What is the offset calculation for a curved rail road?

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Discussion Overview

The discussion revolves around calculating the offset for a curved railroad, specifically the offset from a straight section of track to a point on a second curved section. Participants explore geometric relationships and methods to determine this offset, with a focus on the transition between different radii of curvature.

Discussion Character

  • Technical explanation, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant describes a scenario involving a straight railroad diverging into a curved section with two different radii (R1 and R2) and seeks help in calculating the offset from the straight section to the second curve.
  • Another participant suggests using the Pythagorean theorem to find the offset, proposing a formula involving the lengths AB and BC.
  • A participant clarifies that if AB is tangent to the first circle at point A, the offset can be calculated using a specific formula related to the tangent length and radius, but expresses uncertainty about the situation at point D.
  • The same participant questions whether the two circles share a common tangent at point D or if a transition curve is necessary between the circles.
  • A later reply indicates that once the position of point D is established, the same method can be applied to determine the offset to point C.

Areas of Agreement / Disagreement

Participants express varying levels of certainty about the calculations and the geometric relationships involved, particularly regarding the situation at point D and the need for a transition curve. No consensus is reached on the best approach to calculate the offset.

Contextual Notes

The discussion includes assumptions about the geometry of the curves and tangents, but does not resolve the mathematical steps or the implications of using a transition curve.

tomtomtom1
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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
 

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Would Pythagoras work?
CL2 = AB2 + BC2

.. BC= √(CL2-AB2)
(this is just a quick little stab at the problem).
 
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
 
Last edited:
Thats correct at D both circles share a common tangent.

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

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