how many locomotives would I need for 100 cars carrying 50 tons each with a 5% grade?

Question

If you have a train with 100 cars and each one carries 50 ton, How many locomotives would you need if the grade is only 5%, how much hp? What other info would I need about the locomotive before choosing one or more?

Thanks for pointing it out and sorry for the mistake. I meant 0.5%

Answer 1

At what speed?

I am assuming this is a model railroad application. If trying to be true to prototype, speed would need to be more than 12 to 15 mph for diesel electric locos to keep them from running in "short time." (Note: 15 mph is a speed that should be avoided, due to problems with "harmonic roll," which is acute at 15 mph.) If sort time ratings are exceeded then you'll burn up the traction motors or cabling that supplies the power.

The formula is simple. Horsepower per ton, times 12, divided by the per cent of the grade will equal speed. Put another way, HPT x 12 / %G = Speed.

So, 7 HP per ton up a 5% grade will get you 16.8 mph. Your train of 5,000 tons would require 35,000 hp to make this speed. The number of locomotives required would be determined by the horsepower of each, since this is a variable. Six 6,000 hp, ten 3,600 hp, etc.

But, again referring to prototype operations, you're talking no more than around 1950 tons on the draw bar at any point in the train before ripping it apart, so you'd be running helpers in several places as you break up the power consists to handle the tonnage properly.

It is interesting to note that in model railroading, the same physics apply, and you will need to position the power in your modles correctly, or risk pulling them off the rail on the inside of curvature due to "string-lining."

Answer 2

3

Answer 3

only 5%. This is a steep grade and one you would not find on the railroads in the U.S. today - perhaps 100 years ago but perhaps not even then. In the CAJON Pass, the grade is much less than 5% and there are generally three to four locos on the front and two pushers on the rear for each of the BNSF trains that traverse the pass.

Answer 4

5% grade i actually quite a grade, you would need 2 loco only if new units were used hp on each is 3,800-3,500 i have handled more tons per brake than that with 2 units and 50 tons per car is not much more than the usual 45 tons on most empty cars

Answer 5

18 and 1/2

Answer 6

.5% grade can be pulled with half a horsepower per ton.
so 5000 tons could be pulled with one SD-40, (barely) not fast for sure cuz a hundred car mixed freight is going to be about 6000' long and length slows you down a lot more than most tonnage charts take into account, unless your RR has no curves.
And tell the gosh-darned track patrolman to turn off his rail greaser!! LOL

Answer 7

Motion resistance in railway is 4 part:
1-rolling resistance
2-gravity resistance
3-radius resistance
4-aerodynamic resistance
your traction must more than sum of this resistance
case 3 , 4 not in your problem
( you have no radius in your path & aerodynamic resistance is in more than 200km/h important)

N*T>(Rr+Rg)*n
N number of locomotive
T traction effort
Rr rolling resistance
Rg gravity resistance
n number of wagon

you must define minimum speed that you can use and locomotive maximum traction effort in that speed
.

Answer 8

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Answer 9

3 diesel electrics--in tandem. The grade is one consideration--maintaining speed is another. the types doesn't matter