Dr.Zook

Calculus, ain't that what you get on your hands from doing manual labour???????

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Dave
the "Doctor"

In woodworking there is no scrap, only firewood.

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Drugstore Cowboy

As long as you can calculate the time it takes you to get out the back door - before her husband comes in the front -- you should be ok math-wise.

Well - ok -- so you also need to know the proper ratio of rum to Coke and enough applied geometry to find your way around a pool table.

AlanWS

You have a lot of flexibility in spacing if you use a sophisticated jig or cut them by hand, or some combination. However, if you are cutting half blind dovetails using the type of jig where you cut both parts in one operation, the spacing must be even. This means the tail at half height must be the same width as the socket at half depth. The point of an equation to describe these is that it can help you to see how to modify the joint with varied bit angle and cut depth. The deeper the cut, the narrower it is at half depth.

The idea is to find the depth where the width of the tail and the recess are equal at half depth. That will depend on the angle of the bit (a), the width of the cutter (c), the bushing size (b), the finger width (f), and the dovetail size (s = the average of the width of a finger and the width of a space between fingers.)

Cut depth d = (s + c - f - b)/tan(a)

Treat this as an approximate setting, try it, and adjust the bit depth shallower if too loose, and deeper if too tight. If your bushing is off by 0.001", your cut depth would change by .007" for an 8 degree bit.

To use the same bit to cut deeper dovetails, use a smaller bushing. Likely it will be easier to use a bit with a smaller angle, or a wider bit of the same angle.

But the equation also shows how sensitive the depth setting is to these measurements: all you need is about 1/64" wider cut to change the depth from 1/4" to 3/8". If the cutter is actually wider by that amount, or if there is that much play between the fingers of the template, it would do it. To measure s most accurately, measure the width of the entire template, including an even number of fingers and spaces, and then divide by the number.

But whatever the measurements, you will need to make test cuts and fine tune the depth for fit. For those who like equations, this can let you use a cheap jig to cut a wider variety of dovetails.

mftha

Harrysin, I teach college students and teach a course in which I use a great deal of math, including calculus. I retain the calculus from roughly 4 decades ago that I need in order to teach my subject. There is absolutey no way I could pass a calculus exam today. If I were serious about it I could probably start today and be able to pass rigorous calculus exam at the end of the summer.

The problem that started this thread does not require calculus; it does require trigonemetry. Again, if I had the summer, I could probably pass a rigorous exam by the end of the summer.

As for the answer to the original question, give me some more time. My year just ended and I am still brain-dead exhausted. (I do not even trust myself to get out my router yet!)

harrysin

Thanks for you're answer mftha, I don't feel quite so inadequate now.

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Harry

FlyMaster

To all:
Thanks for all the feedback! This is definitely the place to go when answers are needed in short order.

AlanWS has the right approach. It’s tangent of the angle not sine. Shows how much trig (let alone calc) I remember…

So if you used the calculation for depth of cut d = (s + c - f - b)/tan(a), tweak it a bit, you get

cut spacing = 2 * bit diameter - 2 * (depth of cut * tan(angle))

Happy routing!

FlyMaster (aka – O.F.I.S.)