One for the mathematician

[rorybbellows]

It's probably of no real practical value, and reed making is not an exact science , but maths and geometry are .
If you know two of the measurements in the drawing below how would you find the other two ?
Say for instance you want a slip of 1.4 thickness and width of 12.8 what diameters are the cane tube and sanding block.

Come to think of it ,is it even possible with only two measurements or do you need three?


RORY

[colomon]

You need three measurements, I think. The unknowns are the diameters of cane tube and sanding block AND the distance their centers are apart.

If you look at http://mathworld.wolfram.com/Circle-Cir ... ction.html, then the radius of the cane tube is r, the radius of the sanding block is R, and the distance their centers are apart is d. Then your thickness T is T = d - R + r, and your width W is W = 2 y, where x^2 + y^2 = R^2 and x is where the intersection is.

But that doesn't get you an answer unless you get rid of one of the unknowns.

[Zeildritch]

Something like this?

[andy_skiff]

[JR]

I prefer a beer bottle to a sanding block.

[daveboling]

You need more. With only two dimensions, there is no vertical relationship between the width, and the bottom (or top) of the thickness. If you know the diameter of the cane tube, or the diameter of the circle (block, bottle, or bong) used to sand the inside arc, you could develop a formula to work out the bits you don't know.

dave boling

[rorybbellows]

Thanks all for your contributions.

you could develop a formula to work out the bits you don't know.

Yes but what is that formula and could it be used if you wanted to change just one of the dimensions .
Take the example given by Andy Skiff 12.83 x 1.4 slip, 90mm block 24mm tube. Say you wanted increase the inside curvature by decreasing the diameter of the block but keeping the same slip measurements ,what would be the diameter of the tube.

For the formula to work you should be able to substitute and one of the dimensions and arrive at four valid working measurements.

RORY

[daveboling]

It can be done, but it may take me a day or two to get something that works. It's just a bit of geometry.

dave boling

[billh]

You're ignoring the edge thickness...

[rorybbellows]

You're ignoring the edge thickness...

Yes, thats correct . Adding an edge thickness would be simple in relation to a formula that I think would be very complicated .

RORY

[Calum]

I have done a quick spreadsheet using the formulae coloman pointed at:

https://docs.google.com/spreadsheets/d/ ... sp=sharing

and pinching Andy's numbers.

There's an error in there, though, and I'm scratching my head a bit to figure out what it is. My figure for the width of the slip is not right. Anyone?

[JordanMcConnell]

Came across this link in geokeenan's blog:

http://southeastpipersclub.org/reedmaking/reedform.htm

[rorybbellows]

Good one Jordan, your very first post and you hit the ball right out of the park.

RORY

[pancelticpiper]

you hit the ball right out of the park.

Interesting to hear what I think of as a baseball metaphor there. Isn't the British equivalent "a six"?

Sorry to be offtopic.

[DarthWeasel]

You guys need to stop over thinking this. It's not that complicated