ALL THINGS N&W 611

the stated tractive effort is 80,000 lbs,
but according to the formula for tractive effort, with a coefficient of .85 is 84,981 lbs
but a locomotive with roller bearings equipted should have a coefficient of 1, which would yield a max tractive effort of 99,977 lbs.
maybe that's why it was so slippery back when it was operational...

oh, the formula is
T = cPd(squared)s / D

t is tractive effort
c is a constant representing losses in pressure and friction; normally 0.85 is used (1 is used when roller bearings are specified)
P is the boiler pressure
d is the piston diameter (bore) (this is squared)
s is the piston stroke
D is the driving wheel diameter

Fan Railer--
You probably know a lot more about this than I do, but do you REALLY have a coefficient of 1 with a roller-bearing locomotive? The bearings will certainly reduce frictional losses in the running gear (but not QUITE to nothing!), but there are other losses in the system: internal restrictions in the steam pipes ("wire drawing" the steam), temperature loss between the header and the cylinders (this is significant: Chapelon found by experiment that reducing it by putting steam jackets around the steam pipes made a major increase in locomotive efficiency), back pressure (reduced by improvement of front end design, such as doble stacks, "Kylchap" blast pipes etc etc). Coefficient c ought to reflect all of these.

Passenger steam locomotives tended (i.i.r.c.) to have an adhesion factor (weight on drivers divided by tractive effort) well above 3: typically closer to 4 than to 3. What was J class weight on drivers? Weight per driving axle of 70,000 (what the New York Central claimed for the Niagara) and a stractive effort of 80,000 would give an adhesion factor of 3.5, which is low enough to make one fear a slippery engine even if the t.e. hasn't been underestimated.

Allen Hazen wrote:Fan Railer--
You probably know a lot more about this than I do, but do you REALLY have a coefficient of 1 with a roller-bearing locomotive? The bearings will certainly reduce frictional losses in the running gear (but not QUITE to nothing!), but there are other losses in the system: internal restrictions in the steam pipes ("wire drawing" the steam), temperature loss between the header and the cylinders (this is significant: Chapelon found by experiment that reducing it by putting steam jackets around the steam pipes made a major increase in locomotive efficiency), back pressure (reduced by improvement of front end design, such as doble stacks, "Kylchap" blast pipes etc etc). Coefficient c ought to reflect all of these.

Passenger steam locomotives tended (i.i.r.c.) to have an adhesion factor (weight on drivers divided by tractive effort) well above 3: typically closer to 4 than to 3. What was J class weight on drivers? Weight per driving axle of 70,000 (what the New York Central claimed for the Niagara) and a stractive effort of 80,000 would give an adhesion factor of 3.5, which is low enough to make one fear a slippery engine even if the t.e. hasn't been underestimated.

you have a good point here, and i was considering those factors. in light of that, i have created an excel spreadsheet of major locomotives and tractive effort calculations, and it is absolutely obvious that when railroads determined the tractive effort of their locomotives, some took into account the coefficient factor very well, while others simply ignored it and assumed a general number of either .85 or 1.
however i apparently can't attach the excel doc because it's not allowed, and i have not completed it anyway, as i still have to add in the hypothetical adhesion calculation factors.
i will try to post the word document format. well, i guess you cant attach anything on this forum (lame), so i will try this: pm your email to me if you want to see the doc, and or help me out with the adhesion factors...

Fan Railer wrote:others simply ignored it and assumed a general number of either .85 or 1.

Who assumed 1?

timz wrote:

Fan Railer wrote:others simply ignored it and assumed a general number of either .85 or 1.

Who assumed 1?

depends on the railroad, and then the locomotive itself. if it has roller bearings, railroads typically assume 1.

Fan Railer wrote:if it has roller bearings, railroads typically assume 1.

Got an example of that?

timz wrote:

Fan Railer wrote:if it has roller bearings, railroads typically assume 1.

Got an example of that?

hmmm, actually i'm still looking, seems that most railroads stick with the .85 assumption, regardless. but there's probably some out there....

My understanding, from years ago, is that the .85 constant had to do with losses in BOILER PRESSURE to the cylinders due to friction and flow restrictions, a function of throttle, drypipe, steam chest and valve design, which is essentially what Allen pointed out. I don't think bearings or rolling resistance had anything to do with the standard TE formula. But then again, maybe its time I go back to school. Hey, we didn't have computers or spreadsheets then-

From what I understand, the tractive effort formula is often symbolized differently:

TE = P x C-squared x L, all over D, all times .85

where

P = boiler pressure (psi)
C = cylinder diameter
L = cylinder stroke (i.e., length)
D = driver diameter
[these last three in inches, of course]

It's the same formula as above, but with different letters.

Source: William Middleton, "Locomotive Power," an article in RAILROAD MAGAZINE in the 1950s. (Sorry, I only have the clipped-out article so I don't know the exact issue date.) Middleton did not include the .85 in the formula, but discusses it in the article where he relates it to a percentage of the boiler pressure. He states that this formula applies to rated TE when starting, but as speed increases the full steam pressure cannot be applied because of valve gear cutoff.

I have frequently used this formula to calculate rated TE when it is not specifically stated, and it always works out. For example, the Canadian National system used to give its engines a percentage rating on the cab (e.g., 40%, meaning 40,000 pounds) and when I would use the locomotive's specifications to refigure the TE it would always approximate that percentage.

The formula is a bit more complicated for a 4-cylinder compound articulated, of course.

Richard Leonard

The factor of 0.85 is generally used to estimate the average pressure loss from boiler to cylinders. Some also equate 0.85 x BP to equal mean effective pressure in the cylinders. Either way, it does NOT contain a friction component as used in the U.S. The higher adjustment reflecting the effect of roller bearings on tractive effort was used by Timken to tout the advantages of its roller bearings. What IS affected by solid or roller bearings is drawbar pull at the rear of the tender. Roller bearings will reduce friction losses within the locomotive and tender and more of the cylinder TE will get to rear coupler as drawbar pull.

Some railroads used adjustment factors lower than 0.85 to reflect the effects of limited cutoff at starting. ATSF used 0.70 to 0.73 for its latest 4-8-4's and 2-10-4s. In both cases, this estimating method understated actual STE and TE at low speeds.

611's TE can be considered understated at 80,000 lbs. Under certain conditions Test reports and graphs from N&W indicate that drawbar pull readings (not TE) of 79,000 to 83,000 lbs below 5 mph could be achieved under ideal conditions. This would be roughly about 82,000 to 86,000 lbs TE.

Keep in mind the relatively large cylinders on a J were not intended to pull up stumps at 1-2 mph. N&W had plenty of Y6's to do that. They were intended to accelerate trains from 25 mph slowdowns going into curves back to 45 mph frequently, and to move 15-car trains anywhere on the railroad, regardless of the grades encountered. Part throttle was usually sufficient to get out of town as fast as most engineers wanted. In the overall scheme of things, the rated 80,000 lbs TE for a J is not that important.

Feltonhill--
Thank you very much for the information on the N&W 600 (& the image of a Y6b being used to pull up stumps!).
Vocabulary question: I think I've somewhere seen what you call "drawbar pull" called "drawbar tractive effort": do you know if this is common alternative terminology? It seems to me as if your "drawbar pull" and (what is usually called) "tractive effort" are related in about the same way as "drawbar horsepower" and "indicated horsepower." Am I missing something here?

This is an interesting discussion. I am not a “steam tech” type or an expert, though I have maintained an interest in such issues for more than five decades, and have some further thoughts.

It seems to me that, logically, neither bearing friction nor the adhesion factor could be figured into tractive effort (there was some reference to these in the preceding discussion). Although they may be significant factors in certain cases, I would think that they would be too variable, even for a specific locomotive class, to be factored in.

In the article I cited, Middleton states that a factor of adhesion (or coefficient of friction) in a range of 4 to 4.5 was the standard railroads generally worked with; it is the ratio of weight on drivers to tractive effort, meaning that a locomotive exerting 40,000 pounds of TE needed at least 160,000 pounds of weight on the drivers. However, the adhesion factor required to take advantage of the available tractive effort without slippage would vary depending on weather conditions, grade, tonnage of the train and other factors. Hence it would be hard to put into a formula.

As to friction in the locomotive “drive train” (so to speak), it seems that any reduction in friction that might be advantageous would begin to assume less importance as the amount of drag from the train itself (journal friction, track curvature friction, etc.) became of greater significance, and would be hard to quantify in a formula. Again, it seems that the advantage of roller bearings on axles or side rods would be more of a maintenance and lubrication issue than a contributor to pulling power.

So we are stuck with the usual formula that takes into account what amount of force the locomotive can apply at the cylinder and main rod. Even that, of course, is an approximation but it does provide a standard means for comparing the pulling power of different locomotives.

However, as I stated, I am no expert on these issues and yield to those more well-versed in the technicalities of steam propulsion, which is certainly not my doctoral field.

Richard Leonard

Oh, I feel stupid!
The tractive effort equation Fan Railer gave (leaving out the units to use, which Rlsteam provides) seemed too simple to me: as if it was missing a factor.... Until I remembered that driving wheels as well as cylinders are round! So, the Pi you use in calculating driving wheel circumference (for how far the locomotive travels in an engine cycle) and the Pi you use in calculating piston area cancel out! Doh! (Bangs forehead.) And then you get the formula given. (Well, for a two cylinder locomotive: double the result if you are doing it for a four-cylinder simple articulated.)
---
So. Using this formula with a coefficient of 1 would give you a "tractive effort" (force) calculated on the assumption that the steam exerts 100% of full boiler pressure on the piston over the full 100% of piston travel(*). This is unrealistic for a whole bunch of reasons, even if we ignore the sort of drive-train friction roller bearings are supposed to reduce. (Cf. posts by EDM5970, Rlsteam, and Feltonhill.) The value .85 for the coefficient is meant to allow for ALL these reasons, AS WELL as drive train friction.

Using the coefficient of .85 does seem to give the published values for early 20th century locomotives. (I tried it on a USRA light 2-8-2 and-- rounding to the nearest hundred pounds-- got the published value of 54,700 lbs t.e.) But roller bearings have to be good for SOMETHING! What coefficient (<1 but >.85) SHOULD we use for roller-bearing steam locomotives? I've found one published hint: in an article on the Norfolk & Western A-class 2-6-6-4 in the July 1993 "Mainline Modeler," Robert LeMassena gives a computed value for tractive effort (105,000 lbs, operating at the original 275 lbs/sq.in boiler pressure), but comments :"This figure was calculated from the AREA(**) formula which includes an 8% reduction for friction. For this engine, with roller bearings on all axles, the tractive effort should have been 115,000 pounds."

So maybe we should think of a coefficient of, say, .92 for calculating t.e. of roller-bearing locomotives?
---
(*) In the 1920s and later, many steam locomotives designed for use at comparatively high speed had "limited cut-off": valves and valve-gear designed so it was impossible to admit steam to the cylinders for the full length of piston travel. I suspect a "deluxe" version of the formula-- sorry, I don't have any steam era technical manuals on hand! -- would include a reduction for this.
(**) American Railway Engineering Association?

Allen Hazen wrote:So maybe we should think of a coefficient of, say, .92 for calculating t.e. of roller-bearing locomotives?

Far as I'm concerned might as well stick with 0.85, and separately note the bearing type. All we're doing is calculating the "nominal" TE as a convenient basis for comparison; we know it's not guaranteed to equal the engine's actual starting TE. When Alco/UP said the 4-8+8-4 had 135,375 lb TE (which is what you get using 0.85-- cyl 23.75 by 32, drivers 68, pressure 300) they probably figured everyone could apply whatever roller-bearing correction they wanted to that figure.

Don't want to have to catalog different coefficients for engines with roller bearings on drivers only, or on the engine but not the tender, or for engines with roller side rods.

Allen Hazen wrote:I suspect a "deluxe" version of the formula-- sorry, I don't have any steam era technical manuals on hand! -- would include a reduction for this.

They might make their best guess, but there won't be any "official" factors.

Allen Hazen wrote:Robert LeMassena gives a computed value for [class A] tractive effort (105,000 lbs, operating at the original 275 lbs/sq.in boiler pressure

Cylinders 24 by 30, drivers 70, so using 0.85 the nominal TE comes out 115,400 lb at 275 psi. Dunno why N&W only claimed 104,500 lb; FWIW, maximum cutoff was around 75%.