13 Oct 2010 23:42 UTCWed 13 Oct 2010 - 11:42 pm UTC
I want to sew a donut. To do that I presumably need to cut a circle in fabric and then another circle inside that. This gives me one ring. Do it again and then sew the rings together, flip it inside out and I should have a donut.
The question is, if I want the final donut to have a height H, outer diameter D1, and inner diameter D2, what should the diameters of the inner and outer circle be for the rings that I cut from the fabric?
14 Oct 2010 11:41 UTCThu 14 Oct 2010 - 11:41 am UTC
A donut generally has a ring with a circular cross-section. I assume that's what you want, however if you need an elliptical cross-section please request clarification.
For a circular cross-section, the outer diameter D1 of the finished donut will be the inner diameter plus twice the height H. As you obviously realize, that doesn't mean that the outer cut of the fabric will be of diameter D1.
Consider the circular cross-section of the finished donut. This cross-section will have a diameter equal to H, and a circumference of pi times H. Each of the two pieces of fabric contributes half of this circumference. However, we are specifying the diameter, not the radius, so we need to account for this "half-circumference" twice.
Therefore we have:
After you fill your donut with stuffing to puff it out to donut-shape, your outer cut will be "pulled in" to the outer finished diameter D1. This will cause the fabric at the outer rim of the donut to bunch up because the outer cut had a larger circumference than it now needs.
If you want a tidy finish, you will need to cut out some slim wedges at regular intervals around your fabric. Overall you need to "waste" an amount of the outer circumference equal to the difference between its circumference as cut and circumference as finished:
Just divide this waste circumference amongst the number of wedges you are going to cut out.
If you don't want to cut wedges out of your fabric (because of all the extra stitching that would be required) you could fold, pin, or gather the outer edge instead of cutting away the waste. But you need to take it in somehow, or else the donut will tend to flatten as the stuffing redistributes.
Also, when you cut the inner and outer circles, you probably want to leave an extra centimeter or so, in order that the seam can be stitched on the exact diameter.
26 Oct 2010 20:27 UTCTue 26 Oct 2010 - 8:27 pm UTC
I'm posting this Clarification to trigger an email notification to alert you to Myoarin's alternative solution. It looks like it's going to be a bumper year for donuts!