N = A / (R x R x 3.4641)
where:
N = Number that will Fit.
A = Area of Big circle or rectangle
R = Radius of a single array.
This treats the circular array as a hexagon (which will interlock) and divides the area (A) of the big circle-rectangle by the area of the Hexagon (R x R x 3.4641). The 3.4641 is derrived from [(Cotangent 30) x 2 x 6 / 2].
Enjoy.
Arthur
--- In , "Roger Malmstein" <starwolf@...> wrote:
>
> I would like to get some quick and dirty rule for how many circles of a
> specified radii I can get into either another circle or within a rectangular
> area.
> This request has something to do with my previous post about updating
> "Traveller Beam Factory". I have plans to enable laser turrets, barbettes
> and bays have more than one laser array if the array diameter is less than
> the diameter or width/length of the mount. It doesn't need to be precice as
> I have seen calculations for this and it just seizes up my brain. It can
> error on the side of fewer arrays as we can handwave it with a certain
> percent of the available area will be lost for technical purposes.
>