Effect of grade on train tonnage and horsepower

[Isambard]

Is there a "simple" formula or rule of thumb for determining the effect of an increase in grade on the train tonnage for a given locomotive horsepower and speed? For example, what rated horsepower would be required to haul a 4500 ton train at 20 mph on a 0% grade as compared to a 2% grade?

[dehusman]

You need the same hp per trailing ton as the grade minimum just to move the train.

You have a 4500 ton train going up a 2% grade, 2 hp/tt, 2 x 4500 = 9000 hp. If you have AC's you need less, if you have 4 axle engines, you typically need a little more.

Dave H.

[csxengineer98]

it kills both.... the tonnage of the train..and the horespower rating of the locomotive....but locomotives are mainly rated on the amount of tonnes it can pull on a given tarritory...not so much the HP.... thus a tonage rating for the locomotives....when i have to figer out if i need a helper or not... you take the locomotives you have...by model...and look them up on a tonnage rating chart for my divistion... and add up all the numbers ..and then subtrack them by the tonnage of the train... if the train has more tons then the overall tonage rating of the power..you need a helper...... thier are also a few other things that determan if you need a helper..such as trailing tonage....that is the amount of tonage behind the first empty long car.... that number is also found in the divistion time table...

csx engineer

[kenneo]

I can tell you that in Southern Oregon between Grants Pass and Eugene, it took 3 SD 40's to move 4700 tons up a 1.8% at 15 MPH. 5 SD9's did the same job at 7 MPH.

[PNWRMNM]

Figure it this way. Rolling resistance on level track is about 4#/ton. This means it takes 4# of pull (tractive effort) to overcome bearing and flange resistance per gross ton. A four axle unit with 60,000 # tractive effort could pull 12,500 tons.

This is equavalent to a .2% grade, so a .2% grade will halve your tonnage rating compared to level track. Easiest way to figure any grade is 20#/ton/percent of grade to lift + rolling resistance = resistance per ton. Rating (tons) = Tractive Effort/resistance per ton.

This analysis is reasonably accurate to the limit of minimum continuous speed. It does not address speed. Resistance increases with speed and, more importantly, tractive effort falls as speed increases beyond minimum continuous. For drag freight this is irrelevant as ratings are based on MCS. If you want to go 20 mph up the grade, you will need about twice the horsepower as MCS, if your MCS is 10 mph, three times is MCS is 7 mph

Mac.