Does weight scale as the cube of size?

[mmagliaro]

The subject line pretty much says it.  Since weight is a function of volume, if an N Scale box car
weighs 24g, would that logically mean we should consider it to be  24 x 160 x 160 x 160 grams, which
works out to about a  "scale" 217,000 lbs?

[ryan_wilkerson]

I like your idea. 217,000 lbs seems reasonable. I think modern cars max out at 286k loaded. Good thing our N scale rail is so strong

[Kisatchie]

That would be a heavy boxcar! Of course, it might scale better if the car sides/ends/roof/underframes were made of scale thickness metal... like tinfoil?


Hmm... an N scale model of
Kiz would have to weigh
a few pounds...

[wcfn100]

Yes.  It would take 160 boxcars in each dimension to be the size of a full size box car.

And since Volume is a cube, N scale isn't 1/2 the size of HO, it's about 1/6th (when using 87/160). 

Jason

[mmagliaro]

Yes, 217,000 lbs, about 200 tons, is absurd.  The loaded weight of a 40 foot car was nominally around
50 tons, wasn't it?   So that means that our 40 foot cars should weight more like 12 grams instead of 24,
which would work out to 108,000 lbs.

It never occurred to me, but this is probably one big reason that N Scale engines can rarely pull the lengths of
train that they pull in real life.  An MT 40' car is about 24g.  That's where I got that number.  So a train made up
of those cars would be twice as heavy as it should be.

Of course, in our N Scale world, we would probably suffer derailments a-plenty if we started making super-light cars.

But some 33' hoppers and some tank cars get down there, about 14g (and people add weight to those cars because
they are a derailment headache)

Thank you folks.  All this feeds into the weight balancing and test running I'm doing with my NP W-5.

[wcfn100]

Hopefully it will end here.  I brought this up several years ago on some forum and it brought the crazies out (myself included).  I'll have to search the A-Board and see if it was there.

edit: LOL, I found it, it's here on TRW, but I'm not going to post it.  It's a 2008 classic for anyone who wants to look for it. 

I miss you old Railwire. 

Jason

[peteski]

Yes, 217,000 lbs, about 200 tons, is absurd.  The loaded weight of a 40 foot car was nominally around
50 tons, wasn't it?   So that means that our 40 foot cars should weight more like 12 grams instead of 24,
which would work out to 108,000 lbs.

It never occurred to me, but this is probably one big reason that N Scale engines can rarely pull the lengths of
train that they pull in real life.  An MT 40' car is about 24g.  That's where I got that number.  So a train made up
of those cars would be twice as heavy as it should be.

Yes, but how about the mass of N scale engines?  Isn't an N scale engine also proportionally heavier than its 1:1 counterpart, so it can pull more of those "heavy" N scale cars? 

There is a lot more to this equation than just mass.  Friction (on smaller scale) probably works differently in 1:160 than in 1:1.  Then there is inertia too.  And probably other  things (like the contact area between the wheel and the rail).

Of course, in our N Scale world, we would probably suffer derailments a-plenty if we started making super-light cars.

There are some out there (VonRyan is one) who believe in making their models as light as possible.

[pnolan48]

I remember writing about my 45,000 ton cat prowling the layout and eating anything with lacquer on it, especially trees. Yes, she was a big Maine coon cat.

[Dave V]

[peteski]

I think I understand what Jason mentioned - if this thread continues, we are in trouble.

[Dave V]

Nah, it's all in good fun.  We have a sizable contingent of scientists on this board so we love these discussions.

Joking aside, let's examine.

D = M/V  <-- Density = Mass/Volume

In this country we have a bad habit of conflating weight with mass.  Mass is independent of location in space, but weight is dependent upon the local gravitational acceleration.  Weight is therefore m*g.  Now, students of Newton will immediately recognizes this as a form of m*a, where a = g (acceleration in this case due to the Earth's gravity).  Hence, weight, by Newton's second law, is really a force.

But I digress.  Scaling weight the same way as we scale length is only possible if the density of the material remains constant.  I think you'll agree that an N scale car probably has considerably different density than a real, steel one.  Even when the car is empty, you can calculate an average density for both, and I think you'll find them quite different.

[VonRyan]

Did someone say lightweight cars? 

Micro-Trains cars are acceptable. In the case of Atlas 40' woodside reefers, I remove the hefty stock weights. They haven't given me any trouble whatsoever. Backwards or forwards. 

[Scottl]

Plastic has a lower density compared to every metal I can think of, except lithium.  How does that explain scaling the model up to 1:1 resulting in an unrealistically high weight(mass)?  I don't think that is the issue at all.

I thought the scaled mass is off because there is a metal base plate in the model that when scaled up is unrealistic and materially affects the mass, given it is a large proportion of the model mass to begin with.  Say the metal plate is 3 mm thick, that is 480 mm 1:1, nearly half a meter thick solid metal.

[Dave V]

Exactly...with respect to the floor weight.

Absent the weight the N scale car would scale up to much lighter, but because we add a disproportionate weight to the car, it scales up heavier.  Averaging the density of the plastic car, the metal weight, and the air gives you a higher density than you would have with an empty steel car.  Plus, think about how thin the walls of an N scale car would have to be when you scale it correctly...  1:160th of the thickness of the sheet metal in a real car.  That impacts the average density too, since we have to make it thicker than it would be if in scale.

So density is still the issue at hand.  We are actually in agreement here.

[learmoia]

Technically the desired weight of your car is printed on it's side.

Volume scales at X'3 (cubed) the rate of length. 
So 12"/160 = 0.075"

160 X 160 X 160 = a scale of 4,096,000

The typical 60' covered hopper weights 32 tons (65,000lbs) when empty. 

So 65,000/4,096,000 = 0.0158 lbs * 16 lbs/oz = 0.25 oz

Lets take a Load:
263,000lbs / 4096000 = 0.064208 lbs * 16lbs/oz = 1.02oz

Lets take a 286K Load:
286,000lbs / 4096000 = 0.06982 lbs * 16lbs/oz = 1.12oz

Where I work, we figure that 1 GP38 can handle 20 loads, or 80 empties.

Soo, with that said.. one GP38 should be able to handle about 20 oz of empties or 20 oz of loads.

NMRA standard states:
0.5+Length*0.15
So 60' freight car * 12 / 160 = 4.5" * 0.15 = 0.675+.5 = 1.175oz

So based on my prototypical example.
One Atlas GP38 should be able to handle 17 NMRA weighted cars on a scale version of our railroad.
.. By that I mean.. we don't have 10degree curves and 2% Grades..

Here is another thing to ponder..
1 Locomotive can handle 20 loads.
2 can handle 45 loads
3 can handle 75
4 can handle 100
5 -- You start hitting other safety and practicality limitations before you max out the capacity locomotives.



3 "ACs" can accomplish the same as 5 GP38s..

These figures are specific to our location.. These numbers would never fly in locations such as (Horseshoe or Cajon)

~Ian