592 PROCEEniNGS OF SECTION H. 



not always desirable. Raukine. in his work on civil engineerings 

 describes the laying out of such, and of late American engineers 

 have adopted it under the name of the "cubic parabola," but with- 

 out the reduction of the radius of the circular arc mentioned above. 

 This seems not only to meet all requirements, but the formulce in 

 connection with it can be made so simple that very little extra time 

 is required for the setting out of such in the field. 



Briefly, then, what is requisite for a transition curve is that the 

 radius shall be infinite at a point on the straight to be determined 

 upon, and shall diminish proportionately with the distance from 

 that point till, at a junction effected taugentially with the original 

 curve, the radius has been reduced to that of the circular arc. On 

 such a parabolic curve, then, the super-elevation is everywhere pro- 

 portional to the curvature. The cubic parabola transition curve 

 has been used with success on railway and tramway lines in 

 America. In New South Wales it was adopted on some deviations 

 made in the Blue Mountains, and South Australia has one or two 

 on existing lines, while on new lines in the future all curves of less 

 radius than twenty chains will be set out with transition curves. 



It will be unnecessary to follow up the reasoning by which the 

 formulae for setting out such were evolved. Below will be found 

 equations of the simplest form and suitable for use in the field 



First compute, in the ordinary way, the superelevation required 

 for the circular arc 



Superelevation in ft. =: ^T^tT ^^ 



g = gauge in feet 

 V = velocity in miles per hour 

 R = radius of curve in feet. 

 Now determine the most suitable grade for the superelevation 

 to be run out on (1 in 360 is adopted in South Australia) 

 Therefore 

 Length of transition curve in feet = superelevation X 360 or 



AC (Fig. 1) _ .._ (2) 



The original circular arc is not set out, but the positions of new 

 tangent points and lines are determined thus : — 



(length in transition curve in feet)' , ^ 



Shift or H Q (F,g. 1) =^-^nMT™ii,Sri„7eit) ' (') 



(or ^ of the offset D C from the tangent for a chord equal to half 

 the transition curve and radius R). 

 Position of point G is found thus : — 



I H = (R + shift) tan. of ^ intersection angle (4) 



Set off H G = shift, at right angles. Tangent lines parallel to 

 the original ones are used for the circular arc which is begun at C. 

 To find C, A E is assumed equal to A C, H G and H A are set 

 off equal to ^ transition curve, then the offset E C = 4 times 

 H G ' (o) 



