TRANSITION CURVES FOR RAILWAYS. 591 



6.— TRANSITION CURVES FOR RAILWAYS AND 

 TRAMWAYS. 



By S. SMEATOX, B.A., C.E. 

 Plate XVII. 

 Theoreticall)' the superelevation of the outer rail on the circular 

 curves of railways and tramways ought not to be continued beyond 

 the tangent points, biit should end abruptly ; in other words, the 

 rails throughout the straight portions of the line should be level 

 transversel)'. As this would necessitate an abrupt rise of some 

 inches in the rails, obviously in practice it is impossible, and it has 

 been customary for engineers on construction to extend the super- 

 elevation along the straight to a point at some distance from the 

 tangent, reducing it from its full amount at the tangent to nil at 

 the point mentioned This "• run out," as it is termed, is on a 

 fixed grade, determined beforehand as most suitable throughout 

 the line, so that its length is directly proportional to the amount of 

 superelevation on each curve. Maintenance engineers subsequently 

 modif;y this an-angement by having the tangent point, with the 

 adjoining portions of the straight and of the curve, pulled over 

 towards the centre. This operation is of twofold advantage : first, 

 the passage of rolling-stock from the straight portion of the line to 

 the curved, and vice versa, is not so sudden, the angular change of 

 direction being more gradual; and, second, the "run out" of the 

 superelevation (which, under the first arrangement, was on the 

 straight, and therefore somewhat detrimental to safety) is now on 

 an arc, the curvature of which at any point is approximatehj pro- 

 jDortional to the superelevation. The gradual and easy passage of 

 the rolling-stock from the straight to the curved portion, and vice 

 versa, contributes largely to the comfort of travellers, and alone 

 justifies this alteration. The chief objections to this alteration of 

 the position of the line are : — First, a curve of less radius than that 

 of the original has to be introduced, in order to leave the greater 

 portion of the circular arc intact ; and, second, the operation has to 

 be performed by eye, and is necessarily somewhat inaccurate. A 

 parahola has long been recognised by engineers as the curve pre- 

 eminently suitable for railway and tramway curves; but the diffi- 

 culty attending the laying out of such in the field — not only on 

 survey, but subsequently during many repetitions on construction 

 — has been an insurmountable hindrance to its universal adoption. 

 To overcome this difficulty Froude suggested that an elastic curve, 

 of short length only, should be introduced at the junction of the 

 straight and curved portions ; and he proposed that the original 

 circular arc, except a short length at the end, should be set out in 

 the usual way, and then transferred nearer the centre by an amount 

 calculated to suit various cases, the position of the straight portions 

 of the fine remaining unaltered. It is obvious that by this transfer 

 of the arc the radius is somewhat reduced. Such a reduction is 



