What if we scaled train weight? or power?

@Will Wilkin posted:

Thinking as Godzilla here, who doesn't do any homework, would not the volume of 1:48 scale be the inverse of 48 x 48 x 48?  If our models had the same density (weight per volume) as the protype, how much would these locomotives weigh at O-scale?  I don't know how to calculate it but I'm sure all the retired engineers here have already worked this problem out?  Would it be the cube root of 48?

Same question for power, or hopefully in similar proportions, either power scaled by weight (traditional measure) or, plausibly valid in modeling, power scaled by volume of the model?  How much power should these model engines have if scaled for power?

May I suggest you visit the NMRA website, and refer to the weights section for both HO and O Scale model weights. Properly weighted locomotives and rolling stock are pretty well covered.

I’ve often wondered the same thing.  For weight, I do think it would involve all three dimensions and wouldn’t scale linearly like size.

@Hot Water posted:

May I suggest you visit the NMRA website, and refer to the weights section for both HO and O Scale model weights. Properly weighted locomotives and rolling stock are pretty well covered.

According to their recommended practices, O scale rolling stock should start at 5 ozs and add one ounce for each inch in length.  

So a 40’ box car would come in at about 15 ozs, which when multipled by 48^3 comes out to 50 tons.  Seems right.

@rplst8 posted:

According to their recommended practices, O scale rolling stock should start at 5 ozs and add one ounce for each inch in length.  

So a 40’ box car would come in at about 15 ozs, which when multipled by 48^3 comes out to 50 tons.  Seems right.

If a one hundred car train had an average of 15 ounces per car, the engine(s) is pulling close to 88 pounds?  John

Are you asking if a real engine weighs, for example, 400 000 pounds, what would the equivalent O engine weigh?

@rattler21 posted:

If a one hundred car train had an average of 15 ounces per car, the engine(s) is pulling close to 88 pounds?  John

Yep.  And not all that unbelievable really.  Remember that’s weight on wheels, not on the drawbar.  The locomotive would only need to overcome the drag of friction which is probably two to three orders of magnitude lower.  So 0.08 to 0.8 lbs.  A lot of modern O scale locomotives can easily manage a pound or two of pulling force.  

However, when climbing a grade the weight of the cars must be factored in.  An 88 lbs train on a 2% grade is about a 1.7 to 1.8 lbs additional drag force.

@rattler21 posted:

If a one hundred car train had an average of 15 ounces per car, the engine(s) is pulling close to 88 pounds?  John

Correct.  If you've ever assembled a long consist, you'd be amazed at the drawbar pull of the set.  I ran a 115 car mixed freight a few years ago at a club function, and when I grabbed the lead car and moved the mass, it was pretty amazing how much force it took.  I also got to see how coupler slack is important with a long consist, my two engines couldn't get it moving without first reversing and putting slack in all the couplers.  Just that little bit of movement was enough to make a big difference.

Your math doesn't work, doesn't take into account, the mass of the material

Weight is a function of volume (3-dimensional) so you have to divide by 110,592 (48^3) to get the scale weight from the prototype weight.  Many items out of the box come pretty close to this.  I remember when I realized this conversion I calculated out the correct scale weight for my Lionel N&W 611, and it actually weighs more than it should (not complaining about that!).

@Dave Koehler posted:

Your math doesn't work, doesn't take into account, the mass of the material

Care to elaborate?

@Will Wilkin posted:

Would it be the cube root of 48?

That's how Lionel figured it for rating transformers in horsepower.

@Cheap&NothingWasted posted:

Weight is a function of volume (3-dimensional) so you have to divide by 110,592 (48^3) to get the scale weight from the prototype weight.  Many items out of the box come pretty close to this.  I remember when I realized this conversion I calculated out the correct scale weight for my Lionel N&W 611, and it actually weighs more than it should (not complaining about that!).

A Big Boy locomotive weighs about 1,200,000 pounds, dividing that by 110,592 gives you 10.85 pounds for an O-gauge scale Big Boy.  My Vision Line Big Boy weights 15 pounds and 11 ounces.

The O gauge engine scale weight fudge factor. I see spread sheets.  Not it! 

@rplst8 posted:

Care to elaborate?

@Dave Koehler posted:

Your math doesn't work, doesn't take into account, the mass of the material

I went back over the math... I'm not sure what we missed...

Here is the NMRA recommended practice for car weight.
https://www.nmra.org/sites/def...ndrp/pdf/rp-20.1.pdf

According to that, a 40' O-scale boxcar should weigh roughly 15 ounces.
40' * 12 / 48 = 10"
5oz + (10in * 1oz/in) = 15oz

Most sources I can find on the subject say that rolling resistance for the prototype is 1/1000th (three orders of magnitude lower) that of the weight of the car on the rails.  So a 100 ton railcar takes about 200 lbs of force to keep rolling.  Starting friction is considerably higher, but not likely more than 2-5x higher.  For reference, the continuous tractive effort of an SD70Ace is about 160,000 lbf but I'm not sure at what speed that is.  The faster you go, the more wind resistance and drag are there, and the less tractive effort you have.

To fit that to our 1:48 world, I'd say that the rolling resistance probably doesn't scale linearly, which is why I left some wiggle room saying that the rolling resistance is likely somewhere 1/100th to 1/1000th the car weight.

Let's take the worst case: 15oz / 100 = 0.015oz

For a train of 100 cars, that results in a drag of 15oz of ~0.94 lbs.

You cannot scale weight from length--or even volume.  You have to scale it from weight.

This has come up before, and I do recall that our 3RO equipment, quite coincidentally, often very roughly approximates the proper "scale weight" of some equipment. (Are those enough "roughly","approximates", "some" to keep me out of trouble?)

"my two engines couldn't get it moving without first reversing and putting slack in all the couplers." - and very prototypical, especially in steam days, as a reciprocating steam loco does not generate the starting tractive effort/torque (Tesla!) that electric motors to in a diesel-electric. The steamers did, however, make more horsepower at speed than the diesels.

"Weight is a function of volume (3-dimensional)"

This question is not what we want to weigh our models - as the NMRA standard or some other theory for good tracking and rolling.    It is a purely academic question of what would equivalent weight of a real car or loco be, if it were scaled down.    Dividing by 48 cubed seems logical, but I am not sure.   I think this topic was discussed some where else some  years ago, and I think the answer was that our model stuff is a lot heavier relative to the prototype.

@palallin posted:

You cannot scale weight from length--or even volume.  You have to scale it from weight.

The density of cast iron is somewhere between 6.85-7.75 g/cm3.  Let’s call it 7 for simplicity’s sake.

A 74’ x 16’ x 10’ block of cast iron (roughly the size of an SD70Ace) would weigh 2,347 tons.

An 18.5” x 4” x 2.5” block of cast iron (roughly the size of an O-scale SD70Ace) would weigh 46.7 lbs.

2,347 tons is ~5.1 million pounds, / 48 / 48 / 48 = 46.7 lbs

You can scale weight by dividing the prototype by 48 cubed.

@rplst8 posted:

You can scale weight by dividing the prototype by 48 cubed.

Granted, but your post above was using length, at least in its explanation.

If you "scaled" weight, then a 100 ton hopper car would no longer be 100 tons. 

the only way to do this is by water displacement as Archimedes did.

so place your engine in a bathtub of water and mark the displacement.   then remove and toss in some cubits to arrive at the same mark..

WHO'S FIRST.

More weight scaling discussions found at OnlineConversion forums.

Looks like you divide by the cube of the scale of the 3 factors - 48x48x48 or 110,592.

One of my 40 ft. steel-sided boxcars has a stenciled empty weight of 63,000 lbs.

63,000 / 110,592 = 0.5696 lbs. or 9.11 oz.

NMRA suggests about 15 oz. for a 10 inch boxcar. It's my understanding that the extra weight is for smoothness of operation and purely staying on the track when many cars are being pulled.

Bill

I was aware of the close proximity of weight.  The one non scale-able would be molecules-atoms.  Which helps to understand why our collisions are not as devastating as in 1:1 life.  I have never telescoped a K-line heavyweight passenger car, yet.

I model in HO. It's 1:87 scale. SO... does that mean:

87x87x87 = 658,503

Weight of prototype engine: 240,000 lbs

240,000 / 658,503 = .3645 lbs(?) in HO scale?

IF so, and if I use 1.6 oz (1/10th of a pound) x .3645 I get .5832? Is that 5.832 oz?

Have I done the math correctly?

If so, than most of my HO 4 axle road/road switcher power comes in at an actual 12-14 oz range. SO... my models are over twice as heavy as they would be at a "scale" weight?

Andre

@Tom Tee posted:

I was aware of the close proximity of weight.  The one non scale-able would be molecules-atoms.  Which helps to understand why our collisions are not as devastating as in 1:1 life.  I have never telescoped a K-line heavyweight passenger car, yet.

I believe the major problem is you can’t scale gravity, therefore you can’t really scale weight. Similar to trying to get a scale speed, can’t really be calculated because you can’t scale time. You can only go for what looks appropriate speed wise and what operates well weight wise.

One way to scale weight would be to find a planet with 1/48^th of the gravity of earth… go there and weight your cars – just a thought.

Tom Stoltz

in Maine

To be truly scale in weight using the 110,592 factor, our models would have to have the same proportions by weight of cast iron, brass, wood, copper, steel, etc., etc. to the prototype.

Look at it in reverse. If a model has an electric motor and gearing that weighs about 1 lb., by the 110,592 factor the prototype would have one that weighs around 55 tons! And don't forget all those spring steel handrails on the models that would scale out at over 4" in diameter on the prototype.

This might help account for the fact that our models seem heavier than "scale" in weight!

Also, consider what would happen if a giant tried to lift the prototype by squeezing it around the "shell" the way we do with our models. The weight of materials that make up our models is distributed much differently than in the prototype.

Then, as Tom Tee said, there is the strength of materials factor that does not scale due to differences at the molecular bonding level!

Jim

Put another way. . .

The Cube Square Law is all we have to approximate scaled weight as modelers do. A mechanical engineer will point out the strength goes up and down with area. So our models are not built with scaled materials.

@timetraveller posted:

More weight scaling discussions found at OnlineConversion forums.

Looks like you divide by the cube of the scale of the 3 factors - 48x48x48 or 110,592.

One of my 40 ft. steel-sided boxcars has a stenciled empty weight of 63,000 lbs.

63,000 / 110,592 = 0.5696 lbs. or 9.11 oz.

NMRA suggests about 15 oz. for a 10 inch boxcar. It's my understanding that the extra weight is for smoothness of operation and purely staying on the track when many cars are being pulled.

Bill

I think you answered your own question there.  63,000 lbs empty.  If the boxcar had a load, it would weigh more.  The NMRA is just suggesting you put a load in your scale rail cars.

@Jim Policastro posted:

To be truly scale in weight using the 110,592 factor, our models would have to have the same proportions by weight of cast iron, brass, wood, copper, steel, etc., etc. to the prototype.

Look at it in reverse. If a model has an electric motor and gearing that weighs about 1 lb., by the 110,592 factor the prototype would have one that weighs around 55 tons! And don't forget all those spring steel handrails on the models that would scale out at over 4" in diameter on the prototype.

This misses the point.  The OP asked "What should a locomotive O-scale weigh?"  The materials don't matter in this context.  You could carve it out of wood and then add lead weights to bring it up to the right amount.

This is what I've used for my scale mass calculations...

Scale mass = (Prototype weight (lbs) x 16 (ounces/lb)) x (1/48)^3

So... in Excel use: =(A3*16)*((1/48)^3)

Thanks!

- Mario

@CentralFan1976 posted:

This is what I've used for my scale mass calculations...

Scale mass = (Prototype weight (lbs) x 16 (ounces/lb)) x (1/48)^3

So... in Excel use: =(A3*16)*((1/48)^3)

Thanks!

- Mario

For what it's worth, there is NO WAY that an EMD GP40 weighs "345,000 pounds", which would be over 86,000 pounds per axle! About the heaviest GP40/GP40-2 units ever delivered were a bit over 286,000 pounds (71,500 pounds per axle).

@Hot Water posted:

For what it's worth, there is NO WAY that an EMD GP40 weighs "345,000 pounds", which would be over 86,000 pounds per axle! About the heaviest GP40/GP40-2 units ever delivered were a bit over 286,000 pounds (71,500 pounds per axle).

IDK What you're talking about?

Thanks,

- MARI

I always understood the NMRA weight suggestions to be based on empirical data of what is too light for a models reliable operation, not derailing as they work they way through turnouts,  and too heavy, again for reliable operation in relation to the pulling power of a single loco, and a prototypical problem of light cars ahead of heavies and their derailment chances, such as string lining in curves.  So, flat car or hopper of a given length, the weights were more or less close, starting with a common start weight of 5oz for O and 1 oz for HO and adding additional weight per inch of car length.  Don't think that has anything to do with gravity and scaling down the actual weight, and I thought the original posters question was along the lines of what should a car weight if just the tons were scaled down to model size, not anything to do with the NMRA standard.

Molecules and atoms don't shrink, so it's impossible to have an O-scale anything weigh what a 1:1 anything would weigh.

Next target: how to scale colors.

@Bob Delbridge posted:

Molecules and atoms don't shrink, so it's impossible to have an O-scale anything weigh what a 1:1 anything would weigh.

What?

Molecules are the building blocks of matter.

A square inch of a 10" strip of metal and a square inch of a 40' long piece of the same metal have the exact same molecular structure.

The 10" piece can maintain shape much better with it's attending rigidity.

Molecules are essentially unscalable.

@Tom Tee posted:

Molecules are the building blocks of matter.

A square inch of a 10" strip of metal and a square inch of a 40' long piece of the same metal have the exact same molecular structure.

The 10" piece can maintain shape much better with it's attending rigidity.

Molecules are essentially unscalable.

Understood.  But a better comparison for rigidity purposes in terms of scale would be a 1"x1"x40' piece and a 20 mil x 20 mil x 10 inch piece.  Indeed, they will not be the same, but scaling it in all three dimensions will yield a closer comparison.

One note, people are using pounds to indicate mass, in the English system mass is weight (in lbs)/32 (something called slugs). In the Metric system mass is measured in KG, the weight is KG*9.8.

Doesn't really matter in terms of this discussion (which is a bit off the rails, pun intended, I think the original poster was just asking what the values would be in 1/48th scale if you scaled down weight and the power of prototype rolling stock). It is pretty easy to see why we can't really scale mass and power down, it is why transformers in the scale world had things like momentum and braking and the command control systems spend so much effort on making the train seem realistic in terms of getting to speed and braking. Open the throttle to 18v and watch how fast our trains move, even just the engine. Obviously most of us don't run mile long trains either, and even long trains in our domain on a big layout if you went full out would accelerate way faster than a train the same length in 1:1.