my build from the start

[m_c]

I get a radius of 20.207.

I'd explain fully, but I'd need to do a drawing.
It involves the constant that all the angles within a triangle add up to 180deg, and a bit trigonometry.

[blackburn mark]

ahh... i get it now, im with m_c on this one 20.07mm radius will intersect 3 points 35mm apart

took me ages to work that out

[h4ppy-chris]

i can find the formula for 4,5,6 but not for 3 :confused:

PCD Calculation Formula
3 stud PCD = S / 0.866
4 Stud PCD = S / 0.7071
5 Stud PCD = S / 0.5278
6 Stud PCD = S / 0.5

[ptjw7uk]

3 stud PCD= S/0.866

peter

[h4ppy-chris]

thanks peter star man, added it to the post :-)

[Jonathan]

Ahh, now I understand the question! You wanted *diameter* not circumference at stated in your post.

It's just cos(30)...

Let x be side length of the triangle the three points form (i.e 35mm).

(see diagram)

Draw in lines on triangle that bisect the angles. So we've now got a smaller triangle with one side length x/2, and we know the angle indicated is 30 degrees, since it's an equilateral triangle and we've bisected the corner angle.

cos(30)=(X/2)/r
r=X/2/cos(30)
r=17.5/cos(30) = 20.2072594...
(since d=2r, d=X/cos(30))

Incidentally to help remember it cos(30) is just sqrt(3)/2 = 0.866025...
Hope that helps. You can get the other PCDs using similar methods. 4 is half root 2.

[h4ppy-chris]

thanks jonathan ;-)

[Jonathan]

Ahh just realised. My method can easily be extended to the general case for n bolts. You just need to know half the angle interior angle of the particular polygon. Then do cosine of that to get the factor...

3 = Triangle, 60/2 = 30, so cos(30)
4 = Square, 90/2 = 45, so cos(45)
5 = pentagon, 108/2 = 54, so cos(54) = 0.5878 (!)
6 = hexagon, 120/2 = 60, so cos(60) = 0.5

The formula to find the interior angle is 180(n-2)/n.
So that means, given n bolts with spacing x.

r=x/(cos(90(n-2)/n))
PCD = x/(2*cos(90(n-2)/n))

enjoy!

[mmcp42]

like the formulae but...
er where is x used??

[ptjw7uk]

x=bolt spacing(centre to centre)
Peter