THE INSTITUTION OF CIVIL ENGINEERS. SESSION 1882-83.-PART IV. SECT.1.-MINUTES OF PROCEEDINGS. 24 April, 1883. JAMES BRUNLEES, F.R.S.E., President, in the Chair. (Paper No. 1830.) “Resistance an Railway Curves as an Element of Danger.” By JOENMACKENZIE, Assoc. M. Inst. C.E. THE friction caused bythe unequal and indirect action of the wheels of a locomotive engine or carriage on curvedrails is a source of additional tractional resistance,l andalso of a considerable amount of danger: from the tendency of the wheels to run off the rails ; and it is entirely with regardto this danger that thesubject is treated in this Paper.3 On looking over the Board of Trade Returnsof Railway Accidents for several years, it will be found, in most of the cases in which enginesleft therails without a tolerably obvious cause, that the engineswere six-wheeled with parallel axles, and in some cases were running at low speeds; indeed in one case the speed was so low that the centrifugal force was more than balanced by the cant of the rails, so that some other agency than centrifugal force was evidently at work. The tendency which a wheel has to mount the railon a curve is evidently caused by the adhesion or friction between the rail and the flangeof the wheel, and thisadhesion will bear some proportion to the side pressure with which the flange is forced against the rail. In the case of the wheel most likely to mountthe rail, namely the outer leading wheel, this side pressure, at low speeds, * Minutes of Proceedings Inst. C.E., vols. xviii., p. 51 ; xxiii., p. 406 : xxvi., p. 310; xxxi., p. 358; lxiii., p. 888. Transactions of the American Society of Civil Engineers, vol. vii., p. 78. 2 ‘‘ The Builder,” vol. xxxv., p. 334. a Appendix I. [THE INST. C.E. VOL. LXXIV.] B Downloaded by [ University College London] on [21/09/16]. Copyright © ICE Publishing, all rights reserved. 2 MACKENZIEONRESISTANCE ONRAILWAY CURVES. p1inutes Of is principally caused by the resistancewhich the treads of the wheels oppose to the sliding motion which takes place in running round a curve. Taking the case of an engine with six cylindrical wheels1 on three parallel axles, all coupled? the middle or driving axle being midway between the other two:-when such an engine is running on acurve, and the clearance is the least possible, so that the flanges of the wheels just fill the space between the rails, then the driving axle is radial, the wheels on the leading axle tend to run outwards, and those on the trailing axle to run inwards. Fig. 1 represents such an engine or carriage as seen from below, showing in section the parts of the flanges which project under the level of the top of the rails. The flange of the outer leadingwheel is pressed hard against the rail. The flange of the inner driving wheel is parallel to the rail, and has of itself no tendency to press against it, but is kept close RG. 1. to it by the trailing wheels : %he outer trailing wheel, although the flange is kept close to the rail by the outer leading and inner driving wheels, has a tendency to leave the rail; and' the inner trailing wheel, notwithstanding the tendency to run against the rail, has the flange kept clear of it by the outer leading and inner driving wheels. If now the flange were removed from the outer leading wheel, the engine would run straight forwards, and (if the flanges of the other wheels allowed it to run so far) this wheel, in making one revolution, would run from A to B; but it is compelled by the flange to move in the direction of the line A C, B tangent to the curve at A, so that it slides sidewaysthrough a distance equalto B C. Appendix 11. Downloaded by [ University College London] on [21/09/16]. Copyright © ICE Publishing, all rights reserved. Proceedings.] MACKENZIE ON RESISTANCE ON RAILWAY CURVES. 3 If this wheel were loose on the axle, it would, in making a revo- lution, run along the rail to F ; but the inner wheel, in making a revolution, would run forwards from H to K, the centre line of the axle being E G ; so that, if both wheels are keyed on the axle,either the outer wheel must slide forwards or theinner wheel backwards. Assuming thatthe engine is exerting no tractive force, and that both wheels revolve at the speed due to the inner wheel,' then the outer wheel will slide forwards from F to G. Take A L equal to B C, and L M equal to F G, the diagonal A M is the distancewhich the outer wheel slides in making one revolution. In the same way may be found the distance which each of the other wheels slides, as indicated by the short black arrows, all of FIG. 2. , them moving approxluately in circles about the point P, where the inner driving wheeltouches the rail, so that the sliding of the wheels is similar to that which would take place if the engine, without moving forwards, were made to revolve about the point P. When the coning of the wheelsexactly suits the curve, the leading wheels, and in this case the trailing wheels, do not slide along but only across the rails ; but the sliding of the driving wheels is increased if the wheels are coned, unless indeed they are coned in the opposite direction to theothers. When the clearance between the rails and the flanges of the wheels is increased to just a sufficient extent to allow the inner Appendices 11. and 111. B2 Downloaded by [ University College London] on [21/09/16]. Copyright © ICE Publishing, all rights reserved. 4 MACKENZIE ON RESISTANCE ON RAILWAYCURVES. [Minutes Of trailing-wheel flange to run against the rail (Fig. 2), then the driving axle is not radial, but has the innerend slightly inadvance of a radial line, and the trailing axle has the inner end slightly behind a radial line, and the sliding motions of the wheels take place round a pointP, situated between the driving and the trailing wheels. In this case the sliding of the trailing, as well as of the driving, wheels is increasedif the treads of the wheels are conical. Whenthe clearance is increased, or the radius of thecurve increased, to a still further extent sufficient to allow the inner trailing wheel to run with the flange just clear of the rail (Fig. 3), FIG3. then the position which the engine takes up on the rails depends somewhat upon the comparative loads on the wheels. The driving wheels, in following the leadingwheels, have a tendency to assume a position with their axis radial;’ but the trailing wheels have the sametendency, and it is impossible that both axles can be radial. If one pair of wheels is much more heavily loaded than the other, the more heavily loaded pair will run with the axis radial; but the tendency of the trailing wheels to run forwards is increased by the tendency of all the inner wheels to outrun the Appendix 11. Downloaded by [ University College London] on [21/09/16]. Copyright © ICE Publishing, all rights reserved. Prooeedings.] MACKENZIE ON RESISTANCE ON RAILWAY cmvEs. 5 outer ones,l so probably the trailing axle is generally radial, and the sliding motions of the wheels take place round a point P, situated where the innerwheel touches the rail. In order to cause these sliding motions, the outer leading-wheel flange exerts against the rail a pressure sufficient to overcome the adhesion or frictionof the treadsof the wheels ; this pressure being exerteddirectly on the leading wheels, andtransmitted to the other wheels through the medium of the engine-framing acting as a lever with itsfulcrum at P. The resistance which a wheel opposes to sliding across the rail probably does not differ much from its adhesion for traction ; and the pressure exerted by the leading-wheel flange to overcome this resistance or adhesion will, for each wheel, be approximately equal to the adhesion of that wheel multiplied by its distance from the wheel which acts as fulcrum, and divided by the distance of the leading axle from the axle on which is the wheel acting as fulcrum. These pressures being taken for each wheel, the sum of them will be the total sidepressure on the outer leading-wheel flange. When the flange of the outer leading wheel is on the point of mounting the rail, the tread, being relievedof pressure and adhesion, need not be taken into account in estimating the pressure on the %ange. The distanceswhich the severalwheels slide varywith the sharpness of the curve, but the adhesion remains constant ; so that although the energy expended in causing the wheels to slide while the engine runs a certain distance along the rails increases with the sharpness of the curve, the pressure in the line of the axle required to effect this sliding is nearly constant, whatever may be the radius of the curve. The pressure exerted by the flange on the rail is, however, slightly greater than that in the line of the axle,as thatline is not at right anglesto the rails, andthis pressure increases as the secant of the angle at which the wheel stands on the rails. As this angle cannever in practice exceed 2" 30', and the secant of 2" 30' does not exceed the radius by one- thousandth part of its length, the additional pressure arising from increasing sharpness of curve may be neglected.