Here is a silly newbie question that I don't have experience or room enough
to answer by experiment: How does pulling power scale? FOr example, a
nice prototype 90 car stack train may take three locomotives. How many
model locomotives does it take to move a 90 car train in, say, HO or N
scale, assuming the cars are properly weighted and all that?
Rolling friction doesn't scale at the same rate as mass, so 90 model cars don't
roll like 90 prototype cars.
The prototype has to move the huge mass from a stand-still, and it has to
overcome "stiction" which is, shall we say, the 'gluing together' of surfaces,
journal to bearing and wheel to rail. Once your 90 cars are rolling, it takes
very little force to keep them rolling on the flat.
The models have very little stiction and relatively little mass, but a
relatively large amount of friction, which needs continual power to keep
You can picture this in reverse: - Turn the power off on the prototype at 60mph
and the train will roll for miles - turn the power off on the model and the
train will stop in inches.
Now we add gradients and curves into the equation:
- the prototype has problems with gradients, so they add more locos.
- the models have less problems with gradients, but we tend to have steeper
ones because of space limitations. (that's probably a draw.
- the prototype has large radius curves which do limit train length.
- we have horribly sharp curves which generally limit us to much shorter
trains, just as they would the prototype.
We would need a football field just to lay out a scale sharp radius curve in
H0. Some of us dream of doing that, while others of us just ignore the fact
that our curves are the sort where dock locos would push one car at 5mph with
all flanges screaming, and get on with running express trains at 100mph.
In summary, you have to find the operating limits of whatever track layout you
put down by yourself. (it's great fun finding out)
My personal experience hits two barriers:
- 25 wagons is the limit with my curves and stock.
- If the train is longer than can be viewed all at once, the mind translates it
to be -l-o-n-g-. Add clumps of view blocking trees, embankments or buildings.
Conversely, if you can see an entire 180 degree curve, it will look like a
It depends heavily on the specific locomotives.
Weight, gearing, motor type, and traction tires all make a difference.
There's several factors which will make a model SD45 not work comparable
with a real one.
-Models (pre-DCC at least) have more problems keeping in synch in a
brace. One goes too fast or too slow, and it drains the lot.
-The same mechanism is often in a whole slew of models. You see three
GP50s on a stack train, we could (entertainingly) stick the same works
in GP7 shells.
The answer is that it does NOT 'scale'. The dynamics of the model train
are VERY different than a prototype train.
Model trains are dominated by FRICTION. Real trains are dominated by
MASS (inertia). They behave VERY differently. Try to get a model boxcar
going a few scale mph to 'drift' a scale mile! A real train moving at 60
or so mph takes more than a mile to stop. A model can be stopped in an
actual foot or so, 87 scale feet.
Also, there's LOTS of variation in models. I have a couple individual
locomotives that will easily pull a 90 car train.
The pulling power of a locomotive, prototype or model, is approximately
the coefficient of friction (rail to wheel, typically something like
25%) times the loco's weight. So, to first approximation a loco will
pull about one quarter of it's own weight. That's actual pulling power
("Tractive Effort") applied to the coupler.
Prototype locos get a bit better factor of adhesion (roughly the same as
coefficient of friction) than models, as steel on steel (especially with
sand) has more friction than nickel silver (wheels) on nickel silver
(track) ... the usual model combination. Using rubber or plastic
'traction tires' greatly increases the factor of adhesion, and improves
pulling power (as the expense of many other things).
A model loco should weigh (scale weight) the cube of the scale factor.
for HO at 1/87, that's (1/87) X (1/87) X (1/87) = 1/658,503. So ... a
real loco that weighs perhaps 200 tons (= 400,000 lbs.) SHOULD weigh, in
HO, about 400,000/658,503 = 0.6 lbs.
Interestingly, MODEL locomotives often weigh MORE than their correct
scale weight. They are often far more 'dense' than the prototype, being
made of almost solid metal with just a thin plastic shell. A real loco
has LOTS of empty internal space, reducing it's density. The end result
of the model often being too heavy, plus it's reduced traction, means
that many models will often pull almost the same as the prototype.
The force needed to move the TRAIN (usually a few thousand pounds) is
FAR less than the train's weight (usually a few thousand tons). The
actual force depends on the grade of the track, the curve of the track,
the type of bearings in the train's trucks, the temperature, and other
A model TRAIN has **FAR** more friction in proportion to it's size than
a real train (in engineering, a so called "square-cube" problem). THIS
is what limits what the model locomotive can pull. If you want to pull
long trains, you should spend a **LOT** more time reducing your rolling
stock's friction (metal wheels, better trucks, etc.) than worrying about
increasing your locomotive's pulling power.
Daniel A. Mitchell wrote:
[snip fascinating analysis]
Tangentially (and at the risk of igniting another religious war ;-):
which kind of wheels are generally better? I don't recall where, but
somehow I picked up this general idea that plastic (presumably Delrin)
wheels were better than metal. I've got (N-scale) rolling stock with a
variety of wheel brands in both plastic and metal. Some (of both
materials) are obvious junk: off-centre axles, binding on side-plates
etc. Ignoring those and comparing, say, a Micro-trains truck against a
metal Atlas one, on an informal flick-down-the-track test they seem
The subject of moving trains, in both the prototype and models,
is very complicated even for engineers and physicists, but for
practical purposes, the involvement can be eliminated. Most
data, in either case, has been derived empirically or from
observation and measurement.
All of the factors involved are not scaled down at the same
ratio. Grades are essentially angles, which can not be scaled.
Since weight involves a volume, its ratio is as the cube or third
power or about 660,773 :1 for HO 87.1 :1. Others fall someplace
Between the prototype and the model static and dynamic
rolling or sliding friction coefficients differ greatly due to
materials used and configuration. Air resistance is not a
factor in smaller scale models.
Loco movement capability is divided into two parts: starting
tractive effort and power (drawbar pull at speed). The former
is limited by weight on drivers and torque at rims. For
traction motors, including our models, the torque is limited by
the gear ratios and the motor stall torque. Prototype steam
locos are more involved.
Power is limited by the prime mover, steam generator or diesel
engine etc.. In models this is the maximum power rating of the
The various factors are covered in depth under related topics on
For more details with methods and extensive discussion of
problems and solutions, see first site below in repowering,
weight, grades and motor evaluation.
Hope this helps.
MODELRAILROAD TECHNICAL INFORMATION
PROTOTYPE TECHNICAL INFO FOR MODELRAILROADERS
(Revised. New address)
MR TECHNICAL HELP GROUP
COUPLER HELP GROUP
The problem is in the axle bearings rather than in the wheels themselves.
The bearings in the trucks is a lot better than what was available in the
'50s and '60s what with the delrin axles and/or sideframes. which reduces
the friction of those bearings quite nicely. Cars used to stay on 2 percent
grades with the old style bearing surfaces and most cars will now roll with
less than 1 percent grades.
To the original question, prototype locos could pull a nice long train on
level track - I've seen a single F7 pull 90 cars or so on level track - but
quickly end up pulling only a few cars on 2 percent grades - that same F7
could only pull about 8-9 cars on that grade.
Model locos can be built to pull about 40 cars on the level but that cuts
down to about 25 cars or so on that same 2 percent grade. Trying to get 90
cars on the level would be rather difficult without using good electric
motors in the loco and lots of weight. I've been there and have locos that
are good pullers but I'd rather not weight my locos that much in normal
servicce although doing so tends to make the different loco drives work
better with each other as they tend to match speeds better with the weight.
Why isn't there an Ozone Hole at the NORTH Pole?
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