**Angle of Crossing in Railway**

The angle which is formed between the gauge faces of the Vee is known as the **crossing angle** or **angle of the railway crossing**. Following are the three methods used to determine the **angle of crossing** in railway.

### 1. Right Angle or Cole’s Method

In this method, a right angle triangle is used to determine the angle of crossing.

**Notation: **

- [latex] \alpha [/latex]= Angle of Crossing
- N = Crossing Number

From this Figure, we can write

[latex] \tan \alpha = \frac{1}{N} [/latex]

Or, [latex] \cot \alpha = N [/latex] …………(1.a)

Or, [latex] N = \cot \alpha [/latex] …………(1.b)

Equation (1.a) shows the angle of crossing.

Equation (1.b) shows the number of crossings.

**Note:** This is the standard method mostly adopted by the Indian Railways.

### 2. Centre Line Method

In this method, the measurement is taken along a line bisecting the crossing angle as shown in Fig.

Now,

[latex] \tan \frac{\alpha}{2} = \frac{\frac{1}{2}}{N} = \frac{1}{2N} [/latex]

Or, [latex] \cot \frac{\alpha}{2} = 2N [/latex] …………..(2.a)

Or, [latex] N = \frac{1}{2}.\cot \frac{\alpha}{2} [/latex] ……….(2.b)

Equation (2.a) shows the angle of crossing.

Equation (2.b) shows the number of crossings.

**Note:** This method is adopted in some countries like U.K. and U.S.A.

### 3. Isosceles Triangle Method

In this case, the measurement is taken along one side of the isosceles triangle as shown in fig.

Then,

[latex] \sin \frac{\alpha}{2} = \frac{\frac{1}{2}}{N} = \frac{1}{2N} [/latex]

Or, [latex] cosec \frac{\alpha}{2} = 2N [/latex] …………..(3.a)

Or, [latex] N = \frac{1}{2}. cosec \frac{\alpha}{2} [/latex] ……….(3.b)

Equation (3.a) shows the angle of crossing.

Equation (3.b) shows the number of crossings.

**Note:** This method is implemented in the case of tramway layout.

More the angle of crossing lesser will be permissible speed and vice versa

**Permissible Speed on Different Crossing**

Crossing | Different Gauge | ||

B.G | M.G | N.G | |

1 in 8.5 | 16 km/h | 16 km/h | 16 km/h |

1 in 12 | 24 km/h | 22.5 km/h | 16 km/h |

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