THEORY OF COMPOUND CURVES IN FIELD ENGINEERING 151 



where in the denominator the positive and negative signs in front of R z 

 stand for reversed and compound curve respectively. Now 



R 2 =l*V7+¥=-^-r ; 



sin 9 



hence the radius R 2 = P0 2 of the required branch of the compound 

 curve (internal tangency) 



» c _ T* 2 + ?V ~ 2 T 2 (R t sin 9 - T x cos 9 ) . 



2(7 1 I sin9 + 2? I cos9— 22J ' (33j 



and for the reversed curve, R 2 r = R0 3 (external tangency) 



p , ?V + 7V - 2 T 2 (2?, sin? - r, cosy) 



2(7, sin ^ + 22, cos ^ + 22, * {34) 



To find the trigonometric tangent of the angle of intersection of the 



two tangents of the second branch of the compound curve, from Fig. 5 



w R 2 C 

 it is seen that the tangent of half the supplement w, tan — = -^ , hence 



lif / w\ 

 for the angle of intersection irf = 180 — w, cot — = cot I 90 1 



w R 2 C 



= tan — = -^- , or 

 2 o 



vf T 2 — 2?, sin 9 + T t cos 9 

 C0t T = — 22, + 7\ sin9 + 2? lC os9 ' (35) 



In case of a reversed curve 



w r T 2 — 2?j sin 9 -\- T T cos 9 

 COt T = R, + 7\ sin 9 + 22, cos9 ' (3 ^ 



