Btw - this is not terribly relevant for model railroading - there you have to test what each locomotive can pull, or just make up some more or less arbitrary rule - like “three cars per driving axle on the locomotive” or some such thing.
A model railroader tend to want to put on more locomotives than a railroad would have used - they try to get away with as few locos as they can, we try to use as many locomotives as we can
Tractive effort will give you some idea of how much a locomotive can start from a standing stop and/or move at low speed. Secondarily, it will give some indication of how much can be dragged upgrade.
Horsepower will give some idea of how much speed a locomotive can achieve, especially up grades.
Entire engineering textbooks have been written on the subject, and I doubt that there has ever been a unanimous opinion on which was more important.
HOWEVER - as Stein said, the entire business is irrelevant to a model railroad. Only a very few of us can assemble and run a prototype length train that would be a challenge to modern motive power or superpower steam. Very few model locomotives could ever exactly duplicate the pulling power of their prototypes. Two examples:
A recent model of a large articulated noted for its ability to handle heavy tonnage proved to have rather modest pulling power, a disappointment to modelers who wanted to put it into drag service.
A solid lead model of a German-built (in 1873!) 0-4-0T can easily pull a ten (modern) car train, at least four times the tonnage its prototype was ever expected to move. It also pulls it at a speed which would have destroyed the loco due to dynamic augment.
Chuck (Modeling Central Japan in September, 1964 - including that 0-4-0T)
There are just way too many variables when it comes to pulling ability. Horsepower is a very unreliable indication of pulling power. The 2 most important are tractive effort and factor of adhesion. A simple explanation is taking 2 locomotives with the same HP rating say 3000. one has a factor of adhesion of 2.5 and a tractive effort 40,000 lb. The other has a factor of adhesion of 5 and a tractive effort of 60,000 lbs. The second loco puts more power into starting a train and powering over the rails. The first may be faster and keep up the power at speed but can not start a train and hill climb without help. TE and FoA are better indicators of pulling capacity.
Prototype railroads rate the pulling capacity in tons, not the number of cars. They have tables showing the tonnage capacity of each class of locomoltive for various parts of route. Besides the raw tractive effort and horsepower, tonnage rating will depend on the nature/extent of grades and curves as well as the desired/anticipated speed.
One thing to keep in mind is that the maximum drawbar pull of an HO scale locomotive not equipped with traction tires is about 25% of its own weight, and many don’t approach that. How that translates into number of cars depends on the rolling quality of the cars, car weight, grades, curves, etc., etc.
I had read that it takes 7 lbs of force to move a ton on railroad trucks, which accounts for friction of the wheels. so, a tractive effort of 50,000 would be able to move 7143 tons. If a loaded hopper, for example, weight 71 tons, then that engine could move a train of 100 hopper cars.
some trigonometry shows that for a 0.3% grade, 7 additional lbs of force are required to pull tons up the grade. this would double the force needed to pull the car on a flat grade. A 1.05% grade would require 7 + 21, or four times as much. A 2.45% grade would require 8 times.
but my understanding is that many steam locomotives were designed for specific routes. So a particular engine may be suitable to start the train out of the yard and get it up to sufficient speed that it could climb up the maximum grades on a specific route, reaching the peak with just enough speed to carry it over and continue to it’s destination. It doesn’t need to be able to haul an train up a grade from a stand still. And then of course there is helper service and using multiple engines
TE and Adhesion to get the train moving, horsepower to maintain speed. Small 1000HP and under switchers could move lines of cars a larger road loco with 2-3x the horsepower couldn’t get started, but they could only move that cut slowly - perfectly adequate for switching duties, but to get the expedited merchandise over the road quickly needs more horsepower.
Yes there are some other factors, including the fact that many switchers had friction bearings and thus even if they could, wouldn;t have been able to sustain high speeds, etc.
FOr models, unless we are blessed with a barn to build in, we have to scale back our trains anyway. If the prototype ran 50-60 car trains, we might be able to run only 10 to keep the loco from chasing the caboose and to keep the train from spreading across 4 towns. Thus the concept of comign up with a ‘tonnage rating’ based not on the absolute pullign power of the loco but on other factors such as number of cars per axle. Using that formula as an example nets you a 12 car train for a 4 axle diesel. A typical 4 axle loco like a Proto 2000 GP-7 can pull way more than 12 cars, however just liek we have to selectively compress the length of track, we have to selectively compress the length of trains proportionally.
A handy rule of thumb is horsepower per trailing ton (hp/tt). Divide the horsepower by the hp/tt to find the tonnage.
Drag freights generally have 1/2 hp/tt, piggyback trains are in the 2.5 to 4 hp/tt range.
Generally a train can get up a grade the same as its hp/.tt.
As with all things, this isn’t accurate in all cases, its just a rough estimate to gauge tonnage ratings. It was used by prototype railroads.
So a 3000 hp engine at .5 hp/tt would handle 6000 tons. If you put the engine on a 3 hp/tt piggyback train it would only be rated for 1000 tons. If the engine was on a 2% grade it would only be good for 1500 tons.
