AJK,  you must have time to

AJK,  you must have time to contemplate the meaning of life!! Good job and the math looks good to me, but then again freshman year was the best 4 years of my life!!!!!!

Scale cubed?

The part where you cube the scale is throwing me off. I've always been told that weight DOESN'T scale, because if you (for example) were to divide the weight by the scale directly, that Z-scale boxcar should be over 400 pounds. Part of the issue, I presume, is the scaling of density and mass, not just weight. 

Mike in CO

Area and weight scaled down

Weight?

Weight only factors into its effect on something else. For example, if I real locomotive splits a switch, it tears up the ties, rips the rails out, and generally creates a mess. If a model locomotive does the same, it derails and you use the old 0-5-0 to just pick it up and start over. When is the last time you had to compute the weight of a model train to determine if your bridge can handle it? Our tracks and bridges are comically over-engineered, so much so that your model trains could never cause any structural issues (unless you made a G-scale bridge out of nothing but balsa or any other scale from pressed dried spaghetti). When something ‘goes on the ground’ it probably won’t dig a hole. I think if one of my boxcars derailed and overturned, the static grass I’m using would likely keep the car from actually touching the ‘ground,’ due to how much I’ve stiffened everything in the effort to make stuff not easy to break or mess up. So, your boxcar weighs dozens of scale tons more than it should? Means nothing, as the bridge it’s crossing can take hundreds (maybe even thousands) of scale tons going over it.

I remember once talking to a scientist studying bugs, and he told me that if you ever could make a insect much larger (as in larger than a man), it'd never stick to walls like the small version does. It's the size that allows it to do what it does, and when that scale changes, a fly or a spider 10 feet across would probably be confused as it's habits wouldn't match how gravity affected it. He said, based on a horror movie he once saw, that a SUV-sized spider would spend much of its time trying to do the things it easily does as an inch across, and unable to grasp why it wasn't working anymore, allowing humans with heavy weapons to easily approach and kill it.

In talking to some engineer

In talking to some engineer friends weight does not scale up or down well  folks have tried for a long time and been unsuccessful.

How things scale

Think about ants. Ants can lift 10 times their body weight, but that's because ants are small. Yes, weight scales the same as volume, by the cube of length. If the inside diameter of a prototype tank car is 10 feet and it's 60 feet long, then making an N-scale tank car with a diameter of 3/4" (10 scale feet) and 4.5" long (60 scale feet) could hold a "scale" amount of liquid. The weight and volume of that liquid would be a ratio of 1/160 cubed.

However, the strength of materials varies not by volume but by area. Strength is listed by how much force a given area will support, in pounds per square inch, or Newtons per square meter. This also applies to muscles, which is why ants are so strong. If the prototype tank car has walls 1.5" thick, then the exactly scaled model would be .009" thick. That would be fine for holding the liquid, and would be over-designed by a factor of 160. This is why our models don't tear up track and ties when they derail, because our track is a lot stronger than the prototype track. Still, compared to our 1:1 scale fingers, that .009" tank wall is very delicate, and you might crush it trying to pick the car up.

When you get into dynamics (i.e. the way things move) it gets a lot more complicated. For instance, our much tighter curves and potentially higher speeds. Centripetal force (which makes cars turn over if they go around a curve too fast) is m x v² / r. For N scale, the m is reduced by 160 cubed. v² is reduced by 160 squared, so the numerator is reduced by a factor of 160 raised to the fifth power. The denominator is only reduced by a factor of 160, so the total force is reduced by a total of 160 raised to the fourth power. This is why we can get away with much smaller curves, and a major problem with designing helices is string-lining (pulling the train off of the inside of the curve). On the prototype, even with broad curves and slow speeds, the net force is outward, and the outside rail wears faster, except under very unusual circumstances.

This may be a little deep, but I hope it helps more than hurts.

The only way to "scale"

The only way to "scale" weight is to design the model so that it behaves in a "dynamically similar" manner, without regard to actual mass. Aeronautic engineers have been chasing this elusive butterfly since the Wright Brothers.

Physics Doesn't Scale, whether it be mass, water, or smoke.

The question is what are you after

When you are scaling anything.  I spent a couple of decades scaling aircraft engine components.  

Volume scales exactly.  Weight is density times volume.  The issues are that the item your scaling from is not a homogeneous block.  It has been designed at minimum thickness for nominal strength and has stiffeners added to provide extra local strength as required for the maximum load requirements.  Inherent in the scale is a smearing of these various volumes.  Even if you took the pieces apart and scaled each individually it would not mean much.  The problem is the 9 mill thickness that was discussed earlier does not provide the scaled stiffness of the original car.  You can get to a situation where, if you could create the scaled object, it would not be able to support its own weight,  the stress would be too high.  

Thus gets complicated in any discussion where the materials change.  The stress to density of the material becomes an important factor here.  The various resins that are used in models all have a lower stress to density level than steel.  So they are less likely to support the structure shape.  Another issue is the minimum thickness that can be successfully cast or molded.  While a variable depending on the material and gate or stiffener locations, it is substantially thicker than scale thickness value.  

Based on this, the actual weight is likely larger than a classic scale would imply.  We had factors based on experience for scale ratios much less than these.  These factors were greater than one.  We were working with materials with similar strength to density values.  

I am surprised the O scale model is as close as it is.  It must have to do with the material density change

Performance of the scaled item is another item altogether. The model truck designs do not provide the scaled resistance for a number of reasons.  The bearing areas are much smaller, thus the frictional resistance forces are much lower than scaled amount, even with the heavier than scale cars.  

Barr is onto something...

Dear MRHers,

Barr is onto something...

...and it is this "...we can caricature, fudge, or otherwise sleight-of-hand the physics in model form so it 'looks/sounds right'..." permission that we give ourselves as modellers, which allows amazing models to be built.

To take a related "physical force" example, Barr and I have long agreed that "sound does not scale",
(simply/only "turning down" a 12"/1' prototype recording is commonly called-out as not "sounding right" when considered in the context of the scale visual "noisemaker" that is alegedly making the sound...)

but that does not mean I/we/you are not allowed to consciously and deliberately apply strategic ammounts of Audio processing (EQ, compression, reverb/delay, Image manipulation)

to create a Scale Sound Model 
(a "conscious caricature" of the 12"/1' scale audio waveform,
designed solely for presentation in the context of a miniature model display),

which "sounds right" relative to the related miniature physical/visual "noisemaker",
(the perceptual frequency spectrum and spread being reproduced "sounds right" at an appropriate scale-viewing/listening-distance", IE your diesel "throbs" right from a scale 100'),

while keeping under an entirely "scale appropriate" 70dB-SPL...
(the family members upstairs don't fear an earthquake is hitting when all you did was fire up your "over-scale" sound-equipped loco... ),

Happy Modelling,
Aim to Improve,

PS similarly, when rail-marine modellers want to model the gentle rocking of a tug or carfloat,
who said mounting the vessel on a bearing-suspended axis and counterbalancing with an under-table counterweight was somehow "off-limits" as a solution?

PPS Ditto for Seuthe smoke gens and simiilar. There are variables to play with in the installation and Oil choice which allow visual results varying from "lazy bunkhouse stove wafting" thru to "steelmill blast-furnace jets". just got to learn _what_ variables are available to adjust, and _how to tweak them to achieve the desired effect...

PPPS "live" water is harder to tame admitedly, but viscosity and flow-rate are fair-game variables...

Pulling Power?

This thread reminds me of my occasional wonderment: why do I see nothing about "scaling down" pulling power of locos? If we're going to deal with scaling down weight, then it seems we should also deal with how hard our locos can pull the weights.

I am quite content dealing just with what weights I need for good operation on my layout, Then how many locos do I need to move at reasonable scale speed pulling a train. If the resulting train looks good, then I don't care if it's "properly scaled down."

drJolS

You can't scale down gravity

The most important word in this discussion is gravity. Weight, mass, density, pressure, etc, are all affected by gravity, and gravity cannot be scaled. Consider a model waterfall - it looks odd because the water is falling freely under 1:1 gravity, ie: at the same speed (or acceleration to be accurate) as a real waterfall. Ideally the water should be slowed down by the same factor as loco speeds are slowed down for any particular scale. Which is more or less impossible (unless some clever person has increased the viscosity of the 'water' to slow it down appropriately - bit of a long shot though I would have thought ).

Tony in Gisborne, Australia

Replies...

The need to scale down pulling power is, I feel, an unintended consequence of the improvement of model pulling power. Gone are the days of traction tires, of only one of the two trucks being linked to the motor, and the pathetically underpowered motors themselves. Better motors, all-wheel traction, and heftier weights mean that whereas a 1950s vintage model could have pulled 6 cars its successor model today can haul 30 without breaking a sweat (note: you have a serious problem on your hands if you ever actually see your locomotives sweating!).

Now, dummy locomotives (if they still make them) can cover for this improvement for eras where the prototype locomotives shouldn't be able to haul that many cars alone. Modern era modelers probably have little to complain about given what I see these tier-X E-MC2-MACEs (can you tell I don't follow the latest in model designations?) handling around this part of Missouri.

 The one thing that comes to mind when the discussion turns to slowing down water is a childhood memory of my neighbor's apartment. Between the living and dining rooms the wide archway was flanked by a pair of gilded sculptures. Between the crown and the base there were clear filaments down which "rain" in the form of some sort of oil slowly dripped.

In theory, the mechanics of those sculptures could be applied to model railroading, but the how of it is beyond me - at least at this hour of the night.

A rain lamp

Oh--kay.... I had to go find out what sort of thing it was that I was remembering, and it was a mineral oil rain lamp:

The visual effect

in it's simplest form  depends on one's familiarity with how real trains move and one's ability to mimic it with a controller knob. All the scale weight in the world won't matte rif the toy trains don't run in a realistic manner....DaveB