Lets say there is an 8 mile grade on a mainline (60mph) in which the elevation rises 137 feet in those 8 miles. The steepest gradient is .38% (I know, not much of a grade, but this is Indiana). Speed limit is 60mph.
What will that sort of Indiana mountain railroading do to typical trains…lets say:
8000 ton merchandise train with 8000 hp
5000 ton intermodal with 8000 hp
17000 ton coal train with 8000 hp
What kind of speed would one expect? A range will do (say 15-25mph or 40-45mph). Dry conditions, etc. Nothing unusual.
Just curious. This is one of those situations where looking at the track, it is not apparent there is a grade, but there is a distinct difference in the speeds of the two directions.
On CSX where the ruling grade between Willard and Chicago is 0.3% a CW44AC is rated for…
Just under 15K tons Eastbound and just over 15K tons Westbound. These are the maximum tonnage ratings for this territory…not the tonnage rating for a train to be able to maintain maximum authorized speed.
We’re assuming the train is running flat out on level track when it hits the foot of the grade, and you want to know how fast it will be going at the top?
We can take a shot at that. Or would you rather specify a speed at the foot of the hill?
Ok, let me give some specifics. This is as Balt AC indicated, the CSX ex B&O mainline in NW Indiana. I have noticed a difference in speeds at the HBD depending on the direction of the trains.
For instance, certain intermodals are carrying 3 locomotives. These are probably hot UPS/Truckload/LTL moves such as Q110. A recent Q110 eastbound topped the grade at 56mph with 72 cars and 7000 ft of train. Pretty good performance coming up the 8 mile grade. Compare that with a WB Q113 with 5992 feet and 67 cars at 58mph. Almost topping out at the limit.
An eastbound coal with 6967 feet and 128 cars with 2 engines was at 18mph. Obviously the grade, assuming clear signals, pulled this train down. That seems to be the observation trend. Eastbounds are mostly in the 30-45mph range (against the grade) while the westbounds are almost always above 50mph, often near 60mph.
Granted, each train handles differently. But with a total elevation change of 137 feet over 8 miles or roughly 17 feet per mile, there is a significant difference in speed.
17 feet per mile is enough to knock about 4 mph off while I am biking (obviously not Lance Armstrong, but I hold my own), so it is obvious, perhaps not so much to the eyes, but to the legs.
Just curious what kind of performance issues this type of grade has on a train.
The average grade is 137 ft. / 8 miles = 17.1 ft. mile; divide by 52.80 ft. per mile for 1.0 % yields an average grade of about 0.32 %. Since those trains are long and moving fast, they’ll likely be governed by that figure rather than a shorter and steeper little ramp.
Go to Al Krug’s “Train Forces Calculator” at - http://www.alkrug.vcn.com/rrfacts/RRForcesCalc.html - and insert your postulated values and play with the numbers. If you have questions even after rading what he has to say, you can ask again here.
FYI - For your coal train, I got about 15.3 MPH upgrade, but 74.4 MPH - so say 60 MPH - downgrade.
If the 5000-ton intermodal train is all TOFC, they might only be able to manage 55 mph on the level with two SD70s, and the upgrade would drop them to 38-40 mph. An 8000-ton mixed freight would do 50+ mph on the level, being much less draggy than the TOFC; it will drop to about 30 on the upgrade. The coal train will do 40-45 mph on the level, and less than 20 on the upgrade.
It turns out that 8 miles is enough to eliminate almost all the initial momentum for all three trains-- they all reach the summit close to their balance speeds.
You pretty much nailed it. As a dispatcher I would expect a eastbound coal train to top out at Suman around 15-20mph. The merchandise train should get up to around 30 mph and an intermodal around 45-50mph. Now that being said I have had a merchandise train crawl up the hill at 3 mph, so you can’t always count on it.
Now you know why grades - and if ‘steep’ enough, HP/ton - matter so much for railroads. John W. Barriger III specified that his ‘Super Railroad’ concept would have grades not exceeding 0.5 %, and I recall that RWM has posted here that a similar 0.3 % would be desirable.
The purely ‘rolling resistance’ is so low and efficient - roughly and grossly simplified here as being on the order of the equivalent of 0.3 % for friction bearings, and only 0.2 % for roller bearings - that your grade example effectively more than doubles that resistance going upgrade - or more than negates it, going downgrade. Then air/resistance starts to become more important.
But you knew that already - bicycles can teach you a lot about train performance on grades, momentum, and air resistance, etc., only on a much smaller scale, and one that we can play with ourselves and get exercise to boot !
I’d like to post more - esp. about the momentum effect vs. the total rise - but I’ve got to head into work to beat the snowstorm effects today.
Thanks n012944 and Paul. Your responses really helped.
The speeds are obviously affected by gravity. As a flatlander, I never really realized how much so. True, there is a pretty good grade on the CN thru town…around .9% that used to regularly stall eastbound coal trains (powered with 2 big UP or BNSF units until they added a third unit at the rear), but for the most part we dont “see” the effects.
This quite clearly points out the need for level routes and makes it obvious the reason NYC went way north for the “water level route” while the PRR route looked much more direct.
Thanks,
btw, plugging in the data on the Krug site, I came up with my 17000 ton coal train at 499.9 mph. Perhaps I had better stick to the slide rule.
That is so true Paul…With a bicycle, one can quickly note where the grades are. Here in Muncie, we have our very popular Cardnal Greenway Trail which was originally C&O ROW. It is continous for 30 plus miles now…And wind is just as important. Actually, when Jean and I have ridden on it…I believe the wind {for a bike}, was just as difficult to overcome…This is almost flatland here but it does contain “sags”, etc., on the original alignment.
Wow…Ed, that seems a bit too steep…especially on a main {if it is}…Saluda, N C, the famous steep ascent into Saluda summit was a max of 5.1, but mostly 4.7 if I remember correctly.
Correction…I missed the {.}, in my first read…Sorry.
The wind is really a factor biking. I bike around 5am in the summer and the first thing done is check the weather conditions. Obviously rain, but also the wind. If it is cool, with no wind…it will be a great ride, but a 10mph wind will really affect the time.
And wind can be just as much of an obstacle for the real trains, too - especially in similar situations out on the prairies, where there might not be steep grades but instead a lot of boxcars with open doors, or other ‘high’ cars, etc. Of course, my pedaling up the steeper hills can also be all too reminiscent of the ‘chuff - chuff’ labored exhausts of the similarly 2-cylindered steam locomotives . . . [swg] But it wasn’t until my college years when I learned about vehicle dynamics and momentum grades, profiles and especially velocity profiles, energy budgets, and the like, that I was able to come up with that analogy.
I’m waiting for Carl/ CShaveRR to weigh in on that remark, as he too is a bicyclist. There may well be others here, but I’m not recalling them right now.
And as I also mentioned over on the ‘‘Concrete vs. wood ties ?’’ thread - if you want to find out for yourself just how much the ‘track modulus’/ stiffness affects rolling resistance for trains, ride a bike - especially one with narrow ‘street’ tires - on grass for a pretty long distance, then on pavement, then back on the grass, etc. You’ll figure it out before too long . . . [;)]
Once upon a time, a long time ago, I remember seeing a piece of literature from one of the geared locomotive companies detailing what tonnage thier locomotives would pull on various grades. It was amazing how quickly the tonnage dropped as the grade increased. I wish I remembered where I saw it at. It’d be fun to look at again.
It takes 20# pull per ton per % of grade. Rolling along at track speed on the level is on the order of 10#/ton. So you can see why the early RR builders went to great lengths to find easy grades, and why the routes with the best grades usually won out commercially over the others.
To perhaps state the obvious - but for the benefit of those who don’t yet know - that’s because since 1 ton = 2,000 lbs., each 1.0 % of grade is 1.0 % of that 2,000 lbs. = 20 lbs. per ton, per 1.0 %.
And so ‘track speed on the level’ of 10 lbs. per ton as Don says is roughly equivalent to a 0.5 % or 1/2 % grade. Now, just the ‘starting resistance’ from rest and at low speeds is roughly 4 lbs. per ton = 0.2 % for roller bearings (was about 6 lbs. per ton = 0.3 % for the friction bearings ‘back in the day’). So, the difference is the effect of rolling at ‘track speed’ as contrasted with just starting at low speed - mainly the air resistance and wind effects, etc. - of about 6 lbs. per ton or 0.3 %, which is roughly about the same or a little more than just the starting resistance.
So at ‘track speed’, a mere + 0.5% grade would about double the total train resistance; and a - 0.5 % grade would about allow the train to coast along at ‘track speed’ without needing significant tractive effort or horsepower from the locomotives.
Curves are just like adding a little more grade resistance when going upgrade - which is why many grades are ‘compensated’ in curves by reducing the gradient percentage slightly there to equalize or ‘handicap’ the grade’s effect on train performance. In contrast - when going downgrade, curves have the effect of reducing the effect of the grade. But that’s a whole 'nother topic for another day . . .
IIRC, the figure is 0.04% equivalent additional grade per degree of curvature. I’m pretty sure that figure is for standard gauge, narrow gauge would be less and broad gauge would be more.
Hope you don’t mind interjecting a thought from the “optimum gauge thread”.
Ok…Don and Paul, it has been years since physics class and even then I was more concerned about other things.
You are saying it takes 20 pounds of effort to move a ton up a 1% grade. Do you mind explaining the math/formula for that? I am having a difficult time getting over measuring motion as speed. I understand there is motion involved and that motion must be expressed in some form. I can visualize speed, but am having a difficult time wrapping my mind around the expression of motion in pounds.
I can visualize the effects of a grade and also a curve, absolutely no problem there, and I can visualize how grades and curves would impact motion, either negetively or positively … it takes more effort (or less) to move the same weight a distance when resistance is added and I can sorta understand that that effort must be measured in some form…but why weight?
Plus, I have a difficult time measuring what 10 pounds on level or 20 pounds on a 1% grade is. Speed yes, weight no.
Actually, no motion is necessary to figure grade resistance.
It’s the old box on an inclined plane problem from HS Physics. If you but a box on an inclined plane (assuming no friction) it will slide down the plane. The force of gravity will accelerated it down the plane. If you want it to stay put you have to apply some force pushing it up the plane If that force is exactly equal to the force gravity is trying to pull it down the plane. It will just sit there. The geometry works out so that force is 20 lbf per ton of box per % of grade
If you took a box car that weighted 100 tons an put it on a 1% grade, it would run away downhill (we are going to assume no friction or aerodynamic drag). If you attached a rope to the coupler and put a giant fish scale in line with the rope and then tied the other end off to a big tree, that fish scale would read 2000 lbf (20 x 100 x 1) Gravity is pulling it downhill in the direction of the slope as hard as the rope is pulling back. This is an equilibrium of forces
When there is an equilibrium of forces a body can be at rest OR moving at a steady speed. So, if I got the box car up to 10 mph by giving it a shove, it would keep going 10 mph as long as I kept pulling on the rope with 2000 lbf.
To finish the physics problem here, consider that if you move a box car from the bottom of a hill to the top, it has gained potential energy. To put potential energy into the box car, I have to do work on it. Work is a force applied over a distance. In this example, it’s the force of the rope x the distance you move along t