Math and Mandrels
Why ring mandrels are not the final answer in ring sizing.





When I began my career in Jewelry making back in 2009, money was tight and I had a limited budget for tools and equipment so, like many of us I made do with second hand tools and value line products from the major Jewelry supply warehouses such as Rio Grande, Otto Frei and Contentti. My ring mandrel in particular was both second hand, and a value line model made overseas. Sure it had dents and dings in the tool steel but the ring size markers were clearly defined and easy to read, and that's all you need in a ring mandrel anyway right? So tools in hand, I started making and selling rings for the market.

My ring making process at the time was the same as how many are taught: wrap the material around the mandrel at the size you want, mark where the ends cross over, saw, file, and solder. Then forge round again over the mandrel and double check the size on the line, so the middle of the ring rests on the line of the mandrel. Standard method right? And for a while everything was good and fine..until the rings started coming back to me for re-sizing...again...and again...and again...

There was clearly a problem.

So I went back to my books. Studied the charts. Scoured the Internet. What did I learn? There is a lot of inconsistency and precious little standardization in the Jewelry industry.

First, there was clearly room for improvement in my method. Wrapping stock around the mandrel creates more waste than necessary. It also introduces variables that make the cut length a bit more random than it should be. How tight do you wrap the material? How close are you to the size line on the mandrel? How accurate are your cut markers? How wide of a kerf does your saw blade take in respect to your cut markers? And so on. So first step: remove the random elements, as much as possible.

Cut length can be calculated accurately and easily with simple math and basic geometry.
A brief review of a circle:

• A circle's circumference is the distance measured around the edge of the circle from point to point.
• The diameter of the circle is the length across the center of the circle from edge to edge.
• The radius of the circle is half the diameter.
• Pi is the mathematical constant that defines the ratio of a circle's circumference to it's diameter. This number is typically expressed as 3.14 rounded to the nearest thousandth.

To determine the length of material needed for a ring of a particular size and material, the formula is:
Length = (Inside Diameter of the ring + thickness of the material) * 3.14
Or if you have circumference:
Length = Circumference of the ring size + (Thickness of material * 3.14)
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Material thickness can be found with a pair of accurate calipers, measured at the thickest part of the material stock. Circumference and diameter of a specific ring size should be a constant defined by the Jewelry industry, for which we turn to readily available charts. The problem though, is that not all of these charts are necessarily accurate either...

So a size 7 should have a 17.2mm diameter and circumference of 54.4mm...wait, a 17.3mm diameter. No, a 17.35mm diameter. Errr, 17.32mm...no, 55mm circumference...no 54.41mm circumference. No, a 55.6mm circumference...?

Huh? What's going on here?

Some of these charts are rounding up. Some round down. Some are calculating based on PI of 3.14. others are using more precision at 3.14159265359...or more...or less. And a couple of them, are just plain wrong. Whichever chart you decide to use for your Circumference and Diameter constants, be sure to cross reference it against other charts. If it varies more than a couple thousandths of a mm...don't use it. A variance of 0.5mm can result in a different ring size entirely. I also suggest doing some random sampling across the chart you use and doing the math to make sure the diameter and circumference values it gives you for a specific size agree with each other. Circumference = diameter * pi. Diameter = Circumference / pi. It's worth the peace of mind to do some verification. Some of these charts don't even agree with themselves.

Now I have everything necessary to find the length of material I need to cut for a specific ring size and eliminate the randomness. I cut material for a ring, size 7 out of 18 gauge stock, 3mm wide, 1mm thick and use my chart's inside diameter of 17.32mm to calculate length: (17.32+1) * 3.14 =57.52mm cut length. I take out my precision digital calipers, make sure they're zeroed out, mark my metal, saw through the line and make the ring. I forge it out on my ring mandrel and lo' and behold, it measures a size 6 ¾. Umm, what? So I get out my calipers and check that inside diameter: yup, 17.33 darn near perfect. It should be a 7...it is a 7...the math proves it...but the mandrel says 6 ¾. Guess what?

My second hand, value line ring mandrel does not size accurately. I grab my set of ring finger sizers and dig around for the size 7 and put that on the mandrel. The sizer on the mandrel shows a size 7 ¼. Now I'm cursing.

I drive down to the hobby craft store and buy one of those black plastic ring size mandrels, racing through the checkout and tearing open the packing as soon as I'm in the car. I put my size 7-by-the-math-ring on it. It's a size 8 ¼. I'm pretty sure I did not step through a portal to the Twilight Zone on my way to the hobby shop.

Over the next few months I try 4 other “professional” stainless steel ring mandrels. I get 4 different results on my size 7-by-the-math-ring. Some are close. Some are wildly off.

Ring mandrels vary wildly by maker and materials.

After a lot of searching, I found a maker advertising precision calibrated ring mandrels. I bought 4. My 7-by-the-math-ring slides on, and it measures a 7 at the bottom edge of the ring, both sides of the ring...on 3 of the mandrels. The 4th mandrel...was a lemon and machined out of round. I kept the 3, returned the 4th. You can never have enough mandrels in the workshop anyway.

At last, ring size Nirvana!

In the years after changing my process to calculate size by math and geometry and finding calibrated ring mandrels that actually agree with the math, ring re-sizing requests have become a rarity at my shop. When it does come up, it is usually due to one of these issues:

1. The ring band is a very wide band or is being stacked together with other rings and the buyer did not account for the added compression on the finger by ordering half a size up to accommodate.
   
   
2. They ordered based on a ring size taken from an inaccurate ring size mandrel, an inaccurate ring sizer, or the maker of their other ring that they are comparing to for size used an inaccurate ring size mandrel in it's making and the ring is actually larger or smaller than the size it was sold to them as.
3. Misreading a ring size on a ring mandrel, measuring size from the top edge instead of the bottom edge aka leading edge.

Minor Quibbles – Measuring rings on a ring mandrel

There is a great deal of debate among Jewelers on the subject of measuring a ring on a ring mandrel by the bottom edge of where the ring comes to a rest on the mandrel, or taking that measurement in the middle of the ring band. My thoughts on this, besides the fact that the math and bottom edge of the ring size agree according to my calibrated equipment - is that when making traditional, flat-stock ring bands with straight sides, only the bottom edge of the ring actually touches the mandrel and so this is the correct place to take the size reading. If I was taking a size on a ring that had a rounded inner ring band, such as a comfort fit band, then taking the reading based on the middle of the band makes sense since that is where the ring touches the mandrel and this is how I size all of my comfort-fit rings. If I was forging flat ring bands on a mandrel and taking the size reading at the middle of the ring band, the bottom edge of the ring would be stretched wider than the middle of the band and top edge. The resulting ring would be cone shaped. If you were then to flip the ring around and forge the ring again so that the size is again in the middle of the flat band, you would have a convex shaped ring with both edges flaring outwards from the middle. I cannot agree with this. A flat ring band should be sized based on the resting place of the bottom edge of the ring, checking both sides of the ring to make sure they are in agreement. Comfort fit rings with a rounded inner band should be measured in the middle of the ring. Very wide band rings should be ordered a half size up to account for the extra compression on the finger. In my mind, this is logical.  

Crappy Illustration: Only the bottom edge of the ring contacts the ring mandrel. This is where sizing should take place IMO, not the middle space that does not contact the mandrel, and NEVER measured at the top edge.   

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Thompson Seedless and Flame grape vines growing along the wall in my southern utah garden.

Pomegranates grow well in our southern utah climate: Dixie sweet, Pom Wonderful and Angel Red

Blossom from a Japanese long onion going to seed. I save seed stock from year to year on my favorite garden edibles.

It's been a struggle for raspberry bushes here in Saint George but I think I'll finally see a crop this year.

I favor plants that are resistant to local pests. Greens such as swiss chard, mustard greens and Asian bok choy, pak choy, chrysanthemum greens and picture below - Japanese shiso, an herb in the basil family. I use the large leaves as wraps in Korean BBQ.

Garlic chives in their second year. The pretty purple flowers are also delicious!

Our favorite spring vegetable, sugar peas. Can't get enough of them!

Red Orach going to seed in the garden. This plant along with shiso is a random "weed" now in the garden. Both plants readily reseed themselves.

Fragrant English Lavender in full bloom. One of my favorite plants.

My pumpkin patch! ;)

It's going to be a bountiful apricot harvest this year. This is a Mormon/Chinese apricot tree with edible sweet kernels.

Purple and gold pansies.

Lemon snapdragons in bloom.

​Thanks for visiting!

#dlcgems #southernutah #garden #saintgeorge #utah #selfsufficency

I ended up with 8 total pieces, 6 slabs, two end cuts, only one end cut suitable for a pendant sized cab. Hairline fractures ran throughout the stone, so the cabbing process would require an extra delicate touch to ensure successful cabochons. I cut the first two cabochons into the natural free-form shape of the stone and sent pictures to the customer for evaluation.

The customer came back wanting to know if we could preserve the natural edge of the slabs. Yes, it's possible I told him however we would have to change the way the stones would be mounted into jewelry as traditional bezel setting would no longer be an option. Heavy prong settings would be required instead with much more labor involved. The customer agreed and I proceeded to cab the remaining 5 pieces, retaining the natural edge. I also completed fabricating the bezel settings for the first two cabochons.

The remaining stones with natural edges required prong settings, and since each stone was unique in size and shape, the prong placements for each stone had to be carefully mapped out to ensure that the stone would be held securely. I wanted to accentuate the natural edge of each stone as well by framing it in silver and mirroring the contours of the rough edge in the silver setting. The final result is that each piece and setting is unique. Seven stars for seven daughters in seven unique settings...sounds like something out of a fairy tale.

I will miss looking at these beautiful stones, I doubt I'll ever encounter another piece of petrified wood like it. 

I mentioned earlier that there 8 pieces of wood, one end cut that was too small for a pendant. So what happened to it? The customer decided he wanted a pair of cufflinks for himself, and this end cut was perfect for the job. Here they are, set in sterling silver:

Fine silver is used entirely for the fabrication of the bezel cup to hold the stone for both the bezel and back plate.  Hard, medium and soft silver solders are used for the fabrication of the setting, and since they contain no copper, they do not cause a reaction with our client.

Finally the stone is set into the completed setting and then polished. The fine silver is quite soft at this stage and must be work hardened after polishing in order to give it some strength. A tumble in stainless steel shot for a few hours does the necessary job. I found that attempting to work harden the setting manually with a rawhide mallet marred the metal, so the tumbler is the best tool for the job in this case.

Our hypo-allergenic fine silver ring is ready to deliver to our client.

Using your flex shaft and coarse diamond bits, grind away the remaining chalcedony to expose the fire layers. Be sure to keep the stone and the diamond bits wet, and keep the pressure light…you’ll just wear out your equipment faster if you try to speed up the cutting by pressing too hard.

If possible leave a thin layer of chalcedony just above the fire layers and then switch to your fine grit diamond bits to remove the rest of the chalcedony, being very careful not to grind into the fire.

In the picture you can see that I’m following the contour of the fire agate layers; carefully exposing the fire but without grinding into the fire itself. The fire layers are extremely thin, so if you hit them you’re likely to grind the color to dust.

Here's the carving after polishing with 1200 grit diamond paste.  Sometimes  ensuring that you've covered the entire stone after each grit can be difficult, so I use a cover coat as a guide on hard stones with fire agate with no fractures.  Black sharpie marker in this case is a great cover coat. When the black cover coat is gone, I know that I've covered the entire stone and can move on.

The fire agate is now polished to 3000 grit diamond. At 3000 the colors start to really show off and shine but don't stop here; your fire agate carving deserves the best polish possible.

I hope you have enjoyed my fire agate carving tutorial, please leave a comment here or on Facebook and let me know your thoughts.  Every fire agate carver seems to have their own techniques and equipment preferences, and I would be curious to hear about yours.

The information and pictures presented here are the intellectual property of Don Christensen and DLC GEMS LLC.  Do not  publish elsewhere without express written consent.

@2014

We will be selling in Ivins, UT through the summer every Saturday as part of the Saturday Market at Tuacahn. Be sure to come out and pay us a visit! Don will be performing fold forming jewelry fabrication demonstrations throughout the day creating cuffs, earrings and pendants using this unusual metal sculpting technique.

Every Saturday @ 9 am to 1 pm through August.

See you there!