Scale vs. mass vs. weight for

[asciibaron]

scale this!

[wcfn100]

I think the point would be...

If an N scale car out-weighs it's prototypical counterpart (as I say it does), is that relevant to a discussion about the pulling abilities (tractive effort) of an N scale locomotive as compared to it's prototype (which is where this started).

I am operation under the assumption that it is.


Jason

[bicknell]

have you factored in the empty space of the car?  simple 3 dimensional measurements do not account for the empty space inside the car  sure you can scale a solid objects mass, but a boxcar is not a solid object, there is plenty of air in the car, even when loaded.  a box car's walls would be super thin if scaled correctly

Hence why the N Scale car is "heavy".  Quarter inch plate walls don't become 0.0015" walls in N scale.

If we shrunk the prototype to exactly 1:160 with the same materials it would weigh 1/(160^3).  That includes thickness of everything; this is the wonka magic television camera.  N scale cars are a lot thicker than that though, so even though the material (plastic) is less dense, there is more of it.  If everything were scaled correctly the plastic car would be "lighter" than the prototype, to the same proportion as if the real car would be made out of plastic (which might be heavier than people think!).

It's an important concept to understand if you want to make realistic predictions about what an N scale locomotive can pull.  Imagine how heavy a real locomotive would be if it was 90% full of lead.

[Dave V]

I've been looking for just the right description and I found it.


"The weight of an object increases as the cube of the scale factor."

If anyone has a problem with that, you can go argue it here:

http://www.worsleyschool.net/science/files/scalefactor/factors2.html


It also says this:

"The mass of an object depends on its volume. For example, if you increase an object's volume by eight times, its mass will also be eight times greater."

Sound like scaling....  Go get 'em.


Jason

Unfortunately, when it comes to science, sometimes people teach the wrong thing because it's easier than teaching the right thing.

The mass of an object depends on its volume

Utter nonsense.  Desnity equals mass divided by volume.  We often use a quanity in fluid dynamics known as specific volume, which is desnity per unit mass.  The above statement is backwards even in solid body physics; assuming a completely incompressible solid, you can increase the volume by increasing the mass, but not the other way around.

In order to increase mass by increasing volume, one must hold the density constant.  This requires adding more mass, somthing that can't be done simply by increasing the volume.  That is, unless we're talking fluids.  Then it's just a matter of the equation of state from basic thermo:  PV=nRT, or as we use it in meteorology, P=pRT (where p represents "rho," the density).

One of my biggest pet-peeves (besides promiscuous waffles) is sloppy science.

[wcfn100]

"The mass of an object depends on its volume

Utter nonsense."


Unfortunately you're reading the statement out of context (my fault).  That statement was solely in regards to how things scale and not about the two physical property being dependant on each other for a givin object.


Jason

[Dave V]

Philosophically speaking, were one to reduce a boxcar to N scale, one would have to remove enough of the mass of that boxcar that it would also weigh 1/160th; that's one that the movies always get wrong.

If you shrank to N scale, you'd theoretically weigh the same as you do now (as you'd have the same number of molecules, right?) unless you lost most of your molecules.  If you somehow retained all of your molecules and still shrank to N scale, you'd be in such a high-energy state, you'd probably be unstable (moreso if you're Steve or Ed).  Electron orbits can be "compressed," but only by adding energy.  Plus, they don't like staying that way for long!  You'd still weigh the same, and probably crush whatever locomotive you tried to board (assuming your benchwork holds up).

To shrink "correctly" you'd lose most of your mass somehow (not sure how that'd work) so you weigh 1/160th of your current weight.  For the average non-model railroader, you'd still weigh what, about a pound?  You'd be the size of an N scale guy, but weigh a pound?  Maybe if you're made of Uranium...

...hence the flaw in the whole scaling argument.  Apples and oranges.  Size and mass don't scale in the same manner.

...and good luck getting back to 1:1 scale...  How do you put those molecules back together? ;D

[DKS]

How do you put those molecules back together?

You'd use the Heisenberg Compensator.

Energize!

[wcfn100]

"Size and mass don't scale in the same manner"

So what happens if you increase a volume of water from 1cu meter to 3cu meters?  What happens to the mass?

You're all trying to tell me it won't increase in proportion to the volume.

Show me the math.

Jason

[wcfn100]

To shrink "correctly" you'd lose most of your mass somehow (not sure how that'd work) so you weigh 1/160th of your current weight.  For the average non-model railroader, you'd still weigh what, about a pound?

If that's how you're going to figure the math on that, then I don't know what to make of your posts..

If you only lost your height, you'd way 1/160 less or a pound from 160lbs.

Your width, 1/160 more.

Your depth, 1/160 more.


Jason

[Dave V]

To shrink "correctly" you'd lose most of your mass somehow (not sure how that'd work) so you weigh 1/160th of your current weight.  For the average non-model railroader, you'd still weigh what, about a pound?

If that's how you're going to figure the math on that, then I don't know what to make of your posts..

If you only lost your height, you'd way 1/160 less or a pound from 160lbs.

Your width, 1/160 more.

Your depth, 1/160 more.


Jason

Exactly!

I was wondering if someone would pick up on that...

We talk about N scale being 1:160th scale...  but that's one-dimensional.  An N scale boxcar occupies 1/160^3 less space... That's why an N scale layout takes up roughly one quarter the space as an HO layout (as opposed to "half the size" which is the usual lame quote).

You'd really have to lose enough matter to weigh 1/160^3 less...!

So you wouldn't weigh a pound.  You'd weigh a fraction of an ounce.  Good catch!  You get the gold star!

But where I can't agree is the idea that somehow "increasing the volume of water increases its mass."  You can't increase the volume of water without adding more water which increases the mass of the whole but not of the original water.  This is becuase water is, to first approximation, considered incompressible.

Now, in compressible gases, you can indeed increase the volume dramatically without increasing the mass one bit.  You simply reduce the desnity.

[3rdrail]

Dave Vollmer posted this in the wrong (old) topic. Reposted here.

"Size and mass don't scale in the same manner"

So what happens if you increase a volume of water from 1cu meter to 3cu meters?  What happens to the mass?

You're all trying to tell me it won't increase in proportion to the volume.

Show me the math.

Jason

The math:

D = M/V, therefore M = D*V.  In the euqtaion, M only increases with V if D remains constant.  Now, for most solids this is the case.

But where it's wrong is in treating mass as a dependent variable.  Mass is an independent variable; in a closed system you always start with a certain amount.  You can't just "make more."  Volume is dependent upon mass, and not the other way around.

[chuck geiger]

Somebody call security!

[up1950s]

Would it be that gravity is not scalable , but a constant , so scaling down volume of a given weight is skewed by the constant of gravity . Weight without gravity is nothing measurable , only assumed . Water in N scale is out of scale because of viscosity , gravity maybe , and surface tension . Those are hard to scale down , if at all possible .

[wcfn100]

But where I can't agree is the idea that somehow "increasing the volume of water increases its mass."  You can't increase the volume of water without adding more water which increases the mass of the whole but not of the original water.  This is becuase water is, to first approximation, considered incompressible.

Well I didn't say increase the volume of water, I said increase a volume of water i.e. increasing the space in which water is held or can take up.

"Volume is dependent upon mass, and not the other way around."

WHAT?

Isn't mass dependant on how much there is i.e volume?

M = D*V

That equation tells me the mass is dependant on the volume of the object and it's density.  I that right?


And it's not about making more, it's about having more.


Jason

[Dave V]

Oops!  I didn't see that it had been moved...  Nevertheless, I've had a little fun at Jason's expense.  Essentially what you're saying is correct, although I would probably give partial credit for that answer...

I enjoy these off-topics; I hope you've had some fun thinking about this too.

Also, my mistake; I meant to say DENSITY depends upon mass...  I'm a little embarassed by that mistake!  I should get a refund on that PhD!

In fact, I am out 10 a$$hat points for this one...