Hi,
The constant is tonnage. Tare is the weight of a car without load.
Payload is the load that you can charge someone for moving.
The lower the tare, the larger the payload.
A train of empty cars can have more cars in it than a train of loaded cars. Simple stuff but saying a loco can haul 7 or 8 or 9 cars is ignoring the fact that 260 tons of rated power on a 4% grade is still the same.
Sort of like watts, amps and volts in electronics. A watt is volts times amps - raise the current and lower the voltage to keep the power (watts) the same.
simmilar to tare and tonnage and payload. Tonnage = tare plus payload. Nothing directly to do with number of cars.
If a car's tare is 20 tons and the payload (say 30 people per car at 200 pounds per person average) is 1.5 tons then a loaded car is 21.5 tons.
Weight of a K36 is about 140,000 pounds or 70 tons.
I do not know if the tonnage rating on say Cumbres eastbound includes the locomotive.
If the tonange of the loco needs to be deducted from the 260 tons, then the train weight is 260-70 or 190 tons. at 21.5 tons per car, the K36 can pull 8.8 cars up Cumbres from Chama rounded down to 8.
If bad weather (rain lubricates the rails and lowers the coofecient of friction) then maybe only 5 cars can be lifted up Cumbres or a helper is needed. If the rails are weed covered and rusty, the total tonnage needs to be lowered also.
Now then, let's consider the C&TS after season hospital train from Chama to Antonito.
Keeping the assumption that the loco needs to be deducted from the tonnage rating, the train weight is still 190 tons. Say three steel cars at 20 tons needs to go to Antonito for a total of 60 tons. this leaves about 130 tons available. If a wood box car is 12 tons and a wood flat 8 tons, you could add 4 box cars (12 x 4 = 48 tons) and ten flat cars (8 * 10 = 80) to fill up the train going up cumbres for a total of 16 cars.
The same 190 tons could lift about 23 empty wood flat cars up Cumbres.
So saying a loco can handle 7 cars up Cumbres is a rule of thumb that might work most of the time but misses the corrrect details of how it is calculated.
The tare weight and the total weight listed on car sides are used for these calculations. For rock and ore loads, scales were used for the exact total wieght of the car (density of coal and/or granite, or gravel changes).
Food for though about how it might really work.
Doug vV
