Factor of Adhesion

I know this has been covered before in other posts in other contexts of locomotive performance but I still don't have my head around it to understand specifically what the factor of adhesion really means, or rather how it relates to locomotive performance.

so maybe some of the experts can help clear this up. I found various well known classes of U.S. locomotives with their factors of adhesion. Now, I am not saying the numbers are correct but they are what I found. Can someone put performance into perspective utilizing the FA data ?

Railroad Locomotive Type Road Number Factor of Adhesion

Erie Berk 2-8-4 3385-3404 3.63
Pere Marquette Berk 2-8-4 1216-1227 4
L&N Berk 2-8-4 1964-1969 4.1

C&NW Hudson 4001-4009 3.92
NYC Hudson 5445-5454 4.6
MILW F-7 Hudson 100-105 4.29
DL&W Hudson 1151-1155 4.08

Frisco Northern 4503-4514 3.92
NYC Niagara 6000's 4.4
CRIP Northern 5100-5109 4.18
N&W J 600 class 3.6
SP 4450 series 4450-4457 3.54
ATSF 2900 series 2900-2929 4.45
DL&W Pocono - 1631 class 1631-1650 3.8*
* as built

PRR 4-4-4-4 6110-6111 4.12

why the NYC RR so high and the slippery PRR 6110 class is over 4........

This whole thing confuses me

Thanks for any help

As for why the New York Central is high... The NYC locomotives you quote (Hudson and Niagara) are designed for high-speed passenger service, and so have comparatively (comparative to a freight type of the same overall size) LOW tractive effort: their cylinder dimensions are small enough (relative to their 79" driver diameter) that they can deliver full power, using all the steam the boiler can provide, at high speeds, and so small enough that the low-speed tractive effort is fairly small. Compare a New York Central (System) freight locomotive: the (Boston & Albany) A-1 Berkshire, built a bit before the first J-1 Hudsons: 69,400 lbs tractive effort (without booster: at low speeds the trailing truck booster brought it over 80,000, but that involved powering an additional axle), 248,200 lbs weight on drivers, factor of adhesion 3.58. I think you'd find similar things in comparing freight and passenger steam locomotives of other railroads. (The Norfolk & Western J-class 4-8-4 is the out-lier: it had very small, 70", drivers for a passenger engine, and so a very high nominal starting tractive effort. I assume that a Norfolk & Western engineer, by the time he was trusted with a crack passenger train, knew enough to start carefully!)

(Will Davis: I think you've made a slip of the "pen" in the second line of the second paragraph from the bottom of your -- typically informative -- reply. Shouldn't it be "Lower than four is slippery"?)

Regarding the "slip of the pen" - now I am even more confused !

If lower than 4 is slippery why the example of the NYC locomotives being slippery and needing a booster with a FA of over 4 ? I understand the math to obtain the number, it is understanding the number and relating it to performanace that I am not clear about. I think the example and possible slip of the pen has now put me into tilt.

If I understand correctly, in the case of the DL&W 1631 class they had a modification done, reducing cylinder diameter I believe that lowered their tractive effort and increased their factor of adhesion from 3.8 to something like 4.1, which seems to make sense that the higher the number the less slippery. But be that as it may perhaps where part of my confusion lies is not so much the maximum TE but when and under what conditions it can be used.

I can totally grasp diesel TE and performance having been a diesel mechanical officer with older Alco and EMD units and the newer SD70's with radial self steering trucks and AC traction etc. - it is just trying to look at data with steam I can't correlate what or how the locomotive should perform. Prime examples are in the case of locomotives above, and we can discount the N&W J class is the difference between the Berks (and I don't have the NKP stats) but how did the Erie Berk compare with the PM and L&N engines, and how is that seen in the FA. Same could be asked for the comparison between the C&NW Hudson which looks like a fine machine and the NYC Hudson noted to be a well engineered and performing piece of power. Track limitations and weight restrictions aside which would be the better locomotive and most efficient ?

Yeah, Allen-- I was LITERALLY dozing off last night when I wrote that and now that I see it again it's a mess! I'll delete it and try again...

Well, it looks like Cactus Jack has answered his own questions!

If you understand diesel adhesion, then you understand steam locomotive adhesion.

The factor of adhesion is simply a calculational value relating rated tractive effort to weight on drivers; it's a ratio. A factor of four might be considered null, with a factor higher than that (above four) being less slippery (since tractive effort is not so close to 25 per cent of weight on drivers) and a factor less than that (lower than four) is a more slippery engine.

You say you want to put that to practical use? If you have two different locomotives built for the same service with roughly the same starting tractive effort, but one of them has a factor of adhesion of let's say 4.2 and the other has a factor of adhesion of 3.8 then the locomotive with the 3.8 will likely be able to start a heavier train under most conditions, especially bad ones. In other words, it's more likely to be able to develop its full rated starting tractive effort with a higher weight on drivers compared to its rated tractive effort.

This exact sort of thing might be found on pre-war, and follow-on wartime engines built to the same design but with wartime engines not using light-weight alloys. This resulted in much heavier wartime locomotives; they'd have a higher factor of adhesion numerically (in other words, be less slippery since they had the same tractive effort and higher weight on drivers.)

My NYC example in the deleted post was wrong.. as I said, I literally was dozing off during that writing and should remember never to post while drowsy! The application of a booster might best be thought of though as helping a locomotive that IS slippery, or might be. That's the only part of that now-deleted comment I'll stick to.

Other than these things, I'm not so sure what else the factor of adhesion might relate to operationally.

-Will Davis

You understand what "Factor of Adhesion" is-- right? Weight on drivers divided by tractive effort? But you seem to be trying to puzzle out some greater significance to the figure. It has none.

I'd say your best plan is to forget you ever saw the term. Tractive effort matters, and weight on drivers matters; you know what they are, so you don't need to bother with F-of-A. (Neither does anyone else.)

New York Central had scores (maybe hundreds) of engines with F-of-A around 6. Why would they choose that? Were they worried the engines would be too slippery with an F-of-A of 5? Presumably not-- presumably they never gave the F-of-A a thought. The engine was inevitably going to have a certain weight on drivers, and (for reasons we can't guess) they preferred small cylinders that gave a low calculated tractive effort. Someone might argue that was a mistake, but F-of-A wouldn't be mentioned in their argument.

Cactus Jack--
NYC Hudsons didn't need boosters because they WERE slippery, but to give them the starting tractive effort that WOULD have made them slippery had that starting effort been exerted through their three pairs of drivers with roughly 60,000 lbs on each.
Timz--
I don't think that's quite fair. Sure, tractive effort and weight on drivers are the independent variables, but slipperiness depends (ROUGHLY! There are several complicating factors) on the RATIO between them: F.A. It's not the answer to all questions about steam locomotive design, but it's a helpful number for rough-and-ready judgments. Too high suggests you could maybe improve things by increasing steam pressure or cylinder dimansions to give more t.e. Too low and you worry about slipperiness.
--
Example of complication:
Wheelslip is PRIMARILY a problem at low speeds, so you'd THINK a drag freight engine should have a higher factor of adhesion than a passenger type, whereas the opposite tends to be the case. (So Timz is part right: here's one interesting fact that F.A. doesn't help us understand.) Reason: passenger locomotives are designed to operate efficiently at higher speeds (so: large drivers, small cylinders) and so naturally don't have the low-speed tractive effort that would give them low F.A.

Another example of complication:
A steam locomotive's drivers are coupled together by the side rods, and this seems to help prevent slippage. (Suppose you have one wet autumn leaf on the rail. This might be enough to get one axle to slip momentarily, and if full power is still delivered the momentary slip will turn into runaway slip, since once an axle has started to slip its adhesion is greatly reduced. But if the axle going over the leaf is coupled to the others, they may prevent it from accelerating long enough to get past the slippery spot on the rail and regain traction. Or at least I think that's the principle involved.) So the number of coupled axles influences the slipperiness of an engine. Result: the PRR I1-sa Decapod, a drag freight engine, was able to get away with an F.A. of only 3.91. (Note that the 25% adhesion traditionally used in calculating tractive effort for diesels is actually optimistic. Most railroads, in dispatching diesel locomotives with pre-1980 control systems, preferred to paly it safe and assume that only something like 18% adhesion could be relied on. Which means that in practice they wanted to operate their diesel locomotives as if they had an F.A. of 5.55!)

Cactus Jack--
As to Berkshires... The NKP Berkshires were just a bit smaller and just a bit less powerful than the Erie's, and I think had a very slightly higher factor of adhesion. Their designers had the data on the Erie's engines in front of them (NKP and Erie both had Van Sweringen links, I think), and I have always assumed (though with no documentation) that they were deliberately a bit more conservative in the specs for the NKP Berkshires than the Erie, ordering in the first flush of enthusiasm about "Super Power," had been.

Thanks to everyone for helping me get my head around this concept.

Just for the record...
The Erie's 1927 Alco Berkshires (the only one I have figures for at hand) had 276,000 pounds on drivers, 70,000 pounds t.e., for a F.A. of 3.94.
The NKP's first series of Berkshires had 261,100 pounds on drivers, 64,100 pounds t.e., for a F.A. of 4.07. (All NKP 700's had the same tractive effort, but later series were a bit heavier, and so had slightly higher F.A.)

Okay, I have chewed on this overnight and here is where I am at.

When dispatching diesels on tonnage the strategy was to bulk up on tractive effort and factor in total gross horsepower for desired speed. Basically put on a batch of SD40-2's or SD70Mac's and start lugging. A like number of GP40-2's would be dispatched on some other assignment that did not involve tonnage mauling.

Now to steam and lets see the example of the DL&W 4-8-4 (I believe Lackawanna referred to them as Poconos). 1631 class - had about 72,000 lbs of tractive effort as built with a F.A. of 3.8. From the diesel perspective this sounds like a good deal. Gutsy engine, good tractive effort, BUT if I understand even though the T.E. is higher as a factor of the calculated FA the engine is slippery. So, Lackawanna reduced cylinder diameter by 1" and raised the FA to 4.1. That sounds good until it is realized that TE is now reduced to 67,000 lbs.

Does my confusion make sense ?

Diesels and steam locomotives have very different power/speed relationships. The diesel, because of its electric transmission, can put its full rated horsepower into wheel-turning at any speed. (Not quite true -- transmission losses vary somewhat with speed -- but close enough for a first approximation.) At very low speeds this vastly exceeds what adhesion can turn into train-pulling (hence cases of diesels on a stalled train seriously damaging the rail under their wheels), but at slightly higher speeds means that pretty much the rated horsepower gets used for train-pulling. Steam locomotives, with the power cylinders directly connected to the driving wheels, have limited output at low speeds: low speed --> low engine r.p.m. --> power much lower than what the boiler can produce. (Hmmm... So for an efficient low-speed steam locomotive you would want a gearing arrangement that would allow engine r.p.m. to be greater than driving-wheel r.p.m. As Ephraim Shay realized!)

The DLW Poconos were expected to do their most useful work at reasonably high speeds: they were passenger(?) or fast freight(?) locomotives. Nobody expected them to do sustained maximum t.e. lugging. (With steam locomotives many more hills called for helpers than with diesels. Sometimes a switch-engine would even have to help a steam locomotive start a train out of the yard, even though the main locomotive was more than capable of keeping it going out on the main line!)

So, reducing cylinder bore might have made good sense. You lose a bit on maximum tractive effort, but maximum tractive effort wasn't that important! Operating at the speeds the locomotives had been purchased for, the cylinder dimensions weren't the limiting factor: at those speeds the locomotive would be operated at a cut-off that prevented steam from being admitted to the cylinder for the full length of the power-stroke anyway.

Reducing cylinder dimensions:
(i) Helped prevent wheel-slip at starting, though I suspect this was a secondary purpose, since a good engineer would be careful about opening the throttle too fast on starting anyway
(ii) Might actually have made the locomotive more powerful, or at least more efficient, at higher speeds, by getting a better ratio between what the steam valves could admit and what the cylinders would use.

Disclaimer: I am not a trained engineer, have no particular knowledge of the thinking of the DLW motive power department, am just guessing on the basis of general knowledge. (As for the DLW, I think there was a lengthy "Trains" article on their 20th C steam power some time in the 1970s. If that's not where you got your information from in the first place, I think I can find a reference for you.)

DL&W info came from a series of books by Thomas Tabor

I used it as a specific example of where my confusion lied in the relationship between FA and TE and general overall trying to figure out how a certain steam locomotive may have performed and why

The "Trains" article I was thinking about was in September 1965, and isn't helpful: general history of DL&W motive power acquisitions, no technical details, nothing about modifications to the 1600s.

It seems to me that you guys are looking at this backwards.

It appears you are under the impression that railroads designed the engines with a certain F.A.

As I understand it, it worked the other way: determine the operating characteristics needed, design the engine to produce those powers needed, and then do the math to see what the FA turned out to be. IF lower than 4.0, engine was considered slippery, and possible design rework before construction commenced.

Another consideration of the FA is the type of transmission involved. A steam locomotive had drive rods, creating a very odd power curve due to the reciprocating masses and the quartering of the drivers used to prevent deadlock at starting. To prevent slipping, the MAXIMUM PEAK tractive effort created had to remain below the adhesion limits. Because of the variable thrusts of the cylinders, the engine's tractive effort would be (real-world) lower than its maximum instantaneous effort due to averaging of the power available during the driver revolution.

Meanwhile, a diesel can provide continuous, even, smooth tractive effort. If designed well, the diesel can produce constant effort at just below the adhesion threshold, thereby producing a MUCH higher tractive effort rating compared to steam technology. This is why a diesel, weighing 425,000lbs can produce 142,000lbs of tractive effort at start where as (choosing a 6-drive axle for comparison) a UP Challenger (3985 model), having an engine weight of 627000lbs and 403700lbs on the drivers only produced 97352lbs of tractive effort.

FA was only used as an indicator of the engine's suitableness for a given job. And, because of the difference between engineering lab math and re-world results, it was only an indicator, an engine that would be expected to be slippery could turn out to be sure-footed, and vice versa.