Question on grades

[brokemoto]

When I was looking to see the number of cars that certain prototype locomotives were rated to pull, I came across a comment that read that a one per-cent grade would cut the number of cars in half.  This was the only comment on the grades that I could find, but it gave rise to another question.  Would a two per-cent prototype grade cut the number in half, again, or would it cut it even more?

As an example:  Prototype Locomotive A is rated at twenty four cars on level track.  A one per-cent grade cuts this number to twelve.  Does a two per-cent grade cut this number to six?  To three?

Does anyone know?


(I am aware that horsepower and tractive effort do come into play, here, but I deliberately oversimplify)

[C855B]

A little bit of math should get you a rough answer, mostly to compute the increase in drawbar load as the angle increases. Difference in wheel-rail traction should be trivial, although the weight of the locomotive is part of the increased load to move.

But since my trigonometry neurons retired decades ago, we'll have to rely on our members who actually use the stuff    for the real answer here.

[jpwisc]

There are too many variables to give a "standard" number. Different routes have different HP/Ton requirements.

As an example I photographed two shortlines last year. On the Blue Ridge Southern (BLU) they have grades up to 4%. They had 4 SD40-2s (Yes I know some are SD45 bodies, but the guts are 40-2 now) and they were maxed out pulling 30 loaded woodchip cars (roughly 4HP/Ton). If they get rain on that line, those same 4 engines may have to drop down to pulling 20 loads (6HP/Ton)

I also photographed my St. Croix Valley Railroad. They have max grades around 1.1% and I have seen their 2 SD40M-2s pull 100 loads of sand (.6HP/Ton).

[nkalanaga]

The "Contemporary Diesel Spotter's Guide", which is quite old by now, has a section on  the back on calculation tonnage limits.  According to their math, rolling resistance on level track is 5 lbs/ton, once the car is moving.  It's higher when the bearings first start turning.

The grade adds resistance at (% of grade) x (pounds of train) = (pounds of resistance).  So, a 10,000 ton train, on level track, requires 50,000 lbs of tractive effort to pull.  The same train, on a 1% grade, would require 50,000 lbs + ((10,000  x 2,000) x 0.01) lbs, which is 50,000 + 200,000, or 250,000 lbs.

Horsepower doesn't really matter, except for maintaining a minimum speed, with diesel or electric locomotives.  Higher horsepower will give more tractive effort at a given speed, up to the adhesion limit, but weight on drivers is the main factor in whether the train can be pulled, as long as you don't care how fast.  Just make sure you stay above the continuous speed for the locomotive, so you don't overheat the motors!

[brokemoto]

The "Contemporary Diesel Spotter's Guide",
The grade adds resistance at (% of grade) x (pounds of train) = (pounds of resistance).  So, a 10,000 ton train, on level track, requires 50,000 lbs of tractive effort to pull.  The same train, on a 1% grade, would require 50,000 lbs + ((10,000  x 2,000) x 0.01) lbs, which is 50,000 + 200,000, or 250,000 lbs.

Thank you, that is helpful.  If you take a fifty foot boxcar, that weighs just under thirty tons that has a capacity of fifty five tons, that means that fully loaded fifty foot boxcar would weigh just under eighty five tons.  A nine car train plus a caboose would weigh somewhat less than eight hundred tons (seven hundred sixty five tons for the cars, twenty five for the caboose which would come to seven hundred ninety tons).  Eight hundred is a nice round number with which to work.

If a ten thousand ton train requires fifty thousand pounds of tractive effort on level track, an eight hundred ton train would require four thousand pounds of tractive effort.  On a two per cent grade you would have 800x2.000=1.600.000x0,02=32.000+4000=36.000 pounds of tractive effort required to get that train up that hill.

A single RS-2 puts out 43.500 pounds of tractive effort at ten MPH.  It could get the train up that hill with power to spare.
A single BL-2 puts out 40.100 pounds of tractive effort at 9,3 MPH.  It could get that train up the hill with power to spare.
The VO-1000 and RS-1 put out 34.000 pounds of tractive effort at eleven and eight MPH, respectively.  Either one would be slightly short, so either one would require help on that hill.
The GE-44 tonner puts out 12.400 pounds of tractive effort at twelve MPH.  It would take three of them to get a train of nine loaded fifty foot boxcars up a two per-cent grade.

[nkalanaga]

You've got it!  No you can figure tonnage ratings for every hill on your railroad. 

The other formula, from the same source, that you might want is for tractive effort vs speed.  That one is simple: ( Hp x 308 ) / MPH = TE.  The actual TE can't be higher than the adhesion limit, so there's a flat area on the graph at low speeds.  That will tell you what your locomotive can do at a given speed.

The example they give is for a 2,000 Hp locomotive.  At 5 mph the TE is 123,000 lbs.  for a 4-axle locomotive, such as a GP-38, based on the traditional 25% adhesion, that would be unachievable, because it would require the locomotive to weigh 492,000 lbs, more than the allowable axle load. At 60 mph, the same locomotive would produce 10,267 lbs, and wouldn't be able to pull much of a train on any grade. 

The formula can be rewritten as (Hp x 308) / TE = mph.  That may be more useful, as it tells how fast your locomotive can pull a given train.

Finally, (TE x mph) / 308 = Hp, which tells how many units you'll need to keep the schedule.

[Missaberoad]

If you are looking at a specific prototype, in the past railroads published "haulage capacity of diesel locomotive" job aids that covered every subdivision...

Today its all done by computer, and we aren't akin to the inner workings, but as a general rule a AC4400 will haul between 6 and 8 thousand tons on 1 to 1.8% grades (two big GE's running conventional are rated at 13,000 tons up our "big" 1.8% grade)

[brokemoto]

Thank you for the replies.  They are helpful.  I am interested in them more for my short line than the "main line" (which in reality is a "safety valve" secondary).  The Short Creek and Nopedale runs steam for passengers and switchers, but diesel for freight (with a large 2-6-0 as back-up).  There is a two per-cent ruling grade (which appeared quite by accident, but it is there now).  I have several possibilities for diesel power for the freight and wanted to pick the best choice.

The power that I mentioned were those from which I really wanted to choose.  I figured that the RF-16 or FA-1 would be allright, but a cab diesel (unless it were a boxcab) just would not work on this railroad.

It appears that the best choices are the RS-2, BL-2 or three 44 tonners.  The VO-1000, RS-1 or NW-2 would be lacking in the tractive effort to get the night freight into Short Creek Junction.

The three 44 tonners might be the "cheapest" option since they could have been bought used from the military after the Second World War.  Two of them could handle the afternoon freight while the third took care of local switching duties during the day.  At night, all three would be required, thus there could be little or no local switching at night.  As it would be unlikely that all three 44 tonners would be in the shop at the same time, I could "white line" one of the back up steam switchers.

Again, thanks.

[nkalanaga]

The main reason I was interested in those formulas, many years ago, was similar to yours.  I was designing my narrow gauge, and needed to know what I needed for various trains.  Mine is similar to yours, steam passenger and diesel freight, but with diesel switchers.  Steam, in 1974, isn't cost effective for freight service, but draws enough tourists that the passenger trains are at least minimally profitable.  In  the summer they do good business, but in the winter not so well.  Winter passenger runs often use diesels, especially during the week. 

[brokemoto]

One that I did forget to mention that I did consider was the FM H-15-44/H-16-44.  According to the on line diesel data sheet, it puts out 52,500 pounds of tractive effort at thirteen MPH.  The New York Central System data sheets for the same locomotive give 48,600 ponds at ten MPH.

Depending on which figure that you believe, it could be that the FM will move that ten-thousand ton train on level track with just a little bit to spare.  On the one per-cent grade,  however, it would require four more helpers.

It is  no small wonder, then, that the railroads that used F-units as helpers (which was the initial job of B&O's FTs) ran them in A-B-B-A consists.  The individual unit puts out forty thousand pounds at nine-point-three miles per hour.  Thus, all four would put out 160,000 pounds of tractive effort.  What is funny is that the FTs, F-3s and F-7s all put out the same tractive effort, despite the horsepower difference.

[nkalanaga]

At low speeds, the diesels are adhesion-limited, so as long as they weigh the same, the tractive effort will be the same. 

According to my BN locomotive book, the NP's FTs actually had a higher starting TE than their F3 or F7, because they were heavier.  And, they had a higher continuous TE, 42,500 lbs vs 42,000 lbs.  But they would reach that TE at a lower speed, 9.8 mph vs 11 mph. 

In some cases, railroads rated similar locomotives the same, choosing to use the lowest rating for all of them, rather than try to keep track of which unit had which TE.  They might lose a car or two of capacity, but if it's that close, it's better to stick another unit on than to risk stalling.

The BN roster doesn't give a speed for the continuous TE, so I had to calculate that.  The B&O's is a little lower than what I got for the BN, so they may have had a different view on motor heating.  Heat is the big factor in slow speed operation.  The continuous speed depends largely on how much current the motors can take.  Below that speed, the motors will eventually overheat.  Above that, they can be kept cool enough to run continuously.  Few, if any, diesel-electrics, or straight electrics, can produce their starting TE indefinitely.

[brokemoto]

Few, if any, diesel-electrics, or straight electrics, can produce their starting TE indefinitely.

I was relying on the continuous rather than the starting, as I had assumed that the locomotive could not keep up its starting rate indefinitely.  A locomotive that was doing yard work might get away with it as it stops and starts, thus there is not constant voltage applied to the traction motors.  I had assumed, as well, that climbing a hill would be more taxing on everything because it would generate heat both to the traction motors as well as the prime mover. 

in fact, the E-7s (which are not a subject of this discussion, as they would not be suited to this type of work---Or the curves on the SC&N) were notorious for overheating prime movers on hills.  This was one reason why you had to run them in pairs, as it became necessary to shut down one  unit and let the other one work.  I am not aware that E-6s, which had a similar configuration, had overheating problems.  It is interesting to note that the E-8s came out with a different ventilation system, though.  In addition, many roads sent E-6s and -7s (B&O even sent its EAs) back to Electro-Motive to be rebuilt into E-8 configuration.

[nkalanaga]

Yes, I saw that you were using the continuous TE, but threw the starting issues in mostly for other readers, who may not be as familiar with electric traction.

Yard service is definitely different.  As you said, they can run at low speed all day, because they cool off during the stops, so never exceed the short-term limits.  Hump duty is an exception, and the NP built slugs (Electric Trailers) for the Pasco yard, to make better use of the available low-speed TE without overheating the motors.  ET-1, 2 and 3 lasted into the BN era, before being replaced with ex-GN SD-9s(?) equipped with special low-speed electronics.  The last time I was out there, in 2011, I think the hump pushers were SD40-2s...

The GN bought E-7As in 1945 and 1947 for the 1947 Empire Builder.  They worked fine on the flatter areas east of the Rockies, but were mechanically unreliable on long grades.  An attempt to put F B-units between them didn't work either, so they were relegated to local trains in flat territory, and the Empire Builder and Fast Mail got F units.  The GN's problem apparently wasn't the prime movers, but traction motor overheating.  The Es didn't like the low speeds on Marias and Stevens Passes, and ran into the starting/continuous TE problem.  F's worked fine, because the same horsepower was spread over more motors.  If EMD had offered a 6-motor E, they would have been ideal.

That's also one of the original reasons for the 6-axle SDs, the "Special Duty" series.  With the same Hp as the corresponding GP, spread over more axles, they could run slower, with more TE, without overheating.  They were also usually heavier, so could use the higher TE without slipping.  Then some roads found that a lighter version was ideal for branch lines, and the extra motors allowed more usable Hp at mainline speeds, and they basically took over from the 4-axle road power.

[brokemoto]

This actually compelled me to make sure that the steam power could get those trains up the hill.  Eight hundred tons is a high figure.  The average night freight going up is about five hundred.  On Saturday and Monday, it might get up to eight hundred tons.  The weekday day freight up the grade is mostly empty hoppers, thirty six foot gondolas and tank cars, so it is relatively light   

As the MP mogul is close to the SP's, I checked the tractive effort on SP #1673, which survives.  It is 28.710 lbs, which means that it would not get an eight hundred ton train up that hill on its own (the model will, but the prototype will not).  A five hundred ton train would require 22.500 lbs of tractive effort to get it up that hill.  The mogul or two of the 44 tonners would do that.  I checked the tractive effort on moguls that are comparable to the B-mann mogul.  They range from 26.000 to 30.000.  Consolidateds comparable to the MDC/Athearn come in at 26.000-30.000, as well.  The WM Scenic LS&I locomotive, which is comparable in size to the B-mann SPECTRUM comes in at 60.500, so it has more than enough.  Sadly, that locomotive can not take the curve on the run-around on one of my industrial areas.  The station switcher at Short Creek Junction is a B-mann USRA 0-6-0.  The prototype came in at 39.100 pounds of tractive effort, which would be more than enough to get the eight hundred ton train up that hill.

The SC&N owns two USRA 0-6-0s, one of which works Short Creek Junction while the other one is in the shop.  Swap outs were made by putting one of them on the afternoon empties train, but, as the prototype's tractive effort exceeds anything on the roster, it appears that the swap out could be done at night, as well.  Further, the Short Creek Junction station switcher could also serve as a helper.  The B-mann  mogul will not get nine cars and a caboose up that hill as it is.  I have run it in tandem with the B-mann USRA 0-6-0 and the two can get those nine cars and a caboose up that hill easily.  The models do run well together in tandem.  I should note here that I do not use DCC.  The B-mann 0-6-0s that I run are the latest issues.  The Short Creek Junction station switcher has the most demanding job on the pike.  It is a testimony to the improvements in the B-mann USRA 0-6-0 that it does so good a job working this task.  Of course, I did upgrade the locomotives by swapping out the stock tender for a SPECTRUM.

The latest Atlas Shay as well as the Atlas VO-1000, FM road switcher and GP-7 also work that task well.  The B-mann 2-8-0 and MDC/Athearn 2-8-0 are not bad at it, but not as good as the Atlas power or the upgraded B-mann 0-6-0.  The LL BL-2 is not bad.  The Kato NW-2 and Atlas RS-1 perform passably at the task.  The Atlas S-2 does not do well at all at the task.  That is a shame, as I like the prototype.

[eja]

This might help .....

http://hm.evilgeniustech.com/alkrug.vcn.com/rrfacts/hp_te.htm