The formula for length of the tangent of a simple curve having angle of deflection θ and radius of curvature R, is equal to:

Explanation:

For Simple Circular Curve

Tangent Length (TL) = (BT1) = \(R \times tan\frac{\theta }{2}\)

Additional Information

For Combined Curve (Cubic Parabola)

Tangent Length (TL) = (BT1 + BT2) = \(\left( {R + S} \right) \times tan\frac{\theta }{2} + \frac{L}{2}\)

 For Combined Curve (Clothoid / True Spiral)

Tangent Length (TL) = (BT1 + BT2) = \(\left( {R + S} \right) \times tan\frac{\theta }{2} + \frac{L}{2} \times \left( {1\;-\frac{S}{{5R}}\;} \right)\)

For Compound Curve (Circular Curve of different radii)

Tangent Length (TL) = (BT1 + BT2) = \(\left( {{\rm{DE}} \times \frac{{\sin {\phi _2}}}{{\sin \phi }} + {{\rm{R}}_1} \times \tan \frac{{{\phi _1}}}{2}} \right) + \left( {{\rm{DE}} \times \frac{{\sin {\phi _1}}}{{\sin \phi }} + {{\rm{R}}_1} \times \tan \frac{{{\phi _2}}}{2}} \right)\)