I just happened upon an old Lima Locomotive ad that touts their New York Central 4-8-2s pulling NYC’s premier Pacemaker freight trains. According to the ad these were 75 car trains in a hurry, so they had to make 65 mph. Now, assuming 75 tons per car plus 375 tons for one engine and tender we have a 6000 ton train rolling better than a mile a minute. Are my assumptions valid? Does anyone have a formula to determine exactly how much horsepower is needed for that performance? I’m sure one of you engineers can do this one in your head, but it is one of those things I didn’t learn in Liberal Arts school.
Come to think of it, I didn’t learn anything in Libarts, although it did get me a commission in the Navy, but that’s another story.
The NYC 4-8-2 could pull a 6000 ton freight at 60MPH all day - on NYC’s virtually grade-free rails. Move the same loco and train to almost anywhere south (or even to the B&A) and the picture would change dramatically.
IIRC, the NYC L-4 tested somewhere between 4500 and 5000 hp at optimum speed.
Where R=Rolling resistance in pounds per ton of train, W=Weight per axle in tons, V=Speed in MPH, N=Number of axles per car, G=Per cent of grade, and C=Degrees of curvature.
As is evident, grade is the largest factor since the locomotive(s) must lift the train instead of just moving it forward. On NYC’s Water Level lines the trains rolled easily.
I think you’re high on the 75 tons/car assumption. The Pacemaker freights were for the LCL business and LCL tended to load light. I’d guess about 26 tons for the light weight of the car and another 26 max for lading.
The Pacemaker freights were about all the dang government would allow the NYC to do as it attempted to remain competitive with the truckers for the lucrative LCL/LTL business. When the truckers first became a competitive factor, in the 1920’s, the NYC introduce intermodal container service to compete. The government regulators put a stop to the intermodal system in 1931 by ordering rates increased to a level that was not truck competitive. This was,
I’m guessing the ad didn’t specify 65 mph for 75 cars on the level? They could have meant 65 mph on the downhill bits?
I’m guessing less.
That’s the Davis formula he quoted; if you run thru it you’ll see it says 65 mph with 75 loaded cars on the level is impossible. Nobody knows how close the formula is, but I bet it’s right about that.
Regardless of what locomotive was up front, a 6,000 ton train of 75 boxcars at 60 mph would require something approaching 8,000 DBHP on level track. No 4-8-2 could manage this. A C&O H8 would be lucky to develop this kind of output on a day-to-day basis.
If the Pacemaker service was LCL, why would the boxcars be loaded to 80 tons? I suspect that the train weight didn’t exceed 3000 tons.
NYC always rated their locomotives very high with respect to DBHP, if you’re considering the curves in Paul Kiefer’s book, A Practical Evaluation of Railroad Motive Power. However, what these curves don’t indicate is the evaporation and firing rates required to develop these readings. They would have to be very high, well beyond what could be economically expected on a routine basis.
So you’re saying that the 1.7% Purgatory Hill and the 1.1% Big Moose hill on NYC’s Adirondack Division might have been a limiting factor? (Not to mention a few 5.5 degree curves…) [swg]
Having read all the above comments I have to agree my guess of 75 tons per car was high. But I think your 3000 ton estimate is probably low. A 75 car train of 3000 tons would amount to only 40 tons per car and even less if the 3000 tons includes the locomotive. An average box car of the time weighed about 26 tons, which leaves only 14 tons payload - probably too little to move profitably by rail. Maybe we could compromise at 50 tons per car.
If I did the math right 75 50 ton cars should weigh 3750 tons. Add 380 more for the loco and tender and you get a requirement of 27503 lbs tractive effort to move the train 65 mph on straight, level track. The ad, btw, said the trains moved “up to 65 miles per hour” (maybe down hill) with “up to 75 cars.” So that leaves a lot of wiggle room.
But the question I am really asking is what amount of horsepower is needed to meet that performance. Felton, your estimate is what I am looking for, but I would like to nail it down mathematically with a formula, if there is one. The Davis formula works for required TE, but there must be something similar for HP. I hope.
IF the Pacemaker ran into the Adirondacks, those would have been limiting factors. Most of its run was on the ‘Water level route,’ and the Mohawks would have run Harmon - Chicago and reverse. Not many grades along the Hudson, the Erie Canal or the Ohio shoreline.
IIRC, the Pacemaker cars were the first significant application of roller bearings to freight cars - which also would tend to skew the curve of train resistance.
Davis equations estimate train resistance and the drawbar pull necessary at the rear of whatever locomotive is attached to the head end. It doesn’t estimate tractive effort. The Davis equation listed above is good enough, although I use a slightly different version for the frontal area third term. Also, since NYC was considered a well engineered and maintained railroad in the 1940s, the modified Davis equation may be appropriate. This is simply 85% of the original equation.
There is a mathmatical relationship between tractive effort, drawbar pull, speed and respective horsepower (indicated and drawbar).
Indicated HP = tractive effort x speed/375
Drawbar HP = drawbar pull x speed/375.
Keep in mind, tractive effort doesn’t pull the train, drawbar pull does. Tractive effort is measured at the cylinders. After subtracting the resistance of the engine and tender, what’s left at the rear of the tender is drawbar pull. Based on the figures you gave, 27,503 lbs TE would be 4,767 IHP. That’s easily within the range of possibility for an L4. However, if you meant train resistance, then you have to consider drawbar pull and DBHP. Now, 4,767 DBHP would be a stretch. Kiefer’s book rates an L4 at 4,300 DBHP maximum in the 50-60 mph range, which would be about 26,875 lbs DB pull. I consider this a very high figure for a 4-8-2 no matter how well designed. When compared to other locomotives and actual test data, I suspect that the figures reflect a high evaporation and firing rate, higher than would be expected during daily service. There’s nothing wrong or fishy about this. PRR did the same thing during many of the Altoona tests in order to determine maximum boiler capacity.
Steam locomotive output figures are a source of great interest, but they are also troublesome if one doesn’t know the purpose of the test, or the conditions under which the test figures were developed.
The ruling grade on the Water Level Route was about 0.7%. It was on the “hill” between Rochester and Buffalo after the RR gets away from the Mohawk River/Barge Canal. The is another 0.7% grade westbound out of Cleveland where the RR climbs away from the Lakefront to get on top of the escarpment along the lake edge.
Checking a few timetables, it looks like the 65-mph limit applied to the listed symbols (NB-1 etc) when they had 60 cars or less-- or maybe a 40-car limit in earlier years.
Overall schedule speed for the fast freights was somewhere around 40 mph, but no idea what they averaged based on running time.