The tonnage rating of the locomotive is based on the gross wieght of the car. There are formulas used to determine how much tractive effort is required to move so many tons of train. Within certain perameters, the total number of cars isn't as important as the total trailing tonnage. To account for the addition curve friction of longer trains, the DRGW added an "adjustment factor" to be figured in the gross tonnage of each car.
There are 3 formulas used for figuring tonnage ratings, and the results of these formulas are added together to determine the tractive effort needed. The 3 equations determine how much TE is needed to move a train on flat ground (basic rolling restance), up grades and around curves. Because a locomotive uses some it its power just moving itself, the total gross tonnage (train and locomotive) must be used in the following equations.
(BTW - this info comes from a Heisler Locomotive Catalog reprint)
Rolling Resistance - 8Lb. X (GW)
Grade Resistance - 20Lb X (GW) X % of grade
Curve Resistance - .8Lb X (GW) X deg. of curve
(GW) = Gross Wieght of Train including locomotive.
Here's a well used and well known example.
Train wieght = 235 tons
Wieght of K36 = 143 tons
Total Gross Wt.= 378 tons
We want to move this around the sharpest curve on the steepest grade (4% grade, 20 degree curve).
Rolling Resistance - 8 lb. X 378 = 3024
Grade Resistance - 20 lb. X 378 X 4 = 30240
Curve Resistance - .8 lb X 378 X 20 = 6048
Total tractive effort needed = 39312
Ah ha!! according to this a K36 can't do that!
Well, we know it can, been there, done that, got lots of cinders down my t-shirt. What we didn't figure is that the grades are compensated for in curves(the grade eases on the curves). We would have to look at a track chart to find the actual steepest grade and the sharpest curve. By cutting the grade back to 3.5% on a 20 degree curve, we come up with 35552 lbs of TE needed.
BTW - 35552 lbs is how much tractive effort a K36 makes at 187.4 lbs. of steam pressure (195 is maximum).
Keep 'er hot, fireboy! (no,... these engines don't work very hard!)
