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Calculating bezel length for oval cabs


#1

Greetings,

Just wondering if there was a way to calculate the bezel length for
an oval cab instead of cutting the bezel long and then cutting it
down until it fits perfect. I’ve found some formulas and even an
online calculator but they haven’t been accurate or I just can’t do
math. A combination of both perhaps. Not sure how to adjust final
bezel length given wire gauge.

Say my cab’s dimensions are 30mm x 22 mm and my bezel wire is 20
gauge (20 gauge for design purposes) what would be my length?

Thanks for your help.
Chris


#2

Chris- After 43 years in the trade I have found the perfect formula
for determining the length of bezel wire needed for a cab.

I take a piece of soft binding or copper wire and wrap it around the
stone. Mark or bend it where it meets. Straighten it out. That’s how
long you make your bezel.

Have fun and make lots of jewelry.
Jo Haemer
timothywgreen.com


#3
Say my cab's dimensions are 30mm x 22 mm and my bezel wire is 20
gauge (20 gauge for design purposes) what would be my length? 

According to Google, 20gauge is 0.9144mm, which seems rather thick
for a bezel (maybe I’m using the wrong gauge; I do wish people would
use universal units - mm or inches - instead of arbitrary gauges).
Anyway, assume that neutral axis is halfway through the thickness of
the bezel, so the effective dimensions of the cab are 30.91mm x
22.91mm.

An oval cab is pretty close to being an ellipse, so a reasonable
approximation for the bezel length is:

PI * SquareRoot of 2 * ((1/2 long axis)squared + (1/2 short
axis)squared). So the length of your bezel is 85.47mm

I cheated and used the calculator at
http://www.ganoksin.com/gnkurl/1mo

Regards, Gary Wooding


#4

Bezel length for oval stones is quite an interesting problem. There
are two approaches, - one is working approximation with very little
mathematics, but steps are not easy to describe. Visual instruction
is required. So I am going to recommend my DVD “Coronet Cluster” for
this.

http://www.ganoksin.com/gnkurl/fp

Another approach is mathematical, but there are number of
complications. First, oval and ellipse are not the same thing.
Mathematically we can only deal with ellipses. So if stone is not
true ellipse, one has to determine the difference and adjust
calculations later on.

From this point on, the discussion only refers to ellipses. Let’s
take a to mean half of major axis, and b - half of minor axis. Also
assume that values were adjusted for metal thickness. If a is less
the 3b the formula is 2(Pi)*sqrt (( a^2 + b^2)/2) (Pi is 3.14). The
result is within 5% of true value.

If a is greater than 3b, more complex formula is required. Pi[ 3(a +
b) - sqrt ((3a + b) (a + 3b)) ]

There are other methods yielding exact values, but methods are quite
complex and involve infinite series. There are no reasons to get into
them here.

As anyone can see, a simple oval contains a lot of mysteries, so in
actual practice it is better to use working approximation than exact
calculations.

Practical: given ellipse of 30 X 22 - a is 15 and b is 11. Since a
is less than 3b, first formula is used

2(3.14) * sqrt (( 15^2 + 11^2) / 2 ) = 6.28 * sqrt ( 225 + 121 ) /
2) = = 6.28 * sqrt (173) = 6.28 * 13.15 = 82.6mm

There are no accounting for thickness of metal in the above example.
Also, the true value is from (82.6 - 0.413) to (82.6+0.413). Whether
one chooses higher or lower value would depend a lot on technique.
As a parting word, let me add that requirement for precision is
increasing as thickness of metal is decreasing. For thicknesses of
0.5mm and bellow, only second formula is recommended, and I have
been called to make bezels in 22k out of 0.25mm. Such bezels are used
to set important emeralds and other fragile stones. For these, exact
methods must be used. I did not describe them due to their
complexity, but on can find them in mathematical literature. Another
option is to use specialized software like Wolfram Mathematica.

Leonid Surpin
www.studioarete.com


#5

There’s enough variation in calibrated cabs so that I stopped trying
the arithmetic approach long ago. Instead, I use thin quilter’s tape
and wrap it around the stone. Make your marks, add a little for the
thickness of the bezel and fit for the stone; I just lay the metal
against the tape and transfer the marks. (Add enough to account for
the loss of material as you true the ends.)

Other thin tapes work too - one friend uses striping tape from auto
parts supply stores.

Don’t throw the tape away until the piece is finished…

best regards,
Kelley


#6

Try 30 + 22 divided by 2 plus .8 mm times 3.1416. I would add a bit
just in case.

Vince LaRochelle.


#7

Chris, To measure bezel material to fit a stone, take the radius of
the stone, plus thickness of the bezel and multiply times pi
(3.1416). In the example you asked about for an oval cab, add the
cab’s width and length and divide by 2 for the radius. So for the
numbers you gave: 30 + 22 = 52. Divide by 2 = 26. add .81 (20 ga. in
mm) and you get 26.81. Multiply by 3.14 and the result is 84.18.
Round it up a little bit, clip and solder. I usually end up a little
tight so I may have to stretch it a little.

Jerry in Kodiak


#8
I do wish people would use universal units - mm or inches - instead
of arbitrary gauges. 

I’m with you. For as long as I’ve been jewelrying (33+ years) we’ve
used millimeters. Some suppliers who will remain nameless, use G&S
gauges as if we’re a bunch o’ machinists. It’s sure confusing and I
too wish they would just stop.


#9
I take a piece of soft binding or copper wire and wrap it around
the stone. Mark or bend it where it meets. Straighten it out.
That's how long you make your bezel. 

I don’t even do that, I just wrap the bezel around the stone. Only
time I measure is squares and triangles. No square roots here…


#10

Hi, Chris

Instead of cutting to some calculated length, I just fit the bezel
wire around the cab, then solder. This way you can make a bezel for
any cab, regardless of the size, shape, etc.

Margaret


#11
I take a piece of soft binding or copper wire and wrap it around
the stone. Mark or bend it where it meets. Straighten it out.
That's how long you make your bezel. 

Most definitely.

For some formulas are the only way to go. But they have never worked
with the way that my brain is wired. I always create an analog
whenever possible, like binding wire, wax or even tinfoil…

Andy


#12
Try 30 + 22 divided by 2 plus.8 mm times 3.1416. I would add a bit
just in case. 

I do not comprehend why anyone would do anything but wrap the bezel
around the stone, mark it and cut it. I am not good at math, I am
good at fabrication.

Richard Hart G.G.
Denver, Co.


#13

My method for figuring out the length of bezel to cab is to simply
wrap bezel strip around stone, mark where the ends meet and cut. It’s
too much trouble to measure bezels any other way for me. I can
really get a lot of bezels cut, sized and made in no time. Another
tip - if you are dealing with pointy cabs, I use a plier of chain
nose or flat nose pliers to make a sharp bend in bezel and then fit
the bezel over the stone. That way I can have a precise fit on the
points. When I solder my bezels, I almost always stick solder my
bezels on the outside, so I can avoid any solder bumps inside of
bezels. Don’t forget you can roller-texture your sheet metal and use
it as a backplate for the bezel, adding another dimension to the
design. I do so many bezels that occasionally lose my touch,
generally Christmas time, and a few weeks away from the bench helps
a lot.

Joy


#14
I do not comprehend why anyone would do anything but wrap the
bezel around the stone, mark it and cut it. 

I can answer that one. One of the first jobs that came up when i
started as Jim Binnion’s assistant was a pair of earrings that were
to contain oval bezels. Jim said he’d calculate the length for me,
and I blithely said, “Oh, I can make those, I don’t need a
calculation”, planning to do as usual-- wrap and cut. Imagine my
chagrin when he handed me a 1mm-thick piece of palladium! Try to wrap
that around a 4.5mm faceted sapphire!

So that’s why.

By the way, I wrapped and cut a piece of paper, added the thickness
of the bezel material, cut a piece of copper to make sure I had it
right, and made the bezels.

Noel


#15

Try doing it as a circle. An oval becomes a circle when the major
axis + the minor axis / 2 = a circle. Make your circle and then
deform it into an oval. It will be close to the mark and if you
allowed a bit of under steer you can hammer it up on a stake and
tweak it with pliers to get an almost perfect fit. Final fitting is
done with a graver.

Al


#16
I do not comprehend why anyone would do anything but wrap the
bezel around the stone, mark it and cut it. I am not good at math,
I am good at fabrication. 

There are several reasons why method of wrapping and cutting, or
wrapping a proxy material is not advisable. It may work in some
instances, but invariably the resulting setting is larger than it
should be, which makes setting of a stone difficult and
aesthetically results are wanting. Besides, the stone is put in
danger. It may be ok for inexpensive material, but emeralds,
tanzanite, amber, and etc., I would not advise it.

A stone in well made bezel, should appear larger. At the very least,
it should not appear smaller. This is only possible when perimeter of
the stone and inside length of the bezel match exactly. Exactly means
just that. There are no tolerances in this type of work. Process of
wrapping leaves small spaces, which leaves setting to big, with all
the problems stemming from it.

There are also instances where knowledge of exact bezel length is
required to distribute stones around a cluster, or many other similar
instances. What about when domed back plate is required to match a
bezel. We need a pattern which would match after the doming. The
blank should be larger by exact amount to allow doming to take place.
The same goes for gallery and lower bezel calculations. In these
cases, there isn’t something to wrap around. There are many examples
where it is important to know the exact length of a bezel and how to
use it in practice.

Let me address very common complaint “I am not good in math”. One
does not have to be good in math to use formulas. One simply have to
take time to get familiar with a formula. Write out variables used;
understand how they function; practice substituting actual numbers.
Very quickly a formula would become like a pair of old jeans, soft
and comfortable. Give it a try.

Leonid Surpin
www.studioarete.com


#17

If you acquire a copy of the " jewelers bench reference " it will
list the mathematical formula for calculating the distance of a
circumference, or you could go to wikipedia and search " ellipse
calculator " for on this - but in the end there will
still be the issue of making the bezel fit as nicely as you would
like and in frustration you will wrap the bezel material around the
stone and cut it solder and fit without the comfort of mathematical
science to support your efforts (just one more reason math should be
a requirement for jewelry students )

goo


#18
I don't even do that, I just wrap the bezel around the stone. Only
time I measure is squares and triangles. 

I have had a lot of squares and triangles that had sides of
extremely slight unequal lengths. I start in the center of one side,
mark where the end should be, saw a light line, use parallel pliers
to bend to the correct angle, mark where the next bend needs to be
made, continue around.

Richard Hart G.G.
Denver, Co.


#19
My method for figuring out the length of bezel to cab is to simply
wrap bezel strip around stone, mark where the ends meet and cut. 

When I was in the turquoise business, I would occasionally set
branch coral. Uncut but polished branches of red coral that looked
like tree limbs.

You start at one end and bend until you get back where you started.
I get opals from a certain maker that are never regular or
symmetrical. I could go on… Somebody said, today, “You can’t
get it perfect by bending…” Well, YOU can’t, I guess. I’ve
been doing it for decades. This topic came up a couple of months ago
and I had a bezel to make, so I thought I’d try the mathematical
way. I found a formula that was posted prominently, did just what it
said, and it came out so very, very wrong. You like the math, fine.
Is it “necessary”? Nope.

Now, rectilinear shapes - squares, rectangles, triangles - need to
be measured partly so they are square and the sides are the same
length. Really small bezels ( like 2mm) are better drilled and
reamed no matter what your measuring method would be otherwise,
unless the metal is really thin.

Somebody mentioned making an oval bezel round first - that’s really
great advice, again, no matter how you measure. Measure, cut, solder
and then it’s far, far easier to put in on a bezel madrel and shape
it from there than to try to wing it and get a perfect oval by eye.

Calculating is fine as long as your stones are calibrated. Well, I
guess… If we lived in a perfect world we’d all be in Tahiti for
the winter… Fitting ANY bezel to ANY stone is another of those
fundamental skills…


#20

One thing to remember about cabs. Most of them do not meet
industrial standards.

They may be 20 mm by 32 mm at the widest & longest, but their shapes
are not necessarily exactly the same. This difference in shape makes
the perimeter dimensions of them different. Thus if you use a
mathematical formula to determine the perimeter, the bezel may fit
on some but not on others.

Folding a strip of bezel wire around the cab & marking it is the
easiest way to get the strip to the correct length.

Dave