The ratio on your spinning wheel gives you insight into how quickly (or slowly) you are putting twist into your yarn -- a lower ratio puts twist in more slowly, a higher ratio puts twist in more quickly. The ratio is the number of rotations of the flyer for one complete rotation of the wheel (typically that also means one complete push of the treadles).
Ratios are basically about how many times your flyer rotates completely around for one complete rotation of your wheel. Typically you have several grooves on the flyer for different ratios (although simple wheels may have only one ratio) and one on the wheel; though some wheels have several grooves on them too -- some of the Majacrafts, for example, and Journey Wheels.
To determine the ratio you can either measure diameters -- the diameter of the groove you are using over the wheel's diameter should be the ratio -- but I don't do that. Instead, I note one leg of my wheel (sometimes with a bright piece of yarn) and start peddling s-l-o-w-l-y while counting how many times my flyer goes completely around. Nothing's on the bobbin or in my hands while I do this. Then I know that the ratio of that particular combination of flyer groove and wheel groove is the-number-of-flyer-revolutions-to-1.
"Typical" ratios are 4:1, 9:1, 12:1 ... "production" ratios are usually 20:1 to 30:1. Charkas go upwards of 100:1.
The higher the ratio, the more twist goes into the yarn for a given pump of the treadles. So, for low-twist, soft yarns set your wheel on a lower ratio and for high-twist yarns, set it at a higher ratio. Or, if you can draft like a demon, set it at a high ratio and go for it!
Some folks settle on a single ratio and that's all they ever use. I tend to pick ratios for the job at hand. If you alter the ratio, you need to watch your treadle -- the same treadle speed will give a different amount of twist. So, at a higher ratio, treadle more slowly at first; at a lower ratio, treadle a little faster at first.
Mabel Ross's book "The Essentials of Yarn Design for Handspinners" discusses treadles and ratios _alot_.
There was a great blog posting on the topic by Abby Franquemont.
There are other caveats -- the Journey Wheel, for example, has an accelerator that also affects the ratio. If you simply note which grooves you use/settings of the wheel you have, and count the treadled wheel for one full revolution against the actual flyer's revolutions, that is the ratio.
(based on a post by me on Spin-List, 15apr07)
(the picture is from May, 2001 -- when I was first learning to spin -- at the Shepherd's Festival in Sequim, held each Memorial Day at Carrie Blake Park. The wheel is a Louet S-10.)
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