How does an engine’s tractive effort translate into number of freight cars it can pull? Is there a formula?
This is a short answer that I hope it will help, but there is a lot of testing and evaluation to setting the tonnage rating on an engine for each railroad. This is done by the individual railroads since each company has different percentage grades and they have rules for all of their divisions.
Tractive effort translate into how large or long a train the engine will start moving but the Horsepower rating is how fast or how well it can keep tonnage moving up grade or how fast on the level.
Railroads used some sort of formula for steam from testing on new power on the grades involved. The tonnage ratings on an engine is still used by railroads and this is important for any major grade or pass when the engines are working at near their maximum performance on tonnage.
Tractive effort is the force due to friction between the locomotives wheels and the rails. Force equals mass multipled by acceleration. The force the locomotive’s tractive effort must overcome is the friction force between the cars’ wheels and the rail, part of the cars weight (if the train is going uphill), and the drag (resistance to move due to air, which is usually negligible). If the tractive effort equals these forces, the train will have zero acceleration (constant velocity). Therefore the locomotive must have more tractive effort than the sum of the other forces to accelerate the train. The amount of cars a locomotive with certain tractive effort and pull depends on the grades the train will operate over, the radii of the curves it will go through, the speed the train will travel at, and the wind.
Short answer is yes there is, sorta. What railroads figure out is the “tonnage” rating for an engine, not how many cars it will pull. The tonnage rating depends on tractive effort of the engine, the grades and the curvature of the track.
It can expressed as a “grade factor” or as a rating for each engine for each track segment or as a horsepower per trailing ton requirement for each segment.
The railroads add up the gross weight of the train and then use that to figure how much engine or how much train can be handled.
Dave H.
Besides tractive effort you have to take into account how steep the grade is.Some railroad timetables used to list how many tons various locomotives could haul.
Quick rule of thumb. On a real railroad running diesels, a train needs the same hp/tt (horsepower per trailing ton) as the ruling grade in %. So if the ruling grade is 1.2% then a typical train will need 1.2 horsepower per trailing ton. A 5000 ton train would need 6000 hp. Higher priority trains need more. Trains with all AC consists need less.
Dave H.
Tractive effort is about 25% of the engine weight for steel wheels on steel track. Some modern diesels get higher tractive effort by allowing the wheels to slip all the time. This is the high pitch whine you hear on tangent track. Horsepower has more to due with speed as stated above. Many engines limit the horsepower at low speeds to stop wheeel slip.
Don’t forget the grade is actually the “ruling or effective grade”. This is a combination of actual grade (elevation change) and track curvature. A 1% vertical grade can act more like a 3-4% grade to the locomotives, if there are significant curvatures in the track. I think there was a nice piece on effactive grade in MR within the last couple of years. This is something very few modelers actually consider when planning a layout.
A lot depends on the bearing type of the cars being pulled. The solid bearings used on cars built before the widespread introduction of roller bearings had a higher starting resistance than rolling resistance (i.e. if the loco could start the train, it could pull it).
Years ago, I read a railroad engineering book from 1931 that stated that generally speaking, a loaded freight car had a starting resistance of 6 lbs/ton of car weight which immediately dropped to 3 lbs/ton once under way. It was common practice for engineers to “take slack” when starting a heavy train with a steam locomotive. IOW, no effort was made to start the whole train all at once. A heavy Mikado with 60,000 lbs TE could actually then start and pull a 10,000 ton train on level tangent track. As a practical matter, however most trains in the steam era were not loaded down to that extent. Even the Duluth, Missabe and Iron Range, which routinely pulled iron ore trains of upwards of 13,000 tons used steam locomotives with nearly twice the necessary tractive effort to get the train started.
None of this really helps, does it? For rule of thumb purposes, a 40 foot box car with a capacity of 50 tons weighs 20 tons empty. Assuming a capacity load (weight wise), the same car would weigh 70 tons loaded and require 420 lbs of tractive effort to start on level tangent track.
Oh yeah, one more thing, rolling resistance, even if it dropped once the car was underway would increase with speed and would increase dramatically on an ascending grade. Just to illustrate, an SP C-9 2-8-0 had 45,000 lbs T.E and could have started and pulled 7,000+ ton train in the San Joaquin Valley. In Tehachapi, the tonnage rating dropped to about 475 tons.
Andre