Equation for accurate bending (kerfing) of plywood

I am planning out my first Instructable. It will be a bent (kerfed) plywood coffee table,

There have been a growing number of projects out in the 'makeosphere,' where people are cutting slits or kerfs that go almost completely through a thicker piece of wood, allowing it to be easily bent. I am on a super-tight budget, and cannot afford to ruin my $22 sheet of plywood, so I was hoping that someone might be able to help me with some measurements for cutting the kerf-slits in the plywood. Here is the idea all sketched out. I need help with the measurements that are in bold. 

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PROJECT DESCRIPTION: 

Materials:
  • 1x | 4 ft. x 2 ft. 3/4 in birch plywood
  • 2x | 3 ft. 5/8 in threaded metal rods
  • 8x | flat washers
  • 4x | standard nuts
  • 4x | "end nuts" 

Steps:
  1. On the sheet of plywood, measure in X inches and mark X number of cross cut lines, X inches apart.
  2. Measure in 2 inches from each end of the board and draw a line.
  3. Measure in 2 inches each each side of the board, and draw another line.
  4. Drill out a 5/8 inch hold at all 4 of these crossed lines.
  5. Thread a standard nut onto each end of the threaded rod and screw it on 1-2 inches roughly, then slip a flat washer over the threaded rod.
  6. Bend each end of the board up to create almost 90 degree angles.
  7. Insert each end of the threaded rod into the holes, slip a flat washer over the threaded rod and screw on each of the four "end nuts." 
  8. Use the standard nuts, and the end nuts to fine tune the bends into 90 degree angles. 
  9. Flip the table over, and enjoy. 
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Stability is more important to me than curve radius. I don't know if spacing cuts close together for a small curve radius is more or less stable than placing the cuts further apart for a larger radius. I've never done this, but I have seen that there is an equation for this. I haven't been able to find the equation actually expressed, I've just heard that there is one. Does anyone know about this area of woodworking/physics?

caitlinsdad2 years ago

http://stusshed.com/2007/07/17/kerfing-bending-woo...

Woodworking is an art. You probably have to experiment with some scrap to see what actually works. It sounds like you are building a big tray with low sides and flipped over to become a table. The table will have a nice curved edge all around but you will be hiding the beauty of the kerfed bend. Maybe you should build a lesser wood frame and veneer with a thinner luan plywood - easier to just score/kerf bend. It would be cheaper but you can get thinner plywood in better choice of woods. Good luck.

Dolmetscher007 (author)  caitlinsdad2 years ago

Thanks caitlinsdad... I agree completely. My piece of plywood is actually 2 ft wide, but I plan to rip off 6 inches to that I can make the table more narrow, and have a 6 inch wide piece to experiment on. I am a huge perfectionist, and I was hoping to have a mathematical equation to work from. I will still test, and I will free-hand it if no one can help me come up with an equation. But I still wanted to ask.

Dolmetscher007 (author)  Dolmetscher0072 years ago

Oh man... thanks! I didn't see the link. Thank you!

The formula was in the comments of that link. Still a lot of variables to account for such as your machinery and the wood. The posts I have seen by people who use lasercutters to kerf it still do it by trial and error, hoping for the best.