Aspect Ratio in Design
The two rings on the left have the same inner diameter but wildly different aspect ratios. The top ring, which is thin and spindly like a hula hoop, has a high aspect ratio. The bottom ring, which is fat like a donut, has a low aspect ratio. The two rings on the right are the same aspect ratio. Any weave that works with one will work equally well with the other.
An aspect ratio of 3 or less indicates a fat ring with a small inner diameter (ID), like a donut. The smaller the ID, the stronger the ring; the fatter the wire, the stronger the ring... so a small aspect ratio means a very strong ring. A large aspect ratio of 5 or more indicates a big, skinny ring that isn't going to be all that strong. Such rings should only be used when the weight of the piece will be distributed over many rings. Never leave a ring with a large aspect ratio to take stress on its own.
Any time your design requires just one ring to take the stress alone, you must either use a ring with a small aspect ratio, or solder the ring closed in order to maintain the necessary strength. If a larger aspect ratio is required and you don't want to solder, then you must alter the design to allow the use of multiple rings in that spot to share the stress. Using 2, 3 or even 5 rings, side by side, instead of just one ring alone can be a really beautiful design element and often looks much better than one ring would anyway, so it's no great hardship to make these adjustments and design for strength rather than resorting to solder.
Butted maille -- meaning chain that's made with butted rings rather than rings that are fused, soldered or riveted closed -- requires more skill of the designer than closed ring chains do. Even an unbalanced and poorly designed chain will stay together if every ring is soldered closed, so when speaking of closed ring chains, strength and design skill bear little relationship to one another.
With butted maille, however, strength is all about materials and design. If you're using stainless steel rings, you don't have to be a very skilled designer to make strong maille. Stainless steel is very hard and strong which makes it unforgiving to your hands, but very forgiving of design errors. *s*
Though our ring making process hardens the metal considerably, sterling and most other precious metals will never be hard enough to cover for poor design. To make really strong butted maille from precious metals, it's necessary to understand aspect ratio and how to use it to your advantage. The rewards of this knowledge are great and well worth the time spent acquiring it. Not only does it enable you to make strong and beautiful jewelry from pure, smooth precious metals and nothing else, but it teaches you how to *design* as opposed to just making stuff... and you can't put a price on the value that brings to your work. *s*