1842.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



263 



MR. VIGNOLKS' LECTURES ON CIVIL ENGINEERING, AT THE 

 LONDON UNIVERSITY COLLEGE. 



LECTURE Vtl. — ON CVEVES OF EAILWAYS. 



This leclurevas devoted (o the consideration of curves upon railways, and 

 Mr. Vignolcs pointed out the principles on which should be compared the 

 economy and ailvania<;es to 1* obtained by the adoption of curves, with the 

 inconveniences attending on them; the saving of expense in form-aion, 

 eanh'.vork, bridging. S;c.. by curving round natural obstacles; the advantages 

 of attaining a more level line, av( iding interference with valuable property, 

 or approa-hing towns, mineral or manufacturing establishments, &c., all 

 entering into the former — the practical inconveniences of additional resistance^ 

 tn motion and retardation of velocily to ensure safety being the set-off; 

 and. among other elements, it was stated that the breadth or gauge of the 

 railway affected the calculation. The Proiesscrthen showed that along very 

 wide valleys, through champaign countries, and where the grounds undu- 

 lated, so that the ridges, dividing the water courses, were successively crossed 

 by the railways at right angles to their general direction, the saving by 

 lateral deviation would seldom be material, and consequently, that the curves 

 may be laid out so flat as to be pracically equivalent to straif.ht lines — the 

 " acciti£?ts dc terrain,'^ to tise a French phrase, being, in such districts, to be 

 overcome by cutting and filling, to the extent justified by the importance of 

 the line and traffic, or by the introduction of undjlating gradients, some- 

 what approximating to the natural surface of the country. But in iracir.g a 

 line of railway along the sides of hills boundiog narrow valleys, particularly 

 where the main valley is broken by lateral rivers, then the economy from 

 curving becomes very ^reat, and the introduction of curves to the greatest 

 possible extent, cons stmt with safety, is allowable. 



Mr. Vignoles then went on to consider the various means employed to 

 obviate the practical inconveniences arising from curves on railways. He 

 begcn by explaining the pecidiar distinction in make between carriage-wheels 

 and a.xles constructed for running on railways and those for common roads 

 — in the former the wheel being keyed fast to the axle, and both moving 

 round together— in the latter the axle being fixed to the carriage, the wheels 

 only moving round. Many aittmpis bad been made by engineers to give the 

 railway vehicle the advantage which the road carriage 1 ad of turning with 

 facility and safety round sharp ben 's. hut in vain, as the wheels always got 

 of!' the rails laterally, at even moderate velocities; it was only on the old 

 tramroads that the wheels were loose on the axles. Railway wheels being 

 thus fixed to the axles have the tendency to move on a straight line, so that 

 on the occurrence of a curve the ellort to continue in motion in the direction 

 of the tangent of that curve creates a certain degree of resistance, as the 

 wheels are only kept upon the rai's by the flanges pressing against the inside 

 edge of the cuter rail of the curve. The Professor then entered into a 

 number of technical details, which he illustrated to the class by diagrams, 

 explaining why the llarge of ihe wheel had now, by common consent, been 

 placed on the inner side of the periphery of the wheel rather than on the 

 outer side ; and also the reason for allowing a certain amount of jday, being 

 the diilerence between the gauge of the rai!s and llie gauge of the wheels, 

 and the manner and cause why the rim of the railway wheel is male some- 

 what conical — that is. tlie wheel, instead of being quite cylindrical, is really 

 Ihe fr«s;rum of a cone — stating at the same time, the rule for giving the 

 proper "cone" to the wheel, being dependent on the minimum radius of 

 curvature on the line to be travelled over, and the maj:iniim velocity. In 

 general, the " cone" was stated to be about one-seventh of the breadth of 

 the lim of the line, giving about one inch for the difierenre of diameter of 

 the wheels at their inner and outer edge, for, when carnages are passing 

 round a curve, the wheel and axle, being connected, roll together as a rigid 

 body, and require the contrivance of the " play and ihe cone "' to prevent 

 too much lateral friction of the flange, and to get the wheel round the curve 

 without dr.-.gging. Mr. Vignoles then showed that on the ordinary railway 

 gauge of 4 ft. 81 in., and in the 3-feet wheels, the above amount of cone ai.d 

 play wou'd be sufficient to meet a curve of only iOO yards radius, which is 

 greater than ar.y which ought to be laid down on a travelling line for high 

 speeds. 



The centrifugal force due to the velocity of the carriage was next to be 

 considered. As Icfore stated, its tendency in moving round a curve is to 

 keep a tangential course ; this force may be accurately computed (being de- 

 pendent on the Velocity of motion, weight of the carriage, and the radius of 

 curvature) by well-known formula, whence is deduced the fractional part cf 

 the weight of the carriage, representinp the centrifugal force. The Professor 

 gave the formula, and worked it out on a supposed velocity of something 

 more than IT miles per hour, or about 25fj ft. per second, on a curve o: 200 

 yards radius, whence the centrifugal force was found to be l-30ih of the 

 weight of the carriage. Mr. Vignoles quoted the following niles— viz., 

 " muhiiMy the square of the velocity in feet per second by the gauge of the 

 railway, and divide the product by the accelerating force of gravity, multi- 



plied by the radius of curvature in feet," which gave an expression, which, 

 though not the fraction of the weight, was what would do very well for 

 practical and ordinary purposes ; it was the height which the outer rail of 

 the way should be elevated, to counteract the centrifugal force, and prevent 

 the wheel flying off at a tangent to the curve. He then stated M. de Pam- 

 bour's more strictly mathematical, bnt more complicated, rule for obtaining 

 the same amount of elevation of the outer rail, and showed the table of results 

 calculated by that engineer and by Mr. M'ood. of which we only give the 

 extremes, by which it appears that, supposing it safe to encounter so sharp a 

 curve as one of 250 ft. radius, at the rate of 30 miles an hour, the outer rail 

 of the way must be eleva'ed 12 in. ; but for a radius of 5000 ft., or nearly a 

 mile, at the rate of 10 miles per hotir, the requisite elevatii.n is rnly l-16th 

 of an inch. Having elevated the outer rail, the axle of the carriage, resting 

 on the two rails, gets such an inclination as will produce on the load a gra- 

 vitating force inwards equal to the centrifugal force outwards; and there 

 will neither be any tendency in the carriages to upset or to press the flanges 

 of the wheels against the rails. The rails once laid, if the carriages run 

 slower than the calculated rate, the centrifugal force is overbalanced by 

 gravitation, and the flanges of the wheel press the inside rails; if quicker, 

 Ihe contrary effect takes place, and the flanges press against the outer rails, 

 so that some medium rate of travelling must be fixed on; and, as the slow 

 trains are in general most heavily laden, any increase of friction has a more 

 powerful effect of retardation than will occur to lighter loads moving at 

 greater speed. Mr. Wood, therefore, advises that the outer rail should not 

 be eLvated more than will compensate the centrifugal force produced at the 

 slower rates of motion with heavy trains. Mr. Vignoles then forcibly illus- 

 trated Ihe practical effects of neglecting these rules. 



He then entered on the subject of laying out curves on the ground, by a 

 succession of set-offs at the end of each length of any given measure — the 

 set-oft' being calculated from the r.adius of curvature, considering the given 

 measure (say a chain length) as the side of a circumscribing polygon ; and, 

 oil the large scale, and ]'ractically. a number of these sides of a polygon 

 become the segment of a circle. Mr. Vigno'es gave a simple approximate 

 rule for finding the sct-ofl' from the radius, or the reverse, by " divide the 

 number 792 (the number of inches in a chain) by the radius in chains — the 

 quotient is the set-off per ch.in in inches.' Thus, the set-off per chain for 

 a curve of a mile radius is 9.9. or, in round numbers, 10 inches. M"hen the 

 curve is of less than one mi'e radius, it is advisable to make the sets-off by 

 half-chains. It was observed incidentally by the Professor, from the same 

 rule, the set-off due to the curvature of the earth was in round numbers, about 

 eight inches per mile, and hence had arisen formerly some curious engineering 

 mistakes, from supposing that a horizontal line was a tangent to the earth's 

 surface ; and, in setting oul canals, an inclination of eight inches per mile 

 had .more than once been given to the water line, wliile it was imagined it 

 had been laid out for a dead level. In conclusion, Mr. Vignoles mentioned 

 that some further observations on curves would occupy the next lecture. 



LECT.KE VIll. — ON CL'KVES. 



I.N- continu .lion of the subject of curves, Mr. Vignoles explained that in 

 many cases it was impracticable or inconvenient to apply, on particular 

 ground, the approximate rule given in the last lecture, of setting out curves 

 chain by chain, or other short lengths, making each the side of a regular 

 polygon, the set-off being constant. In that method the given length was 

 strictly a secant, and not a tangent, to the curve. Another formula was 

 mnre generally applicable, and sharp curves on hill sides, tlirough thick 

 woods, had been quickly and accurately set on therefrom. It was this; 



offsell = radius — (radius — tangent)- ; the demonstration of this was given, 

 and illustrated by a diagram. For the field, tables calculated beforehand, 

 for Ihe greatest number of usual curves, should be prepared ; but. on the 

 occurrence of any peculiarcases, the calculation could be very readily made, 

 with the help of a pocket table of natural sines. The Professor then reca- 

 pitulated St me of the leading points that had been gone over in detail at the 

 last lecture, observing that on the three principal expedients for counteracting 

 the injurious eflecis of curves, the usual mcasun-ments might be easily 

 remembered— viz., half an inch for the " cone '' of the tread of the wheel ; 

 one inch as a maximum amount of " play " of the wheels between the rails (it 

 being disadvantageous to allow too much play) ; and one inch for the 

 extreme elevation of the outer rail in laying the way, that being the measure 

 due to a velocity of 2-5 miles an hour, on a curve of half mile radius. Mr. 

 Vignoles then observed that the "cone" being given to the wheels, on 

 account of the curves, when the line of road was perfectly straight, this 

 conical formation of the tuyere was not required, and the general disadvantage 

 of such a fo.'-m of wheel, not bearing upon the whole face or upper button of 

 Ihe rail, preponderated. It had, therefore, become customary to incline the 

 rail, to meet ihe cone of the wheel, and this should always be done, both 

 on straight lines and on curves whose radii are not small. This inclination 

 of the surface of Ihe rail is obtained by casting the receiving chair accord- 

 ing'y on rails ; having a continuous bearing on longitudinal sleepers, or 



