Surprising amount of missing volume compared to theoretical coin

Hi all – I'm surprised by the amount of "missing" volume / weight in circulation coins compared to a smooth cylinder/coin made of the same density alloy. For example, take the modern US quarter:

1. Diameter: 24.26 mm
2. Thickness: 1.75 mm
3. Volume if it was a perfectly smooth cylinder (no upsetting, stamped design, etc.): 0.809 cm³
4. Mass of such a smooth cylinder made of 91.67% copper, 8.33% nickel: 7.22 grams (Copper and nickel have almost identical densities, so the proportions don't matter much – I used 8.92 g/cm³ as the combined density.)
   
5. Mass of actual quarter: 5.67 grams
6. Missingness: ≈21.4%

That is, the mass is 21.4% shy of a featureless coin blank of the quarter's dimensions, which means that the volume is 21.4% short as well. I knew that it would be short, but I'm having a hard time understanding how it can be that short. Looking at the coin, the field's recession from the rim doesn't look deep enough to account for such a drop in mass/volume. A 20% shave would require the field to be recessed a tenth of the coin's thickness/height on each side, and that the field was flat and smooth with no design on the coin.

But the quarter has a lot of design on both sides that rises up from the field, which means there's more volume and mass there than there would be if the coin was featureless. This in turn means that the field's recession or sunkenness from the rim must be even deeper to make up for the volume and mass of the elevated design features. I don't see it, and my calipers can't measure the thickness of the coin at its thinnest points, recessed field to recessed field. I can only measure the rim thickness, which is the max. Anyone know what the thickness of a quarter is at its thinnest?

The only other angle I can see is the reeded/milled edge. That would create some missing volume and mass compared to a smooth cylinder. If the highs and lows are equal in area around the rim, the average diameter of the coin would be reduced to the nominal diameter - (the depth of the lows/2). Maybe that ends up shaving half a millimeter from the diameter – no idea, but it's another aggregate hole in the coin cylinder.

Anyway, I'm surprised by how unintuitive this looks to me, as far as the amount of lost volume and mass, from just eyeing the coin. I'll note that the reality is similar with other circulation coins. Canadian steel coins have nominal densities of 5.62 - 6.36 g/cm³, even though mild steel is around 7.87 g/cm³ (not to mention the few percent of copper and nickel plating they have, with a density of 8.92 g/cm³). By "nominal density", I mean the computed density of a perfect coin cylinder of the dimensions of the relevant coin, given the weight of the coin (I have a spreadsheet with nominal volumes and densities for dozens of coins, along with the usual measurements). It's always less than the density of the coin metals because coins are always lower in volume than a cylinder of the same dimensions. For some reason Mexican coins have the highest nominal density relative to their material, even though stainless steel is a bit lighter than mild steel (their coins are made of 430 stainless) – they must have less sunkenness from the rim.

 

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Totally disagree with that. There is no added volume to a struck planchet that gives it its features. It should still be the same volume/weight at any instance.

 

The weight of the planchet should remain the same, but the volume will change due to the density change in the metal cause by it being struck into a coin.
#2 should be the thickness of a type 1 blank, not a coin which has a thicker edge.

 

When these coins are struck they are struck wit tonnage the metal flows into the recess's of the die. Well struck coins are just that Well Struck. Planchets have tollerances, They weigh within 100ths/g of each other.

 

Duh?

 

Meow

 

I'm referring to the design features being higher than the field, not claiming that striking adds volume, which is impossible for solid metal at normal temperatures. I'm talking about the state of the finished coin, and eyeballing the depth of the field relative to the rim. Since the field doesn't look deep enough to account for 10% of the coin's thickness, it's even stranger when considering that you still have to account for the volume rising up from the field – the design features. This means the field must be more than 10% deep (ignoring the effect of the reeded edge).

 

Right, agreed, never said there's a change in volume. Note however that the mint says the strip or planchettes arrive the same thickness as the final coins, which is confusing. They say only the diameter of the blanks is different – larger – and this gets reduced by the upsetting mills. The thickness of the coin must increase at the edge due to the upsetting, so I don't know what they mean. And the main body or field should get thinner when struck, since the design is flowing up from it into the die.

 

A boat floats on water despite being so heavy. A few coins will float on water as well because they are usually concave on one side or the other and other is convex. Coins are made so they will stack and to protect key elements from wear since coins wear from the outside in.

It should be noted that struck coins vary more in thickness than any other parameter. A roll of 1984-P quarters has enough room to add three or four more and only 38 1965 quarters fit fit in a roll. Thickness is a striking characteristic rather than being defined by the mint.

 

You can get more than 50 1965 quarters in a roll if you pull them from circulation today.

Banks have a mild heart attack if you take back rolled old coins because they can't believe those short rolls have even 40 coins in them. But even after they are heavily worn they still stack and as long as you have a mixture of coins they can be counted very quickly by stacking.

 

That'll be tricky because of all the different designs, but my fine Amazon-sourced caliper -- if you can't trust BEIGEFAMU, who can you trust? -- has a little thing that sticks out the end of the scale that's exactly for measuring depth.

On a fresh Maya Angelou quarter, I get a diameter of 24.15mm, a rim thickness of 1.74mm. The deepest relief I measured on the obverse or reverse was about 0.20mm. (I've never been trained, so my measuring technique may be really bad.)

Density in alloys does funny things; as you say, the densities of copper and nickel are similar, but I'm not sure the density of the cupronickel alloy is the same -- but some quick Googling indicates that it probably is.

One other factor: the "diameter" presumably counts across the ridges of the edge reeding. The grooves take away a measurable amount. But, yeah, the overall result is a little surprising.

But. But. Measure and weigh a stack of slick SLQs. Their thickness may have decreased by a full 20%, but their weight by a mere 7%. Those half-dollar tubes that are precisely cut to hold exactly 20 coins? I've got one with 26 Barbers in it, and the lid all the way on. It weighs a lot more than a roll of 20 1964 Kennedys.

It doesn't fully address your question, but it does shed some more light on volume vs. weight.

 

Hey @-jeffB using your calculation, what is the rim thickness and deepest relief of a Washington. Silver or clad. Well circulated and mint state?
I don't have the tools or I would do it.

 

If I get a chance, I'll check. Need to fish out a slick Washington, I don't have as many of those as the slick earlier stuff.

 

The problem I see is that we are missing exact information. How thick and wide are the original blanks, and where do they measure the thickness of a finished coin (presumably at the rim)? You speculate that the difference between the thickness and therefore volume in the thinnest areas of a coin versus the rim "doesn't look deep enough" to account for 21%, but that's only speculation. We need to know the thickness and diameter of an unmilled, unstruck blank, and I can't easily find that information. The mint does state that "they have a slightly different diameter, but the same thickness, as a finished coin" which gives us a clue that the discrepancy is due to the diameter of the blanks, but I'm not convinced that the thickness is exactly the same either. Metal has to flow into the raised areas, and that metal has to come from somewhere.

 

Size. Collar. Pressure. Stuff happens.

 

No, I was just noting that the coin has less volume than a perfect cylinder of its diameter and thickness/height. A coin isn't a perfect cylinder. It's got a lot of the volume scooped out by the recessed field and milled edge.

The blanks they use are larger in diameter than the final coins, before upsetting. And the nominal thickness of a coin is its max thickness, along the rim. It's thinner everywhere else.

 

Yeah, I was puzzled by the Mint's claim about the "same thickness" too. It would be nice to have a simple table of all dimensions at each step in the production process. All they mention is that the blanks are wider than finished coins. But the thickness can't be the same if they're starting with perfect, flat cylinders, since the official thickness they give for their coins is the max thickness, which is at the edge formed by the upsetting mills. That means the blanks must be thinner than the official coin thickness.

And then there's your point on the strike. The design rises up from the field, so that metal has to come from somewhere. I wonder if anyone has put together a video enactment of the coin strike in slow motion. Even just a graphic, cartoon video would work. Given a flat blank surface, except for the edge, it's not clear to me how you end up with a raised design. The die is a negative, like a mold. So how does it force solid metal up into itself? If it just forced its way into a flat metal surface, it seems like it would have to create a new, deeper field immediately surrounding the design features, while the rest of the blank would be elevated over that. That's not how most coins are, including US coins. Does it depress the surrounding field to force metal to flow onto the die? That would thin out that part of the blank. All of this has to happen in an instant, less than a second.

 

Absolutely. With every strike, a die forces metal out of the fields (low areas) and into the devices (high points). That metal movement produces wear on the die. And that's how we get flow lines, which produce luster!