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# Maths formula for circumference pcd

## 11 posts in this topic

I have to mark out 5 holes equally spaced on a 72mm dia,

whats the formula again ?

I know its 72 deg but i haven't got a dividing head,

,i have compass,dividers and vernier caliper etc.

thanks Matt

ps Like on a car wheel stud pattern, 5 studs.

pcd=72mm

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dont get what your looking for.. you have your two polar coordinates, distance and angle, thats all you need to locate a point

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you are trying to find coordinates of 5 holes on a 72mm diameter to drill/mill them on a mill?

First hole will be at angle "0" (3 oclock). 360/5=72 degrees between holes.

If the center of the bolt circle is 0,0, then the first hole will be at (36,0)

Second will be at (36*cos(72),36*sin(72))

Third will be at (36*cos(144),36*sin(144))

4 at (36*cos(216),36*sin(216))

5 at (36*cos(288),36*sin(288))

Make sure the calculator is in degrees mode. Using the whole angle referenced from polar 0 will give you correct sign in x,y depending on what quadrant you are in.

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you are trying to find coordinates of 5 holes on a 72mm diameter to drill/mill them on a mill?
If he were doing that, I'd think it would be simpler than anything else just to use a rotary vise.

But for those less familiar with applying trig to this sort of thing, maybe you can elaborate on the process a little (especially here, where the angle between points and the diameter are coincidentally both 72).

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i was thinking

pi x d = circumference / 5 =

so

3.1459 x 72 / 5 = 45.2389

But after trying it i was wrong,

i think its got to do with straight lines and curves.

Cheers.

and im only using a drill press, so i need to scribe them, centre punch and drill.

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It does "have to do with curves", as you said. If you had a realistic way of measuring along the circumference, your answer would have worked.

Layout a full sized pattern on paper using the compass method from wiki if you can't do it on the work itself. Transfer it to your work and punch it in.

Aaron's trig solution will do it, too.

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Thanks, i got 42mm divider setting through template transfer (on paper first ) i should have marked it out before i bored the center hole

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Here is the math solution to find the chordal distance between holes; use Aaron rectangular data and calculate the XY rectangular coordinates for the holes.

X & Y values for the first hole are 36,0 and for the second are 11.125, 34.238. The XY differences between these two holes are 36-11.125 and 0-34.238, or 24.875 & 34.238. Use these numbers for a new triangle. The hypotenuse of this new triangle is the square root of 24.875 sqd + 34.238 sqd, or 42.321. Set your dividers to this new value and you should be able to scribe the location of the holes on your 36 radius circle. How close you close on the beginning hole will indicate accuracy.

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protractor and compass, no math needed.

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If he were doing that, I'd think it would be simpler than anything else just to use a rotary vise.

But for those less familiar with applying trig to this sort of thing, maybe you can elaborate on the process a little (especially here, where the angle between points and the diameter are coincidentally both 72).

Elaboration:

This is a trig problem very common with CNC machining..and since I have CNC on the brain lately it is the solution I chose. All trig identities will sign themselves correctly (aka have x and y as positive or negative according to which way they are pointing) if you use an angle referenced from 0, which in the case of a cartesian coordinate system is the positive x axis.

If you start at 10 degrees for example you have a thin triangle constructed just above the x axis. The hypotenuse is the radius of whatever bolt circle you are making. The adjacent side is the x position of the hole, and the opposite side is the y position of the hole, where the hole is at the far end of the radius/hypotenuse.

Sin solves for Y and Cos for X. We have to multiple these by the radius to get correctly scaled values for the size circle we are solving.

The beauty of doing it this way, to me, is there is very little room for error so long as your angles are correct. You can set up a spreadsheet to solve for everything, and make changes very quickly.

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