How do you precisely calculate a coin's off-center distance

1Bustcollector · June 5, 2011 8:41AM

It has been awhile, can anyone assist?

ambro51 · June 5, 2011 8:47AM

I would say a simple measurement would suffice. Say, a Lincoln cent is 19 mm in diameter, if the off center border is lets say 3.8 mm in from the edge, it would be 20% off center. That would be correct, wouldnt it?

1Bustcollector · June 5, 2011 9:03AM

Perfect. Thanks ambro51! That was too simple..........

Sonorandesertrat · June 5, 2011 9:35AM

Depends on if you're the buyer or seller.

goodmoney4badmoney · June 5, 2011 9:43AM

in my experience it's far easier to just look at it and rough estimate, rather than try and measure somehow.

Aegis3 · June 5, 2011 11:38AM

I was able to devise a method by measuring the distance between the two "points" on the rim of the coin between the struck and unstruck portions of the coin. Of course, it got kind of complex and used an inverse trigonometric function. It's just as well to guess it by visualization.

I suppose you could also do some Photoshop/GIMP work and measure some areas in pixels also.

coinman23885 · June 5, 2011 12:07PM

I find your mathematics approach fascinating; would you care to share?

Aegis3 · June 5, 2011 12:16PM

I don't know where I wrote it down, so I'd have to re-devise it. I'll post it tomorrow if I can figure it out again. If not consider it as homework for the forum.

1Bustcollector · June 5, 2011 1:27PM

I printed the obverse on a white gloss sheet of paper, then printed the reverse on a transparency sheet (Each side was blown up to 7 inches in diameter). Then I overlaid one on top of another to match the offcenter placement as best as possible.

I found the image was off center about .900" of an inch. So I divided .900/7.00 which got me just under 13%. This sound correct?

coinman23885 · June 5, 2011 1:42PM

<< <i>I don't know where I wrote it down, so I'd have to re-devise it. I'll post it tomorrow if I can figure it out again. If not consider it as homework for the forum. >>

It sounds like a lot of fun. I'll try to devise it myself as well. I always enjoyed mathematics in high school and the courses that I took in college.

coinman23885 · June 5, 2011 1:42PM

It sounds right, but I would round the number!

astrorat · June 5, 2011 2:25PM

Cut or file away the unstruck portion and then weigh it. Since the standard coin weights are known, it's just a simple ratio of the amount remaining to the known weight. Bingo! There's your answer!

yosclimber · June 5, 2011 3:59PM

If you want to have fun with the math, the struck area of an off-center coin would be about
equal to two circular "segments", and you can construct the ratio of the blank (non-struck area) to total area of the circle/coin.
http://mathworld.wolfram.com/CircularSegment.html

Although first you might want to ask the question of whether "% off center" is measured in terms of non-struck/total area of
the coin, or just a linear ratio measure of how far the center of the die was from the center of the planchet,
say relative to the diameter of the planchet.

Aegis3 · June 6, 2011 11:21AM

See bold edits first

<< <i>If you want to have fun with the math, the struck area of an off-center coin would be about
equal to two circular "segments", and you can construct the ratio of the blank (non-struck area) to total area of the circle/coin.
http://mathworld.wolfram.com/CircularSegment.html

Although first you might want to ask the question of whether "% off center" is measured in terms of non-struck/total area of
the coin, or just a linear ratio measure of how far the center of the die was from the center of the planchet,
say relative to the diameter of the planchet. >>

The Mathworld link seems to work at the problem the same way I do. The goal is to have the area of the "pie slice" and of the triangle connecting the center, and the two other corners of the slice. My method approximates the off-center area to be defined as the sum of two circular segments. The only variables are the distance between the two edges of the off-center area (alpha or (a) in Mathworld) and the diameter of the coin (d). Since we want a percentage I defined the ratio A/C to be the area of the off-center portion vs. that of a normal coin.

So I got the following:

A/C = {(2/pi) sin(-1)[a/d]} - {[2a sqrt(d^2 - a^2)]/[pi d^2]}

I realize that may be difficult to understand as text.

EDIT: Rechecking this, it looks like I made an error somewhere, as I worked out the cases for a normal struck coin (a=d) and a blank (a=0) and they don't work out correctly. I'll have to try again.)

EDIT #2: I found the "error." A/C measures the fraction on-center. You want 1-(A/C) to get the fraction off-center.

ambro51 · June 6, 2011 12:11PM

difficult to understand?

thats an understatement!

I like my method in post number 2. Us D students in Math can understand that!

chaze215 · June 6, 2011 12:51PM

<< <i>difficult to understand?

thats an understatement!

I like my method in post number 2. Us D students in Math can understand that! >>

I was always decent in Math, however......

Aegis3 · June 9, 2011 7:07AM

This will be more understandable. "d" is the diameter of the coin/blank, and "x" is the distance between the two ends between the off-center/normal areas.

A/C is the fraction on center. Thus, the percent on center is just that multiplied by 100. Use that for items like brockages, indents, and the like.

The fraction off-center would thus be 1-(A/C). And the percent off center would be that times 100. Use that for items like off-centers, double strikes, and the like.

FredWeinberg · June 9, 2011 7:18AM

I just take a ruler, measure the
normal coin's diameter with it,
in either MM's or fractions of an
inch, an then put the ruler on
top of the coin, and see what
percentage of the BLANK area is
showing, compared to the normal
coin's diameter.

You can't measure an Off Center
coin from the struck portion; only
from what is showing of the blank
area. Metal flow, uniface strikes, etc.
are factors that might make the coin
look more off center than it is.

Don't forget, it's an Off Center Strike,
not a 'what's showing strike'.

renomedphys · June 9, 2011 8:18AM

This is a funny discussion. I guess what it boils down to is: is it the total unstruck area, or the total unstruck diameter? A coin with 50% unstruck diameter would have far more than 50% unstruck area. The struck area would be the overlapping area of two circles. This is a difficult math problem for those uninitiated to the subtelties of trigonometry.

Thus, one must conclude that the standard used in the coin industry would involve the simplest calculation, ie. the ratio of the unstruck diameter to the total diameter of the coin. For this, you only need a ruler and your phone's calculator.

One thing I've learned about how these things work: folks always go for the simple way.

How do you precisely calculate a coin's off-center distance

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