Two straights, D1T1 and D2T2 in Figure 10.1, are connected by a circular curve of radius R:

(1) The straights when projected forward, meet at I: the intersection point.

(2) The angle  at I is called the angle of intersection or the deflection angle, and equals the angle T10T2 subtended at the centre of the curve 0.

(3) The angle φ at I is called the apex angle, but is little used in curve computations.

(4) The curve commences from T1 and ends at T2; these points are called the tangent points.

(5) Distances T1I and T2I are the tangent lengths and are equal to R tan/2.

(6) The length of curve T1AT2 is obtained from:

Curve length = R where  is expressed in radians, or

Curve length =  where degree of curve (D) is used

(7) Distance T1T2 is called the main chord (C),

(8) IA is called the apex distance and equals

(9) AB is the rise and equals R − OB = R − R cos /2

These equations should be deduced using a curve diagram

Circular curve

Curve designation:
Curves are designated either by their radius (R) or their degree of curvature (D◦). The degree of curvature is defined as the angle subtended at the centre of a circle by an arc of 100 m

Thus a 10◦ curve has a radius of 572.9578 m.