Thread: Diameter Of A Circle

Is the 18mm between the holes a straight distance (ie a chord of the big circle) or a distance along the circumference of the big circle ?

Bill

Originally Posted by steamingbill

Is the 18mm between the holes a straight distance (ie a chord of the big circle) or a distance along the circumference of the big circle ?

We're assuming a straight line.... I think lol


Hi Ray,

You mean like this?(the red lines that is)
But how do you get 18mm between the holes?



Stuart

Originally Posted by steamingbill

Is the 18mm between the holes a straight distance (ie a chord of the big circle) or a distance along the circumference of the big circle ?

Bill

Straight line.

Here is my crappy diagram, you only have to solve for one hole, to be able to calculate the radius.. the angles for all the other holes and spaces are the same

circles_1.jpg

Hope that makes more sense.

Ray

Originally Posted by Stustoys

We're assuming a straight line.... I think lol


Hi Ray,

You mean like this?(the red lines that is)
But how do you get 18mm between the holes?


Stuart

I see what you are getting at, It could be either way... I assumed equal angles for holes and spaces.. imagine they are all holes, not spaces between holes, and they are all 18mm diameter and all centered on the circumference.

The other method you are suggesting is that the distance between hole edges is 18mm, that would lead to unequal angles and spacing for holes vs spaces..

I guess either is a solution...

Ray

when I have a maths problem I now know where to come and ask......

Originally Posted by eskimo

when I have a maths problem I now know where to come and ask......

So do I, ask Stuart... I just get confused.

Here is the problem... (again) when the spacing between the holes is specified, then there are multiple options as to how to measure the spacing between holes. It amounts to constructing a 2n sided polygon around a circle of radius r, for large enough values of n the error is very small, the worst case is when n is small, so take n=3, that means a polygon of 6 sides.

Supplied
h is the side length ( or hole diameter )
n is the number of holes.

Derived..
a is the angle between vertices.
r is the radius
D is the diameter (what we are looking for)



The polygon can be constructed outside the circle as follows..





Or it can be constructed inside the circle...


Either way is valid, there are probably other solutions as well .. but my guess is that the answers will be very close to the same if n is large.

I think inside looks better?

Ray

Originally Posted by RayG

So do I, ask Stuart... I just get confused.

Here is the problem... (again) when the spacing between the holes is specified, then there are multiple options as to how to measure the spacing between holes. It amounts to constructing a 2n sided polygon around a circle of radius r, for large enough values of n the error is very small, the worst case is when n is small, so take n=3, that means a polygon of 6 sides.

The polygon can be constructed outside the circle as follows..


Or it can be constructed inside the circle...


Either way is valid, there are probably other solutions as well .. but my guess is that the answers will be very close to the same if n is large.

I think inside looks better?

Ray

this is getting out of hand...I have NFI what you are talking about

Oh "Either way is valid, there are probably other solutions as well .. but my guess is that the answers will be very close to the same if n is large."...are you telling me that close enough is good enough???...if so I must inform you that it didnt want to work when I made that knurler...

Originally Posted by eskimo

...are you telling me that close enough is good enough???...if so I must inform you that it didnt want to work when I made that knurler...

Close enough is always good enough, when you can't measure the error it's time to stop

When do I get my knurler?

Ray

You mean we're not having fun yet?

There is a third way. Just using n. that gives you 18mm between the holes at their closest point.

I think

Stuart

p.s. sorry about butchering your drawing Ray.

Originally Posted by RayG

Close enough is always good enough, when you can't measure the error it's time to stop

When do I get my knurler?

Ray

I have'nt finished using it yet

I see one flaw with both of those images. The circles are not spaced correctly if we want the minimum distance between to be 18mm, which is what i took the original drawing to mean
I'd rather draw a triangle, with the corners on the center of the holes. This way the holes are centered on 36mm and the distance between them is 18mm.....I'm on the shop PC right now, its a little hard to do drawings.

Ew

Too slow, i see Stu is on to it. That is how i worked it out the fist time.

Originally Posted by Stustoys

You mean we're not having fun yet?

There is a third way. Just using n. that gives you 18mm between the holes at their closest point.

I think

Stuart

p.s. sorry about butchering your drawing Ray.

That's probably the best solution.. ( I see Ewan's suggesting that as well.. )

I'm away for the afternoon, so I'll leave you to derive the formula..

Ray

Wow ... Can you lads do tomorrow's tatts numbers too ?

Originally Posted by Glenn.Visca

Wow ... Can you lads do tomorrow's tatts numbers too ?

they have lost me Glen...maybe I should have listen to the teacher afterall

But seriously, I wish I was able to do what they do tho