Allegheny Tractive Effort Table

[Anonymous]

Im not sure, you might want to search Dynometer car data through the historical society.

Tell a steam engineer "Your choo choo aint got the...."

and watch him go to it.

[Anonymous]

Who wouldn't like to see hers/his favorite steamer see run. again? Still after 60 years they are fascinating, thank you for sharing thoughts...

[timz]

What is the grade at Blue Ridge, and how long is it?

The Blue Ridge grade doesn't have any settled value-- it varies, with the maximum being something over 1%, maybe as much as 1.2%. But don't bother with Blue Ridge-- anything you read about a performance there isn't much help, since you don't know what the exact grade at that location was. Instead look at the climb from Walton to Christiansburg, which stays pretty close to 1.0% compensated for six miles. Final Y5/Y6 rating there was 5150 tons of slow freight.

So what TE would it take to start a 5150-ton train that happened to get stopped on the 1%? We don't have much idea-- nobody knows exactly how much TE it took to start a friction-bearing train. Maybe 125,000 lb was enough, but for all we know maybe they'd need 140,000 lb or more. So could they reliably start a 5150-ton train that got stopped on the 1%? We don't know that either. 

However, builders specified starting TE was just 152.000 (simple) and 126.000lbs in compound mode.

That's the nominal (i.e. calculated) TE; we don't have much idea how realistic it is. Here's how they calculated it.

You know the usual formula for a two-cylinder engine: you assume the mean effective pressure in the cylinder is 85% of the boiler pressure, and you assume that the total work done by that pressure, acting on the piston of known diameter, through a known stroke, is equal to the work done at the rim the driver of known diameter during half a revolution. Run thru the algebra and the two pi's cancel out, so you're left with

nominal TE = 0.85 x pressure x bore squared x stroke, divided by driver diameter

(Yeah, I knew you'd notice: the thrust on the back of the piston is less than on the front, since the piston rod cuts the effective area. Apparently that factor is included in the 0.85.) 

Dunno how many formulas there are for compounds, but N&W used the simplest one, assuming that the total of the MEPs in the high- and low-pressure cylinders was the usual 85% of boiler pressure, and assuming that in compound the TEs of the two engines should be equal. In other words (since the Y6's LP piston area is 2.4336 times as large as the HP) the MEP in the HP cylinder should be 2.4336 times the MEP in the LP cylinder, and the two MEPs should add up to (0.85 x 300) = 255.

Do the algebra and you get LP MEP = 74.266076. We use that in the usual way to get the TE for the LP engine: 63415.4 lb. We're assuming HP TE is the same, so total for the whole engine is 126,830.8. Apparently a typo converted that to 126,838 which is the figure usually given for the Y5/Y6. How do they get simple TE? Multiply by 1.2. Why 1.2? Nobody knows, but 1.2 times 126,838 gives the usual 152,206.

That's for a 57-inch driver engine, not a 58-inch. 

[timz]

The highest starting tractive effort from a successful, regular production steam-piston locomotive was, IIRC, about 176,000 lb from the Virginian XA 2-10-10-2's.

ALCo claimed 176,600 lb simple from the 2-10+10-2; dunno what formula they used to get that-- just something empirical, I assume. If you use the same formula that N&W used you get 135,200 lb in compound and 162,200 lb simple.

Note they supposedly had 617,000 lb on drivers, only a bit more than the N&W engines had after they got their extra weight, after 1950 (?). 

[BigJim]

Ogden - Wasatch

Ruling grade 1.14%

What is the grade on Blue Ridge?

Ruling grade 1.2%

Lars,
   Let's look at the facts as given in William Kratville's book "Big Boy". There were three tests of the Big Boys. Trains of 3479 tons, 3883 tons and 3539 tons. Average speed from Echo to Wahsatch, all up hill and mostly 1.14% grade, was respectively 14.6 mph, 14.8 mph and 17.4 mph. After the tests, tonnage ratings were readjusted. Designed for 3600 tons, they were regulary given 4200 tons. In the final steam years they were rated at 4450 tons.
   This compares to the 4600 tons for the Y6 on the 1.2% grade of Blue Ridge. Mr. Timz seems to make light of the Blue Ridge's 1.2%, but remember, we are trying to make a comparision as closely as possible. As famous as the Blue Ridge grade has become over the years, there were heavier grades going North, South and West out of Roanoke. Timz' Christiansburg grade pales in comparision to the 25 miles of grade from Glyn Lyn into Bluefield. Also keep in mind that once all of that tonnage was on the grade it was dead weight no matter if it be three, five, ten or 25 miles long.
   If you must fixate on tractive effort ratings, the N&W never published a TE rating after the Y6 locos were improved and weight was added to the front engine frames. One can only guess. I'll say this, tonnage ratings for the "Improved Y6" (that is what they were referred to by the N&W) jumped an average of 500 tons per district. I'll let you lads do the math.
   Now, let's deal with Mr. Le Massena. Mr. Le Massena has been very kind in his writings of the N&W locomotives. However, since the Steam vs. Diesel tests, he has been consumed in the assumption that there were "ringers" involved in the tests. He contends that there was a "Super Class A" and "Super Y6". This myth has been shot down by people that were intimately involved in the tests. The Class A's and Y6's were all super, without having to cheat. I don't believe the 190,000 lb. figure to be very accurate.
   Let's clear up the simple and compound operation. Simple operation, if needed, could be used up to about 15mph, after which compound operation was used. If tonnage didn't require starting in simple, compound was used. There was a sort of "booster" valve that could also be used up to about 15 mph that added a little more power while in compound.
   In this narrative I have referred only to the Y6. This class includes all of the Y6, Y6a and Y6b locos and along with the Y5 class after the improvements, all were basically the same. 
   BTW, the Y6 had 58" drivers, not 57".

With all of this said, I'll politely bow out and let the number crunchers continue.

[timz]

once all of that tonnage was on the grade it was dead weight no matter if it be three, five, ten or 25 miles long.

Agreed, the weight never springs to life. Question is, how much of Blue Ridge was 1.2% and not 1.1%? That problem doesn't arise (not so much, anyway) with the climb to Christiansburg. Or with the eastward climb to the Elkhorn tunnel, after 1950.

BTW, the Y6 had 58" drivers, not 57".

Lessee-- the Y5 had 57" as built, and the Y6-- probably the Y6a too? For all I know they all ended up with 58 inches, but the TE calculation was made when they still had 57 and was never updated.

[selector]

So, let's suppose a bystander uses his dusty boot toe and slides the representation of a Z-1 into the circle.  Does this add more worms to the can?

[Anonymous]

@timz and BigJim

thank you for extensively answering my questions and showing more facts for the Y6.

Can we draw following conclusion: at a ruling grade of ~1% ratings for Y6 was 5200tons and at ~1.2% it was 4600tons ?

 

 

[dredmann]

re: "So what TE would it take to start a 5150-ton train that happened to get stopped on the 1%? We don't have much idea-- nobody knows exactly how much TE it took to start a friction-bearing train."

That's very true. But we can say that some theoretical frictionless train of 5150 tons (assuming 2000 lb tons, not long tons or metric tons) will require a constant force of about 103,000 lb to pull up a 1% grade. An old rule of thumb has been reported, that a friction-bearing train needed maybe 25% more than simple frictionless calculations based on tonnage and grade would indicate, which would take you to about 129,000 lb. Also, with friction, the starting force will have to be somewhat higher than the rolling force, so yes, starting the train is the hardest part. I will readily grant you that old rules of thumb have questionable accuracy and less-than-stellar precision! But, well, that's probably about as good an idea as we're going to get, Monday-morning-quarterbacking N&W operations of fifty years ago.

By the way, it is my understanding that all or virtually all of the Y5 & Y6 class locomotives got new tires that were 0.5-inch thicker, which then increased the outside diameter of the wheel-and-tire set from 57 inches to 58 inches.

[BigJim]

Question is, how much of Blue Ridge was 1.2% and not 1.1%?

Timz,
   And how much of it was 1.3%, 1.4%, etc. I don't have the Blue Ridge track chart here in front of me to give you a specific answer, however, be gauranteed that my question is just as relevant as yours. Heck, the ruling grade may even be 1.3%. I was just going by what was written in a book. I tried to get a track chart yesterday, but , things were in such disarray they could spare the time to make a copy for me.
   The ruling grade is somewhat of an average of all of the different little grades and curves involved. There can be steeper sections, called "momentum grades", that are very short but slow you down further for a short time or the grade may ease up enough to gain a tiny bit of speed. Curves factor into the equation because of their is resistance. Put 'em together and have you got? Bibbity Bobbity Boo! Sorry couldn't pass that one up. No, put them together and you have a "Compensated" ruling grade.
   So, while your analogy may be a good one for Dynometer Car test purposes (Dyno Cars like constants), in the end, only so much tonnage is going over that hill.

Can we draw following conclusion: at a ruling grade of ~1% ratings for Y6 was 5200tons and at ~1.2% it was 4600tons ?

Lars,
   I wouldn't pin it down to those figures just yet. When I get my hands on a track chart for those districts, I'll get back to you. I do have the track chart between Roanoke and Shenandoah, Va. The timetable breaks the district up into two tonnage segments because of grades and turnaround local jobs of the day.
   The ruling grade northward from Roanoke to  Greenville (52 miles south of Shenandoah) is 1.6% on which the Y6 is rated at 3200 tons. The ruling grade southward is 1.64%, the Y6 being rated at 2850. Just to stir up some more fuss, on these same grades, a Dash-9 or SD70 is rated at 2950 tons and 2750 tons respectively.

[Anonymous]

So much thank you, BigJim!

hope nobody got bothered with this thread, fine it's still alive . Any other figures (this should no become a Black vs. White thread, please) for other specific combinations are welcome!

Maybe, the aim to compare engines just by their drawbar or tonnage pull at certain speeds is not as exact as I thought first. There seems to be many more factors than just engine related ones: achieved speeds, range of fuel or moving tonnage just beyond stall weight.

What do you think about the achieved average 3500hp and 70000lbs TE effort on the BB test runs (Kratville, P. 23)?

If we compare some diesel classes on specific runs, can we draw trends for steamengines? I tried to do this here: http://www.trains.com/trccs/forums/1268000/ShowPost.aspx

Excitingly waiting for your charts...

Lars

[feltonhill]

Timz,

You're correct, the Y5, Y6 and Y6a all had 57" drivers as built.  Following WW2 they were equipped with thicker tires, which raised the driver diameter to 58".  The Y6b's were built with 58" drivers, starting in 1948. 

Where did you find the info regarding N&W's method of computing TE for the Y's?  I've never found a specific reference at the NWHS archives, at least not yet.  I only have three days a month there, and detailed computation books are few and far between.  Only found three so far.  Lacking any specific info, I assumed they used the formula found in various text books and that differences were caused by N&W's experimentation with valve timing on the Y's as they tried to get more "production" out of them.  This would cause variations in the MEP.  Best I understand it, the Y5/Y6's had a form of limited cutoff, with an adjustment factor averaging around 75%.  If you found a reference I can guarantee that at least two people here (Big Jim and me) would be very interested in getting a copy of it to the NWHS archives.   Although a lot of information on N&W locomotives has survived, this is one area where there is less than I would like to see.

If you prefer to contact me off line, my e-mail is still the same.

[Anonymous]

For their grades, at least at sherman, it seems to be UP used BB as a 120.000lbs cont. pull@15mph Machine...compared to diesels...

-EDIT-

Not that true, sorry, better 110.000lbs@15 mph. Quite similar to BigJims's posted SD70.

 

 

[timz]

An old rule of thumb has been reported, that a friction-bearing train needed maybe 25% more than simple frictionless calculations based on tonnage and grade would indicate, which would take you to about 129,000 lb.

Best forget that rule of thumb. Like you said, 103,000 lb to overcome gravity on a 1% grade with 5150 trailing tons (plus more for the engine and tender), but the train's friction resistance won't be 26,000 lb at low speed, once the bearings have warmed up. (I'm assuming it's a 5150-ton loaded coal train. If it were 5150 tons of empties, might have to reconsider.)

[timz]

I looked at the chart for the eastward climb over Blue Ridge. As everyone knows the first few miles is easier, then once the grade stiffens it climbs 234 ft in (scaling off the chart) 4.04 miles, which equals 1.10% average. Curvature in that distance totals somewhere around 278 degrees of total angle; using the usual curve compensation formula (0.04% per degree of curve sharpness) that makes the average compensated grade 1.15%.

The last 1.28 miles to the west end of the vertical curve at the summit averages 1.24 or 1.25% compensated: 79 ft altitude gain, 120 degrees of curvature plus maybe a few degrees of that concave-south curve at the summit.

[erikem]

An old rule of thumb has been reported, that a friction-bearing train needed maybe 25% more than simple frictionless calculations based on tonnage and grade would indicate, which would take you to about 129,000 lb.

Best forget that rule of thumb. Like you said, 103,000 lb to overcome gravity on a 1% grade with 5150 trailing tons (plus more for the engine and tender), but the train's friction resistance won't be 26,000 lb at low speed, once the bearings have warmed up. (I'm assuming it's a 5150-ton loaded coal train. If it were 5150 tons of empties, might have to reconsider.)

A rule of thumb from the article on grades in an early 1968 issue of Model Railroader, figure 0.3% (6lbf/ton) for journal bearings and 0.2% (4lbf/ton) for roller bearings. The figure for roller bearings is probably vaild down to zero speed, but journal bearings can be as high as 10 to 15 lbf/ton below 1-2 MPH. The 25% increase is correct for 1% grades, but understates added friction for lesser grades and overstates for steeper grades.

(lbf = "pounds force" or simply pounds) 

[timz]

figure 0.3% (6lbf/ton) for journal bearings and 0.2% (4lbf/ton) for roller bearings.

In 1926 Davis said loaded cars (say, 80 tons on four axles) needed around 3 lb/ton at low speeds. No reason to think he was wrong.

journal bearings can be as high as 10 to 15 lbf/ton below 1-2 MPH.

That seems to be a persistent legend-- that friction bearings get draggier at low speed. But if N&W 2-8+8-2s really could start 5150 tons on a 1% upgrade (or if they could start their rated 13500 tons on the 0.3% upgrade on the line to Columbus) 10 lb/ton at 0.5 mph sounds unlikely.

Then again-- for all we know maybe they couldn't start their trains on the ruling grades. 

[timz]

I assumed they used the formula found in various text books and that differences were caused by N&W's experimentation with...

You're right-- I thought I had been thru the figures and they agreed, but they don't. The Cyc shows 101480 for a Y3b when the formula says 101465, and Jeffries says 114154 for a 270-psi engine with 58-inch drivers when the formula says 114148 with 57-inch drivers, and the X1-Y1-Z1-Z1b are off by larger margins as you're no doubt aware.

I don't remember seeing cutoffs or lap-lead figures for the Y's, either before or after the circa-1950 change. "An adjustment factor averaging around 75%" of what? That's before 1950?

[erikem]

figure 0.3% (6lbf/ton) for journal bearings and 0.2% (4lbf/ton) for roller bearings.

In 1926 Davis said loaded cars (say, 80 tons on four axles) needed around 3 lb/ton at low speeds. No reason to think he was wrong.

I'm looking at a graph from a circa 1920 Baldwin publication that shows the minimum rolling resistance for a passenger train as 4.5 lb/ton at 8 to 10 MPH. The 0 MPH intercept on the graph appears to be 15 lb/ton, 2 MPH looks to be about 10 lb/ton, 5 MPH is about 6 lb/ton. The caption stated that this graph was  valid for car weights of 45 tons and higher.  Even though this was intended for passenger cars, the rolling resistance for freight cars at low speeds should be about the same.

 

journal bearings can be as high as 10 to 15 lbf/ton below 1-2 MPH.

That seems to be a persistent legend-- that friction bearings get draggier at low speed. But if N&W 2-8+8-2s really could start 5150 tons on a 1% upgrade (or if they could start their rated 13500 tons on the 0.3% upgrade on the line to Columbus) 10 lb/ton at 0.5 mph sounds unlikely.

Then again-- for all we know maybe they couldn't start their trains on the ruling grades. 

I would be more inclined to think that the trains could not be started on a ruling grade - you're heard of a "grade" marker on some signals - a heavy train is permitted to pass a "stop" specifically because the train may not be able to start again after stopping on the grade. This is also why engineers would take up slack before starting, they would only need to get a couple of cars started at any given instant, minimizing the number of cars at near zero (high drag) speed.

Journal bearings rely on the journal riding on a film of oil on the axle end. At low speeds, there isn't enough oil being carried in to maintain that film against the weight of the car thus increasing friction.

[feltonhill]

The 75% adjustment factor I referred to would be substituted for the more usual 85% of Boiler Pressure in the standard TE formula.

According to my estimates, and that's all they are, the as-built Y6's had valve timings that reflected an adjustment factor of about 74%.  The final Y6b's and the improved Y6's were closer to 82%.  This is for starting TE only and the percentages are "plug numbers" I used to adjust the TE formula to reflect N&W's test data re: TE and drawbar pull.

There were several interviews with N&W engineering personnel (Pilcher, Pond, McGavock.....) that were used background information for Jeffries' book, N&W Giant of Steam.  Pilcher specifically discussed valve events and cutoffs, but no exact timing data was mentioned, IIRC.  Still, we're lucky to have that kind of first-hand info.  This is where I got the idea that the increases in TE/DBPull were the result of increased MEP caused by modified valve timing.

So far I don't recall seeing any specific detailed data regarding valve settings in NWHS archives material, but several of us keep looking every month!

[timz]

a circa 1920 Baldwin publication that shows the minimum rolling resistance for a passenger train as 4.5 lb/ton at 8 to 10 MPH. The 0 MPH intercept on the graph appears to be 15 lb/ton, 2 MPH looks to be about 10 lb/ton, 5 MPH is about 6 lb/ton.

Supposedly N&W A's took 12500 tons to Columbus, climbing an 0.3% grade a few miles long, and C&O 2-10-4s supposedly took 13500 tons on their 0.2% grades to Columbus. Think it would be hopeless for either one of them to restart if they happened to get stopped on the ruling grade? Come to think of it, if rolling resistance were 10 lb/ton at 2 mph they likely couldn't even start on the level.

(Yeah, I know-- you're figuring they can sequentially jerk each car from 0 to 3 mph, using the slack in the train to get past the purported drag at 2 mph. I'll have to think about that a little more-- I suspect pure inertia will rule it out. How much slack do you think we should allow per car-- a foot, or two, or what?)

[timz]

The 75% adjustment factor I referred to would be substituted for the more usual 85% of Boiler Pressure in the standard TE formula.

According to my estimates, and that's all they are, the as-built Y6's had valve timings that reflected an adjustment factor of about 74%.

The 1938 Cyc gives the usual 126,838 TE for the Y6, requiring 85%. Did N&W itself assume less?

The 1930 Cyc's TE for the Y3b also requires 85%.

[Anonymous]

Very impressive dig'in into formulas and sources here...Go ahead, please!

Lars 

[erikem]

Supposedly N&W A's took 12500 tons to Columbus, climbing an 0.3% grade a few miles long, and C&O 2-10-4s supposedly took 13500 tons on their 0.2% grades to Columbus. Think it would be hopeless for either one of them to restart if they happened to get stopped on the ruling grade? Come to think of it, if rolling resistance were 10 lb/ton at 2 mph they likely couldn't even start on the level.

(Yeah, I know-- you're figuring they can sequentially jerk each car from 0 to 3 mph, using the slack in the train to get past the purported drag at 2 mph. I'll have to think about that a little more-- I suspect pure inertia will rule it out. How much slack do you think we should allow per car-- a foot, or two, or what?)

I've seen several references to trains crews being surprised and delighted with not having to take up slack with diesels as opposed to steamers. Being a bit too young to remember railroading in the days of steam, I can't vouch for engineers needing to take up slack before starting, but I've seen many references to the practice. I recall a couple of references to have to take a couple of iterations to get the train moving, the back and forth should ensure that oil gets in the bearings of the cars in the front of the train.

The figure that sticks in my mind is 6 inches of free slack per coupler. 

[timz]

Oh sure-- I didn't mean to suggest that the idea of taking slack was a myth. But offhand I'm guessing that if train resistance at 2 mph really were 10 lb/ton, taking slack wouldn't be enough of a help to allow a 2-10-4 to pull 13500 tons.

[erikem]

I didn't think you were suggesting taking slack was a myth.

Assuming the train was starting on level track, the difference between the 4.5 to 5 lb/ton rolling resistance at 10 MPH and the 10 lb/ton rolling resistance at ~2MPH is equivalent to a 0.25 to 0.275% grade. If the train can't start at 10 lb/ton on level track, it certainly couldn't go up a 0.3% grade.

Doing a bit of Googling turns up a starting TE of 93,000lb plus another 15,000lb from the booster for the C&O T-1, which is probably just enough to get the train going by taking up slack (works out to be 8 lb/ton of available tractive effort for the whole train). Interestingly, the article stated that the trains usually got a helper when ascending the 0.3% ruling grade.

I'm also wondering how much the low speed rolling resistance of journal bearings depended on ambient conditions and recent (as in the last few minutes) operation.

 

[dredmann]

Feltonhill wrote: "Best I understand it, the Y5/Y6's had a form of limited cutoff, with an adjustment factor averaging around 75%."

I am not 100% of what you are getting at, but I will tell you this. Just last night I was re-reading the relevant sections in the revised edition of N&W: Giant of Steam, and the report there was that the Y5/Y6 originally allowed steam admission over, IIRC, 90% of stroke in the HP cylinders and 88% in the LP cylinders, but that this extreme amount of steam admission was found to provide little extra TE, while causing the valves to work less optimally at lower cutoffs. So they rebuilt the valves, and among the changes the new maximum cutoffs were 80% and 75%.

Also, just to point out, there are so many issues and fudge factors that I don't have any confidence that anyone can come up with a precise answer to the main points being discussed here.

One of the main things I neglected to mention previously, that someone else did mention, is that usually there is some slack, so the locomotive is not really simultaneously starting the train. How you can really account for this, precisely, with all the various experimental figures being discussed is certainly beyond me.

Frankly, I think the whole system is so complicated that there's no way to answer the question today, and even in 1952 or whenever, the only reliable answer would have come with a freshly-shopped loco, a skillful engineer and fireman, and a dyno car. Other than that, we're guessing. (Not that it can't be fun to guess and discuss.)

 

[dredmann]

re: "I'm also wondering how much the low speed rolling resistance of journal bearings depended on ambient conditions"

I suspect they did make a real difference. The lube would have appreciably different properties if sitting cold for a while and hitting an ambient temperature of 10 deg. F, versus sitting in the summer sun and hitting 90 deg. F, versus temperature after operating (what 150 deg. F or more?).

Q: Does anyone know whether the used different lubricants at different times of the year? Or for different train weights? I.e., would they maybe use a thinner lube on a heavier train, to give the locomotive a better chance to pull it, at the expense of increased wear?

 

[timz]

a circa 1920 Baldwin publication that shows the minimum rolling resistance for a passenger train as 4.5 lb/ton at 8 to 10 MPH. The 0 MPH intercept on the graph appears to be 15 lb/ton, 2 MPH looks to be about 10 lb/ton, 5 MPH is about 6 lb/ton.

Supposedly N&W A's took 12500 tons [unassisted] to Columbus, climbing an 0.3% grade a few miles long, and C&O 2-10-4s supposedly took 13500 tons [unassisted] on their 0.2% grades to Columbus. Think it would be hopeless for either one of them to restart if they happened to get stopped on the ruling grade? Come to think of it, if rolling resistance were 10 lb/ton at 2 mph they likely couldn't even start on the level.

Let's look at a C&O 2-10-4 trying to start its 13500-ton, 160-car train on level track, supposing the train needs 10 lb/ton = 135,000 lb to roll at a constant 2 mph on the level. Once the slack is all stretched they have to be going faster than 2 mph, or the train will refuse to accelerate (since the engine's TE of 109000 is less than 135000) and shortly grind to a halt. So we'll aim for 3 mph when the slack is all stretched-- how about we say 7 lb/ton train resistance at 3 mph?

First off we have to bunch the slack, which will be a struggle in itself, but say we manage that. We flip the Baker to full forward gear and accelerate the engine and the first few cars to 3 mph, 4.4 feet/sec. For now we'll assume a foot of slack per car--  so one after the other the cars are accelerating from 0 to 3 mph in 0.227 seconds, which requires a pull on each car of around 104,000 lb for that time just to overcome its inertia -- whatever it takes to overcome its friction is additional. Meanwhile more and more of the engine's TE is being absorbed by the already-stretched part of the train-- when we've stretched the first 120 cars they're demanding 70000 lb to maintain 3 mph. So clearly we can't maintain 3 mph. As the front of the train slows it's easier to tug the slack out of each remaining stationary car-- but supposedly the resistance of the already-rolling cars is increasing as their speed drops toward 2 mph. I'm too lazy to program the calculator to solve that problem, but wouldn't you agree it looks pretty hopeless?

So you need more slack. Any chance for 2 ft/car? I'm guessing not, but what do I know.

Additional complication: what if we haven't bunched all the slack -- the last ten cars are stretched? The 150th car, moving at, say, 2.5 mph, meets the last ten stationary-with-no-slack cars, that have to be accelerated to 2.5 mph in 0.27 seconds, requiring 700,000 lb or so... 

[timz]

If the train can't start at 10 lb/ton on level track, it certainly couldn't go up a 0.3% grade.

The N&W timetable rated the A at 12500 tons up the 0.3% to Kingston (Ohio). No idea whether they actually did that-- but if they did, you figure anytime speed dropped below 5 mph on the 0.3% they were doomed to stall?