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http://www.n0kfb.org/rail/railphs.htm "Horsepower is pull times speed. You can have pull with _no_ HP. Example: A 15,000 ton coal train sitting on a 1% grade and being held there by the engine brakes alone has 300,000 lb pull on that first coupler. But there is no horsepower being produced. The factor of adhesion for a steel wheel on a steel rail is between 20% and 30% of the weight on the wheel. So to prevent that coal train from pulling (sliding) those locos back down the grade the locos need to have at least 300,000 lbs of adhesion. This means they must weigh at least 1,000,000 lbs because 30% of 1 million is 300,000 lbs. The maximum weight per wheel, to prevent crushing the rail, is 35,000 lbs (70,000 lbs per axle). So we need a loco with at least 29.6 wheels, each of which is weighted to 35,000 lbs. 30 wheels is 15 axles or four 4 axle units minimum. It could also be 3 six axle units which would be 18 axles. Or it could be two 6 axle units and one 4 axle unit for a total of 16 axles. The point is that you have to have that one million pounds on the wheels and you are limited to no more than 35,000 lbs per wheel. Adhesion as described above and Tractive Effort are closely related and can be though of as the same thing in many cases in that the amount of adhesion limits the maximum TE that can be used. TE is usually quoted at a specific speed. TE is the pull at the drawbar. HP is the amount of pull (TE) times the speed. So while our coal train is just sitting there on the grade there is no HP required. But try to move it at 1 mph up that hill and HP is required. The required HP is the TE needed (300,000 lbs) times the speed (1 mph or 1.47 ft per second) divided by the definition of a HP (550 lb-ft per second). So the HP required is 801 HP! Yes just 800 hp will move this coal train up the hill. Amazing isn't it? But will one 800 hp unit do it? No! Because that one 800 hp unit must have at least 1 million pounds on its drivers to prevent it from sliding back down the hill. You MUST have the adhesion required. This means each wheel of an 800 hp 6 axle unit would have to have 84,000 lbs on it. Oh my the busted rails that would leave behind! As I said above, the minimum number of axles we need to spread out the required weight is 15 axles. Now it doesn't matter whether we have one 800 hp 4 axle unit and three 4 axle slugs, or whether we have four 200 hp units. It is all the same to the coal train. " quoted from Al Krug; a discussion on locomotive and train dynamics
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