Now that I've assembled my parts for building a charkha I've started assessing everything. I decided to start with determining what drive ratios I want to create, as this will dictate the main components. Drive ratios on traditional spinning wheels are pretty straight forward. For each complete turn of the drive wheel, how many times it turns the driven object (such as bobbin or flyer) is the drive ratio. This is determined by dividing the diameter or circumference of the drive wheel by the diameter or circumference of the driven object. Abby's Yarns has a good in depth post of basic drive ratios that goes into that further. For a charkha, or 'accelerated' wheel, there are two drive wheels, and the ratio of each is multiplied together to determine the final spinning ratio.

So using my set up as an example (I've used metric here because hey- it's easier math) the formula is:
A1 / A2 = C
B1 / B2 = D
C * D = Drive Ratio
So we get, 108 / 22 = 4.9 and 50 / 12 = 4.2 which gives us 4.9 * 4.1 and a ratio of 20:1

Here you can see my actual pieces that will give this ratio. Basically, the greater difference in size between wheels of one drive band, the higher the ratio. I've found a variety of those little wooden spools work great, already predrilled to the desired size and interchangeable. I also have a 1/2" or 12mm spool I can use for A2 that I've calculated will give me an even higher ratio of 37:1. If I want to push that even higher, I'm looking for a smaller spindle pulley (around 1/4") that would allow me to interchange spindles to change ratios- up to 75:1. This would be closer to the true Indian charkhas that typically have ratios around 80:1 - 125:1, great for cotton.

In the other direction, I've calculated a simple flip of B1 and A2 from the above illustration would produce a 4:1 ratio with spindle 1 or an 8:1 with spindle 2. Thus lowering it enough to be suitable for longer staple fibers such as wool.

Can you tell I've had fun playing with numbers? Here are a few other notes on the wheels that I've learned. At one point I had thought about having the second drive band simply connect to the spindle/knitting needle rod directly, with washers on each side to hold it in place. This would obviously push the ratio way up, but I have since realized with such little surface area for the drive band to grab onto, traction, and therefore slippage, becomes an issue. Additionally, the farther apart the wheels are placed helps create more surface area contact between band and wheel and again, improves traction.