In the thread “how to cut copper sheet?”, I gave a couple of mathmatical answers for calculating rolling staples, so I am asking for some expert advice as to what is the best formula for calculating a staple blank. In the example a 4.0mm inner diameter was called for. The person asking thought that a blank of 4 x 3.14 = 12.56mm wide copper would be what was needed. I pointed out that the inner diameter is not what should used to calculate the width of the blank. Early on I was told that one should add the thickness of the material to the result as a factor to make a rolled tube. Using this, the example would be 4 x 3.1416 = 12.57 + 0.5mm (copper thickness) = 13.07mm width. Another machinist told me that for every 90 degree bend, 0.2 of the material thickness should be added. That would yield 0.8 times the material thickness yielding a factor of 0.4mm to add for a total blank width of 12.97mm. Looking up bending calculations showed me that one would need to know the k-factor of 0.020 copper in order to figure this out. I was in over my head at this point, so I am asking if anyone on this forum could enlighten us on the proper fudge factor to add into these calculations. I have used the 0.8 times the copper thickness and it seems the staples just close on the mandrel using it. Seems pretty close, but close only counts in horseshoes and hand grenades.
Wow. You’re really over thinking this. Even if you cut and filed a piece of copper to what you think are the perfect demensions the act of rolling the copper around a mandrel and squeezing/hammering to it’s final shape will to some degree strech the copper. If you’re mandrel is too fat then the copper will get streched.
Making reeds is a craft and is trial and error. Make a bunch of staples of slightly different sizes and see which one gives you the best tuning in both octaves.
You won’t get you’re first staples perfect. It takes practice.
There is no good reason to hammer a staple around a mandrel, and many reasons not to. Just fold the copper carefully in half around the mandrel and then wipe it from end to end, alternating on each side of the seam. Whilst gripping the mandrel in the left hand fingers, grip the u-shaped copper with the thumb against the back of the mandrel (the “back”, or “middle” of the copper slip) to keep it from spinning around the mandrel, and wipe the sides of the seam with a round hard piece of wood or the round shank of a phillips head screwdriver and use as much pressure as you can with your hands. Then roll it in the usual way on the table, using as much pressure as you can with your body over it, with a 3/4 square x 24ish scrap of cold rolled steel that has been sanded perfectly flat on the side as well as its neatly rounded corners. If, when you try to roll it, the copper with the mandrel in it skids across a metal surface, roll it on a butcher block or maple bench surface and that will give it more traction until it is well rounded and will readily roll on the metal surface. If you have a slight bit of gap somewhere in the seam, roll it even harder in that specific spot to close the gap. There is no need to solder the seam, and there are good reasons no to. The hemp will seal any leak, but a tidy job will not allow any air going through anyway, for at that point, you have made a really handsome seam.
I’ve been watching various pipemakers on this DVD over the last week, the DVD gives a good insight into the various approaches by the different makers.
http://store.pipers.ie/store/product/1213/Heart-of-the-Instrument,-The--/
to state the obvious i belive Ted already knows this 
I’ll second madfortrad on this one.
Thanks for all the advice on rolling 
. Having rolled thousands of them, I think I have that part down. My question is strictly anal. I am looking for a machinists or jewelers fudge factor for calculating the width of the blank. I’m sure I am very close but was looking for an experts knowlege of the mathmatics of copper bending. I have not found copper wanting to spread much when rolling over a mandrel, but the I don’t anneal the blank prior to rolling, or ever, if I can help it. I do use a plastic-headed hammer to tap the edges of the copper around the rolling mandrel while it is setting in a semi-circular groove routed into a hardwood block. I have not seen spreading occur with this method. The only steel I use is the mandrel. I reproduce quite accurate staples this way. I have found a 0.005" diffrerence in width of the wide end of a staple blank gives a noticeable difference in the tuning of a staple.
Hi Ted,
I was going to PM you about this in the other thread. The trick is to add the thickness before multiplying by Pi. In your original example of a 4mm I.D. tube of 0.5mm copper, you’d need (4+0.5)Pi = 4.53.14159… ~= 14.137mm initial width.
The principles are of course the same for hand-rolled ferrules.
For really thick rings, there’s indeed a correction factor that accounts for the fact that the mid-diameter, i.e. at which 50% of the copper is on the inside and 50% on the outside, is actually a bit bigger than (I.D.+t). I think it’s a smaller effect than the “stretching” of the copper sheet, so the actual perfect width for your staple blank will depend on the rolling technique - the two effects work in opposite directions.
For what it’s worth, I anneal my copper before rolling - not because I can’t roll the half-hard stuff, but because it gives me a more uniform result. Rolling the blank on the mandrel provides enough work hardening for me. If I solder a seam - which I do occasionally - I often spin the result rounder afterwards, which accomplishes some of the same.
Bill- you are the man! Thanks for that. I don’t know how I forgot to add the wall thickness BEFORE multiplying by pi. Total brain f*rt. Old age must be getting to me. I looked at some older calculations I did some time back and had done it correctly. I somehow slipped up when first answering the other post, without thinking it through completely.