Motto: “This blade doesn’t want to be drawn! I don’t want it to want to be drawn!” B.S. Delavrancea – Sunset

Curves without transitions

In 2015, the Institution of Civil Engineers (ICE) published online a collection of proceedings of the institution which contains papers and discussions of the Railway Engineering Division of ICE from 1952.

One of these papers is called “Recent Developments in Railway Curve Design”.

The paper can be found here: https://www.icevirtuallibrary.com/doi/10.1680/ipeds.1952.11271

and the discussion is published here: https://www.icevirtuallibrary.com/doi/abs/10.1680/ipeds.1952.11272 

The document presents the results of the experiments carried out by British Railways to determine and define limits and rules for designing the railway curves.

It is also the first public document I found which mentions the concept of “virtual transition” in British railway literature.

The authors present the results of the experiments carried out and their conclusions and recommendations with regards to the calculation of the horizontal alignment and cant design parameters.

These were later adopted by the British Transport Commission and became the Civil Engineering Handbook No 3 – Railway Curves. Rules for speed of trains in relation to radius, cant and transition.

All the tests were carried out on curves with transitions and cant. But, when defining the design rules, the authors present their view with regards to curves without transitions.

This is a snapshot from the paper:

The authors assert that “when a coach moves from a straight to a curve, the whole vehicle begins to acquire radial acceleration when the leading bogie passes the tangent bogie. It continues to gain radial acceleration until the trailing bogie reaches this point, after which is subject to uniform circular motion. The change of motion is thus completed in a distance equal to the length between the centres of bogies. The shortest distance between the bogie centres on the British standard coaches, namely 40 feet, has therefore been accepted as the length of the virtual transition.

The deficiency of cant is considered as being gained within the length of 40 feet, commencing on the straight 20 ft before tangent point.”

Please remember, dear reader, the underlined words.

When the grandfathers were right

After the paper was presented, the subject was discussed, and these discussions are collected in the second part of the paper. A certain gentleman called Brinsmead raised an interesting point:

“Mr Brinsmead had mentioned the effect on passengers standing over the bogie at the end of the coach. The point should not be overlooked that the fortunate passenger in the centre of the coach travelled over a path which was that of the virtual transition, but the passenger over the bogie was subjected to an instantaneous application or relief of radial acceleration as the bogie passed over the tangent point.”

A personal note

Mr Brinsmead comment correctly stated that the radial acceleration is not the same for the centre of the coach and for the point above the bogie, contradicting the authors’ initial assessment that the “whole vehicle” acquires the radial acceleration.

If I would have been in the room that day, my perverted mind would have quickly replied to this challenge:

“All right, the radial acceleration is not the same for all the points along the coach. But you know what is the same for all these points, but has no connection whatsoever with the cant deficiency variation?!”

You noticed already, dear reader, that there is no causality statement connecting statement A and statement B. The way the cant deficiency varies over the length called “virtual transition” is a “consideration”.

Revelations 22:18-19

The proposal presented to the Railway Engineering Division of ICE, in March 1952, was later adopted by British Railways in what became Handbook No 3 – Railway curves. The earliest version I could find is from 1962.

This handbook contains almost all the sketches and rules presented in the 1952 ICE paper.

Section 2 – Curves Without Transitions, has this cosmeticized definition of the Principle of Virtual Transition:

“The vehicle moves with uniform velocity in a straight line until the bogie centres C1 reaches TP. Here the motion of the vehicle begins to change as it passes on to the curve, and the vehicle gradually acquires angular velocity. The change continues until the bogie centre, C2, reaches TP, after which the vehicle moves round the curve with uniform angular velocity. The change of motion of the vehicle from straight to curve conditions takes place in a distance B feet. The length B may therefore be considered as a virtual transition.

Deficiency of cant is considered as being gained in the length of the virtual transition, commencing on the straight 20 feet before TP, and terminating on the curve 20 feet beyond TP.”

For the happy few

Let’s read that quote again:

“Mr Brinsmead had mentioned the effect on passengers standing over the bogie at the end of the coach. The point should not be overlooked that the fortunate passenger in the centre of the coach travelled over a path which was that of the virtual transition, but the passenger over the bogie was subjected to an instantaneous application or relief of radial acceleration as the bogie passed over the tangent point.”

But now, with no mention of radial acceleration, the problem is solved, isn’t it?

Would it be a surprise to you, dear reader, if I would tell you that these are the only two instances in the entire Handbook No 3 where “radial acceleration” was replaced with “angular velocity”?

The most anticlimactic movie twist ever remains for me the one at the end of the Maltese Falcon, when we find out (50 years old spoiler alert?) the precious falcon statue everyone was fighting over was a fake. The 1952 paper beats this.

Angular Velocity

Post scriptum

With no connection whatsoever to the above sections, I give here, for your entertainment, dear reader, the animation of a crankshaft piston. I call that three-dotted green arm “the eternal virtual transition”.

Why?

Because, you see dear reader, all three points on that arm have the same angular velocity.

But the blue one moves on a line – it has ZERO radial acceleration.

The red point moves on a circle – it has a constant radial acceleration.

The mid point moves on an ellipse – for half of its movement it has a radial acceleration almost double of the red point and for the other half of the movement it has close to half of the red point radial acceleration.

(to be continued …)

References

• Loach G. C., Maycock M. G. (1952) Recent Developments in Railway Curve Design, ICE, Proceedings of the Institution of Civil Engineers, Volume 1 Issue 5, OCTOBER 1952, pp. 503-541
• Loach G. C., Maycock M. G. (1952) Recent Developments in Railway Curve Design – Discussions , ICE, Proceedings of the Institution of Civil Engineers, Volume 1 Issue 5, OCTOBER 1952, pp. 541-572
• *** (1962) Railway Curves – Civil Engineering Handbook No 3, British Transport Commission.