174 



RAILROAD CURVES 



superelevation of the circular curve, at the P. Sj. At an? 

 intermediate point distant I stations from the P. Si, it is there- 

 fore equal to 



Angle of Deviation and Angle of Deflection. Let CA, Fig. 1, 

 be a spiral connecting the tangent RT with the circular curve 

 AB. Let P be any point on the spiral and HN a tangent to the 

 spiral at the point P. 



The angle that a tangent drawn to the spiral at any point P 

 forms with the original tangent RT is called the deviation angle 

 for the point P. It is represented by the Greek small letter 

 (called delta). 



When the point P coincides with the P. 82, the deviation 

 angle becomes LKT, which is represented by the Greek capital 

 letter A (catted delta) . 



Since LKT = A EC, it follows that A is the whole central 

 angle of the spiral, which measures the whole change in direction 

 of the track between the original tangent and the P. 82. 



The angle between the original tangent and a chord drawn 

 from the P. Si to any point of the spiral is called the deflection 

 angle to this point. It is represented by the Greek letter 

 6 (called theta). In Fig. 1, TCP is the deflection angle 

 for the point P. It is the angle that must be deflected at 

 the P. Si from the original tangent in order to locate the point 



P of the spiral. 



By using the pre- 

 ceding notation, the 

 following formulas 

 are derived: 



and = i 8-N. 

 in which the value 

 of 2V can be taken 

 from the accompanying table. Intermediate values of N may 

 be found by interpolation. Angle NPC=d 0. This is tht 

 angle that must be deflected from the direction of PC to bring 

 the line of sight tangent to the spiral at P. 



