February 4, 2009

How to calculate and create a snug cover for a pot

A pot is basically the bottom portion of a cone. To make a pot cover, you must finish the cone in theory to create the dimensions. A cone is also just a portion of a much larger circle. It's important to remember these things so it all makes sense as you're doing the calculations.

I apologize that it isn't easier, but it's not super easy to make something fit well when precision is everything. I made these instructions based on easy to take measurements that would be more accurate than other measurements (e.g., circumference rather than radius and length rather than height). I'll be posting pictures once I've gone through this procedure and have successfully made a pot cover.

Ugh, this problem has been bugging me for a while, but I was too lazy to actually sit down and devise a plan. Now I finally did it, and it seems correct and easy enough to do.
  1. Take the circumference of the wider portion, and this will be called Ca.
  2. Take the circumference of the narrower portion, and this will be called Cb.
  3. To find the radius, use the age old equation of: C = 2πr. Do this for both Ca and Cb to make ra and rb, respectively.
  4. Measure the distance along the pot between the wider portion and the narrow portion. This will be called La. This is necessary to get an accurate measure of the height of the theoretical cone.
  5. Take the difference ra and rb. This will be called Ba.
  6. Using a2 + b2 = c2, you can now calculate the height of the pot. La is the hypotenuse, and Ba is b in the equation. Call this height Aa.
  7. Now it’s time to use proportions. The smaller triangle you just calculated is directly proportional to the larger triangle for the theoretical cone. So: ra/Ba = Aa/Ab. Ab is the height of the theoretical cone and is also the radius of a much larger circle as cones are really just a portion of a circle that’s been rolled up.
  8. Set a compass or a length of string to the same length as Ab.
  9. Mark where you set the compass in the center of a piece of paper and draw a circle using this point as the center of the circle.
  10. Subtract La from Ab, and this will be called Lb and will be the radius of a smaller circle to fit exactly within the larger circle.
  11. Set a compass or a length of string to the same length as Lb.
  12. Draw a circle using the center you drew for the larger circle.
  13. Cut this circle out, fold it in half, and cut at the half-way mark.
  14. Calculate tan(Ba/Aa) to find the angle. You can plug this into Google to get the calculation if you don’t have a scientific or graphing calculator.
  15. Mark the angle on the half circle and connect the points to the larger circle.
  16. Cut out this large piece of the pie leaving a little extra on one side. This will extra will become a tab that will be hidden.
  17. Cut along the edge of the smaller circle.
  18. At an angle, cut tabs off the extra portion so it looks like a trapezoid. This will require only two cuts.
  19. Phew! After all that, you’re done. You should have something that will snuggly wrap around your pot.

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