58. Let A X B, fig. 26, represent the angle formed by any two tangents which it is required to connect by a circular curve. It is plain that knowing the angle of deflection of the lines A X, B X, we obtain also the angles A C X, X C B. The manner of laying these curves upon the ground is by placing an angular instrument at any point of the curve, as at A, and laying off the partial angles E A a, E A M, E A G, etc., which combined with the corresponding distances A a, a M, M G, fix points in the curve.
These small chords are generally assumed at one hundred feet, except in curves of small radius (five hundred feet) when they are taken less.
The only calculation necessary in laying out curves, is, knowing the partial deflection to find the corresponding chord, or knowing the chord, to get the partial angle.
As the radius of that curve of which the angle of deflection is 1° is 5730 feet, the degree of curvature for any other radius is easily found. Thus the radius 2865 has a degree of curvature per one hundred feet of
5730
2865 = 2°;
again,
5730
2000 = 2°.86 or 2° 51.6.
The radius corresponding to any angle is found by reversing the operation. If the angle is 3° 30′, or 210′, we have
5730 × 60
210 = 1637 feet radius.
The following figures show the angle of deflection for chords one hundred feet long, corresponding to different radii:—