Nominal Tractive Effort

[sturrock]

Modern locomotives have their true tractive effort measured in purely scientific terms and directly relate to their actual performance, but in the earlier days of steam when most things were done by ”rule of thumb”, a group of the then current locomotive engineers (known by various titles) frequently met to share many of their ideas one of which was about comparing the power outputs of of locomotives.

At a meeting of one of the many organizations, (others may have more details) in the early years of the 20th century a group of eminent locomotive engineers came up with a formula for this purpose. Although some had access to actual performance details via their newly established dynamometer cars and loco mounted indicators it was decided that a formula for calculating nominal potential performance could be useful using known specifications such as boiler pressure, cylinder size, number of cylinders and the driving wheel diameters.

The initial formula they agreed on was as follows based on 85% of boiler pressure (although some subsequently used 80 or 100% so take this into account when reading specifications)
.85 BP x bore squared x stroke (square pistons and rectangular cylinders?) multiplied by number of cylinders all divided by the wheel size.(BP was in lbs/sq inch and the others were in inches.)

When this was compared to actual data from the dynamometer car they must have found it to be about double the measured figure and it was decided to divide it by 2.
To give an example an 1899 NER class R 440 calculated by this method would show the nominal tractive effort as 31,134 pounds (lbs), but current dynamometer figures indicated a maximum pull of about 7 (then used, long) tons, i.e. 7x2240=15680 lbs, so it was probably decided to divide this calculated figure by 2 making a more realistic 15,567lbs.

The formula adopted -
.85 BP (in lbs per sq. inch) x bore x bore x stroke (all in inches) x number of cylinders.
Divided by the driving wheel diameter (also in inches)
Divided by 2.

i.e. .85 x BP x B x B x S x n All divided by 2
Divided by wheel diameter

I like to simplify this to what I call “the .425 formula” as follows-

.425 x BP x B x B x S x n
Divided by wheel diameter in inches.

Remember this figure is “nominal” only and actual performances were influenced by other factors such as restrictions in steam passages, limitations and state of boilers, advent of superheating, positive valve events, grate restrictions and other factors limiting or maintaining the accessibility of each locomotive to that estimated power .

Also good luck in calculating compounds !

PS- I have forgotten my formula for “adhesive factor” -can anyone refresh my memory?

Regards, Jon.

[Hatfield Shed]

As above it was quickly realised that for a 2 cylinder simple - easily the most common steam loco format - the force estimate was better aligned with measured force at the drawbar if the estimate was based on a single cylinder. This is reasonable as the cylinders effectively deliver the force alternately. (Never let anyone tell you this is an estimate of the power output potential of a steam locomotive, as a moment's reflection makes clear: power is a measure of work, and the maximum capacity for work of a steam locomotive is fundamentally limited by the rate at which steam can be supplied, and its temperature and pressure. Grate area, boiler pressure and superheater:grate area ratio are most useful for this estimate.)

(For any wishing to go compounding a search on 'tractive effort estimate von borries baldwin chapelon' should provide entertainment.)

The factor of adhesion estimate is mass on the driven wheels divided by the tractive effort estimate (obviously the same units for both). It was generally considered that a value of 4 or higher was desireable. It is readily appreciated that as a steam locomotive in service is subject to maintenance, increases in cylinder diameter and reductions in driven wheel diameter will increase the tractive effort estimate, while making some small reduction in the loco's mass; and this reduces the factor of adhesion, but this was never of significant effect.

[sturrock]

Thanks Hatfield Shed
Really appreciate your memory refresher on adhesive factor, do I use 2000 or 2240? (short or long tons) -I think what we now call long tons was the one in use before the '60s?
Your comment on steam generation rate is of course the most valid, but my dissertation was specifically on this vague idea of tractive effort ---
On your point about single cylinder, don't forget inertia, (or flywheel effect) - a steam engine is not a static entity and when moving has strong positive inertia, particularly its crank and wheels, so 2, 3, or4 cyls become important in maintaining this, as well as increasing its rate.
Always good to hear from you as your insights and knowledge are usually spot on'.
Regards Jon.

[65447]

Thanks Hatfield Shed
Really appreciate your memory refresher on adhesive factor, do I use 2000 or 2240? (short or long tons) -I think what we now call long tons was the one in use before the '60s?

2240 was (and still is) the number of Imperial pounds in 1 ton; 112 pounds (lb) to the hundredweight (cwt) and 20 cwt to the ton. The metric equivalents are 50 kg approx= 1 cwt and 1000 kg (1 metric tonne) approx= 1 Imperial ton.
If you wish to use the metric value then you should amend the formula to use all metric values throughout for, as in cooking and baking, the measures are not necessarily interchangeable (1 egg still = 1 egg, but is it of the same size?)
The 'long' ton is the Imperial ton at 2240lbs, whereas the 'short' ton is the US measure at 2000lbs, in the same way that the US short-changes liquid measures.
My old text books are in English

[sturrock]

Thanks 65447
Of course you are right -my only excuse is that being an automotive engineer in the past I'm used to the metric system I could'nt think straight and it was late at night.
Jon.

[Hatfield Shed]

..Always good to hear from you as your insights and knowledge are usually spot on'.

Jon,
I owe it all the late father of a long ago schoolfriend (who tragically died in his teens). This gentleman had served an apprenticeship at Inchicore, latterly under Bulleid, and from him came the foundation of my knowledge of steam locomotive engineering. A truly marvellous power of description was at his command, and he could convey to this eager listener all the flexing of the machinery and frames, and the movements thereby generated (in addition to the desired direction along the track!) by the off centre forces of each piston stroke.

[Pyewipe Junction]

What is the theoretical speed in this formula? At start-up or some other speed?

[sturrock]

First of all I believe the idea of nominal tractive effort was instituted to give a comparison of classes of locomotive's potential vis-a-vis each other -it clearly was " pseudo-scientific"

However as steam gives instant torque even from standstill, Hatfield's point about them using only one cylinder seems valid, but as I point out Inertia (i,e."positive" inertia) also has an influence (and the whole train becomes integral to this).
I would think that the maximum pull measured at its optimal point was the figure they were aiming at. This was via the Dynamometer car and usually measured in tons. For instance a small wheeled mineral loco's indicated maximum pull would be at slow speed, a large wheeled express loco at a higher speed. Each class would be tested using their designed load capacity.

I like nominal te , I identify it with certain locos -and I love technical statistics -but as I point out, dynamometer figures are reliable, remote calculated nominal te is not.

[Hatfield Shed]

What is the theoretical speed in this formula? At start-up or some other speed?

Further to the above, this is a good question. It is a static estimate, but can be considered to apply to the 'dead slow' movement of starting a train, because the conditions haven't departed significantly from static. And it is something of a worst case guess. Factors such as fire, superheater, valve and cylinder temperatures, valve gear type and settings, aren't considered. Talk to any footplate crew about the difference starting a heavy load with a locomotive that has been standing for hours with the machinery 'cold', and how that same locomotive then gets away after a brief halt following an hour of power production on the road.

[sturrock]

- my engine driver dad used to say "An engine doesn't pull a train, -it moves a train."