That's great planning. Not everyone thinks of how they're going to get something in place until just after they say 'ahh sh..'
Haha. Here's what I did. Not exactly master mathematician, but brute force approach. With a minimal wood shop, this is what I do. I have a $150 Sears table saw and hand tools do do this:
- Confirmed that 13 inches inside diamond dimension would hold 16 bottles.
- Measured space. Determined rough horizontal/vertical dimension which would maximize bottle volume.
- Drew out plans, with prodigious use of Pythagorean Theorum, to estimate how big it would need to be to maximize full diamonds. Due to 3/4" board width and 45 degree angles there was some uncertainty here.
- Fixed vertical dimension and constructed the frame. Left horizontal framing pieces uncut. Prayed I would be close enough to make it work as I knew there was 1-2" play in my predictions.
- Cut first 13" piece in bottom right.
- Cut rest of pieces leaning parallel, ended up I believe 16.5" vertical difference drop top of prior board to bottom of next one. I would measure the estimated length of each one, cut the first 45 angle, then cut the board 1" longer then predicted. Then I would shave it down until it fit "perfectly". There is calculation then there is reality, and I bank on reality.
- Similarly cut boards going the opposite direction.
- Carefully put opposing boards in place on top of the first set. Marked edges of dado slots.
- Disassembled and cut dado slots in first set.
- With length established for full diamonds, fixed length of rack and cut horizontal frame boards.
- Cut boards for top left corner to clear stair decline.
- Reassembled and checked fit by inserting second set of boards. Marked exactly 2 needed adjustments.
- Made small top left corner frame piece.
- Disassembled affected pieces to make small corrections.
- Reassembled, with 2nd set boards now in slots, marked them for dados.
- Cut second set dados.
- Fit boards. Everything fit.
Now to countersink all screw holds (3 per joint), sand, clean, finish, and final assembly.