How much could this steam engine pull

Good luck getting a straight answer. I asked a similar question and never did get a good answer.

 But I'll take a guess.. a light Pacific, and 1.5%?? I'd say 4-5 streamlined cars, and 3-4 heavyweights..

I'm not sure about the car numbers, but as for speed, you have to remember that Steam is different from diesel in that tractive effort is not speed linked.  IF a steam engine can start a load, it can pull it at its full speed capability.  If your Pacific can start the consist, it can reach its full speed.  THis varies per engine, but a rule of thumb has always been in the superheater era that the max cruise for a well maintained steam Locomotive is its driver diameter in inches plus 10.  IE if your engine has 60" drivers it should do 70 MPH. 

THere are exceptions to this.  THe Milwaukee Hiawatha engines, and the Nofolk "J"s were so superbly balanced they could do higher rpms, thus exceeding this rule by some degree.

With the right data, you can calculate it with the info in this link:

http://www.alkrug.vcn.com/rrfacts/hp_te.htm

from a previous post by Wyhog in:

https://ogrforum.com/d...nt/11144471728537363

Thanks for those replies. I did forget to say that the engine has 68" drivers.

CofG

"The Right Way"

There is usually information called "Tonnage Rating" on web sites. This is the rating at which the engine will handle the tonnage on the steepest (Hopefully without stalling.)

If I understood the WM 2-8-0's they would be able to handle something like 6000 tons on the level. But throw in the Black Fork Grade at something like 3% you are down to maybe 800 ton.

Thus a train of 60 odd cars of coal probably needed about 8 to 12 of these 2-9-0's to make the trip without stalling... hopefully.

The second thing in tonnage is coupler strength. I think you could not put more than 350,000 pounds onto a set of couplers or you will break them.

It works on downgrades under retained braking as well as upgrade. Drape the train across a bunch of hills and valleys as would happen in say.. Ohio... gives the Engineer a headache.

The third thing with tonnage is a Y6b with 130,000 pounds TE can walk all day up, down, sideways and around on the eastern rails at about 25 mph or so. But you could not keep schedules with it out west. So... out west you brought in the Big boys rated for 50 mph.

Finally but not least, a engine usually has about 25% of it's total weight on just the driving wheels. I think the value is called Cohesion coefficient. The more weight the better.

Sometimes railroads like the C&O and others are able to call in a yard desiel (Or any deseil really) to give that shove necessary to get the steam engine and it's train out of town... Just hope it does not stall out.

If it did, it will cut the train in two or threes to double or triple the hill... something that Dispatchers hate to see.

 But I'll take a guess.. a light Pacific, and 1.5%?? I'd say 4-5 streamlined cars, and 3-4 heavyweights..

CofG

I agree with Steam Fan's estimate.

you have to remember that Steam is different from diesel in that tractive effort is not speed linked.

Drydock

NOT TRUE!  That notion has had several proponents.  Some of them should know better but have repeated it anyway.

Steam locomotives lose drawbar pull as their speed increases.  You can't avoid it unless you live in an alternate universe without friction. 

Steam locomotives lose drawbar pull as they increase speed but they tend to lose it more slowly than diesel electrics.

Finally but not least, a engine usually has about 25% of it's total weight on just the driving wheels.

Drydock

Not quite.  A locomotive like a 2-8-0 will have 80% or more of its weight on the drivers.  A widely used rule of thumb with steam locomotives was to design for a tractive effort of 25% of the weight on the drivers.  The term factor of adhesion is the ratio of weight on drivers to TE.  A tractive effort of 25% of the weight on the drivers gives a factor of adhesion of 4.0 to 1.  Locomotives with a factor of adhesion less than 4 are more prone to slip when operating at full power under less than ideal track conditions.

Tractive Effort is ALWAYS "speed linked" to use your term. The amount of tractive effort developed, combined with the speed at which it is developed is how you calculate the horsepower of the locomotive...diesel or steam.

Think of it this way...

DIESEL LOCOMOTIVE - a constant horsepower, variable torque machine

A diesel has tremendous starting torque (tractive effort) but a fixed amount of horsepower. The HP is limited by the HP rating of the diesel prime mover. Consequently, as the diesel goes faster, the torque (tractive effort) drops, because the horsepower remains constant.

STEAM LOCOMOTIVE - a constant torque, variable horsepower machine

A steam locomotive does not have tremendous starting torque (tractive effort) like a diesel. However, the torque that it does have remains constant as the speed increases. If the torque is remaining constant as the speed is increasing, that means the horsepower is also increasing as the speed goes higher. This is why it is said that if a steam locomotive can get the train started, it can pull it at speed.

This is always a difficult comparison to understand because we are comparing two very different types of power generators - an electric motor and a reciprocating engine. The two have extremely different power curves.

This is also why it is so difficult to answer the OP's question about how many cars the locomotive can pull. There are too may variables to come up with a pat answer. You have to add the qualifier by asking, "How many cars can it pull, under these conditions..." The conditions then specify whether it is on level track, if there are grades, what is the ruling (steepest) grade, do the cars have roller bearings, etc., etc.

To put this in everyday context, when we pulled the New River Trains on the former C&O with the 765, we regularly pulled 34 car trains on that route at speeds up to 70 mph. The ruling grade on that route is only .48%. This year, on the 1.7% grade at Horseshoe Curve, we could only maintain 11 mph with the equivalent load of about 18 cars. Grades make a HUGE difference.

Rich

Whenever a locomotive operates at less than full cutoff the percentage of the stroke that steam acts on the piston at full pressure is reduced. 

That increases efficiency but it lowers torque.  

Having ridden the New River trains in the '80's behind 765, I was absolutely stunned by the enormous trains pulled - 34 cars! I thought, My Gosh, Amtrak would need about 16 locomotives to pull this train! Then, with further thought, a 34 car passenger train is probably equivalent to a 68 car freight train - just an average day in the life of a NKP Berk!

I know, but I'm trying to keep this explanation simple and basic.

Let's not get too technical by bringing cutoff into the picture.

Please remember that a steam engine is a heat machine and the TEMPERATURE of the steam acting on the pistons, i.e. EXPANDING is all important. By limiting the valve stroke, the volume of steam out of the throttle may be reduced but, since that steam spend more time in the superheater units, the steam thru the valves is actually HOTTER and thus does more "work" on the pistons. The end result is INCREASED horsepower as the machinery accelerates.

By keeping "full stroke" on the valves, the horsepower is actually reduced because the steam temperature is reduced, since that larger volume of steam is unable to spend a long enough time in the superheater units.

This guy did some homework and there are references to a USRA Pacific:

http://model-railroad-hobbyist.com/node/3978

Re: Power to Tonnage Formula

Tue, 2011-01-04 07:31 — cmawdsley

Hi

I'm in the process of developing something like this for my own use.  There are quite a few variables* to consider, beyond horsepower and train length

The horsepower is actually more directly tied to how fast a train of a particular weight can be moved.  Whether or not it can be pulled is a function of Tractive Effort.  (Before anyone jumps on me for that, I am aware of Starting TE, Continuous TE, but we're trying to keep this simple)

Continuous Tractive Effort (CTE) data is available for a wide variety of prototype locomotives, both steam and diesel.  (Probably electrics, too, but I haven't bothered to look.)  HP for diesels is also readily available, and for steam engines, it can be approximated as 40 multiplied by the firebox grate area in square feet.  (Again, don't flame me about cylinder bore and stroke etc., we're trying to find something simple-ish)

Ok, so we know the HP and CTE ratings for our locomotive roster. We also need to know the weight of the locomotive and tender, to include in the total train weight, i.e. the weight of all the loaded and empty cars, caboose etc. that the engine needs to pull.

Now we can calculate the tractive effort required to pull the train:

TE = train weight in tons multiplied by (2.5 + (ruling grade mult. by 20))

An example:

Weight of train, 12 boxcars plus caboose is 930 tons

Ruling grade is 1.5%

TE required for cars = 930 X (2.5 + (1.5 X 20))

TE = 930 X 32.5 = 30,225 lb.

For a USRA pacific, CTE = 40,750lb, HP = 2700, weight is 208 tons.

TE required for train = (208 + 930) X 32.5  = 36,985 lb.  Engine has more than this, so ok.

Next up, is how fast this engine can move this train.

Trust me on this formula, it approximates several variables we don't generally have access too (e.g. power train efficiency, rail conditions ... )

Speed (MPH) = HP X 340 / TErequired.

For the train in the example:

Speed = 2700 X 340 / 36,985 = 24.8 mph.  Plenty for a freight train.

You can also turn this formula around to calculate the required HP for a specified speed.

HP = Speed X TE / 340.

Example 2: Passenger train, 4 80' coaches plus 1 express box = 623 tons. 2% ruling grade, min 30 MPH

TE(cars) = 623 X (2.5 + (20 X 2)) = 26,478 lb

An EMD FP9 with F9-B has 66,000 lbs TE, 3500 HP and weighs 256 tons...

TE (train) = (623 + 256) X 42.5 = 37,358 lb ...  ok

HP required for 30 MPH = 30 X 37,358 / 340 = 3296 HP ... ok.

I use a spreadsheet to calculate this.  It allows me to enter my engine roster and it then shows me which engines are acceptable to use.

Sorry for the lengthy answer, but that's about as simple as it can be reduced to.

Chris Mawdsley Bruce Peninsula, ON, Canada

Refs: 

http://www.scribd.com/doc/3340.../Tractive-Effort-PDF

http://www.vnerr.com/training/intro_loco_app.pdf

Plus the site in LKandO's post.

Variables required to approximate engine selection:

HP of engine CTE of engine  (lb.)

Weight of engine (and tender)  (tons)

Weight of train  (tons)

Ruling grade the train will encounter  (percent)

Speed the train is expected to achieve.  (mph)

SIMPLE? You're kidding, right? My eyes glazed over less than 1/3 through all that.

The SIMPLE answer is...about 7 cars.

O.K. now my head hurts trying to make heads or tails of this. So those who have a definite answer how many lightweights could this light pacific of 28,000 of TE, 69" drivers, 180lbs steam psi. pull up a ruling grade of 1.5% while trying to maintain a speed of atleast 20-30mph rated track conditions? And yes this train will start on level ground and will remain on level ground for the first 7 miles before the grade starts.

CofG

"The Right Way"

I wondered about that constant myself, Wyhog.

The SIMPLE answer is still about 7 cars...

I don't blame you, CofG.  It's complicated.

Here's an idea.  If your engine had a prototype, and if the railroad that operated the prototype of your engine published tonnage ratings for ruling grades in its timetable or special instructions, you can find out how many tons it was rated for.  The railroad already did the math.  They made it available in some publication for Conductors and Engineers.  The question is, "Where did they publish it?"

The rolling resistance is a much smaller factor when there is a significant grade involved, and slower speeds, so it can be overlooked for rough estimates.

http://www.alkrug.vcn.com/rrfacts/hp_te.htm

The Rolling Resistance of the Train.

Now we'll look at rolling resistance. Assume the same train as above, ie., 15,000 tons plus 840 tons of locos (4 SD40-2s) rolling at 10 mph on a 1.0% grade. Using the well known Davis formula we get the following values:

Resistance  Pull  HP 

Grade  316,800 LBs  8447 HP 

Rolling  41,880 LBs  1116 HP 

Total   358,680 LBs  9563 HP

Got that link from you in another thread, Thanks Wyhog !

What's the purpose of the original question, anyway? To emulate prototype with models? In the modelling world we usually just do whatever our engines are actually capable of, and/or whatever looks good.

A simple "back of the envelope" calculation is as follows:

The grade resistance of a train on a grade is 20 lb/ton/1% grade, so a 1.5% grade the grade resistance is 30 lb. per ton (includes locomotives).

The train resistance varies with speed, and starts at about 3lb/ton and "one estimate" is 8 lb/ton on the grade. (Speed would be low so no high resistance due to wind, etc.)

If there is one or more curves on the grade, their resistance value has to be included.

Most grades also have curves but since none was identified, I have not included curve resistance in what follows.....

So total resistance is 30+8 or 38 lb/ton.

With a starting tractive effort of 28,000 lb, you would normally calculate trailing tonnage by dividing the 28,000 by 38, so total tons on the grade would be 736 tons.

NOW subtract the weight of the steam loco and tender in tons.

If you assume the 28000 lb tractive effort is available AT STARTING and the locomotive weighs four times that (25% adhesion), then the engine must weigh about 112,000 lb, or 56 tons.

The weight of the tender is a guess, but lets assume it weighs 40 tons.

So the trailing train weight on the grade is: 736 minus 56 minus 40, or 640 trailing tons.

NOW.............

Since this is a steam locomotive and the 28,000 lb is a STARTING TRACTIVE EFFORT and not the CONTINUOUS TRACTIVE EFFORT of a diesel, I would DEDUCT about 20% from the 28,000 lb and assume 22,400 lb. are available at some "reduced" speed on that grade.

The reason for this deduction is that the crossheads of ALL steam locomotives on each side of the locomotive actually go through ZERO tractive effort/driving wheel torque TWICE in each wheel revolution. (This ignores any change in cutoff and assumes that the engine would be on the grade at its full stroke/in the corner as they say.) At very low piston speeds the engine may "quarter slip" or, if wheel to rail adhesion is low enough, stall! (The TE of the engine is never "zero" since the crank on the right side of the engine (except for PRR) is 45 degr ahead of the left crank (2 cyl engines only)).

So the trailing tonnage for an "assumed capable" tractive effort of 22,400 is 22,400/38, or 589 tons, minus 56 minus 40, or 493 trailing tons.

If you assume that a lightweight car weighs 65 tons, that would be 493/65, or 7 cars (actually 7.58, but you can't haul 0.58 cars...)

AND.......

A better way to do this is to determine the in service weight of the engine and go from there, and assume 18% adhesion. (Due to rail and wheel condition, weather, and presence or absence of sand, etc. you cannot assume that you can apply 25% adhesion, and 18% is a safer bet. PRR dispatched trains at 16%. In addition, all steam locomotives fall from their starting tractive effort rating as soon as they start to move.)

For example, if the engine weighs 56 tons, then 18% of that is 20,160 lb TE.  Divide by 38 and the result is 530 tons or 530-56-40 which is 434 trailing tons.

With 65 ton cars, this is 6 cars.....

Depending on the length of the grade, an engine with only 28,000 lb starting TE will struggle with 6 cars...........

The last two paragraphs are "back of the envelope". Everything above that is "front of the envelope"!

Hope this helps!

The SIMPLE answer is still about 7 cars...

How would you know?  You a friend of his or something? 

Thanks Rich, 7 lightweight cars over this mountain with this pacific. I guess since it would be 7 lightweights can I assume about 4 heavyweights?

CofG

"The Right Way"

The difference in actual weight between a "lightweight" and a "heavyweight" car is not significant enough to be a factor.

The answer remains....about 7 cars...ANY kind of cars.

Thanks Rich. That's just what I wanted to know.

CofG

"The Right Way"

Oh one more question Rich, would this engine be able to maintain a 20-30 mph ( due to class of track ) or would it have to slog it out at a lower crawl speed?

CofG

"The Right Way"

Depends on the grade. With 7 cars on 1.5% it is not going to set any speed records.

Rich, I figured it wouldn't be high ballin'. I just figured that it would have to maintain a minimum speed before it would stall being that it has 69" drivers which was not meant to operate at real slow speeds a.k.a. drag freight speeds.

CofG

"The Right Way"

A higher drivered engine with a shorter stroke would be more prone to slip down than a lower drivered longer stroke engine.

I believe that the engine could do 6 cars in almost any kind of weather, tempered by the fact that most likely there are curves that were not identified. The use of six cars would also make the running speed on the grade higher than seven cars (obviously).

If Rich believes that six cars is "about" seven cars, I agree.

Rich, please define "about".....!

"About 7 cars" - as in "between 6 and 8." 

I will never again attempt a simple answer.   

Stay tuned for next weeks episode of Calculus de Locomotive ! 

Well now it would be real interesting to know how much a heavy USRA Pacific could pull on a 2% grade with 8-degree curves. That is if it had a running start at the grade. If it could it make it up 5 miles of grade with X number of cars, could it do 8 miles of grade? And what if it was raining, the rails would be more slippery. And what if it was cold and the train heat was on, that draws steam, would that affect the hauling capacity much? And if the engine had a single leaky flue, would that drag it down much? And what about lightweight cars versus heavyweight cars, how many cars of each could it pull? And roller bearings or not. And what if the fireman was having a bad day and couldn't keep up with the shovelling too well, how much difference would that make? If the engineer had to blow the whistle a lot, could that make it stall on the grade? What about oil burners compared to coal burners. Can the same engine pull any more or less depending on the fuel. How much could this steam engine pull?

ACE

The NP rated their heavy Pacifics at 5 cars on the 2.2% grades in the mountains of Montana and Washington.  They were not a USRA design but were similar in size.

The NPs next passenger locomotives were the worlds first 4-8-4s.  They were designed to pull 9 heavy weights over the 2.2% grades without helpers.

The NP would doublehead one of their Class A Northerns with a heavy Pacific to get up to 14 cars over the 2.2% mountain grades.  Over 14 cars and they would add another locomotive, often a Mikado, as a pusher.  That must have been something to see!

Ted, that is rather interesting. Without looking up the data, I recall that NP had some long stretches of 2.2% grades.

Speaking of which, I recall reading a story some years ago (I forget where) about a roadmaster firing a typical (for the time) Mikado locomotive on the eastbound mainline haul over Stampede Pass. He intended to prove the point that if a train couldn't make the grade with the rated tonnage, the fireman wasn't doing his job (or it might have been a test for higher tonnage ratings over the district). But the result was that mechanical stokers were specified from then on. Hand-firing some of those locos was a potential man-killer if you worked up a drenching sweat in winter conditions and then have to take water in the tender, part of the fireman's job. The "good old days" of steam.

Alright folks I have more details about the grade. It is in fact a 1.2% ruling grade and the tightest curve on the grade according to the tracklayout is in fact 8 degrees. The grade is like a roller coaster and eveytime it starts uphill it last for about 2 miles before dropping back down hill. There is even one section where the climb last for 4 miles. This up and down ride last four about 15miles. So how does this fair my little pacific?

CofG

"The Right Way"

Excellent suggestion. Find an operating timetable with special instructions with the locomotive tonnage ratings for the line that you are interested in. I've seen this kind of info in my assortment of older SP and UP timetables.

Maybe you can find your loco data in here:

fficial-list-51-steam-locomotives&catid=29:motive-power">http://www.cofg.org/index.php?option=com_content&view=article&id=168fficial-list-51-steam-locomotives&catid=29:motive-power

Then find an operating timetable with the tonnage ratings. Have you joined the Central of Georgia Railway Historical Society?

Ace

Yes, the NP had several stretches of 2.2%, especially for passenger trains.

I recall reading a story some years ago (I forget where) about a roadmaster firing a typical (for the time) Mikado locomotive on the eastbound mainline haul over Stampede Pass. He intended to prove the point that if a train couldn't make the grade with the rated tonnage, the fireman wasn't doing his job (or it might have been a test for higher tonnage ratings over the district). But the result was that mechanical stokers were specified from then on. Hand-firing some of those locos was a potential man-killer if you worked up a drenching sweat in winter conditions and then have to take water in the tender, part of the fireman's job. The "good old days" of steam.

I recall reading a similar story, perhaps the same one.  It took place on the NP Sumas line where they interchanged with the CP and British Columbia Electric.  Maltby Hill north of Woodinville was the ruling grade at just under 2%.  If a helper wasn't available at Woodinville freights often had to double the hill.  There are still 3 tracks at Maltby left over from the steam days for just such circumstances.  In the 60s the NP would assign 4, 5 or 6 diesels (often FTs) to trains on the line to avoid the need for helpers or doubling the Maltby Hill.

As an example of things not authorized by the time table or other operating rules take a look at this photo of a NP ten wheeler with an 11 car POW train.  NP photographer and dispatcher explains why he made it happen.

The NP could have fired me for this picture. I was working as Chief Dispatcher at Missoula and ordered the power and crews for this military special. We were extremely short of power and had only two engines available, the 1382 and the 2245 (a heavy Pacific). I ordered the 1382 and the roundhouse foreman nearly had a fit because he said such a small engine wouldn't handle 11 passenger cars on a 1 percent grade. I knew engineer Stewart could do it, besides we might have had to send 2245 to Helena. My reason for ordering 1382 was that I didn't have any pictures of an S-4 engine hauling more than 4 cars. If the 1382 had stalled I would have been in very serious trouble for not using the 2245.