Wheel size effect on performance

This comes out of some of the New build threads... It seems to me that I don't altogether understand the practical implications of wheel size on locomotive performance, the steam engine being such a different beast to internal combustion.
Yes, I get the obvious stuff - that with smaller wheels you get greater tractive effort which means, subject to adhesion, better ability to start a train, and that large wheels mean lower piston speed which obviously means a higher speed before the locomotive disintegrates.
What I'm not sure about is the relationship between rpm and power delivery which seems utterly different to petrol and diesel, and also at what point boiler capability comes into it.
Also how does rate of wear come into it? On a 25mph line a large wheeled loco must do many fewer revolutions per day than a small wheeled one: does this mean things like tyres and motion wear more slowly?
How much does boiler come into it? Does it essentially deliver much the same amount of steam to do the same trip at the same speed, or are there differences in the life of that most critical component?
Seems to me the tradeoffs could be very complicated indeed.

 

If we look at the physics, there are three formulae to be considered:

Power = Torque x Angular Velocity (call it rpm for simplicity)
Power = Force (Tractive Effort) x Velocity (speed for simplicity)
Torque = Force x Distance at which it is applied.

The steam engine delivers its maximum torque at zero rpm, irrispective of wheel diameter. That force at the crank pin becomes torque within the wheel. It is then delivered as Tractive Effort at the wheel rim, where the Torque is divided by the wheel's radius, so the bigger the wheel, to lower the Tractive Effort for any given torque. So a large wheeled engine will deliver less tractive effort than an otherwise similar one but with smaller wheels, e.g. Black Five versus 8F.

Once the engine begins to move, the TE will begin an initially slow but exponential decline as rpm rises. As the rpm rises less slowly with a large-wheeled engine, so it will maintain its TE for longer. So the large-wheeled engine will still be pulling at higher speeds when the small-wheeled engine's TE has dropped to zero. Since Power is TE x Speed, the former is still able to produce power where the latter can no longer do so. But on a railway subject to a 25 mph speed limit, the smaller engine will produce the required power more easily.

The bigger wheels do though confer some advantages, even at low speed. As you say, lower rpm gives less wear, counter-balanced to some extent by the requirement to work the engine harder to produce the same TE on starting, but lower piston speeds not only reduce wear in that area, but also the magnitude of the reciprocating out of balance forces which rise with the rpm.

The boiler is the key to power production. Unless it can provide sufficient steam to meet the power demand from the cylinders, pressure (and water level) must fall and the driver must reduce regulator opening and / or cut-off to compensate, so the TE and power output fall away. Big cylinders provide a high Tractive Effort but can in a short time overcome the boiler's output. This works well enough with a shunter, which runs for only a short time with the regulator open, but can move for a short period very substantial loads. But when faced with lighter trains over longer periods can struggle for steam.

 

Good stuff mr 2968. One other factor regarding wheel size, and it doesnt always follow, but a 6 coupled 6ft 8 is longer than a 6 coupled 5ft 8 which is likely to result in more rail/wheel/axlebox wear on curvy lines....

 

As you say it doesn't always follow. For example many Midland designs (and derived ones on the LMS ) used a standard 8' + 8' 6" wheelbase irrespective of wheel diameter. So a 'Jinty' and a 2-6-4t had the same wheelbase despite having wheels over a foot different in size. Ray.

 

That pretty well sums it up. I've said several times on this forum that big wheels are not a problem when it comes to slow running so a big wheeled loco is not, in itself, unsuitable for use on a 25mph line. Big wheels can go slowly but small wheels can't go fast because, as LMS2968 says, the T.E. falls off with increasing speed for a variety of reasons. Most conventional steam engines (and I mean engines and not locomotives) were designed about a maximum design speed of about 360 rpm. There were many faster rotating ones but you are getting to a practical limit at 600 rpm unless the engine is very small.
Steam locomotive design is a complex subject. the starting point is the T.E required and the speed at which it is required. A loco required to produce 15,000lbf of drawbar pull at 60 mph is going to be a different beast from one required to produce 15,000lbf of drawbar pull at 30 mph. The loads they are required to pull may be the same but the former will require bigger wheels, bigger cylinders and, above all, a bigger boiler.

 

Crank throw is also another factor to consider, but that is tied in with cylinder size anyway.

 

I believe a lot of early engines had rather large driving wheels in order to minimise piston speeds for a given running speed, on account of the primitive lubrication at the time.

For many years, the LSWR used to construct pairs of near-identical 4-4-0s, with 7'1" drivers for east of Salisbury; and 6'7" drivers for west of Salisbury, which were supposedly better for hill climbing on the tougher gradients in the west. (The preserved Adams T3 is one of the smaller-wheeled engines, with the Adams X2 being its larger wheeled sibling). But in practice, very little difference was found between them; maybe the difference in wheel diameter wasn't sufficient to be significant.

Another issue of significance on many preserved lines, which are often rather twisty and where the locos spend half their time running backwards, is the carrying wheels, which help lead the loco into curves and thereby reduce flange wear. It would be interesting to know, for lines that have examples in service of similar classes, whether, say, a 2-6-2T has reduced wear over a 2-6-0 tender variant of the same loco (say Ivatt class 2MT vs 2MT tank; GWR large prairie vs WSR 9351 class, etc etc).

Tom

 

Wear of tyres can be significant without a guiding wheelset in a bogie or truck to lead the coupled wheels into a curve. When the 8F arrived at the SVR, she had a virtually brand new set of tyres, but after 150,000 miles of preservation use, there are now worn to their limit. The cause was flange wear to the (unguided) trailing coupled wheels as they bit into the curves which, as you said, was 50% of running. To restore the flange thickness meant turning down the tyre treads, not only on the trailing wheels, of course, but all of them. And so now they require renewal.

When we first got her, I remember thinking: they're so thick they'll never wear out! Ho humm...

 

Using 6'-7" drivers as against 7'-1" drivers will give the loco a slightly greater T.E. but the advantage would be largely lost if the adhesive weight wasn't increased. Did this happen, do you know?

 

DL Bradley gives:

X2 class

Driving wheels: 7'1"
Adhesive weight: 15T 5C + 14T 8C = 29T 13C (A later series had another 13cwt between the two axles, i.e. 30T 6C)
Cylinders : 19" * 26"
Boiler pressure 175psi

Which gives a TE @ 85% pressure of 16,425lbf
Factor of adhesion = 4.04 (adhesion divided by TE)

Incidentally, can't resist this picture: was there ever a finer sight than a late Victorian engine in all its finery?
http://en.m.wikipedia.org/wiki/File:4-4-0_LSWR_X2_Class_No_577.jpg

T3 class

Driving wheels: 6'7"
Adhesive weight: 15T 15C + 14T 16C = 30T 11C
Cylinders : 19" * 26"
Boiler pressure 175psi

Which gives a TE @ 85% pressure of 17,673lbf
Factor of adhesion = 3.87 (adhesion divided by TE)

To put that last number in context, a Schools class has a factor of adhesion of 3.74.

So the smaller-wheeled locos did have greater adhesion, but not sufficient to give the same factor of adhesion - indeed, the factor of adhesion on an Adams T3 was not much greater than of a Schools class, generally reckoned to be near the upper end of the ratio of TE to adhesion.

The line from Waterloo to Basingstoke was one of the very early mainlines and was laid out without major gradients (but significant earthworks). However, west of Salisbury, the line was built using the "roller coaster" theory, where it was assumed that time lost on the climbs would be regained on the descents. As I understand it, the typical driving practice in LSWR days was to try to keep the demands on the boiler near constant, i.e. run fairly gently uphill, but then run hard downhill. So on the one hand, that probably didn't lead to big risks of slipping of an engine being driven hard uphill, but on the other hand, did mean downhill speeds were very fast; probably the peak speeds west of Salisbury were faster than the larger-wheeled engines were achieving east of Salisbury!

Tom

 

That is a pretty low factor of adhesion for a Victorian loco. The Schools, at least, had the advantage of three cylinders to even out the turning moment. I produced a table of locos used on the NYMR a while ago and it is quite interesting to see how the different locos stack up in this respect.
The K1 is well up near the top and the WC is well down the list. The K1 does pack a lot of T.E. into its small size, though but, even so, I don't reckon it has a problem with slipping. I've used an adhesion ratio in the table so you need to take the reciprocal to get a comparable factor of adhesion.

 

Interesting figure for a WC/BB given their reputation, but I guess that is based on 250psi boiler pressure - when built they had 280psi. That gives an adhesion ratio of 0.248, equivalent to a K1 and just below a Schools - or just below an LSWR T3!

Somewhat OT: The Adams 4-4-0s were very highly regarded in their time. Many had working lives of around 50 years from the 1880s to the 1930s, albeit later on secondary duties. That should have been the end, but the war intervened and many were placed into store on a "just in case" basis, which was why the NRM's T3 survived long enough for it to be officially preserved by the Southern Railway. They returned it as far as possible to Adams condition and steamed it for the Waterloo Centenary celebrations, alongside the LSWR Tri-composite coach also in the NRM.

Tom

 

Regarding slipping the percentage difference between peak and mean is very important.
Driving wheel diameter is not so great a matter as it once was. Once we had driving wheels of 8ft. in diameter. In the 1940s and 50s express passenger (though sometimes referred to as mixed traffic) locomotives were fitted with 6' 2" diameter wheels.
We're these types more sluggish than their predecessors?
Unless your engine happens to be 160A1 then at low rotational speeds you will have significant losses. Again if you have a steam circuit that does not allow high rotational speeds you have another problem. Current thinking is that you should design a locomotive to have a maximum working rotational speed of 504 rpm. That sets your design wheel size. Though it might be thought that this should the primary consideration you are better designing the best possible exhaust system.
If you are wanting to maintain as high a tractive effort as possible as speed rises then you don't use simple expansion. In tests carried out in Germany the Norwegian 2-8-4 compound could deliver a performance superior to that of the German Pacifics because of the type's capacity for acceleration - it could not reach as high a maximum speed but in the real world the performance traits of the design were far more useful.
Do you have to accept a wear and tear disadvantage if you adopt this policy? No, have a look at the N&W class J as one example.

 

what about the number of wheels (2, 4, 6, 8, or 10?) how does this affect things?

 

The more wheels that you have the greater your mechanical loses all things being equal. The number of wheels that you have depends on the power that you have to deliver and the restrictions imposed on your design by civil engineering considerations and restrictions. The locomotive that you design should carry as large a percentage of of the total design weight on the driving wheels as possible. The C & O Allegheny carried far too much weight on undriven wheels. The design was hamstrung when compared with the N&W Y6b, it could produce more power than Roanoke's finest but could not be relyed upon to deliver that power because of the many tons sat on undriven axles. The C & O machine was designed to outperform the N&W Class A, which it did but on a simple pro rata basis the 2-6-6-4 was a far better machine that offered far better value. The N&W engine was superior to the UP Big Boy too, it had a better power to weight ratio and in terms of maximum output there was little to choose betwen them.
If you can design an engine that weighs 65 tons or so that produces the same amount of power as one that weighs 95 tons and you can deliver maximum power to the drawbar as required then you have 30 tons approx to play with as extra payload. So on the understanding that engines should be as small as possible, and large wheels weigh more than smaller ones, then driving wheels should be no larger than the traffic requirement demands. As to the number of driven wheels, no more than is required to transmit the cylinder horsepower to the rails.