148 BROOMALL : 



This curve, wliich satisfies the condition that the radius 

 decreases and the superelevation increases in proportion to the 

 length, is one in which the centrifugal force is always bal- 

 anced by the inward pull of gravitation. In other words, the 

 rails suflTer no side pressure from the wheels. 



To find the value of k, consider equation (3). There 

 obtains for any point on the transition 



kl = 

 At B this gives 



From which 



(6) 



1. Re 



and therefore the equation of the transition curve becomes 



y = _!^ (7) 



6 l.R.. 



In order to make practical use of such a curve it is neces- 

 sarj' to establish certain of its characteristics, as follows: — 



(A) From equation (7) it is seen that the offsets from 

 the tangent increase as the cube of the distance along the 

 curve. 



(B) From equation (4) it is evident that the sine of the 



/dv \ 



angle I — 1 between the tangent to the curve and the ori- 

 ginal tangent increases as the square of the distance along the 

 curve. Since this angle is always small, its sine may be 

 taken as approximately ecjual to the arc, so that the second 

 characteristic may be stated as follows : That the angle 



