Math help with metal wire spacing

[joegreen]

I feel like this is pretty straightforward but i cannot seem to figure it out. I have a rectangle that is 330mm wide and i have metal rods that are 2.5mm in diameter. I want to lay the bars across so it looks like a grill grate or oven rack. I want to lay the 2.5mm bars evenly so there is an 8mm gap between each bar. The 8mm gap doesn’t have to be exact. How do i calculate how many 2.5mm bars are needed to span the 330mm gap while keeping the gap between each bar around 8mm?

 

[BrendanC]

If you take 330mm and divide by 10.5mm (8mm + 2.5mm), you get 31.42. This sounds like to me you need 31 or 32 rods if you aren’t set on an exact 8mm gap.

 

[Gyro Gearloose]

Each rod plus the spacing occupies 10.5 mm. The last rod would not include a space and would take up 2.5 mm of your rectangle, therefore there are 327.5 mm to be occupied by the rod /space groups. 327.5/10.5 = 31.19 rod/space groups, plus the end rod makes 32 rods total.

If you are just trying to form a grid across the open space of the rectangle without starting and ending rods, then obviously 2 less.

 

[joegreen]

Oh wow thanks. I knew it was simple but i kept trying to figure it out without adding the 2.5mm and the 8mm.

 

[dnewton3]

The two answers above are correct, but I want to make it more generic; this can be applied to anything with multiple elements over a distance. For example, this could also be used for spacing stile rails for a deck railing system, etc ...

T = total distance to be covered
W = component width
S = desired spacing in between components
Q = quantity of components

Hence:
T = (W + S) x Q

* Algebraically, this can be solved for any one unknown element when the other elements are known ...
* Often, the result will not be a whole number. You'll have to round up/down by one component to make it work and slightly adjusting the spacing. The larger the component is relative to the spacing, the more "adjustment" you have to make. When the component is very small relative to the spacing, it's very difficult for the eye to notice at a glance.
* Always make sure the units of measure are the same; inches to inches, cm to cm, etc ...
* The formula above presumes only one type of component, all of the same width. If you have components of varying widths, the formula becomes more complicated and then depends if you want to defer to equal spacing between components, or equal component centerline spacing ...

 

[BrendanC]

The two answers above are correct, but I want to make it more generic; this can be applied to anything with multiple elements over a distance. For example, this could also be used for spacing stile rails for a deck railing system, etc ...

T = total distance to be covered
C = component width
S = desired spacing in between components
Q = quantity of components

Hence:
T = (C + S) x Q

* Algebraically, this can be solved for any one unknown element when the other elements are known ...
* Often, the result will not be a whole number. You'll have to round up/down by one component to make it work. The larger the component is relative to the spacing, the more "adjustment" you have to make. When the component is very small relative to the spacing, it's very difficult for the eye to notice at a glance.
* Always make sure the units of measure are the same; inches to inches, cm to cm, etc ...
* The formula above presumes only one type of component, all of the same width. If you have components of varying widths, the formula becomes more complicated and then depends if you want to defer to equal spacing between components, or equal component centerline spacing ...

If only my professors would’ve taught it this simply