A question about traction.

I was browsing though old mags today and came across an article about Russian Class 'O' locos by Harvey Smith in EiM (April 2012). He mentions that '... smaller diameter wheels give higher traction ...' . I assume that is an empirical fact, but can anyone explain why it is so? My guess is that it must be something to do with the way the way the wheels/track deform (elastically) to give grip.

This is idle curiosity - I don't build locos - hence tea room. But it's bugging me!

Robin.

Smaller wheels give higher tractive effort for a given set of cylinders. I'm not aware of any relationship between wheel diameter and friction, but I'm open to offers

I'm not too convinced about that. Locos with small wheels will often have a higher tractive effort, but that is because the effective gearing is lower, like being in first gear in a car. Like the car, they also can't go as fast.

The actual grip between the wheels and track depends mostly on the coefficient of friction and the weight on the wheel. The civil engineering department gets upset if you increase the weight on any one axle too much, so to get more tractive effort you need to add more axles. Eventually the civil engineers will start to complain about the length of your fixed wheel base spreading the track on curves. so to keep the wheel base reasonable you make the wheels smaller, which will tend to limit the top speed. So hence express locos with fewer but larger wheels, and goods locos with many smaller wheels.

John

As an example of what John Olsen says, B R used 8 coupled locos, but the 9F 2 -10 - 0s had the centre drivers without flanges to allow them to negotiate the same curves as 8 coupled freight locos.

Howard

There must be some deformation between the rail and the wheel due to applied pressure, steel is not infinitely hard. For a given weight on a wheel a smaller wheel will have a smaller contact area so more deformation will occur as the pressure is higher. The actual friction force will not increase as that is dependent on both pressure and area so I can only imagine that an increase in traction is due to a either a greater deformation taking place with a smaller wheel or the increase in pressure effectively cleaning the rail surface better.

Martin C

The statement "the smaller diameter wheels give higher traction" should read, "higher tractive effort". A somewhat sloppy mistake.

The basics mean that smaller wheels have lower gearing and hence can start a higher mass train from rest. It has nothing to do with friction between the rails and wheels. Any such effect is of a miniscule second order.

Andrew.

P.S. All bets are off if the wheels slip on the rails!

Edited By Andrew Tinsley on 29/10/2021 09:54:35

Shock/Horror … sloppy use of technical language in a Hobby magazine

… Whatever next ?

MichaelG.

Going into the workshop to do some lathing of course

At a graduate engineer BR management training course some 40+ years ago I encountered an M&E engineer and asked him what kind of coefficient of friction was seen between a locomotive wheel and a rail. He stroked his beard thoughtfully and said, "Well, it normally lies between 0 and 1."

Presumably it depends on the type of leaves on the line!!

Thanks! I assumed that 'traction' was to do with the grip of the wheel on the rail, and would therefore be proportional, all other things being equal, to the area of contact between the wheel rim and rail. So I was trying to think about how elastic deformation would work out with different wheel diameters. Duncan and Andrew's explanations make sense though - not to do with friction, just 'gearing'.

It was an interesting article though, written by someone who is (was?) obviously knowledgeable about steam engines, and perhaps he used the term as a sort of shorthand, assuming that the cognoscenti (not me) would know what he meant.

Robin.

I was thinking with good traction the smaller wheels will have lower gearing, but seeing it is metal on metal and not tyres on a tarrred road, I was thinking if the larger wheels start to spin and sand applied, it will keep on spinning easier than the smaller wheel turning faster at same speed of locomotive, not sure, but maybe if the experts can elaborate about large locomotives what will happen most likely if sand is applied to tracks with a comparison between locomotives at same angle pulling same weight but one with smaller wheels(Low top speed)and one with larger wheels(high top speed), which one will slip more...I would like to think there will be a difference from this perspective, or is the difference in contact area(Metal-sand-Metal) so little it can be ignored in practice-? Then theres also similtanuesly the argument when slipping starts for both the one with larger wheels will be travelling at a higher speed, but this throwes my suspicion in the other direction, now I am more confused-?

We either need to be talking about static friction, where the wheels are not slipping, or dynamic friction, where they are. The coefficient of friction is very different, and usually much lower for the slipping case. The coefficient will also be liable to change with slipping as things heat up, and in any case prolonged slipping is liable to quite quickly lead to catastrophic damage.

For the static case, the area in contact makes very little difference to the friction force. The two main factors affecting the friction force are the force normal to the contact, and the actual coefficient of friction. The diameter of the wheel is unlikely to make much difference. Neither is deformation of the wheel or the rail, at least so long as both remain within their elastic limits. Deformation will increase the area in contact, but decrease the force per unit area.

Note things are a bit different with rubber, which can give a coefficient of friction of more than 1, which is not usually possible with other substances. The point of wider tyres is not in itself to give more area, but to allow more rubber so that softer compounds can be used, to give more grip than harder ones do. But the softer ones would wear faster, so by widening the tyre there is more rubber available for a given tread depth. The downside is of course that the wider tyres will aquaplane much more readily.

Sanding will tend to increase the coefficient of friction, and I doubt if the diameter of the wheels makes much difference to this effect, compared to other factors like the wetness of the rail, the depth of leaves or snow etc. One thing I have been told about using sand is that you don't want to overdo it, as you will have to drag the whole train over the sanded rail. The sand that has been embedded in the rail by the weight of the locomotive will roughen the surface and so increase the rolling resistance of the train. Apparently this is noticeable if you use too much sand, eg leave it on once you are past where you were slipping.

John

John Olsen Interesting...My father was a steam train driver retired when diesel came, never involved in an accident , he had lots of stories to tell, I know being on time was a big issue, and as a child I have seen some accidents on corners, lots of metal off the track.

I remember him telling sometimes if they get slippage and sand does not help, they reverse back and make a new attemp at higher speed, those days there were no communications like today, so they do what they can, or walk back and place explosive caps on tracks to warn next trains. If the reverse does not help, they must half the load and try that, and come back, or get another locomotive. There was also a conducter in his own wagon at the back, and his stories about conducters and kicking them off with shunting was funny as they run towards stop blocks..

So there seems to be something in slippage and speed over slipery area, or is it more momentum in practise.

One rightly expects the coefficient of static friction to be greater than that of sliding friction.

However, apparently,and very surprisingly, the coefficient is maximum at 15% slip!

This is employed in the low speed ground radar controlled wheelslip locomotives such as the General Motors manufactured BR Class 59, and their Class 66 successors.

Not long after the 59s were introduced I was able to witness the difference between a 59 with 100 ton hoppers and a 47 with 20 ton wagons., when checked by a yellow. The more heavily loaded 59 accelerated without problems while the 47 smoked and had to have the throttle "jockeyed" to pass the same signal post.

Howard

Somewhere I have a paper about friction and slipping speed. The coeff of friction doesn't fall off a cliff as soon as it starts slipping. If there is any interest I'll try to find it, but it will take a while, so I'll not bother if no interest.

double post, no idea how

Edited By duncan webster on 30/10/2021 18:20:41

I was passing the bookcase and there it was

it appears that coeff of adhesion is max just before it starts slipping as I expect. 15% slip doesn't mean a lot, if the loco is trying to start a train from rest 15% of what? I suspect that the motor current is controlled so that the wheel is just slipping, as you can't detect just not slipping . It gets very complicated with steam locos, as the tractive effort has a pronounced cyclic ripple. If it starts slipping on the peak, will the wheel have accelerated enough by the time the peak has passed so that the now reduced coefficient of adhesion is insufficient to stop the slip?

Apparently, the ground radar slip control cuts out above 5 mph, which ties in pretty well with Duncan's graph

Howard