| Angle of deflection. | Radius, in feet. | |
|---|---|---|
| ¼° | or 15′ | 22920.0 |
| ½° | or 30′ | 11460.0 |
| ¾° | or 45′ | 7640.0 |
| 1° | or 60′ | 5730.0 |
| 1¼° | 4585.0 | |
| 1½° | 3820.0 | |
| 1¾° | 3274.0 | |
| 2° | 2865.0 | |
| 2½° | 2292.0 | |
| 3° | 1910.0 | |
| 3½° | 1637.0 | |
| 4° | 1433.0 | |
| 4½° | 1274.0 | |
| 5° | 1146.0 | |
| 5½° | 1042.0 | |
| 6° | 955.4 | |
| 6½° | 822.0 | |
| 7° | 819.0 | |
| 7½° | 764.5 | |
| 8° | 716.8 | |
| 10° | 573.7 | |
Points in any curve may also be fixed by ordinates, as a b, M D′, G F, or by E a, K M, etc.
For the details of locating, of running simple and compound curves, and of the calculations therefor, the reader is referred to the works of Trautwine, and of Henck.
Fig. 27.
59. Suppose now that we have the surveyed lines m m, and n n, fig. 27, one of which is to be finally adjusted to the ground. The shortest line is the straight one, which is generally impracticable. The most level line is the contour line, which is also impracticable. Between these two lies the right line, which is to be found by an instrumental location. The line A n n n n B, on the plan, gives the profile A n n n n B. The line A m m m m B gives the profile A m m m m B, while the finally adjusted line A 1 2 3 4 5 6 gives the profile A 1 2 3 4 5 6 B.
Fig. 28.
60. Again, in fig. 28, the straight line A n n n B gives the profile A n n n B, requiring either steep grades or a great deal of work. By fitting the line to the ground, as by the line A a b c d ... m n o B, we obtain the profile A a b c ... m n o B.