ON A SIMPLE PLAN OF EASING RAILWAY CURVES. 



(One Plate.) 

 By Walter Shellshear, Assoc. M. Inst., C.E. 



[Bead before the Royal Society of N.8.W., June 6, 1888.'] 



Although universally admitted that it is a desirable thing to 

 ease off the junction of the straight and curved portion of railways, 

 also to ease off the junction of two reversed curves by a gradual 

 increase of curvation, yet hitherto, with few exceptions, little has 

 been done by English engineers when setting out railways, in the 

 way of putting this into practice. 



The object of this paper is to bring under attention a simple 

 plan by which this can be done, without adding materially to the 

 work of the surveyor, or overtaxing his brains with obtuse 

 formula. 



Of all curves the circle is most easily set out in the field, and 

 for this reason, no doubt, the more complicated elastic curves 

 have with few exceptions been carefully avoided. The circle 

 being the easiest curve to set out, it will no doubt continue to be 

 the one generally used, and if supplemented by a short curve of 

 adjustment where it joins the straight line, the circle leaves little 

 to be desired in the way of suitability. 



Eroude's method of easing curves, as published in Rankine's 

 " Civil Engineering," although sound in principle, is somewhat 

 tedious in application. 



The problem that is required to be solved, is to find a curve 

 which deviates from the point of zero curvature by a perfectly 

 gradual increase curvature, and to see how such a curve can be 

 applied to ordinary circular curves. 



The cubic parabola is a curve which meets our requirements, 

 as it deviates from the point of zero curvature by a perfectly 

 gradual increase of curvature, and for a small portion of the curve 

 the curvature is small, and is proportional to the distance from 

 the point of zero curvature. 



Now as the curvature in the cubic parabola deviates from the 

 point of zero curvature by a perfectly gradual increase of 

 curvature, it follows that at some point in the curve its radius of 

 curvature is equal to the radius of a circle of any particular radius, 

 and that it can therefore be so located that it will make a perfectly 

 gradual curve of transition from the straight line to the circle. 



