10.1 CIRCULAR CURVES

Two straights, D ₁ T ₁ and D ₂ T ₂ 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 T ₁0 T ₂ subtended at the centre of the curve 0.

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

4. The curve commences from T ₁ and ends at T ₂; these points are called the tangent points.

5. Distances T ₁ I and T ₂ I are the tangent lengths and are equal to R tan ?/2.

6. The length of curve T ₁ AT ₂ is obtained from:

   Curve length = R ? where ? is expressed in radians, or

   
   

7. Distance T ₁ T ₂ is called the main chord ( C), and from Figure 10.1:

   
   

8. IA is called the apex distance and equals

   
   

9. AB is the rise and equals R ? OB = R - R cos ?/2

   
   

Figure 10.1: Circular curve

These equations should be deduced using a curve diagram (Figure 10.1).