MrNaz
Enlightened
I have noticed a few threads regarding this, and I see that people are doing things like playing with coins and using other imprecise methods of calculating these values. I derived a few formulas a while ago, and have been using them ever since. They are easy to apply, and windows calculator in scientific mode can be used to calculate them effectively. I have included a simple factor, so you don't even have to apply the formula, just multiple the diameter of the inner circles by the factor to get the outer diameter.
3 Circles:
Dt = Di + (Di / cos(30))
= 2.15 x Di
4 Circles:
Dt = Di + Di x sqrt(2)
= 2.41 x Di
5 Circles:
Dt = Di + Di / sin(36)
= 2.70 x Di
6 Circles (can contain 7, as 6 circles can have one more in the middle):
Dt = Di + Di / sin(30)
= 3.00 x Di (duh!)
From these I saw that you can generalize the formula to:
n Circles:
Dt = Di + Di / sin(360/2n)
E.g.,:
I was building a battery tube for 3P 18650 batteries. To calculate the battery tube's inner diameter, I did this:
Dt = 18 + 18 / cos(30)
= 18 x 2.15
= 38.78mm
You don't need the first line if you memorize the values. 2.15 for 3 batteries, 2.51 for 4 batteries, 2.70 for 5 batteries and 3 for 6 (or 7) then you can easily work out the diameter of battery or optic arrays with a single multiplication.
Be aware that when applying the values, make sure to leave yourself a little breathing room for manufacturing tolerances. See this post for a bit of discussion on this point:
https://www.candlepowerforums.com/posts/2997327
I hope this is helpful.
3 Circles:
Dt = Di + (Di / cos(30))
= 2.15 x Di
4 Circles:
Dt = Di + Di x sqrt(2)
= 2.41 x Di
5 Circles:
Dt = Di + Di / sin(36)
= 2.70 x Di
6 Circles (can contain 7, as 6 circles can have one more in the middle):
Dt = Di + Di / sin(30)
= 3.00 x Di (duh!)
From these I saw that you can generalize the formula to:
n Circles:
Dt = Di + Di / sin(360/2n)
E.g.,:
I was building a battery tube for 3P 18650 batteries. To calculate the battery tube's inner diameter, I did this:
Dt = 18 + 18 / cos(30)
= 18 x 2.15
= 38.78mm
You don't need the first line if you memorize the values. 2.15 for 3 batteries, 2.51 for 4 batteries, 2.70 for 5 batteries and 3 for 6 (or 7) then you can easily work out the diameter of battery or optic arrays with a single multiplication.
Be aware that when applying the values, make sure to leave yourself a little breathing room for manufacturing tolerances. See this post for a bit of discussion on this point:
https://www.candlepowerforums.com/posts/2997327
I hope this is helpful.
