- 160 sq.ft. 207 50 lbs. - 3 in. in, Stroke 16 in. or Wheel Friction Heating surface Effective pressure in boiler - 50 lbg. Range of the slide 3 in. Lap over the apprtures · - in. Engine with cylinders 12 in. or 1 ft. Stoke 18 in. or Wheel Friction Heating surface Effective presssure in boiler Lap over the apertures From these results we see that too great a lead detracts a considerable portion from the power of the engine. It is therefore necessary not to exceed, in that respect, certain limits. It is, besides, easy to know the lead, or to regulate it at any degree. After having opened the chamber situated under the chimney, and taken off the top of the slide-box, in order to see the slides work, the engine must be pushed gently forward on the rails, until the crank of the axle be perfectly horizontal. Then the piston is at the bottom of the cylinder. If at that moment the passages which the slide opens to the steam be measured, it will give exactly the lead. 0. 0. 26.16 26.57 27.41 28.86 19.85 20.16 20.80 21.90 15.99 17.64 16.24 16.75 13.93 14.15 14.60 15.37 13.09 13.30 13.72 0. 0. This operation whenever the piston ready to the open pas exccentric in that position. concluded, it is clear that crank is horizontal, or the begin its stroke, the slide will sage to the degree required. There are some ways of altering the lead without opening each time the chimney chamber; but they are not quite exact, and some of them are injurious to the engine. In the experiments we have related above on the velocity of the load of the engines, the Vesta engine was the only one in which the lead was considerable enough to have a remarkable effect on the speed. If we wish to alter the lead, we keep the crank in the same position, and loosening the driver which is fastened to the axle only with a screw, we turn the exccentric, unti§ the slide, which moves at the same time, opens the passage as much as is wanted. Then we replace the driver so as to fix the CHAPTER VII. OF THE CURVES AND INCLINED PLANES. ARTICLE I. proper to the engine, that may either favor or impede its effect. We have still to examine two external circumstances that may have a similar influence on the motions. The curves offer on the railways an additional resistance, which is so much the greater according as the degree of their incurvation is more considerable. The wagons being of a square form, tend to continue their motion in a straight line. If, therefore, they are obliged to follow a curve, the flange of the wheel does no longer pass in a tangent along the rail without touching it, as it does in a direct motion. The rail, on the contrary, presents itself partially crosswise before the wheel, and opposes thus its progress, by forcing it to deviate constantly from its direction. Moreover, the wheel that follows the exterior rail of the curve has naturally more way to travel than that which follows the interior rail. Now in the wagons at present in use, the two wheels of the same pair are not independent of one another. They are fixed on the axletree that turns with them. If therefore the road travelled by one of the two wheels be less than that of the other, the latter one must necessarily be dragged along without turning on the difference of the two roads. Finally, on passing the curves, the wagons are thrown by the centrifugal force of the motion against the outward rail, the result of which is a lateral friction of the flange of the wheel against the rail, which does not exist in the direct motion. It is impossible to construct the wheels of the wagons and the railway itself in such a manner that these three additional causes of resistance may be destroyed. The mode we are going to describe, in order to obtain that effect, is that which is already known; viz., the conicalness of the tire of the wheel, and a greater elevation of the outward rail at the place of the curve. But those means have until now been employed only by approximation, and fulfil more or less imperfectly the intended purpose. By sumitting them to calculation, we trust we shall be able to deduce general rules, which will make us certain that the required effect will be cbtained. The particular resistance owing to the passage of the curves, is composed of two distinct parts, as to their causes and their effects. The first, according to what we have seen above, is occasioned by the waggons being obliged to turn along the curve, which produces an opposition of the rail to the motion, and a dragging of the wheel. The second is owing to the centrifugal force, and produces the friction of the flange of the wheel against the rail. The first of these two resistances will evidently be corrected, if we succeed in constructing the wheels of the wagon in follow such a manner that the wagon may of itself the curve of the railway. For that, it will be sufficient to make the wheel slightly conical with its greatest diameter inside; 1. Of the conical form of the Wheels and that is to say, towards the body of the wagsurplus of elevation of the Rails, calcula-on, as appears on the engine in fig. 2. ted to annul the effect of the Curves. By that disposition, when the centrifiugal We have considered the dispositions force throws the wagon on the outside of OF THE CURVES. Our intention being to produce that effect, by pushing the wagon aside on the road, the question is, how much the wagon must be laterally displaced. This point depends evidently on the degree of conicalness of the wheel. the curve, the wheel on that same side wil|| a (D-D'); this displacing will produce on the thickness in order that the centrifugal force of the of the tire expressed by. The two wheels Let D be the diameter of the first wheel, and D' that of the second, being the ratio of the circumference to the diameter, we shall have pro This difference on the diameter will be Thus the lateral motion to be produced is a e D { a ( D — D) = 2 ( r + e ) We know at present what must be the lateral displacing of the wagon, in order to destroy the first species of resistance. The question now is, to make use of the centrifugal force to produce that effect. It is its natural tendency; but it is evident mm' D, and a.. = D'. that that force must produce exactly the Now the two arcs being both terminated by necessary displacing, else the defect would the same radius, we haveby no means be corrected. The effort of this force exerting itself in the direction of the radius, its effect will be to push all the wagons out of the curve. If the two sides of the railway are of equal elevation, the wagons will be stopped in the lateral motion only by the friction of the flange of the wheel against the rail. But if we give to the outward rail a surplus of elevation above the inward one, it is clear that, in increasing sufficiently that elevation, we shall be able to master at last the centrifugal force, in such a manner as to permit it only to produce just the displacing we want. In fact, by raising in that manver the outward side, we change the railway in an inclined plane. The wagons placed on that plane ought, by virtue of their gravity, to slip towards the lower rail. On the other hand, the centrifugal force pushes them against the outward rail, which is the highest. We create, then, by that ans, a counterpoise to the centrifugal force. Let us call y the surplus of elevation given to the outward rail (fig. 30); 2e being the breadth of the way, the inclination of the plane on which the wagons are placed, is y On this plane, the gravity If we represent by r the radius of curvation, by V the velocity of the motion, and of a body, the weight of which is P, is exby m the mass of the body moved, the cen-pressed by trifugal force produced on the curve will be, as is known, expressed by V 2 f = m But P being the weight of that same body, and g the accelerating force of gravitation, we have thus 2 e D f: rte P V2 g This equation shows the difference that which is the expression of the centrifugal must exist between the diameters of the force of a body of a given weight P, movwheels, that the required effect may be ob-ing with a velocity V, on a curve the radius of curvation of which is r. tained. a e D 2 (r+e) we must endeavor to find out what is the necessary inclination. Let us then suppose the train already displaced as much as required. Let us imagine, for instance, that the train has been pushed from the position ab to the piston cd (fig. 30;) that is to say, that the point of the inside wheel that was at a be come to c, at the distance from the first point, and that at the same time, the point of the outward wheel that was at b, be come to d. In this situation, the inclination of the plane on which the train is, will tion of which must thus be added to Consequently the outward side of the wagon will be raised above the interior 2μ side of a quantity equal to y+ ; and as a y eVi gr 2 aD Let us suppose that we have to employ inclination of the tire of the wheel, e, half breadth of the way, 2.35 ft. For instance, on a line, the most abrupt curve of which has 500 ft. radius, with wagons having wheels of 3 ft. diameter, and a play of 1 in. on each side of the way. the equation shows that the least inclination one ought to give to the tire of wheel is 1⁄2 ; but a more considerable inclination will answer, a fortiori. On the Liverpool and Manchester Railway, the most abrupt curve, which is the one at the entrance of Manchester, has a radius of 858 ft. This results a conical inclination of, and this would answer in all cases; but having said that a greater inclination will fulfil the same object, we are free to adopt a greater inclination, if it suits other purposes better. It is customary to give an inclination of The motive for making it so considerable, is to prevent all possibility of the flange If we wish to construct on that railway a rubbing against the rail, either in case of a curve of 500 ft. radius, on which the wag strong side-wind, or in case of some fortuons may experience no additional resistitous defect in the level of the rails, by ance the equation will give which the wagons would be thrown on the y= 0.236 ft. or in inches, y = 2.83 in. lower rail. Having seen above that, with We must, therefore, for that curve, with an inclination of, there would be no danthat wheel and that average velocity, give ager of the flange rubbing in the curves, that surplus of elevation of 2.83 in. to the out-danger will be still more impossible with an inclination of 4. ward rail. Adopting the surplus of elevation of the rail deduced from that equation, we render it impossible, the first species of resist ance, which the passage of the curves tend to produce. However, as we only destroy that resistance by a certain lateral deviation of the wagon, it might be feared that that deviation might go so far as to make the flange of the wheel rub against the rail, in which case we would only have substituted one resistance for another. This is, therefore, the point we have still to consider. We conclude that, with wheels having that inclination, the surplus of elevation of the rail which we have determined above, will correct the first species of resistance of the curves without creating the second, and that, consequently, the train will pass over curves without any diminution of speed. the From what has been said, the surplus of We have, until now, supposed the inclielevation that must be given to the outward of the tire of the wheel to be railin the curves, is determined by the follow nation 1 a eV 2 y gr given a priori. But as it is on that incli-ing formulæ : nation that depends the degree of deviation the wagon must undergo on the rails, it the base which separates the two bearing must evidently be such that, even on the points is measured by 2ep, the final re-most abrupt curve of the line, the lateral sult is that the wagon will be in the same deviation of the wagon may never be concase as if it were placed on a plane, the in-siderable enough to bring the flange of the clination of which should be wheel in contact with the rail. If, therefore, the wagons have, for instance, y, surplus of elevation to be given to the outward rail of the curve, over the inward rail, expressed in feet and decimals of feet. Solving these formulæ in the most usual ing table which dispenses with all calculations in that respect. OF ELEVATION TO BE GIVEN TO THE OUT- SURPLUS WARD RAIL IN EFFECT OF THE CURVES, THE CURVES, IN PRACTICAL TABLE OF THE A Surplus of elevation to be given to hour, being 30 miles. €90'0 Designation of the Wagons and the Way. Radius of the curve, in feet. 10 miles. 20 miles. ft. in. in. in. 5000 0.28 0.66 Wagon with wheel ARTICLE II. . OF THE INCLINED PLANES. § 1. Of the Resistance of the Trains on Inclined Planes. Inclined planes are a great obstacle to the motion on railways. present the resistance that would be offered jare helped in passing the plane by an en- the engine, which ought also to enter for its share. On the Darlington Railway, the accli vities are much too numerous for an adIn speaking of the fuel, we shall sce that ditional engine to be placed at each of the inclined planes of the Liverpool Rail them. The load of the engine must thereway, which at first sight appear quite in-fore be limited so that it may ascend with significant, oblige, however, the engines to that load the most inclined of the planes. a surplus of work, which amounts to a The locomotive engines acquire, howsixth part of what they would have to do ever, a considerable augmentation of power, on a level. By this we see how important at the moment of their passage on an init is, in establishing a railway, to keep it clined plane, because their speed being on as perfect a level as possible. It fre-suddenly considerably reduced, the cylinquently happens that, by avoiding to level ders consume a smaller quantity of steam. a part of the road, that is to say, to cut The fire, strongly excited by the preceding through a hill, or to form an embankment rapidity of the engine, continuing to furthrough a valley, a great economy is ex-nish the same quantity of steam, a great pected. This is, however, a great mis- part of it must escape through the valve. ake, for, in most instances, the only eco- But the passage of the valve is too narrow nomy is that of the first outlay, whereas, to emit freely all that steam. Besides, the the annual augmentation of expense sur-spring that presses on the valve opposes passes by far the interest of the capital more and more resistance, in proportion as saved; so that, instead of an economy, we the steam tends to raise it higher, in order have in reality a greater expense. This to get a wider passage for itself. The conadditional expense may even, in some cases, go so far as to paralyze completely all the advantages of the undertaking. In suffering inclined planes to subsist on a line of railway, it not only becomes inpossible to lower sufficiently the freight of the goods; but, what is much more important, frequent accidents occur while descending those steep acclivities, the least As soon as the trains reach these in- inconvenience of which is to destroy puclined planes, they offer a considerable sur-blic confidence in the safety of the conplus of resistance, on account of the graveyance. It is, therefore, necessary to lay vity of the total mass that must be drawn down as a principle, that the end to be up the plane. aimed at in the construction of a railway, sequence is that the steam, not being able to escape as quickly as it is generated, suffers an increase of pressure in the boiler. This increase of pressure evidently depends on several circumstances: the size of the valve, the evaporating power of the boiler, the previous excitation of the fire, and finally the length of the lever at the extremity of which the spring-balance acts. In some engines this increase may amount to 10 lbs. per square inch, as we have remarked in speaking of the pressure. In that case, if the usual effective pressure of the engine be 50 lbs. per square inch, it may, on ascending the inclined plane, increase to 60 lbs., that is to say, in the proportion of, which is considerable. This must, therefore, be taken into account when it is required to calculate the load the engines are able to draw on these planes. But it is necessary to observe that this is effectual only when the inclined planes are not of too considerable an extent, because, in that case, the fire ceasThe loads must either be regulated so that ing to be excited in the same proportion, they may not exceed the power of the enthe surplus of effect will be reduced. The gine in going up the plane, or it is neces- weight of the engine must, besides, always sary to give the engines the help of one or give sufficient adhesion of the wheel to the more others, according to what is required. rail, as we shall explain in the following Chapter. Let us suppose a train of 100 t. drawn by an engine. Having seen that on a level the friction of the wagons produces a resistance of 8 lbs. per ton, the power required of the engine will be 800 lbs., when When, however, it has been impossible travelling on a level. But let us suppose to avoid the inclined planes, and when the the same train ascending an inclined plane use of stationary engines has been rejected at On that plain, besides the resis-on account of the interruption they untance owing to the friction of the wagons, avoidably cause in the service, there are a fresh resistance occurs, which is the gra-only two ways that can be resorted to. vity of the total mass in motion on the plane. That gravity is the force by virtue of which the train would roll back if it were not retained; and it is equal to the weight of the mass divided by the number that indicates the inclination of the plane. If, therefore, in this case, the load of 100 t. is drawn by an engine weighing 10 t., the total mass placed on the inclined plane will be 110 t. or 246,400 lbs. ; and thus its gravity on the inclined plane, at, will be 2,464 lbs. The surplus of traction required of the engine, on account of that circumstance, is, therefore, 2,464 lbs., and, as we have seen that on a level 1 t. load is represented by 8 lbs. trac- The trains that are too heavy for a single tion, we also see that those 2,464 lbs. re-engine, as are commonly those of wagons, On the Liverpool Railway, the trains of coaches never being very heavy, are seldom above the power of the engines on the which the engines are obliged to exert an most inclined parts of the line, viz. in the additional effort. That is at the moment two acclivities of and In general, of starting. We have seen, in fact, that the therefore, the engines ascend these inclined power which, when the motion is once planes without help; and during the rest of created, need only to be constantly equal the trip, on the level or descending parts of to the resistance, must, on the contrary, the line, their speed is regulated by par-surpass it at the instant that it is to put tially shutting the regulator. the mass in motion. The reason is plain : in the first place, it is only necessary to maintain the speed; in the other it must be created and maintained. It is this addi-elsewhere, or by its adhesion, as shall be This table, assimilating the trains drawn on inclined planes, to trains drawn on a level, gives the means to learn by the former The starting is, therefore, a difficult task tables, either the loads the engines will be for a locomotive engine heavily loaded. able to draw on given inclinations, or, vice However, at that moment the engine ac-versa, the inclined planes the engines will quires, as well as on the inclined planes, be able to ascend with given loads. CHAPTER VIII. OF THE ADHESION. a considerable increase of power. Here rails. § 2. Practical Table of the Resistance of the Trains on Inclined Planes. In the preceding paragraph, we have seen in what manner the resistance of the trains on the inclined planes must be calculated. The following table presents the result of that calculation in the cases which occur the most frequently on the railways. It is clear that, by the weights inscribed in the following table, it is only intended to show the resistance offered by the train, and not the weights the engines are able to draw, those weights being limited either by the power of the engine, as we have explained A PRACTICAL TABLE OF THE RESISTANCE OF THE TRAINS ON INCLINED PLAINS. Designation of the Engine. Engine weighing 8 t. Engine weighing 10 t. helping engines, the work by the adhesion of their four wheels, as has been said elsewhere. The ATLAS is the only one of the former class that differs from the othersin that respect. This engine has six wheds, four of which are of equal size, and worled by the piston. The two others, whch are smaller, and have no flange, an be raised out of contact with the rals, by the action of the steam on a moveable piston. That ingenious arrangement, which may have more than one us:ful application, in permitting the weight of an engine to be distributed upon six whels, without making the engine more embarrissing than if it had only four, is due to Mr. J. Melling, of Liverpool, who, in this instance, made use of it in order to give the engine a much larger firebox, and corsequently the power of generating a greater quantity of steam. We have remarked in describing the enWe have now expressed the adhesion, by gine, that the power of the steam being ap-giving the measure of its effects; but the plied to the wheel, the engine is in the same situation as a carriage which is made to advance by pushing at the spokes. Thus, as in that action, the only fulcrum of the moving power exists in the adhesion of the wheel to the rail, if that adhesion is not sufficient, the force of the steam will indeed make the wheels turn, but the wheels, but the wheels slipping on the rails instead of adhering to them, will revolve, and the engine will remain in the same place. power itself may be expressed in a direct manner. The load of 244 t. produced a resistance, or required a traction of 1,952 lbs.; the adhesion was thus equal at least to 1,952 lbs., else the wheel would have Now the adturned without advancing. hering weight was 5.5 t. or expressed in pounds 12,320 lbs.; we see then that the force of adhesion was equal to about of the adhering weight. Considering that en-traction of a ton on a level, this expression is every 8 lbs. force corresponds with the exactly similar to the first. The more considerable the train the gine draws, the more power it must employ, and the more resistance it must consequently find in the point on which it rests, for executing the motion. It was therefore to be feared, that with considerable trains, the engines would be unable to advance; not that the force would be wanting in the moving power itself, but in the fulcrum of the mo tion. The experiments related above, establish riments, not one is to be found where the du ring a part of the journey, that engine drew 50 199 161 170 201 251 302 402 The engine advancing with that load, the adhesion must necessarily have been sufficient. Now the weight of the and dirty, in consequence of damp weather, In winter when the rails are greasy the adhesion diminishes considerably.— However, except in very extraordinary cir to draw a load of 15 wagons, or 75 t., tencumstances, the engines are always able der included, that is to say, 14 times their adhering weight. In other words, the resis adhesion is always at least of the adhertance of 75 t. being 600 lbs., the force of ing weight. Adhesion being indispensable to the creation of a progressive motion, two conditions are necessary in order that an engine may draw a given load. 1st. That the dimen sions and proportions of the engine and its boiler enable it to produce on the piston, by means of the steam, the necessary pressure, which constitutes what is properly termed the power of the engine: and, 2nd, that the 150 239251 298 371 145 592 FURY is 8.20 t,, and that weight is divided weight of the engine be such as to give a 25 45 50 5 74 91123 75 125 135 155 194 234313 100 162 178 203 254 306408 175 279 305 348 434 521 593 sufficient adhesion to the wheel on the rail. in such a manner, that 5.5 t. are supported These two conditions of power and weight own mass. We have said that the FURY engine ad- |