Carpentry conundrum

[Donkeyshed]

A wood panel is 1740mm long. It has two joins along its length. The first is at 606mm. The second is at 1188mm (This creates three sections of 606mm+582mm+552mm).

Stripwood is required to cover these joins. It is available in widths of either 15mm, 21mm and 25mm.

The stripwood will create smaller panels on the surface of the larger panel. However, it is important that each panel is equal in width. Extra small panels may be added, as long as each has equal width (taking the stripwood width into consideration). It is preferable to use the same width of stripwood throughout.

I need a calculation to work out where to place the stripwood along the length of the larger panel in order to create a series of smaller, equal panels. The two joins must be covered by stripwood.

Any help would be very gratefully received!!

 

[Donkeyshed]

Just to clarify: Here is the panel diagram. Broken lines are where the main panel is joined.

The irregularity of the joins on the main panel is problematic; it is crucial that these joins are covered by stripwood.
This gives an idea of what I need to do:

 

[Cubist]

My attempt to "draw" the situation...

           CASE 1      CASE 2

|-----|    |-----|    |-----|  0
|     |    |     |    |  s  |
| 606 |    |  p  |    |-----|
|     |    |     |    |  p  |
|     |    |-----|    |     |
|-----|    |  s  |    |-----|
|     |    |-----|    |  s  |
|     |    |     |    |-----|
| 582 |    |  p  |    |  p  |
|     |    |     |    |     |
|     |    |-----|    |-----|
|-----|    |  s  |    |  s  |
|     |    |-----|    |-----|
|     |    |     |    |  p  |
| 552 |    |  p  |    |     |
|     |    |     |    |-----|
|     |    |     |    |  s  |
|-----|    |-----|    |-----|  1740

Panel width is "p" and strip width is "s".

Are we talking about case 1 or 2? From your image it appears like case 2 is accurate. And does the stripwood cover the 2 "ends" wholly, or could say the 15mm stripwood only cover 5mm at the ends (because you need 10mm of the stripwood to hang over the end for example). And could there be a gap at each join (which is hidden by the stripwood)? Potentially quite complicated!

 

[Donkeyshed]

Hi, many thanks for your reply.
The ends are both covered by an L-shaped corner moulding, which has a 3.2 width. I have already subtracted that (at both ends) from the overall length to give me 1740mm. I can get away with having these two strips being at a different width, as they are corner mouldings (and it would keep it symmetrical). That's my thinking anyway.

I'm hampered by the width of stripwood available to me. I don't (at present) have the ability to cut it (accurately) to a particular width myself.

 

[Donkeyshed]

Sorry- therefore Case 1 would be most suitable (I think!)

 

[Cubist]

OK, then I think you're out of luck (unless my calculations are wrong). Here's my working...

We are looking at "case 1" in my diagram. And the total width 3p + 2s=1740 therefore p=(1740 - 2s)/3

If we take the widest strip of s=25mm, then p=563 1/3mm

The first strip would go from x position "p" to "p+s" which is from 563 1/3mm to 588 1/3mm. This doesn't reach the first join position at 606mm.

--

How about a solution where you put the shortest panel in the middle, and have two equal size panels either side of it? This might look OK? (I don't know if the math would work out yet, but it might have more chance of success)

 

[Donkeyshed]

Hi, yes- please go for that! Alternatively, a wider panel in the middle and two narrower on the left ands right? Also, would it work if further panels were created (eg, have 5-6 narrower panels?)

Greatly appreciate you looking at this for me.

 

[Cubist]

If you can accept the central panel being wider than the outer two, which will at least look symmetrical, then I think there's a solution but you need to check this yourself before committing...

|-----|    |-----| 0
|     |    |     |
| 550 |    |  p  |
|     |    |     |
|     |    |-----|
|-----|    |  s  |
|     |    |-----|
|     |    |     |
| 638 |    | p+x |
|     |    |     |
|     |    |     |
|     |    |-----|
|-----|    |  s  |
|     |    |-----|
|     |    |     |
| 552 |    |  p  |
|     |    |     |
|-----|    |-----| 1740

Let x be an increase in the size of the center panel. (You could make x negative if you want to investigate a smaller center panel). I assumed the corner overlap is 32mm, since 3.2mm seemed very small. I used this assumption to swap the boards around as seen above.

Now 3p+x+2s=1740 therefore p=(1740 - 2s - x)/3

I think s=15mm and x=80mm will cover the joins (the width of the two outer panels ought to be 543 1/3mm).

 

[Donkeyshed]

Hi,
thanks for this. Not sure I understand though. In the first diagram, if the first panel is 552mm wide, adding a strip would not reach the join at 606mm. The existing panels cannot be swapped around as they are fixed in place.

In your summary, you state that the two outer panels will be 543 1/3 wide. That will also be too narrow to reach/cover the first join at 606mm.

However, I may well be missing something (I am not a mathematician).