How to layout circular curve with ordinates method

In this construction video tutorial, S.L. Khan, the eminent civil engineer, has briefly explained the ordinates method (ordinates from chord of curve) that is very useful to lay out horizontal curve whether it is a circular road curve or railway curve.

The method can also be applied if a building contains a horizontal curve.

To obtain ordinates from chord, the following formula is used :-

O1 = √(𝑅^2−𝑥^2 ) − √(𝑅^2−𝑎^2 )

Here,
O denotes Req offset.
R denotes Radius of the curve.
x denotes interval or distance b/w mid offset and required offset.

Suppose a road is going to be deflected with some angle known as deflection angle. Now, it is required to lay out a horizontal curve among the two lines called as tangent lines. To start with, you have to find out the start point and end point of the curve as PC and TP. PC stands for the front of the curve and TP for tangent point. The two points are situated if the tangent length of the curve is defined.

The tangent length is computed with the following formula :-

Tangent Length (T.L.) = R(tanØ/2),

Here, R denotes radius of the curve and Ø denotes deflection or central angle.

To get the complete details, watch the following video tutorial.

Video Source: SL Khan