Hopper Coal Load
Hopper Coal Load
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This is one for the railroad engineers.?
How many SD40-2's would it take to pull a 100 care loaded T100 hopper coal train up a 2% grade. Would they need mid engine helpers?
Hmmm... three ex-SP hoggers in a row... there goes the neighborhood...
But:
The first thing you need to do is calculate total horsepower need, with speed as a factor.
Out target speed is no less than 12 mph. At 12 or above, the locomotives will not go into their "short time rating." Simply put, short time rating is a speed at which the traction motors are seeing the maximum amount of amperage they can handle without over heating.
To calculate speed, the formula is HPT x 12 / %G = Speed (horsepower per ton, times 12, divided by the % of grade will equal speed).
Next, figure where the power needs to be placed to stay within the limits of the draft gear. Standard draft gear is rated at 240,000 lbs. To figure the pull, the "Rolling Train Resistance" formula is used. This will give us the figure of the load on the draft gear of a moving train: This formula is: 20 lbs per ton for each % of grade, + 5, or (20 x T) x %G + 5 = force. If the math arrives at a number higher than 240,000, then a helper must be entrained to shove enough tonnage to reduce this number below 240,000.
Finally, to figure the force levels when STARTING a train, the formula is 30 lbs per ton for each % of grade, or (30 x T) x %G = f.
So, your train is 10,000 tons and needs to ascend the grade 2% at 12 mph. Your SDs are 3,000 hp each. So, we use our formula to solve for "x": X x 12 / 2 = 12 mph. We find that 2 hpt will allow us to operate at 12 mph. Since we have 10,000 tons, it will take a minimum of 20,000 hp. So, a minimum of seven SD40s would be needed to supply 21,000 hp.
Next, use rolling train resistance formula to determine drawbar force levels. 10,000 tons, times 20 = 200,000, times the 2%G +5 = 400,005 lbs. We are way over 240,000. We need to split the power up.
Using the formula further, you can calculate how much tonnage the road engine will handle and how many locos should be in the road consist and how many should help. SP always made it a point to operate at the max, but if a higher target speed is desired, then more power will be needed, distributed accordingly.
There is one other thing to consider. When placing the helper, it must be entrained such that it shoves 1/3 of the tonnage it will handle and pull 2/3s of the tonnage. This will keep the helper from shoving the cars ahead of it off the track. If the tonnage trailing the helper exceeds 240,000 lbs of force, then another helper must be added to reduce these forces as well. When running with two helpers entrained, the first is referred to as the "swing" helper, with the other being the rear helper.
Often times prospective new hires will ask here, "How much math do I need?" This is one example. Most times, most of the math is done for you, with locomotive ratings and drawbar tonnage limits printed in the Timetable for the district you are on. But, if you ever need to figure it out on your own, this is how its done... But, you'd probably wind up running 3 by 4, or 3 by 5 (more likely), IF the power-chief can scrape up another loco... It always a good idea to have one more unit in the helper consist than the road engine has... Either way, a good helper engineer is worth his weight in gold, because he has the hammer...


US $90.00
























