176 RAILROAD CURVES 



The distance CR, measured along the original tangent from 

 the P. Si to the foot of the perpendicular PR, is represented by x. 

 This distance is somewhat shorter than the distance CP meas- 

 ured along the curve: the difference in length between CR and 

 CP is called the * correction, and is given by the formula 

 x correction = .000762 a 2 / 5 



This formula gives the quantity to be subtracted from CP, 

 expressed in feet, to obtain the length CR, in feet. 



EXAMPLE. Find the values of PR and CR to a point of the 

 spiral 310 ft. from the P. Si in the preceding example. 



SOLUTION. In this example, a = 2, and 1 = 3.1, and from the 

 table, using interpolation, M = ,003+|(.010- .003) = .004. 



Substituting these values, 



y = .291X2X3.13-23X.004 = 17.31 ft. 



Substituting known values in the formula for the x cor., 

 x cor. = .000762X22X3. is = .9 ft. 



The distance / = 310 ft.; therefore, the distance C7? = 310 .9 

 = 309. 1ft. 



The Spiral Offset and t Correction. Let the circular curve 

 BA, Fig. 2, be produced backwards until at a point E it 

 becomes parallel to the original tangent that is, until the 

 tangent H IV to the circular curve becomes parallel to R'T. 



The point E at which a spiraled circular curve, if produced 

 backwards, becomes parallel to the original tangent is called 

 the point of curve, and is denoted by P. C. 



The offset EV from the point of curve to the original tangent 

 is called the spiral offset. It is represented by F, and its value, 

 in feet, is given by the formula 



F = . 072709 aZ.3 



If M' , Fig. 2, is the middle point of the spiral that is. 

 a point half way between the P. Si and the P. 82 it will 

 always be found that the spiral offset cuts the spiral at a poin 

 M that is a very short distance to the left of M'. The di 

 tance CV will therefore always be slightly less than the 

 distance CM'. The difference between the half length of 

 spiral, CM' , and the distance CV from the P. Si to the foot 

 of the spiral offset is called the / correction; it is denoted by 

 t, and its value, in feet, is given by the formula 

 * = . 000127 a'L' 



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