How to Find Crossing Angle in Railway – Mathematical Problem & Solution

Find the Crossing Angle – Problem & Solution

Mathematical Problem:

Find the crossing angle of 1 in  8\frac{1}{2} crossing by using all the three methods(Right angle, centre line and isosceles triangle method):

Use Dot Product to Find the Angle b...
Use Dot Product to Find the Angle between Two vectors

Solution:

1. By using right angle method

We know,  \cot \alpha = N = 8.5 [N =  8\frac{1}{2} = 8.5]

So, Angle of Crossing =  \alpha = 6^{\circ} {42}' {35}''

2. By using centre line method

We know,

 \cot \frac{\alpha }{2} = 2N = 2 \times 8.5 = 17

So, Angle of Crossing =  \alpha = 6^{\circ} {43}' {59}''

3. By using Isosceles triangle method

We know,

Or,  \alpha = 6^{\circ} {44}' {41}''

Read More:

Angle of Railway Crossing Methods