Calculate Motive Power Needed

Simple calculations to determine the number of locomotives needed to power a train.

Basic Calculations:

Tractive Effort:
(Horsepower x 308)
Miles Per Hour
Tonnage Rating:
Tractive Effort total from above
(2000 x % of grade)1
Locomotive Total:
Train tonnage
Tonnage Rating from above

Sample Calculation:

So, here's a calculation based upon my planned model of Cajon Pass.  The ruling grade is 2.2%.  Motive power will be 4400hp GE Dash 9's, pulling a train weight of 7000 tons.

Tractive Effort:
(4400 x 308)
= 54208
Tonnage Rating:
(2000 x 2.2)
= 12.32 (1232 tons)1
Locomotive Total:
= 5.681, rounded up,
6 Dash 9's needed2

1Use first 4 number w/o decimal point, i.e. 12.32 = 1232.
2Rounding up to the the next even number works fine.  However the .681 can be made up with a locomotive that provides ~75% of the power of the Dash 9, ~3300hp.