Grades and usage of locomotives....

[jimrice4449]

Actually the steepest mainline grade in the US was in the East on the Southern at Saluda NC between Spartanburg and Asheville. I believe it was 4.5% (that is a 4ft. 6 in rise for every 100 ft of horizontal motion). There was an even steeper (but not mainline) grade in Indiana, of all places, Near Madison. It ran from the bluff along the Ohio river down to the riverbank and the Pennsylvania had to use a specially equiped SD-9 for the service.

[timz]

Sure-- but it's a 0.2% grade that roughly doubles a train's rolling resistance.

[Anonymous]

no. 2' rise in 100' run is 2%.

[timz]

QUOTE: Originally posted by PBenham

A 2% (2' up for 100' distance) grade cut a trains pulling power by half, or doubled the resistance of a train.

0.2%, he meant to say.

[PBenham]

The exact formula as to how much additional power is required is over my head. Usually,in the steam era a locomotive's tractive effort times 25(?) equalled the amount of tonnage it could handle on level trackage. A 2% (2' up for 100' distance) grade cut a trains pulling power by half, or doubled the resistance of a train. As to who had the steepest Transcontinental (west of Chicago) the Rio Grande approaches to Tennessee Pass were the heaviest at 3.5%, while UP's Overland route was the easiest. Santa Fe bypassed the brutal 4% portion of their main over Raton Pass, by running to the south via Amarillo, TX in the mid teens. A 4000 ton train typical of the steam era after WWI on that 4% grade had a 2-10-2 road engine and a second 2-10-2 helper in the middle of the train and yet another 2-10-2 had to push at the rear of the train. Santa Fe did not like mallets, as theirs cost too much to operate for their liking. Other Transcons had no problems with 2-8-8-2 helpers (UP, NP,GN). While GN had the oddest of all, 2-6-8-0s. But GN liked them enough to run them from the pre WWI era right up until dieselization. SP innovated with their "cab forwards", which kept the lead engine's crew away from the smoke inside tunnels and snowsheds in the Sierra Nevada range. On a 2% grade their best 4-8-8-2 was good for 1000 tons each up to Norden, CA on or near the summit of that grade. Then EMD delivered F3s and F7s.To all of the Transcons. Game over.

[JanOlov]

How did the the railroads work out how many, and where to use their steamlocomotives and later diesels in their frieghts and passenger trans over their heavier grades? How many helper stations did they have and where were they placed?
I'm thinking of Milwaukee Road, Northern Pacific, Great Northern, Southern Pacific and Rio Grande. Which probably had the heavier grades, or am I wrong? Who had the worst mainline grades?