# Switch Angle in Railway

22nd December 2019

## 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 trains 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 case of fast-moving trains. But, in case of slow-moving train or station yards, greater switch angle is recommended.

Switch angle depends upon 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
• $\theta$ = Switch Angle

Now, from the above fig.

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

Switch Angle = $\theta$ = $\sin ^{-1}\frac{d}{D}$

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

Let,

• t = Thickness of tongue rail at toe
• $D_{1}$ = Actual length of tongue rail
• $D_{2}$ = Theoritical length of tongue rail
• x = Difference between $D_{1}$ and $D_{2}$

From the above equation and fig, we can write

• Actual Length of tongue rails $D_{1}$= $\frac{ ( d - t ) }{ \sin \theta }$
• Theoretical Length of tongue rails $D_{2}$ = $\frac{d}{ \sin \theta }$

Now, x = ( $D_{2}$$D_{1}$ ) = $\frac{t}{ \sin \theta }$