Hi, Douvgg,
Not to add to the confusion, but TE is more a measure of how much weight the engine can set in motion, forget speed. HP is a measure of what a locomotive can haul at speed. Generally, you need one unit of HP per ton of train, up to 60 mph. Then you really have to pile on the HP. I think at about 80, you need 19HP per ton of train. Also, and this is very important, you have to figure in the grade. Once you start up grade, all bets are off, your hauling capacity is greatly reduced, so pile on the HP. Going upgrade is really more dependent on TE than HP. Also important if to recognize HP is always IHP, indicated HP. Once you determine the HP, multiply by .85, to get the IHP. That's because many unspecified factors affect HP, such as valves not closing properly, etc. How to convert TE into HP? Good question. The formula I recall is that you divide the TE by 7. For example, it is said that Big Boy could haul a train five miles long. Probably true. But that is going purely on TE. The train would probably be rolling along at about 5-10 mph. To get any real degree of speed out of a Big Boy, the train would have to be kept to a mile or so long. Also important is the fact that both TE and HP have P (pressure) in their formulas. If the engine can't keep up P, then forget it. I think that the ratings for most steam locomotives were based on the MAWP (Maximum Allowable Working Pressure).
Traditionally, engine crews didn't give a hoot about al; these formulas and loved to make disparaging remarks about the so-and-so's who calculated them and what they didn't know about stem locomotives. The crews went strictly on their experience with the locomotive.