustion is less violent. The combustion is also less perfect, because the strong draft does not allow time for a perfect combination of the gases which produce combustion.

The supply of steam which a locomotive boiler must furnish is also much more irregular than the demands made upon any other kind of boiler. At one time the fire must be urged to the greatest possible intensity in order to furnish steam enough to pull a train up a steep grade. When the top is reached the demand ceases, and the boiler can be cooled. The load which a locomotive can pull over a given line of road is usually limited by the utmost capacity of the boiler to supply steam at these critical periods.

QUESTION 424. _What relation is there between this irregular action and the size of the boiler?_

_Answer_. The smaller the boiler, or rather the larger the amount of steam which must be generated in a given time in proportion to the heating surface, the more must the fire be urged; and therefore the smaller the boiler in proportion to the work it must do, the less will be its economy. In order to produce a rapid combustion in a small boiler, it is necessary to contract the exhaust nozzles in order to create a draft strong enough. In doing this the back pressure on the pistons is very much increased, and when the blast becomes very violent a great deal of solid coal is carried through the tubes and escapes at the smoke-stack unconsumed. At the same time large quantities of unconsumed gases escape, because there is not time for combustion to take place in the fire-box. The fact that with a violent draft the flame and smoke are in contact with the heating surface for a sensibly shorter period of time also has its influence; as less heat will be imparted to the water if the products of combustion are only ¹⁄₁₀₀ of a second instead of ²⁄₁₀₀ in passing through the tubes.

There is another consideration which should be taken into account in this connection, which is, that if a boiler is so small that it is worked nearly up to its maximum capacity at all times, it will be impossible to accumulate any reserve power in it in the form of water heated to a high temperature to be used as occasion may require. With a boiler having a great amount of heating surface and capacity for carrying a large quantity of water, the latter can be heated at times when the engine is not working hard, and the heat thus stored up in the water can then be used when it is most needed. Thus we will suppose that to pull a train of cars on a level 250 lbs. of steam are consumed per mile. On a grade of 30 feet per mile the resistance will be three times what it is on a level, and therefore three times the quantity of steam will be consumed, so that the boiler must then evaporate 750 lbs. of water per mile. Now to convert 250 lbs. of water heated up to a temperature due to 130 lbs. of effective pressure, or 355.6 degrees, into steam of that pressure will require 216,575 units of heat. If at the same time that this steam is being consumed, we pump into the boiler 250 lbs. of water of a temperature of 60 degrees, 73,900 more units of heat will be needed to raise the water to the temperature due to 130 lbs. effective pressure, so that on the level part of the road it would be necessary to transmit to the water in the boiler 216,575 + 73,900 = 290,475 units of heat in a mile. If there is no room in the boiler for storing a surplus quantity of hot water, it will be necessary on a grade as fast as the steam is consumed to feed an equivalent amount of cold water to take the place of that which was converted into steam, so that on a 30 feet grade it would be necessary to convert at the rate of 750 lbs. of hot water into steam in a mile, which would require 649,725 units of heat, and at the same time heat an equal amount of cold water to a temperature due to the pressure of the steam, which would require 221,700 more units. So that it will be necessary to transmit at the rate of 871,425 units of heat to the water per mile. Now if the boiler was so large that more water could be pumped into it and heated than was used on the level portion of the road, and could there be stored up for future use, the pumps might be either partly or entirely shut off when the engine was working the hardest on the grade. In this way, instead of being obliged to convert hot water into steam, and at the same time heat an equal amount of cold feed-water, there would be a surplus of hot water stored up already heated. It would therefore only be necessary to convert this hot water into steam, which will require a transmission of heat to the water at the rate of 649,725 units of heat instead of 871,425. It must be remembered that on nearly all roads there are certain difficult places which practically limit the capacity of the locomotives on that line. If therefore the capacity of the engines can be increased at those points, their capacity over the whole line is increased. It will be seen by the above illustration that by having a large boiler it is necessary for it to do very much less work at the critical period, when, as every locomotive runner knows, it is often of the utmost importance to make use of every possible available means in order to pull the trains. It is true that on a very long grade the supply of surplus hot water would soon be exhausted, but even in such cases there is usually one place, owing to a curve or other cause, which is more difficult to surmount than any other, in which case it will be necessary to use more steam for a short time than the locomotive can generate if the boiler is fed continuously. For such cases a surplus of water can be used. But even if the resistance is equal over the whole length of the incline, still the large boiler will have the advantage, because it can at all times generate more steam than a smaller one. It may therefore, we think, safely be assumed that locomotive boilers should always be made as large as the weight of the locomotive will permit.

QUESTION 425. _What effect does the size of the driving-wheels have upon the combustion and evaporation of locomotive boilers?_

_Answer._ As small wheels make more revolutions in running a given distance than large ones, there will be more strokes of the piston with the former than with the latter, if the locomotive in both cases runs at the same speed. As smaller cylinders are usually employed with small wheels, the blast up the chimney is then composed of a larger number of discharges of steam, but each one of less quantity, than when larger wheels and cylinders are used. In the one case the “puffs” of steam are many and small, and in the latter few and large. If the cylinders are proportioned by the rule which has been given for that purpose, the amount of steam discharged in running any given distance will be the same with engines having large and those with small wheels, the only difference being that it will be subdivided into a greater number of discharges in the one case than in the other. Now, it is found that the draft of engines is much more effective on the fire when the blast is thus subdivided, that is when small wheels and cylinders are used, than it is with large ones, and therefore more steam is generated with the former than with the latter.

QUESTION 426. _What relation is there between the size of the wheels and that of the boiler?_

_Answer._ As has been explained, the size of the boiler is limited by the weight of the locomotive. The boiler and its attachments of an American locomotive, when the former is filled with water, weigh about half as much as the locomotive; therefore unless we increase the weight of the latter or decrease the weight of the machinery, we can not increase the size of the boiler. Now, large wheels are heavier than small ones; they require larger cylinders, stronger connections, heavier frames, and in fact nearly all the parts of the machinery used with large wheels must be heavier than are required when small wheels are used. Therefore, by decreasing the size of the wheels all the other parts of the engine proper can be made lighter than is possible if large wheels are used, and thus the size and weight of the boiler can be increased without increasing the whole weight of the locomotive. There is of course a practical limit below which the size of the wheels can not be reduced, because the speed of the piston would become so great as to be injurious to the machinery. By reducing the stroke, however, with the diameter of the wheels, the evil referred to may be obviated to a great extent. A cylinder with a large diameter and comparatively small stroke has also the advantage that there is less surface exposed to radiation of heat than there is in a cylinder in which these proportions are reversed.