Thank you Sheldon. That is very useful information.
Regards,
CG
CentralGulf ATLANTIC CENTRAL On several of the layouts in our round robin group, one of which I designed the track plan, we have run trains in excess of 100 cars. A single Rivarossi Allegheny and a single BLI N&W Class A were each able to pull over 100 cars up 1.8% helix curves with out any problems. Sheldon, do you have any information on what a Bachmann Spectrum Light 2-10-2 might haul up that particular helix? I know you mentioned they are difficult to add weight to, so I assume they aren't going to come close to that 100 car number. CG
ATLANTIC CENTRAL On several of the layouts in our round robin group, one of which I designed the track plan, we have run trains in excess of 100 cars. A single Rivarossi Allegheny and a single BLI N&W Class A were each able to pull over 100 cars up 1.8% helix curves with out any problems.
On several of the layouts in our round robin group, one of which I designed the track plan, we have run trains in excess of 100 cars. A single Rivarossi Allegheny and a single BLI N&W Class A were each able to pull over 100 cars up 1.8% helix curves with out any problems.
Sheldon, do you have any information on what a Bachmann Spectrum Light 2-10-2 might haul up that particular helix? I know you mentioned they are difficult to add weight to, so I assume they aren't going to come close to that 100 car number.
So I did quick test this afternoon, Bachmann Spectrum 2-10-2, drive is stock.
Rolling stock used (I have about 50 of these all the same) - 4.3 oz Athearn piggyback flats equiped with Kadee sprung trucks, refitted with Intermountain metal wheelsets.
Level track, some curves, all 36" radius and larger, the 2-10-2 comfortably handled 30 cars. It was obvious at startup that this was right on the edge of slipping, 5 more cars made starting nearly impossible.
Train stopped on 2% grade - the loco could not start the 30 car train, it slipped. It could start a 20 car train on that grade, again, right at the edge of slipping, but once underway handled the train fine on the grade.
As I have noted earlier, and as Selector has noted just above, Steam locos in particular loose pulling power quickly on grades. Our models pull less on level track, but do better on grades than the prototype. A good argument for mountain modeling and double heading......
So two Spectrum 2-10-2's which might have only handled 40-50 cars on 2% grades on the prototype, can come close to that in model form, even if they cannot match the prototype on the flat.
Also, keep in mind, my 4.3 oz piggys are heavier than most rolling stock, but they are very free rolling....
Sheldon
gregc ... If I did the trig correcrly, a 1% grade requires an additional 35 lb per ton. Roughly double that for 2%. ...
... If I did the trig correcrly, a 1% grade requires an additional 35 lb per ton. Roughly double that for 2%.
...
The prototype consist requires three times as much horsepower to lift it up a 0.5% grade, so about six times for a 1% grade at the same speed. It's actually more, but for easy figuring here.... If you are willing to crawl up the hill, it's possible in a diesel for less horsepower, but a steam locomotive will be hooped. It produces most of its horsepower in the mid-high speed range limited by the running gear.
I would guess about 30 cars max with that kind of grade. I may be able to do some sort of test on my layout later. I will let you know.
The boiler of the Spectrum 2-10-2 is die cast metal, but the drivers lack any suspension, unlike their 4-8-2 cousin, and long wheel base locos loose traction on our tight curves.
There is likely a big loss between straight/level and grades/curves - which justifies two of them on the point.....
The Rivarossi Allegheny and the BLI Class A both have traction tires.........
Some BullFrogSnot may work for the 2-10-2, I just have not had time to give it a try, busy at work and trying to rebuild part of the layout.
Opinions vary, but for me, trains don't look long enough to justify 3-4 first generation diesels, or double headed steam until they approach about 40 cars.
That is my typical mainline freight train, and it takes two Mikados to handle 40-60 cars on my 2% grades.
dehusmanOr.... If your engine can haul 25 empties then it should be only able to haul about 5-6 loads.
That 5-6 cars is almost laughable seeing a D9-44CW can haul 70 loaded hoppers on NS Sandusky Line so,our model D9-44CW should be able to haul 25 cars and would look right as far as length-if you actually seen a 25 car model train on the straight it appears to be a "mile" long to the eye. Its a optical illusion.Even switching 8-10 cars places the engine far away from the switchman figure standing by the switch.
Larry
Conductor.
Summerset Ry.
"Stay Alert, Don't get hurt Safety First!"
Weights and pulling power don't scale.
A model of 1000 hp engine has the same motor and gearing as does a model of a 4000 hp engine.
On a real railroad a house car has a empty-load ratio of about 1:2 or 1:3 and bulk car has about a 1:4 or 1:5 ratio. So a empty hopper car that weighs 25 tons when empty weighs about 125 tons loaded. End result is that if you can haul 25 loads, you should be able to haul about 100-125 empties. Or.... If your engine can haul 25 empties then it should be only able to haul about 5-6 loads.
Either way you go it doesn't scale.
Your best bet is to use a relative pulling power based on "horsepower" and your engine's actual pulling power.
Dave H. Painted side goes up. My website : wnbranch.com
Since this thread has taken a different direction, I will offer just a few more thoughts.
I use Aristo Train Engineer throttles. They use push buttons to control speed and direction. There is a "FASTER" button, and a "SLOWER" button.
The rate at which the voltage increases is controlled by a momentum feature, but even with that setting on "zero", there is still a fixed rate of voltage increase or decrease while the buttons are pressed.
This very minimal "momentum" effect is very good at providing realistic acceleration and braking without a bunch of complex controls on the throttle.
There is an "EMERGENCY" button for when you really need to stop quick......
I run long trains, and just like the prototype, it takes careful use of the throttle to control them, but the Aristo throttle provides more than enough realism in that area for me.
I do have tonage ratings for my locos, and most trains need all or most of the power assigned to them. Most trains are pulled by 3-4 diesels or two steam locos.
BRAKIE gregc I thought the original discussion was with respect to the laws of physics -- the effect of the weight of the train on the locomotive speed. True dat but,the only way I know how to mimic that is through momentum in DC or in DCC adjusting the momentum,sped step and start volt which I think may be better then adjusting the acceleration and deceleration CVs. Other then that I truly don't know.
gregc I thought the original discussion was with respect to the laws of physics -- the effect of the weight of the train on the locomotive speed.
True dat but,the only way I know how to mimic that is through momentum in DC or in DCC adjusting the momentum,sped step and start volt which I think may be better then adjusting the acceleration and deceleration CVs.
Other then that I truly don't know.
doctorwayne provided some interesting links discussing engine horsepower. These reminded me of my high school science teacher who said no matter how hard we push against a wall, we do no "work" if it doesn't move. Likewise, horsepower is "pull times speed". So no horsepower is generated if the wheels are spinning and speed is zero.
Our models typically have this problem, the motor is plenty strong but the wheels spin: zero horsepower, zero tractive force, zero pull.
While our models have no problem "jerking" a 2 or 20 car train to speed without sufferring the effects of momentum, their wheels start spinning pulling a short train up a grade.
Adding weight to the engine can solve the grade problem, but also results in an unrealistic model locomotive with up to 10x the pulling power of a prototype loco.
So I think a weighted locomotive with a smaller motor could more realistically
But this may only be true if the motor can actually turn slower at max voltage because of the load and turn faster as things start moving without damage.
When a prototype locomotive starts pulling a train, some amount of power is applied to the wheels to generate the force/torque needed to accellerate the train. But the wheels are barely moving. They gradually turn faster, but if the acceleration is constant, the force/torque and power must be constant as well.
As I said earlier, this must generate a lot a heat and the motors are designed to tolerate it and protected from damage.
greg - Philadelphia & Reading / Reading
BRAKIENow allow me to add this tidbit. While half of a long train is going down grade the other half may still be coming upgrade and after these cars reaches the peak and starts down grade there is a second run in of slack that pushes the engine....
You're absolutely right, Larry. Just for the heck of it, I ran a train of just over 70 cars around my layout. It was fascinating (and a bit scary, too) to watch the slack run in and out in different parts of the train, often at the same time and at more than one location within the train. I have numerous up and down grades, many on curves, so careful train handling was a must.
BRAKIEI've always suspected the first half of the train going down grade may help pull the second half of the train upgrade.
I think so too, and I'm sure that came into play with my long train.
gregcanother aspect of the models, because of the worm drive, is that there is no need for braking. A model locomotive won't let a train roll down a hill.
You're quite right, Greg, but a heavy train can still push the locomotive, either as slack runs in or due to the weight of the bunched-up train when all slack has run in. The loco's wheels won't turn any faster because of the worm drive, but if the loco has excessive gear lash (play between gears) or excessive end-play in the motor, then the loco will speed up until the gears temporarily lock-up due to being slightly out-of-mesh. The loco stops for a fraction of a second, then restarts, pulling out some slack until the rest of the train begins rolling again, then, as the slack runs in again, the process repeats itself. Steam locomotives without gearboxes (worm on the motor shaft and the worm gear on an axle) can be adjusted for gear lash by shimming the entire motor appropriately, and thrust washers can be used to limit end-play in open-frame motors.
Locomotives with gearboxes generally have decent gear alignment within the gearbox, and it's easiest to reduce motor end-play by adding thrust washers at the ends of the worm, rather than by opening the motor.
I recall reading several very interesting offerings from Al Krug, a poster perhaps in the Trains Forum, or one whose site was linked-to therein. I couldn't find his former website, but his discussions on tractive effort and horsepower as they relate to real trains was extremely informative.
Here's a LINK to an interesting article by him. It will certainly give the OP (and anyone else who's truly interested in this stuff) some insight about how real trains perform.
...and this is a post copied from the Trains Forum, which itself was copied from Krug's original website. This is the discussion which I most remember, especially the part about the weight of the train being able to pull the train's locomotive back down the hill!
Anonymoushttp://www.n0kfb.org/rail/railphs.htm "Horsepower is pull times speed. You can have pull with _no_ HP. Example: A 15,000 ton coal train sitting on a 1% grade and being held there by the engine brakes alone has 300,000 lb pull on that first coupler. But there is no horsepower being produced. The factor of adhesion for a steel wheel on a steel rail is between 20% and 30% of the weight on the wheel. So to prevent that coal train from pulling (sliding) those locos back down the grade the locos need to have at least 300,000 lbs of adhesion. This means they must weigh at least 1,000,000 lbs because 30% of 1 million is 300,000 lbs. The maximum weight per wheel, to prevent crushing the rail, is 35,000 lbs (70,000 lbs per axle). So we need a loco with at least 29.6 wheels, each of which is weighted to 35,000 lbs. 30 wheels is 15 axles or four 4 axle units minimum. It could also be 3 six axle units which would be 18 axles. Or it could be two 6 axle units and one 4 axle unit for a total of 16 axles. The point is that you have to have that one million pounds on the wheels and you are limited to no more than 35,000 lbs per wheel. Adhesion as described above and Tractive Effort are closely related and can be thought of as the same thing in many cases in that the amount of adhesion limits the maximum TE that can be used. TE is usually quoted at a specific speed. TE is the pull at the drawbar. HP is the amount of pull (TE) times the speed. So while our coal train is just sitting there on the grade there is no HP required. But try to move it at 1 mph up that hill and HP is required. The required HP is the TE needed (300,000 lbs) times the speed (1 mph or 1.47 ft per second) divided by the definition of a HP (550 lb-ft per second). So the HP required is 801 HP! Yes just 800 hp will move this coal train up the hill. Amazing isn't it? But will one 800 hp unit do it? No! Because that one 800 hp unit must have at least 1 million pounds on its drivers to prevent it from sliding back down the hill. You MUST have the adhesion required. This means each wheel of an 800 hp 6 axle unit would have to have 84,000 lbs on it. Oh my the busted rails that would leave behind! As I said above, the minimum number of axles we need to spread out the required weight is 15 axles. Now it doesn't matter whether we have one 800 hp 4 axle unit and three 4 axle slugs, or whether we have four 200 hp units. It is all the same to the coal train. " quoted from Al Krug; a discussion on locomotive and train dynamics
quoted from Al Krug; a discussion on locomotive and train dynamics
Wayne
gregcI thought the original discussion was with respect to the laws of physics -- the effect of the weight of the train on the locomotive speed.
BRAKIEI'll toss this out how about CV settings? I'm using combination of momentum,acceleration and deceleration CVs and I feel like I'm moving freight cars since it takes time to get things rolling and stopped..
while the electronically controlled throttle settings do mimic momentum, they don't reliably represent the weight of the train or grades. Unless modified for conditions, the momentum should be adjusted for length of train and grade.
I thought the original discussion was with respect to the laws of physics -- the effect of the weight of the train on the locomotive speed.
another aspect of the models, because of the worm drive, is that there is no need for braking. A model locomotive won't let a train roll down a hill.
The DC motor and gear train don't model the mechanical aspects of a locomotive.
doctorwaynemuch like our models, cresting a hill and beginning a downhill run. The run-in of slack pushes the loco, which then speeds up momentarily, until the next car runs in, etc., etc.
Now allow me to add this tidbit. While half of a long train is going down grade the other half may still be coming upgrade and after these cars reaches the peak and starts down grade there is a second run in of slack that pushes the engine.
I've always suspected the first half of the train going down grade may help pull the second half of the train upgrade.
gregc...how often have you seen a locomotive stall (wheels stop turning) with power applied but unable to move because of either an excessive load, either too many cars or too steep a grade?
Hopefully, not too often: if the train's stalled (not moving) and the wheels won't slip with the power applied, you're doing damage to the motor. I've seen this with an underpowered locomotive that's too heavy - there is a limit to how much weight can be added to any locomotive. In many cases, it can't be reached, as there's usually insufficient room inside the loco to overcome the generally powerful motors available nowadays.
BRAKIEI'm using combination of momentum,acceleration and deceleration CVs and I feel like I'm moving freight cars since it takes time to get things rolling and stopped..
I get the same starting effect even on my DC-powered layout, because the trains are usually heavy, occasionally enough so that the engineer needs to take slack to get things rolling. Prototypical deceleration, though, is all careful throttle work (unless I'm using a throttle that has a separate brake function). In that case, the engineer needs to know what he's doing, as brake response is definitely not anywhere near instantaneous.
Braking, regardless of throttle type or DC/DCC control, is a real variable when comparing prototype to models, since despite relationships of any sort involving weight, power, or rolling resistance, our freight cars depend solely on the locomotive stopping the entire train, while a real train has brakes on every car.
I've seen real trains, like an SW900 pulling 4400 tons of loaded ingot buggies without brakes, trying to stop at perhaps 20mph. The brakes on the locomotive more-or-less lock-up, and the slack on the buggies begins to run-in violently, bumping the locomotive forward as each buggy bumps the one ahead of it.....much like our models, cresting a hill and beginning a downhill run. The run-in of slack pushes the loco, which then speeds up momentarily, until the next car runs in, etc., etc. Okay if you're running an industrial layout, I guess, but not so realistic on a mainline.
gregcwhat would it take for a model to mimic the behavior perhaps a relatively weak(?) motor in a heavily weighed locomotive such that with a relatively heavy train, the motor develops a proportional amount of torque but cannot turn the wheels because they won't slip.
I'll toss this out how about CV settings?
I'm using combination of momentum,acceleration and deceleration CVs and I feel like I'm moving freight cars since it takes time to get things rolling and stopped..
Based on the numbers I quoted before, I calculated that 5000 ton train (100 50-ton cars) pulled by an engine with 380,000 lbs tractive force will take about 2 minutes to reach 20 mph on level ground.
consider what the wheels and motors on the locomotive are doing when a locomotive starts moving and compare it to what you think a model will do.
The prototype locomotive is going to feed the motors as much power as possible which is going to apply a torque to the wheels causing them to slowly turn as the train starts to move.
the motors are going to get hot while all this power is going thru them and I assume there is some mechanism to cool the motors and limit how hot they get before being damaged.
And as the train picks up speed, there will be point where less power is needed because the motor just need to maintain speed.
what would it take for a model to mimic the behavior
perhaps a relatively weak(?) motor in a heavily weighed locomotive such that with a relatively heavy train, the motor develops a proportional amount of torque but cannot turn the wheels because they won't slip.
Eventually, once the train is moving, there is little problem maintaining speed, until, of course there is a grade.
how often have you seen a locomotive stall (wheels stop turning) with power applied but unable to move because of either an excessive load, either too many cars or too steep a grade?
ruderunner...My original was basically to determine if one can draw some inferences about prototype pulling power and model pulling power. Not too many variables involved, loco weight, tractive effort and trailing tonnage. How does prototype compare to model?....
I think that you have to include all of the variables, because we have so many that the prototype doesn't have: grades steeper than most prototypical ones, much tighter curves, no wheelslip detectors to automatically decrease power to traction motors, the amount of slack built-in to our couplers, and the lack of dynamic brakes on our locomotives, and, on downgrades, the lack of any brakes on the trailing train.I think that you'd get more useful data by establishing "tonnage" ratings for all of your locomotives, and do so for each extreme operating condition which exists on your layout.I started by using loaded Athearn 2 bay hoppers, all pretty-much identical, with unremarkable rolling charactersistics - not really free-rolling but not sluggish either. Each weighed 8oz., and I also included a standard 4oz. caboose, similar to what would be used on all freight trains. Most of my grades are 2.5% and most are on curves, so the initial tests were done on such a grade where there were two curves, forming an ess-bend with a short length of straight track between the curves. Theoretically, this would be the worst grade/curve combination (both have a negative impact on locomotive pulling performance). I do have a much longer grade at 2.5%, but it has a longer section of straight track between two reverse curves, but both curves are also much longer. I've not yet done formal tests on this grade, as it's been a dead-end at its top until just recently.
The test train is 12 cars, plus the caboose, for a total trailing weight of 100oz. I had diesels which could easily pull this train, but my operation is now all-steam. None of my locomotives alone will pull the test train up the grade, even though some can move it easily on straight, level track. I simply removed hoppers, one-at-a-time, until the train could make it up the grade with minimal wheelslip, and noted the results by assigning each hopper a nominal prototype weight of 70 tons. I also assigned the same weight to the caboose, to keep things uniform.
Some locomotives benefitted when their trailing train became short enough that the train would be in only one of the curves at any time.
After all locomotives were tested, I then performed the same tests using two locomotives and did so in a manner which paired-up all possible combinations of wheel-types....basically anything which would be used on the layout.
Not many of my trains are loaded coal trains, but this gives me benchmarks to which I can compare performance with other car types and also with heavy, loaded cars mixed in with lighter ones. Hands-on experience will give you a better idea of your layout's requirements than will any comparison to the prototype, although when you've completed your test runs, you will have data with which you can make comparisons if you wish.
A couple of comments after a quick read of the posts...
1. The assumption that there should be a connection between model engine and model car weight is probably flawed. A heavily weighted engine with a weak motor is probably going to pull less than a light engine with a good motor.
2. I don't know if it would be possible to fiddle with engine and car weights to make a 1:1 ratio between how much 'tonnage' a real engine could pull compared to a model one. The new Walthers "critter" HO switcher appears to be much stronger than the real one was, whereas I suspect MTH's new HO DMIR Yellowstone can't approach the real engine's 120-140 car ore trains.
Modeling the Cleveland and Pittsburgh during the PennCentral era starting on the Cleveland lakefront and ending in Mingo junction
ruderunner My original was basically to determine if one can draw some inferences about prototype pulling power and model pulling power.
My original was basically to determine if one can draw some inferences about prototype pulling power and model pulling power.
I think the answer is no. The laws of physics in Lilliput are different.
ruderunner As for my layout, I'm not modeling mainline trackage yet, I'm still stuck in the industrial area. As construction progresses, longer stretches of track will become available for use. Longest planned train is expected to be 30-40 loaded ore cars . . .
As for my layout, I'm not modeling mainline trackage yet, I'm still stuck in the industrial area. As construction progresses, longer stretches of track will become available for use. Longest planned train is expected to be 30-40 loaded ore cars . . .
My longest trains are about 30 or so cars, too. Pulled by two SD-70s. Coal, not ore. My coal porters have the option of removing the loads, and would you believe it . . . my empties weigh almost exactly the same as the fulls. Not so in the 1:1 world. Your mileage may vary.
I'm with Sheldon. I don't think I can offer anything else to this discussion.
Good luck.
Robert
LINK to SNSR Blog
7j43k I've seen an SP SW1500 pull 47 cars on a straight flat at "road speed". If models can pull more than the prototype, I look forward to hearing how many cars a model SW1500 can pull. Ed
I've seen an SP SW1500 pull 47 cars on a straight flat at "road speed". If models can pull more than the prototype, I look forward to hearing how many cars a model SW1500 can pull.
Ed
Ed,I did a lot of terminal switching at a club I was a member around 15 years ago my BB SW1500 could easily pull 22 free rolling cars on the level at 23-25 there was wheel slip but,she would barely move the cars and anything above 25 was total wheel slip.These was stock weight cars-that's the weight the car came with.
IMHO those 22 cars was a impressive sight. I don't know but looking back a six axle unit or 2 end cab switchers may have looked better.
ruderunnerMy original was basically to determine if one can draw some inferences about prototype pulling power and model pulling power.
is it fair to say you're interested in knowing what it would take to have the same momentum issues as the prototype does?
ATLANTIC CENTRAL ruderunner And that is an excellent point. However, horsepower tends to get speed, not necessarily pulling power. We know model trains can usually exceed their prototype speeds. Actually, run on the original NMRA Standard 12 volts, or anything reasonable close to it, most HO model trains produced in the last 20 years run very close to their prototype top speeds. BUT, DCC, and other factors have prompted some to run trains on higher voltages....or supply higher track voltages for sound, decoder losses, etc. Many inexpensive DC power packs over the years put out much more than 12-14 volts.....until the load increases a lot. So with todays low current motors, they will runs trains way too fast. I use regulated 13.8 volt power supplies and Aristo Train Engineer radio throttles. Full voltage at the track of about 13.5 volts provides prototypical top speeds for most locos. Simple fact, in my view, your idea simply has too many variables, and respectfully, if your layout requires 18" curves and limits trains to 20-30 cars, it will be hard implement. Personally, I have never warmed up to the idea of considering a 20 car train long enough to represent a Class I mainline train requiring multiple diesel locos. If that was my space restriction, I would build a switching layout or a branch line. But that's just me. I think I have offered all that I can here. Sheldon
ruderunner And that is an excellent point. However, horsepower tends to get speed, not necessarily pulling power. We know model trains can usually exceed their prototype speeds.
Actually, run on the original NMRA Standard 12 volts, or anything reasonable close to it, most HO model trains produced in the last 20 years run very close to their prototype top speeds.
BUT, DCC, and other factors have prompted some to run trains on higher voltages....or supply higher track voltages for sound, decoder losses, etc.
Many inexpensive DC power packs over the years put out much more than 12-14 volts.....until the load increases a lot. So with todays low current motors, they will runs trains way too fast.
I use regulated 13.8 volt power supplies and Aristo Train Engineer radio throttles. Full voltage at the track of about 13.5 volts provides prototypical top speeds for most locos.
Simple fact, in my view, your idea simply has too many variables, and respectfully, if your layout requires 18" curves and limits trains to 20-30 cars, it will be hard implement.
Personally, I have never warmed up to the idea of considering a 20 car train long enough to represent a Class I mainline train requiring multiple diesel locos. If that was my space restriction, I would build a switching layout or a branch line.
But that's just me. I think I have offered all that I can here.
OK I see where you are coming from on the speed aspect, I'm not referring to orders of magnitude. Nor does it really have any bearing on the he question I originally proposed.
My original was basically to determine if one can draw some inferences about prototype pulling power and model pulling power. Not too many variables involved, loco weight, tractive effort and trailing tonnage. How does prototype compare to model?
Other posters brought up many other variables, most I specifically indicated are not part of the original question. Can they be explored later? Absolutely. But to bring them up now is pointless and confusing.
As for my layout, I'm not modeling mainline trackage yet, I'm still stuck in the industrial area. As construction progresses, longer stretches of track will become available for use. Longest planned train is expected to be 30-40 loaded ore cars, running longer will be possible but why?
And, for the record, how many locos is not really necessary info for my question. Another variable added by a responder.
ruderunnerAnd that is an excellent point. However, horsepower tends to get speed, not necessarily pulling power. We know model trains can usually exceed their prototype speeds.
ROBERT PETRICK But when you go the other way, the little electric can motors in model locomotives would work out to about 12,000 HP to 15,000 HP in HO scale and about 60,000 HP to 70,000 HP in N scale. Each.
"the other way"?
Are you using the same factor of 650,000?
I don't see that, just because it works for weights and volumes, it would work for horsepower.
7j43k Greg has pointed out how the weight of freight cars scales down nicely using the NMRA formula. Let's also do that for a locomotive. A typical B-B diesel weighs about 250,000 pounds. Divide that by 650,000 and you get a scaled model weight of 6 ounces. Which kinda suggests our locos weigh too much. My Athearn F7 weighs a pound. But, still, going with orders of magnitude, the scaling "works". Ed
Greg has pointed out how the weight of freight cars scales down nicely using the NMRA formula.
Let's also do that for a locomotive. A typical B-B diesel weighs about 250,000 pounds. Divide that by 650,000 and you get a scaled model weight of 6 ounces. Which kinda suggests our locos weigh too much. My Athearn F7 weighs a pound.
But, still, going with orders of magnitude, the scaling "works".
An interesting tidbit. And if you know the makeup of the train a data point to start. Though we can assume empty cars. So can a model sw1500 pull 47 model cars? Can it pull more? In either case, what would we need to make the model tonnage weigh to match the observation?
Note, I'm deliberately leaving scale and car weight out of the question. If my theory works, scale is irrelevant.