**Switch Angle in Railway**

**Switch angle** or angle of switch divergence is defined as the angle formed between the gauge lines of the **stock rail** and **tongue rail**(Switch rails).

If the **switch angle** is more, the entry of the train will not be smooth and consequently, the speed of the train will have to be reduced. On the other hand, a **small switch angle** will increase the overall length of the turnout.

Hence, small **switch angles** are provided in the case of fast-moving trains. But, in the case of slow-moving trains or station yards, a greater **switch angle** is recommended.

**The switch angle** **depends on **the length of tongue rails and heel divergence, which is given below:

**Case:1 **When the thickness of tongue rails at toe = 0

**Let,**

- d = Heel divergence
- D = Length of tongue rail
- [latex] \theta [/latex] = Switch Angle

Now, from the above Fig.

[latex] \sin \theta [/latex] = (heel divergence / Length of tongue rail) = [latex] \frac{d}{D} [/latex]

**Switch Angle = [latex] \theta [/latex] = [latex] \sin ^{-1}\frac{d}{D} [/latex] **

**Case:**2 When the thickness of tongue rails at toe = t

**Let, **

- t = Thickness of tongue rail at toe
- [latex] D_{1} [/latex] = Actual length of tongue rail
- [latex] D_{2} [/latex] = Theoretical length of tongue rail
- x = Difference between [latex] D_{1} [/latex] and [latex] D_{2} [/latex]

From the above equation and fig, we can write

- Actual Length of tongue rails [latex] D_{1} [/latex]= [latex] \frac{ ( d – t ) }{ \sin \theta } [/latex]
- Theoretical Length of tongue rails [latex] D_{2} [/latex] = [latex] \frac{d}{ \sin \theta } [/latex]

Now, x = ( [latex] D_{2} [/latex] – [latex] D_{1} [/latex] ) = [latex] \frac{t}{ \sin \theta } [/latex]

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