Learning Opportunities

That's me. As in today, I've learned that I should not attempt to go into the HTML edit level on this tool. Ironic, isn't it? 25 years ago I started this whole process by editing my HTML directly in Notepad... But thou shalt not do it here. 

I was blathering on in the draft I don't dare go back into about woodworking.  I had stumbled into yet another chance to make a  cooper-topped chest, this time I'm working backwards.  With the chest I made for my son's wedding, I started with the lid, then tried to build a box while avoiding plywood.  This time, I downsized rather significantly.  The current chest will be about 19" wide by 14" front-to-back.  It looks like the eventual height will be around 15 or 16 inches tall, once I finish that lid.  

This time, I went in trying to apply math.  There's a way to calculate this lid, and I don't know it.  What I did do, though, was approach it from left field.  I looked at the angles.  I thought if a piece of wood is standing vertical, that is, at 90-degrees to flat, then the "travel" across the horizontal is, well, zero.  I know that's part of my problem, but bear with me.  If the piece of wood is, well, flat - that is, it's laying down, then the width of the wood is 100% of the distance.  So if I'm using a piece of wood 2 inches wide, if it's standing on edge, it's going nowhere.  If I lay it flat, then it moves me a whole 2" from side to side.

So, there's angles.  Right?  And I started by trying to figure out how to calculate the triangle, then it hit me.  But I suppose I've skipped a step.  When you want to cooper a lid, what you do is cut the edge of the wood at an angle.  To make an even curve, what I do is cut the edges of long pieces of wood then cut them to length.  The trick is your angle is going to be twice what you set on the saw.  

Huh?  Well, here goes.  Let's say you want a 12-sided figure.  Think a clock.  A circle is 360 degrees, right?  So if you divide by 12, each side is 30 degrees from the previous.  But if you're cutting wood to get that, you need to cut the edge of the wood at 15 degrees each, because when you put them together, the two angles are additive.  If you cut 30-degree angles, your figure will have only six sides.  

But it also occurred to me.  If I look at the angle, well, if I cut each edge at 10 degrees to make a total 20-degree angle, 20 degrees is 22.222% of 90.   So shouldn't the run of that piece of the lid be 77.778%?    Or in other words, that first piece should travel 1.555 inches while dropping 0.44 inches?  I mean, it made sense to me.  

So with a flat piece that is 3 1/2" wide, the first piece on either side of it should make the lid 2.72" wider, each, and the second  piece at 40 degrees will travel only 1.95".  Or in the end, my simple CAD tool told me the lid should come out a little (as in 3/8") wider than my 14" I need.  The practice piece I made turned out about an inch and a half wider, which is fine.  It's always easier to cut a bit off, because my board stretcher still doesn't work.  

Obviously,  my math was off, but closer than well, what the heck, let's see how it works...