1930] New Method for Laying Out Circular Curves ■19 



As a check in taking deflections from the table, it should be noted 

 that the 1st + 9th = 2d J- 8th == 3d-f 7th ^ 4th -f 6th = 180 

 + A = 220°00'. 



The above points on the curve are not at full stations ; but the 

 chainmen, on their way back from the P. C, can very easily set stakes 

 at full station and -(- 50 foot points as follows : the rear chainman 

 holds the -\- 51.1 division of the tape at the P. C, and aligns the front 

 chainman by sighting to the 9th point of the curve ; then a right 

 angle offset on the P. I. side of the curve, at a certain fraction (see 

 Fig. 3) of the middle ordinate for a chord of 50 feet (see Table III), 

 locates Sta. 60 (in this case the middle ordinate is 0.44 ft. and the 

 offset is less than 0.1 ft.) ; next the rear chainman holds the zero end 

 of the tape at Sta. 60 and aligns the front chainman by sighting from 

 the 9th point to the 8tli point, in order to locate Sta. 60 -f- 50 which is 

 so near the 8th point it does not have to be shifted. The other stations 

 are established in a similar manner. 



Example 2. 



Given A = 20^20' ; P. I. at Sta. 37 + 18.2. 

 T = 50.532, E ^ 4.5 (Table II). 



Suppose T = 100 = approx. desired length of tangent. 

 Eatio = 2, hence L = 200, T = 101.0, D = 10°10'. 

 P. I. = 37 + 18.2 

 T = 1 + 01.0 



P. C. = 36 + 17. 

 L = 2 



P. T. = 38 + 17.2 

 200 



:= 20. Use 40-ft. chords applied five times. 



10 



Points Deflections 



P. T. A° 



2d 21°40' 



4th 35° 13' 



6th 165°07' 



8th 178°40' 



10th P. C. 180°00' 



2d + Sth = 4th + 6th = 200°20'. Check. 



The quantities in Tables II and III are based on the definition 

 that the "degree of curve" is the central angle subtended by an arc 

 of 100 feet instead of a chord of 100 feet. The radius of a one- 

 degree curve is found by means of the following proportion : 



36000 36000 

 1° : 360° =: 100 feet : 2f;R feet, hence R = = = 5729.578 



feet. 



2(3.14159) 



