Calculating Rings

    The problem here deals with the floor of the carousel. I do not know if it is my tension, or an incorrect pattern, but the ring counts on the doily for the floor do not work. As one person said, those rings were tortured into submission. I don't like it. they were pulled to ovals. Here I am going to go through the math to calculate the correct number of rings. Then I will tat it and see if the calculations worked. They should.
    Just so you know, for those of you not familiar with my job, I draw steel. The software I use puts the " mark between the whole number and the fraction, so I am just used to doing it that way.
    First I tatted a few rings and measured them. The 6 count rings are right about 1/4". The 8 count rings are about 5/32". I measured the doily at its present stage and found it to be 6"7/8. I added the quarter inch (1/8" each side) and got 7"1/8. The circumference, (pi*d), then, is about, 22.38. I divided that by 1/4 for the smaller ring and got 89.5, so I need 90 rings at 1/4" to make a circumference, at the center of the ring, that is 22.5".

    I drew the rings in AutoCAD because it will do some of the math for me. I can just measure a few things.

    Next, I measure the 8 count rings on the outside of the round. Those are about 5/32. 90 of those make a circle of just under 8"1/16, so I laid them on a circle that size, offset from the smaller rings by half.
    Now that I have the small rings in place and the larger ones in place and offset, i can measure the bare thread length I need. Just barely under 1/4", so I will be making 1/4" bare threads.

    Now that I know how many rings I have to have, I can figure out the chain round that separates the sections. I know the previous section had 60 rings to attach the chain to. Those will be lock joins. I need 90 picots to join the next round to, that is what we figured out above. Now, how many stitches do I need between the attachments? I will work one segment, then repeat it around 10 times.
    I have 10 segments and 60 attachments so that makes 6 per segment. In those 6 attachment sections I need 9 picots. The distance from ring to ring to attach is about 3/8". I want a little more so the chain will arch a little and snug so I will use 1/2" of chain or, from the photo, 14 stitches. 14*6 is 84 per segment. I need that divisible by 9 for the rings and 6 for the attachment. 84 is not divisible by both, but 90 is so 6*15=90 and 9*10=90. I will attach every 15 stitches on the chain, and there will be a picot every 10 stitches to attach the next round of 6 count rings.

Whew! What a process. And that is just for these 2 rounds. After I get this tatted, I have to do this for the next 4 sets.