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Please note: This is not a homework question. I work in Engineering.

Firstly Thank you for reading my post.

I am trying to learn a technique called Hallade which is used on the Railway to design curves.

I have some notes (attached).

The bit I fail to understand is on page 8.

Three equations are presented:-

1) Sin (Alpha) = 4V/C

2) Sin (Beta) = Sin(2Alpha)

3) Sin (Beta) = 8V/C

I understand how equation 1 was derived but I do not understand how equation 2 & 3 was derived???

I was wondering if anyone could help shed some light into how equation 2 & 3 was derived, please do not miss any steps.

I have been working on this for the last few weeks and got nowhere so I really appreciate any help you can give me.

Thank you for your help.

Please note: i have been informed by a few people that equation 2 could actually be wrong and should be Sin(Beta) = 2Sin(Alpha) but either way i still dont undertsand how its dervied.

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# Railway Engineering Curve Design Through Hallade Method

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