Locomotive wheels and flexing

I am currently in the process of reading "The Midland Railway North of Leeds", and have come across a reference to an article by E.L. Ahrons, dating from the late 1800s.
The reference states that Ahrons thought that Midland train speeds were increased by the introduction of higher tensile strength steels for locomotive tyres, and the use of 109Lb/Yard rail. This, he believed, would have reduced the tendency of locomotive driving wheels to run "flat", and the rails to compress slightly under the locomotive's weight. He stated that locomotives previously running quite slow times, were running faster after the above modifications.

My question is this: How much flexure is there in a locomotive's driving wheels? I am guessing that the larger its diameter, the greater the degree of flexure, but just how "flat" does a loco's tyre run? Does anyone know what the contact patch of a tyre on the railhead is in regard to area?

My apologies if this sounds like a daft question - I am not a qualified engineer, just a very interested amateur!

Richard.

 

Does anyone know what the contact patch of a tyre on the railhead is in regard to area?

About the size of a 10p piece per wheel.

 

Thats a lot of Lbs per sq inch. Saw some footage of one of the 'Kings' hurtling into a bend and subsequently 'bouncing' . even modern metals certainly have some flex in them, but i wouldnt think that a cast wheel has much flex in it, and although a steel tyre would, its been shrunk damn onto the wheel...

 

Try typing 'rolling contact fatigue' into Google.

These are two reasonble documents ...

http://www.arema.org/eseries/script...library/2004_Conference_Proceedings/00011.pdf

www.eprints.whiterose.ac.uk/781/01/lewisr7.pdf

But the best document is ....

The exact theory of the motion of a single wheelset on a perfectly straight track by A.D DePater

 

There was a time that I could have followed the vector mechanics in that last paper but not any more. This does highlight one of the issues raised in this thread http://railways.national-preservation.com/showthread.php/24908-Making-Engineering-quot-Sexy-quot?p=353846#post353846

When is an engineer not an engineer? It's important because modern technology requires an increasing number of people who can understand advanced technical mathematics but rather fewer of the traditional skilled fitters who do such a stalwart job of keeping our beloved steam locomotives running better than ever. Unfortunately for this country, the numbers of students graduating from mathematics, physics and engineering courses continue to fall. The Con-Dem's changes to the education system are unlikely to change this.

 

I think 'flexing' probably gives the wrong impression. What is happening here is that the tyre is being compressed by the weight of the vehicle, so that there is a continuous 'flat spot' on the tyre as it rolls over the rail.

This quite a separate matter from the 'flexing' that does occur in the rail and might occur in the wheel rim and the spokes. Stanier introduced the triangular wheel rim on the LMS - which was continued by Bond on the BR standards - and Bulleid introduced his version of the 'Boxpok' wheel to minimise this phenomenon. The problem was known about in the 1920s if not before and 'dishing' of a wheel was frowned upon in loco design offices precisely because this feature put stresses on the spokes which could lead to fractures.

On the modern railway spokes are unheard of as are tyres.

Regards

 

Loco wheels for the BR Standards had a degree of dishing and they we designed in the 50s. A modest amount of dishing provides a desired degree of flexibility.