Scale weght


T

trailrider

Well-Known Member
We all know that HO scale is 1/87th of actual size. But have you ever considered how our models "scale" compared to the prototype? Weight (or more properly "mass") is a result of three dimensions times the density of the volume. Therefore, the weight of, say a typical Mikado locomotive and tender should be 1/87x87x87 or 1,52 x 10^-6. If a "typical" Mike and tender weighed about 850,000 lbs, then a scale model "should" weigh about 1.29 lbs. I weighed one of my old Mantua Mikes on an old baby scale, and it came out to about 1.75 lbs, or equivalent to 1.15 million lbs...a bit on the heavy side, but close enough considering the boiler is solid metal, and Mantua steamers are probably a bit heavier than average in the HO scale modeling world. I haven't weighed any box cars, so I'm not sure how they compare with the prototype and the NMRA standards. Just sayin'!;)
 
Engineer:

I believe the 87:1 refers to scale or "size" and not mass.

Not an engineer, just my 2 cents worth.

Thanks.

Greg
 
The scale is a linear not a volume measure. You would need to compare volume to weight. Since Density = Mass/Volume, you are basically comparing density. You can substitute weight for mass for this. Divide the 1:1 weight by 1/(87.1 x 87.1 x 87.1).
 
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trailrider said:
We all know that HO scale is 1/87th of actual size. But have you ever considered how our models "scale" compared to the prototype? Weight (or more properly "mass") is a result of three dimensions times the density of the volume. Therefore, the weight of, say a typical Mikado locomotive and tender should be 1/87x87x87 or 1,52 x 10^-6. If a "typical" Mike and tender weighed about 850,000 lbs, then a scale model "should" weigh about 1.29 lbs. I weighed one of my old Mantua Mikes on an old baby scale, and it came out to about 1.75 lbs, or equivalent to 1.15 million lbs...a bit on the heavy side, but close enough considering the boiler is solid metal, and Mantua steamers are probably a bit heavier than average in the HO scale modeling world. I haven't weighed any box cars, so I'm not sure how they compare with the prototype and the NMRA standards. Just sayin'!;)
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And all pointless anyway since one would have to also scale the earth and its gravity. Physics in general don't "scale down".
 
All care is that the HO rolling stock and locos stay on the rails.

Nice question anyways.

Thanks.

Greg
 
Good thing they aren't real. No way this table would hold em up! I'm using the vid on you tube that shows a quite handy little gage a guy made to get the weight 'right' to NMRA standards. Tech challenged so sorry no link, I don't know how and don't want to learn at this time.
 
G'day Trailrider and all....I recall a similar question some time ago .. Re 1:87 and re physical dimensions , quite accurate in scale size of course but weight is naturally a different matter stating the blooming obvious..If it was possible to meet ACTUAL one 87th of scale weight , an SD70 Ace (around 450,000 lbs) would need to be way more than the weight of two real family cars or so ..Absolutely impossible to condense that much weight into such a small item.unless your layout was situated in a Black Hole in space .If you could scale a 6 foot tall , 180 pound human to one foot in perfect scale size ,then the weight of him/her would need to be 30 pounds...equally impossible..I'ts funny though to think of a model locomotive that was so heavy that it'd fall through the floor . Imagine needing a crane to fix a derail but WOW...imagine the tractive effort....and the power of the wound pole motor to push a 5000 lb model around your layout!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!.......IMPOSSIBLE BUT FUN....Cheers Rod...
 
I still think that the "scale weight" would be the cube of 87 divided into the prototype weight. That would make your 450,000 lb SD70 about 10.8 oz. Oh, well, whatever...
 
Trailrider has the answer. That's why i suggested you look a density (technically average density). Take the dimensions of a 1:1 SD70 ACE (as suggested above) then calculate the average density (d = W/(WxLxH)). However you can also multiply the 1:1 weight by 1/(87.1x87.1x87.1). So, in the case of the SD70, your "scale weight" would be 0.68 lbs, approximately. That's too light for a model. Reason: gravity doesn't scale.
 
OldGuyHO said:
Trailrider has the answer. That's why i suggested you look a density (technically average density). Take the dimensions of a 1:1 SD70 ACE (as suggested above) then calculate the average density (d = W/(WxLxH)). However you can also multiply the 1:1 weight by 1/(87.1x87.1x87.1). So, in the case of the SD70, your "scale weight" would be 0.68 lbs, approximately. That's too light for a model. Reason: gravity doesn't scale.
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One of my HO scale engines weighs about 11 oz. (.69 pounds). IF 87.1^3 worked, that would make the prototype 454,284 lbs. It is TRUE that gravity doesn't scale, and I'm not sure how much an actual F7A would weigh. The thing is, we don't have a scale 567, traction motors, generator, etc. inside the model. What we have is an electric motor, flywheels (which are quite heavy), and the die cast chassis, which, it is TRUE does not scale. Oh, well... just too much time waiting to get over the stomach grippe...
 
Even at 'scale weight' its nearly impossible to model a 'bump yard', there are just some things we CAN'T do in HO scale.

Seen attempts at it but it never quite works out without some kind of 'help'.

Pesky physics.
 
trailrider said:
I still think that the "scale weight" would be the cube of 87 divided into the prototype weight. That would make your 450,000 lb SD70 about 10.8 oz. Oh, well, whatever...
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Yes it would.

Imagine a 100" x 100" x 100" block of steel.

If you reduce *only* the height from 100" to 1", you can see it would be 1/100th of the original amount of material. If you reduce all three sides to a length of 1", it's not 1/100th of the amount of material, it's 1/1,000,000th of the original material.

If you similarly reduced an SD70 in all dimensions and details, using the same materials, to scale size*, it would NOT be 1/87th of the original mass, but far, far less than that. A "scale weight" of 450,000 lbs is a basic misunderstanding of math and geometry.

*(Of course the details and materials are NOT the same, but the multiplication by 1/(87x87x87) does get you something to compare to.)
 
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This all reminds of an episode of Mythbusters when Adam had a 1/6th sized action figure (12" tall) and he needed to determine how much it should weigh. So he divided his weight by 6 and got 25 pounds. Jamie said "So you're saying it needs to be made out of depleted uranium." Adam was figuring the weight of someone 12" tall, but the same width and depth of a normal human.

As others have pointed out, you need to divide by the scale cubed. Adam's little action figure should have weighed about 0.7 pounds.

Steve S
 
O.K., let's look at Z scale then, what should the coupler cut bar on a GP38-2 weigh in 1/220th scale?
 
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