RAILROAD CURVES 16V 



thus determined will be Station 9. Next the chord BF is 

 prolonged 100 ft. to D; BF is only 75 ft., DG is computed from 

 the preceding formula; thus, do = 3.49 (1+^fe) = 6.11. This 

 distance is measured at right angles to BD; the point G thus 

 determined will be Station 10. The point H, which is Station 

 11, and the P. T. of the curve, is determined in the same. 

 manner, except that, as the chords FG and GH are each 100 

 ft. long, the regular chord deflection of 6.98 ft. is used for 

 EH. A stake is driven at each station thus located. Although 

 a chord deflection is not at right angles to the chord theoreti- 

 cally, yet the deflection is so small, as compared with the 

 length of the chord, that for curves of ordinary degree it is 

 usually measured at right angles. 



Middle Ordinate. The middle ordinate of a chord is the 

 ordinate to the curve at the middle point of the chord. The 

 following formulas give the relation between the length of the 

 chord c, the radius of the curve R, and the middle ordinate m. 



To Determine Degree of Curve From Middle Ordinate. It is 



sometimes necessary to determine the radius or the degree of a 

 curve in an existing track when no transit is available. By meas- 

 uring the middle ordinate of any convenient chord, the degree of 

 the curve can be calculated from the relative values of the ordi- 

 nate and chord. As the track is likely not to be in perfect aline- 

 ment, it is well to measure the middle ordinate of different chords 

 in different parts of the curve; as, also, the middle ordinate of a 

 chord measured to the inner rail will somewhat exceed the middle 

 ordinate of the same chord measured to the outer rail, the ordi- 

 nate of each chord should be measured to both rails and the 

 average of the two taken as the value of the ordinate. Having 

 measured the middle ordinate of one or more chords, the 

 degree of curve D c can be found by the formula 

 45.840m 



