When cutting a slot in a piece of pipe using my rotary table, for some reason the chord length always ends up a bit shorter than it should be.
I’m sure it’s because I can’t simply subtract the cutter diameter from the desired chord length and still use the central angle that my calculator supplies.
The problem is that I have no idea how to compensate for the cutter diameter when dealing with a cut measured in degrees.
I’m not sure I’ve even provided enough information to properly explain my problem, but hopefully someone will be able to set me straight before I pull my hair out.
I’m sure that I don’t know what your talking about…
not that I’ll let that stop me…
shouldn’t it be the radius instead of the diameter?
chord length is a fraction of the diameter of the cutter
yep…don’t know…bad time of day to wade into things not touched for 30+ years 
Well, say I have a workpiece with a 1" diameter, and I want to cut a slot with a chord length of 5/8".
I should need to cut out 77.364 degrees, but how do I take into consideration the bit diameter?
If I’m using a 1/8" diameter bit, I’ve already made a cut with a chord length of 1/8" before I ever turn the rotary table… see my problem?
And if I try and compensate by subtracting the 1/8" for the bit then and calculating the cut for a chord length of 9/16" (68.458 degrees), then the resulting chord length ends up a bit shy of the desired 5/8".
This method of compensation would be correct for a flat surface, but the curve is throwing me off.
I should have taken math more seriously back in high school! 
Could you post a sketch/diagram?
Does the rotary table sit on a mill?
It sounds like you want to subtract half the bit diameter from the circumferential distance, not the chord distance. On a 1" diameter piece, an angle of 77.354 degrees gives a circumferential distance of (77.354/360) * (pi * 1) = 0.675 inches. Subtracting half the 1/8" bit diameter to compensate gives 0.675 - 0.0625 = 0.6125 inches. Since circumferential distance is proportional to the angle, the angle you want is (0.6125/0.675) * 77.354 = 70.192 degrees, which is a bit more than you were using.
Maybe. 
yes, circumference…I new I was too tired last night when I screwed that up and went to bed anyhow!
MT’s sounds good…bit like music & fencing…you have to count both ends or think in radius instead of diameter. So yer 1/8 becomes 1/16
As an ex high school math teacher, this sounds a little bit like the story problems that I would give the students. When I did this, I usually got groans from my class. Sometimes it is difficult for us to translate words into numbers and equations. Of course, a photo or diagram would help our understanding.
Here is a different take on the matter. Instead of using deductive reasoning, where you try to figure everything out mathematically, why not try inductive reasoning, also called “trial and error”? If your chord length is too short, you need to cut a little more off. Keep a record of your saw settings until you get exactly the chord length that you were looking for.
…and if ya get real good at trial and error you can call it successive approximation!
Ya do need to reduce the error bit for that.
Well, it seems as though I’ve come up with a workable solution, but I have only tried it on a couple of scraps so far.
If I subtract the degrees of a cut with a chord length of 1/8" instead of simply subtracting 1/8" from the desired chord length, it seems to solve the problem.
So a 1" diameter workpiece with a chord length of 5/8" and compensating for a 1/8" bit diameter would be 77.364 - 14.362 to equal 63.002 degrees of revolution on the rotary table to make the cut… I think!
That’s exactly what I would recommend! Once you have the right length, go back and figure out how the calculation would have worked.
well, fine then just come at it from both sides at once
ain’t the brain weird!
Yep, that amounts to the same thing mathematically. Compensate either the circumferential bit width or its equivalent angle.
But before, you said that an angle of 68.458 degrees gives you a slot that’s too short of 5/8". If so, then 63.002 degrees would be even shorter! 70.192 degrees would be a hair longer. I calculated using half the bit width because that’s what you used in your previous post (9/16" chord length), assuming that’s how your table works.
Anyway, let us know how it turns out.
Well now I’m really confused, but the important thing is that my cuts are coming out right now.
I must have somehow set up my mill incorrectly last night when I was having all the problems, which wouldn’t surprise me a bit! 
Thanks to everyone who tried to help me out.
I’ve been waiting for someone else to ask, but since they haven’t, I will: what is this “chord” you refer to?
djm
You know, like a D major chord. When you are making whistles, you need to set your saw so that it cuts the right chord. I think that what he means. I may be wrong, though.
From a mathematical point of view, a straight line that bisects a circle is called a chord. Actually, to be more specific, the chord is the line segment which is inside the circle, while the rest of the line, seen or unseen, is chordless.
I knew if I waited long enough, someone else would ask.
Or with any calculator:
a = 2 * arcsin(c/2r)
l = (a/360) * (2 * pi * r)
h = r * (1 - cos(a/2)) OR h = r - sqrt(r^2 - (c/2)^2)
where
a is the included angle (in degrees)
c is the length of the chord
r is the radius of the circle
l is the arc length
h is the chord height
now MT if you’re gonna do twisted sinnin’ you’re on the wrong forum…shame on you, sir 
I see. Yes, now it all becomes clear.
I thought all you had to do was drill holes or something.