Surprising amount of missing volume compared to theoretical coin

I think we just have to accept that there's actually 21% less volume in a US quarter than the raw rim and diameter calculation gives us, due to the fact that a significant percentage of the coin is narrower than the rim dimension used for the thickness. I think the mint's contention that a blank is wider, but the same thickness, as a finished coin is just wrong. Watch the animation in this video starting at about :18.



The upset mill squeezes a coin blank into a narrowing space while raising a rim edge. It clearly shows the blank getting thicker, and while it's only an animation, I think that it's an accurate depiction, because that squeezing force applied to the metal isn't just transferring metal to the raised rim lip, it's also making the blank thicker.

Empirically, we know that the quarter weighs what they say it weighs, and it's pretty easy to measure the diameter accurately to confirm that too, so to me we accept that the average thickness is 21% less than the stated measurement.

 

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Yep. Mass is conserved, and while it is possible to change the density of some alloys with phase changes, that's not what's happening here.

A struck coin is a complex shape. The easiest way to get its volume is to weigh it, then divide by the metal's known density. Next easiest would be to dunk it in liquid and measure its displacement.

 

And that's super-important if you're in a diving or climbing airplane, or in space, or on the surface of some planet other than Earth. @Sunbird, you are on Earth's surface while you're weighing these coins, right?

If you have a coin whose gravitational mass differs from its inertial mass, you need to get it to the folks in Stockholm, stat.

 

Yeah, I forgot to reply to that bit. It has nothing to do with anything I'm talking about. I was saying how surprised I was that US coins like the quarter were "missing" 21% of their volume/mass compared to a full cylinder, since eyeballing them it seemed like the field wasn't deep enough relative to the rim to account for a 21% hit, especially given all the raised design features that would partly offset the volume loss from the recessed field. It was just an expression of surprise and maybe mystery. I'll need to do some submersion tests, and figure out how to measure the field-to-field thickness, maybe with those micrometers or calipers that have the mouthy/toothy shape instead of the flat beak style I have – the ones where you can go around the edge of an object and measure an inner depth.

I learned the difference between mass and weight as a kid. That distinction doesn't matter in this context, where Earth is assumed and mass and weight are equivalent. There aren't two different values here, a mass A and a weight B that don't match or something. The quarters weigh what they should – the ones I weighed recently are less than one percent off, with one 0.62% under and the other 0.53% over the official weight of 5.67 grams.

 

Here's a micrograph of a small area of a Lincoln cent showing the difference between rim depth and field depth. Maybe it helps to visualize where the "missing" volume is. Of course it would be nice to see one for a cross section of a whole coin.

 

Yeah, that thickness claim must be wrong. (Unless the strike knocks the rim down some from what it was coming out of the upsetting mill, while maybe also reducing the field-to-field thickness, forcing both of the "found" volumes of metal into the die for the design features.)

The average thickness doesn't have to be 21% less than the rim thickness to account for the 21% missing volume. There's also the reeded edge. I did some quick math and came up with a 4% volume loss just from the reeded edge, assuming the rim is 1 mm wide (so it accounts for 2 mm of the quarter's 24.26 mm diameter), that the sunken parts of the rim are halfway deep, so 0.5 mm, and that the sunken and raised parts of the rim have equal area around the rim (they're equally wide looking at rim edge-on, and distributed evenly, 50/50). These are all just ballpark guesses, but they might be in the neighborhood of the actual values.

I didn't see a thickening in that animated video. The perspective kept changing – they never gave a fixed lateral view of the blank, so I didn't really know what I was seeing, and of course it's just an animation someone created. It would be cool to see a slow-mo video with a fixed angle. Also, the 3D model files of the coins would be super. They must have them, and there are standard file formats like DWG that people can easily open using free viewers, some of which are online.

 

The problem with your reeded edge theory is that the material isn't chopped out of the coin.

 

That's fascinating, thanks. It's interesting that the design features, like the text (letter E in this case), are almost as high as the rim. This makes it more surprising and unintuitive for me, since it means that the fields must each be more than 10.5% deep (out of max thickness). A 21% volume hit means 10.5% per side. But with the design features rising up to near-rim thickness, then the baseline must be lower. To get an average reduction of 10.5% per side might mean an 18% field depth or something, which I just don't see with my Mark 1 Eyeball. It's quite surprising. (Pennies don't have reeded edges, so all volume loss has to be in the fields.)

 

No chopping necessary. It's based on the assumption that the official diameter of the coin is the max diameter, since a reeded edge gives a variable diameter.