Is there a formula to be able to find tractive effort for a steam locomotive?
Not really, ben. There are too many variables involved. However, one can come up with a broad ball-park figure by using the weight on the drivers (NOT the total weight) and multiplying by 0.1. That will probably be within a factor of 2 or so, if the locomotive has big enough cylinders and enough steam pressure and so on. Otherwise, one could also figure an approximation by knowing the boiler pressure, cylinder diameter, driver diameter, and crankpin radius of action and doing a little math.
do you want a quick rule of thumb, or something specific to certain classes of locomotives?
the quick rule of thumb is that tractive effort will never excede 25% of the weight on the drive wheels. In reality it’ll probably be much less, particularly at low speeds.
to get more in depth, you’ll have to know piston area, steam-chest pressure, stroke, etc,etc,etc. . . there are formulae out on the web.
you’re probably best off checking one of the railway guides or doing a search for your particular locomotive on the web and see what the manufacturer claims.
The steam locomotive is supposed to have lower tractive effort because the reciprocating forces result in an uneven pull, but on the other hand, on a non-articulated rod locomotive, all of the drivers are coupled.
The Diesel hydraulics had coupled drivers – not through siderods but through gears, almost like on a model railroad locomotive. They were supposed to have higher tractive effort than the pre-electronic wheel slip-controlled Diesel-electrics, but at the pain of making sure that the wheel diameters didn’t wear to different values. That was supposed to be a big minus for the Diesel hydraulic, but now the EMD AC’s have all the wheels on a truck electronically connected in speed through the one-inverter-per-truck arrangement and this doesn’t seem to be that big a problem.
I am kind of thinking that maybe per weight on driver, steam did a little better than pre-electronic Diesel electrics in multiple unit on account of the most-slippery traction motor effect along with weight transfer on the early truck designs, but a multiple unit Diesel just had so much more weight on drivers because it had so many drivers it was no contest.
There was this article in Trains a few months back about how Super Power steam had too many unpowered axles and too much HP for the powered axles. Were the railroads running shorter but faster trains in the steam days and the effect of the Diesels was to go for lugging heavy trains and lower speeds? It is only recently that single unit Diesel HP is anywhere near the HP of Super Power steam.
Dear ben13,
There is a formula:
TE = (kPS[B ^ 2])/D, where:
TE = Tractive effort (pounds)
k = Constant of mean effective pressure (usually 85% or 0.85)
P = Boiler pressure (in psi)
S = Piston stroke (inches)
B = Piston bore (diameter) (notice that it is squared)
D = Driver diameter (inches)
I hope I have helped,
Daniel Parks
By the way, I must respectfully disagree with Mr. King’s article.
-Daniel Parks
The above formula for tractive effort (with 0.85 BP factor) is used for computing starting TE at zero mph. TE will decline slightly up to 15 or 20 mph, then fall off fairly rapidly as speed increases. The reason for this is that the boiler on a modern steam loco will supply more steam than the cylinders can use in full gear up to about that speed. After that, TE is limited by the boiler capacity. That’s why shorter cutoffs must be used as speed increases. The explanation gets worse from here…
TrainJunky29 -
Do you disagree with the article because of a sound economic analysis, or just because you’re a fan of the UP or ATSF or C&O or NYC or PRR or N&W - well, you pick one - and that railroad could do no wrong?
The premise is one of actual use of a locomotive’s maximum drawbar horsepower. If it wasn’t used regularly, then the railroad paid more for its power than it needed to.
I haven’t got any figures to support it, but I think it’s a good bet that the Southern Railway got more gross ton miles per train hour per dollar (first cost, maintenance, operating) out of its USRA heavy 2-8-2s than C&O did out of its 2-6-6-6s.
When you factor in the dollars, some of the so-called great ones don’t look so good any more.
Old Timer
A similar analogy can be made with diesels. BRC could buy SD70ACe’s for their tractive effort and put them on Clearing’s hump but it would be a huge waste of money when the SD40/slug sets can do the same work for a lot less.
The N&W got it right for modern steam power. Their J 4-8-4 passenger jobs had 72" drivers, not the 80" typical, and were good for their fastest passenger trains. The had the A articulates for high speed freight, and yes they did run coal at 70mph on the eastern portion of the system to save buying and maintianing more coal-carrying cars, but they also had lots of MODERN Y-class 2-8-8-2 mallets for drag freights and nearlly all freight traffic in the mountains, where A’s would also handle passenger trains.
After electrification, the PRR relied on its WWI design locomotives right up to WWII when they mistakenly bought some J 2-10-4’s. Their postwar duplex experiments were not particularly successful. The fact that they could compete against the Central with lots of older power supports King’s article.
How did PRR get it wrong with the T1 and other duplexes? A duplex looks like a simple-expansion double-engine articulated put on a rigid frame. I guess the advantage of that is lighter rods and a disadvantage is increased wheel slip because you have just lost the property of making all the wheels turn at the same speed. Other than that, how hard could a duplex be? Did they ruin it with exotic valve gear or something?
On the subject or romance vs dollars and cents with regard to steam, I am too young to be a steam nostalgic – the closest thing to nostalgia I experienced lately was that I was sat in the back of a DC-9 right next to those 60’s vintage low-bypass fanjets that a certain power settings make a sound like the GE vacuum cleaner my mom used when I was young, and as the engines revved, I told myself to enjoy the experience while I still could.
I used to think that steam was, well, thermally inefficient and as for being replaced by Diesels, it was about time when it happened. These days, my attitude on steam is that it was a particularly elegant solution to getting a lot of power with fairly simple machinery, and given the cost differential between coal and oil, the thermal efficiency was not the big cost issue that killed it. I believe the cost issues were 1) the lack of M.U., and 2) the maintenance and inspections required to operate a boiler.
I am curious about the “could-have-beens” about the final days of steam along with the speculative "might-be"s about things such as the ACE 3000. We could run out of oil although I suppose the economics favor running Diesels on coal-derived liquid fuel instead of bringing back steam.
I suppose steam could have lasted another 10-20 years if steam people had made all the right decisions and the Diesel people hadn’t. I guess the clincher for Diesel over steam is that even the QE-II (the Cunard ocean liner) got reengined as a motor ship and lost its steam power plant and steam power will eventually go away in
I respectfully disagree with your comment referencing the PRR J 1 2-10-4.
PRR had a need for War time power to move the traffic that just groaned over the railroad. The USRA did not permit railroads to have any specific locos as they tightly controlled which railroad got what power. PRR needed power to move that freight and NOW. so…
The PRR elected to use the C&O T-1 as a starting point to BUILD a possible engine which finally was born as the J1. The J1 went on to become one of the largest non articulated and possibly the most powerful engine ever to hit the rails.
First some details. N&W J’s had 70 inch drivers not 72 inch. As far as A’s doing 70 mph with coal trains, 45 is more like it. Old Timer has more and better info than I do. I hope he checks in.
Paul raised some questions about PRR’s T1 duplex. There are as many myths concerning the T1 as there are accounts written about it. Most do not stand up in light of recent research (past 10-15 years). Early on (1960-1990), the same, sometimes incorrect, anecdotes were repeated over and over and the locomotive’s history suffered as a result. There was way too much entertainment and not enough fact. Current findings indicate the T1 was not as unusual as originally thought.
The duplex concept was valid from an engineering standpoint, but like most intended improvements, it had consequences that may not have been properly considered. A pair of two-axle engines is inherently sensitive to rail conditions, so particular attention would have to be given to locomotive components (e.g., suspension, sanding), the railroad’s physical plant, and proper handling methods. A duplex needed good rail contact and skillful operation to realize the benefits of the design. For these reasons, locomotive and track structure condition were more important than they would be for conventional locomotives. This attention was not free, and performance would have to be good enough to justify the expense.
The T1 has been endlessly called slippery. Part of this legend is true - the two prototypes were slippery for various reasons. It is also unarguable the T1 could be more prone to slip compared to a conventional 4-8-4 under identical rail conditions. This is a disadvantage of the duplex drive concept and cannot be ignored or dismissed. A conventional 4-8-4 will always have better adhesion under highly variable rail conditions. It stands to reason if a railroad cannot provide good track, consistent maintenance, and competent handling, a duplex will not be a reliable performer.
There a
Mark - Thanks for the kind words and motivation. It’s summary of about ten years’ worth of work. Keep an eye out, there’s more coming.
Felton – You’ve obviously spent a good bit of effort researching the T1!
Have to admit I’ve always sort of wondered what the T1 would have been like if a really good wheel-slip control, fast acting, had been available at the time (of, course, it wasn’t).
Don’t want to sound too picky but I think you’re confusing wars there, HighIron. The USRA was created during and dissolved not long after WW I. I believe it was the WW II War Production Board that limited PRR to purchasing locomotives of existing, proven design. There was still an awful lot of “Standard Railroad of the World” thinking and not a whole lot of innovation there at the time.
I’ve always thought that the WPB (or whichever of FDR’s alphabet soup agencies did it) did PRR a favor. I kind of doubt that Altoona would have arrived at as good a locomotive as the J1 if they had not been limited as they were.
Chuck
I agree with the analysis, and sorry added two inches to the J’s drivers, but I made a valid point. These were great 4-8-4’s and despite smaller drivers, could provide all the speed one could want. Basically, the duplexes did not make sense because they added additional mechanical complications and thus maintenance. An N&W J could have done anything the T-1 did and do it more reliably and economically. Of course you are right about the Pennsy’s J, but the King article made the very good point. If they had been speeding very long freights along the double track Crestline to Chicago their boiler capacity and horsepower could have been put to good use. But the PRR used them Enola - Altoona - Pittsburgh and they ended up simply substituting for 2-10-0’s that did the same job just as economically and that was the mistake.
I don’t blame the PRR for wierd ideas in general. The DD-1 was surely wierd machine, but they did the job and survived on the LIRR into the diesel era, both freight and passenger work. As a kid I saw a DD-1 on a local freight on the Long Beach branch.
Our thread has wandered away from the original question, which was a request for the formula for tractive effort of a steam locomotive. On the original question, for those who do not want to do the math, a quick estimate would be to take the weight on the drivers and multiply by the listed factor of adhesion (listed on the same spec sheets which have e.g. piston diameter and stroke). This does not take into consideration driver diameter – the overall number goes down as diameter (and with it speed capability) goes up – but often design made up for that.
With regard to steam design, remember that the one characteristic of steam locomotives was the individual targeting of their design. N&W Js were designed with small drivers because the locomotives were expected to pull passenger trains in relatively hilly country at certain anticipated speeds (driver diameter does make a difference here as well). Js probably could not have out-muscled a U.P. 800 on flat terrain, but they were not meant to. The 800s were designed to haul passenger consists at speeds of 80-100 mph. They came off the drawing boards at a time when railroads were truly private companies and could set their own speed limits and safety rules. The federal government subsequently limited passenger speeds to (I recall) less than 74 mph. That of itself took away at least a little from the 800s’ performance while the good ol’ Js kept right on going.
Re the remainder of this thread, thermal efficiency and fuel cost, as well as labor and maintenance, very much factor into the decision to dieselize – just look at the railroads which kept their steam to the end. N&W and U.P. in effect enjoyed free fuel, since they owned their own coal mines; and, since that made a difference on the bottom line, for them steam stayed around, even though Jabelmann for U.P. wanted to dieselize before WWII.
Thermal efficiency is another factor, since how much fuel one has to burn to get a given amount of power also figures into fuel
One very important factor thus far not included: DYNAMIC BRAKES. Diesels have a tremendous advantage in bringing a train down a grade with the car wheels cool.
The 0.58 BP factor included in the formula for tractive effort (given much eariler) may also be explained thus:
“Broadly speaking, in a two-cylinder engine, the arrangement of the cranks is such that … if the mean tractive effort be 40,000 lb. at one point in the (driver) revolution the tractive effort will rise to 50,000 lb., and unless there is sufficient weight on the drivers the engine will slip.” Locomotive Cyclopedia, Seventh Edition - 1925, p. 198.
A couple of points, here. First, my old neighbor Vernon Smith worked for Franklin Railway Supply Company which provided the poppet valves for the Pennsy T1, and he makes the very valid point that for a limited time - until diesels - the T1s did their job and took everything that came their way. He thinks the slipperiness was over-emphasized. He spent a lot of time with the T1s as a Franklin representative (he also worked on Burlington’s poppet valve 4-8-4 and Santa Fe 3752).
But one can say that the Duplex concept came along too late in steam’s reign to be properly developed; I don’t think they ever got the T1s weight distribution right and as noted above, two four-coupled units will be more slippery than one eight-coupled one.
Another point is this: It might have been, and there is no documentation for this other than what happened on other railroads with the same situation, that the T1s were not operated properly because each one replaced two crews - the guys running the doubleheaded K4 Pacifics they replaced. If you read accounts of their operation, you will note that some crews didn’t have the trouble with slipperiness that others did, because the engineers took the time and used the patience to handle the engine properly at low speed. But others did not.
As far as the N&W was concerned, it carefully matched the engines it designed to the jobs it wanted done. It designed the J to be able to start 15 car trains at the foot of a crooked hill and accelerate out of the hole; to handle the same train at track speed up a mountain with more than 1.3% grades. It designed the A with a horsepower curve that would permit handling heavy trains on less graded territory at high speeds. It designed the Y-class to lug tonnage on crooked mountains, which it did. These were the things that kept N&W at or near the top of the heap in the early 1950s when it was still all steam in the categories of Gross Ton Miles per Train Hour and Gross Income carried over to net. These were the