178 



RAILROAD CURVES 



P. Si to the foot of the spiral offset. Consequently, the spiral 

 offset and the spiral very nearly bisect each other; the point 

 M at which the spiral cuts the offset is almost exactly half 

 way between the P. C. and the original tangent. 



Tangent Distance. The tangent distance of a transition 

 spiral is the distance of the P. Si from the point of intersection 

 of the tangents at the points of spirals. When the lengths 

 of the two spirals are equal (Fig. 3), 



TC = f length of spiral - 1 cor. + (R + F) tan $7 

 in which R is the radius of the circular curve and F the spiral 

 offset EV. 



FIG. 4 



When the lengths of the spirals are unequal (Fig. 4), the 

 tangent distance of the shorter spiral is 



rC- i length of spiral-/ cor. + (/?+F) tan * 7+^^ 



sm 7 



and the tangent distance of the longer spiral is 

 TC= | length of spiral -t cor. + (R+F) tan J I-(F'-F) cot 7 

 F' and F denote, respectively, the spiral offsets of the longer 

 and shorter spirals. 



