What is the offset calculation for a curved rail road?

[tomtomtom1]

Hi all

I work on the rail roads and I am trying to solve a geometry problem which I was hoping someone could help me with.

My problem is this:-

I have a straight rail road. At point A trains can divert onto another road, the other road is curved with a radius (R1), the curvature of the road changes to R2.

If I was to continue to travel along the straight rail road then what would be the offset from some distance traveled along the straight (AB) to the top of the 2nd curve.

In simple terms how is offset BC calculated.

I’m not much of a math’s wiz so I could really use a hand. I have made a drawing to illustrate what I am trying to calculate.

I really want to understand where and how it is calculated.

Can anyone shed any light?

Thanks guys

 

[huntoon]

Would Pythagoras work?
CL² = AB² + BC²

.. BC= √(CL²-AB²)
(this is just a quick little stab at the problem).

 

[Studiot]

I am assuming from your description that AB is tangent to the first circle at A.

The perpendicular offsets from a tangent to circular curve are given by

Offset = (length along tangent)² / twice radius

This will get you as far as D.

At D I'm not sure what happens.

Are you saying that at D the two circles have a common tangent?

Or do you need to insert a transition curve between the circles?

https://www.physicsforums.com/showthread.php?t=640859&highlight=offset

 

[tomtomtom1]

Thats correct at D both circles share a common tangent.

I am assuming from your description that AB is tangent to the first circle at A.

The perpendicular offsets from a tangent to circular curve are given by

Offset = (length along tangent)² / twice radius

This will get you as far as D.

At D I'm not sure what happens.

Are you saying that at D the two circles have a common tangent?

Or do you need to insert a transition curve between the circles?

 

[Studiot]

So once you know where D is, you can use the same method to get to C.