172 RAILROAD CURVES 



correct. When the curve is finished, the transit is ^c up at 

 the P. T., and the bearing of the forward tangent taken, which 

 affords an additional check upon the previous calculations. 

 The magnetic bearing is recorded in the fourth column, and the 

 deduced, or calculated, bearing is recorded in the fifth column. 



SUPERELEVATION OF OUTER RAIL 



The difference between the elevation of the outer rail and 

 that of the inner rail of a circular track is called the supereleva- 

 tion of the outer rail. If the degree of curve is denoted by D 

 and the velocity, in miles per hour, by V, then the supereleva- 

 tion e, in feet, is e = .000058 DV 2 



The accompanying table gives the values of e, corresponding 

 to all values of D and V, that are likely to be required in 

 practice. This table is computed from a more accurate for- 

 mula than the one just given. The formula given is, however, 

 sufficiently exact and may be used if no tables are at hand. 



TRANSITION SPIRAL 



DEFINITIONS, PRINCIPLES, AND FORMULAS 



Transition curves are introduced for the purpose of connecting 

 a tangent with a circular curve in such a manner that the 

 change of direction and elevation from one to the other takes 

 place gradually. A transition spiral is a transition curve in 

 which the degree of curve at any point increases directly as the 

 distance of this point, measured along the curve, from the 

 tangent. The degree of curve is zero at the tangent, and, at 

 the point at which the spiral meets the circular curve, it is 

 equal to the degree of the circular curve. 



The point at which the transition spiral joins the tangent is 

 called the point of spiral, and it is denoted by P. Si. The point 

 at which the transition spiral joins the circular curve is called 

 the second point of spiral; this point is denoted by P. 82. 



The unit degree of curve of spiral is the degree ot curve of the 

 spiral at a point 100 ft., or one station, from the point of spiral; 

 it is equal to. the degree of curve of the simple circular curve 

 divided by the total length of the spiral, measured in stations 



