Friday, March 14, 2014

Happy pi day 2014

But, I want to point out, Pi is (still) Wrong!

Vi Hart explains:


When sewing neckbands on t-shirts, I recommend using your preferred circle constant, the minimum circumference necessary to pull over your head, the stretchiness of your fabric, and the width of the neck band to determine the optimal circumference.

For thicker neck bands and smaller openings, the 90% of neckline rule will result in a neckband that is too loose.  Do you need a drawing or an you visualize it?

Suppose you want a neckband that is 1 cm (about 5/8") wide and your neck opening is about 43 cm/17" (7 cm radius).  Using the 90% rule, you'd cut the band to finish at 39 cm circumference.

But, wait!  The radius of your opening is not at the sewn edge; it's at the inside edge, which has a radius of 6 cm and a circumference of 38 cm.

Your 39 cm tube will be too wide and floppy!

On a larger, scooped neckline, say 55 cm circumference and 8.75 cm radius, the inside edge would be 48.7 cm or 7.75 cm.  That's awfully close to 8.75*0.9 = 7.875.

Anyway, the 90% rule does come from geometry, but it only works for a range of neck opening circumferences.

Other sewing gurus say 85% of opening.  They mean smaller openings.

When in doubt, it's best to go back to first principles and calculate what you need based upon:
  • the minimum circumference necessary to pull over your head
  • the stretchiness of your fabric
  • your neck opening measurement at seam line
  • your neck opening at the folded inside edge
Your neck band should be a tube with a circumference a bit smaller than the inside, folded edge. Yet, it should not be so small as to distort (gather in) the shirt neck opening. If you have trouble with distortion, then change to a lighter neckband fabric, or reduce the difference between the two circumferences by either cutting a larger neck opening or using a neckband that is less tall.

Read past pi-day entries.

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