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I've been studying your drawing for a few minutes and think it is a good plan for the shape of the space and the number of lights you have. I am concerned that there might be a couple of places between the lights at the sides of the room that won't be lit well. I wonder if doing a mock up of the spacing with zip ties, string, or whatever to suspend the lights would confirm that the spacing is right before cutting the frame pieces.
Good suggestion. rather than hang the lights I decided to do the test using eggs.
8 eggs in rows of 3-2-3: Note the space where the shag carpeting below the eggs shows through the gap.
9 eggs in rectilinear rows of 3-3-3: Note the spaces between eggs are much larger. The overall shape went from rectangular to square.
9 eggs in staggered rows of 3-3-3: Note the shape is now more rectangular and the spaces are small again.
One conclusion to be drawn is that staggered lines of circles provide more even coverage than rectilinear lines of circles. You will never get a true tesselation using circles, there will always be gaps. The young man pointed out that hexagons give full coverage, and they are pretty close to a circular shape.
I decided to skip a smashed egg hexagon test
A second conclusion to be drawn is that adding 2 lights, one at each end, would change the end lighting from an "inny" to an "outie" which might be more useful since I tend to grow plants more in an 'outie" circular shape than an "innie" bowed in shape on one end.
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In the egg layouts there is a fixed distance between the centers of each egg. I had assumed in my drawing that there was 16" between each light center and that the centers of the lights formed equilateral triangles (creating equal distances between all lights.) This was bad geometry. Equilateral triangles form 3 dimensional triangular pyramids and hexagons.
In the layout I have drawn each light was supposed to be 16" away from each other light, but they can't be because of the whole hexagon thing, the distance between lights at the short end of the grid should be the same as on a hexagon with one point in between - so x times the square root of 3 - about 28" between centers, 32" overall. That is a foot more than my posted plan.
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I'll go back and do some careful measurements and recalculate
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The cat closely observed me setting out the eggs for the photos. After I removed the semi-spherical egg toys, he decided to stretch out on the sheepskin (not really shag carpeting )