230 RAILROAD LOCATION 



1.1602X5.5 = 6.3811 ft. The elevation of grade at Sta. 44 

 +25, the P. C. of the 9 curve, is 142.90095; hence, the eleva- 

 tion of grade at the P. T., at Sta. 49+75, is 142.90095+6.3811 

 = 149.28205 ft., which is recorded on the profile together with 

 the grade, + 1.1602. The end of the line is at Sta. 53, giving a 

 tangent of 225 ft. = 2.25 sta. The rise on this tangent is 

 1.4302X2.25 = 3.21795 ft., which is added to 149.28205, the 

 elevation of the P. T. at Sta. 49+75. The sum, 152.5 ft., is the 

 elevation of grade at Sta. 52. 



The sum of the partial grades should equal the total rise 

 between the extremities of the grade line. The points where 

 the changes of grade occur are marked on the profile with small 

 circles, which are connected by fine lines representing the 

 grade line. These points of change are projected on a hori- 

 zontal line at the bottom of the profile. The portions of this 

 line that represent curves are dotted, and the portions that 

 represent tangents are drawn full. The P. C. and P. T. of each 

 curve are marked with small circles on this horizontal line, and 

 are lettered as shqwn in the diagram. 



Where the grades are light and the curves have large radii, 

 there will be no need of compensation for curvature. Where 

 the grades exceed .5 % and the curves 5, compensation should 

 be made. 



VERTICAL CURVES 



If the grade of the center line of track changes at any point, 

 the two grade lines that intersect at this point form with each 

 other an angle more or less abrupt. 

 If this angle points upwards, it is 

 called a spur; if it points down- 

 wards, it is called a sag. 



The angles CVD in Fig. 1 (a) 

 and (6) are spurs; the angles CVD 

 in Fig. 2 (a) and (b) are sags. 

 Vertical Curve at a Spur. If A V and BV, Fig. 3. are two 

 grade lines meeting at V, a vertical curve CM D must be intro- 

 duced to join these lines. Between C and D, the actual grade 

 is established along the vertical curve CMD, instead of along 



