From previous calculations, dimensions of interior area:
13' 2.6875"
10' 10.6875"
Round up to nearest inch:
13' 3" or 159 total inches
10' 11" or 131 total inches
Calculate width of 6" rising sides, from 9' walls to 9' 6" center, assuming 5/12 roofing.
6 / (5/12) = 14.4
So, center portion is reduced by 28.8" in width. Since we already rounded up by 0.3", we can take this subtrahend as simply 29":
10' 11" = 131" - 29" = 101"
So the center portion is 159" x 101"
The sides are 14.4 in horizontal width, but we have to include rise, along the 5/12 slope. So we multiply 14.4" by 1 / cos(5/12 * pi / 4) or (the latter being approximately 1.056). (I had to repeate this calculation several times and think a lot, it boggles my mind that the number would be so small.) Thus 14.4 * 1.056 is 15.2064. That just doesn't seem right, that 1" buys us 6" of rise (though it could be true, maybe).
Instead, I'll take a more generous allowance for the rise, and simply add it to the sides, giving 20.4 inches, and then round down to 20 inches
So the ceiling consists of 2 sides 20" by 101", and 1 center portion at 159 x 101".
Total square inches is 16059 + 4040 = 20099 sqin
Total square feet is 20099 / 144 = 139.6 or, rounding up 140.
Each 4x8 panel is 32 sq ft.
If there were no waste (unlikely), it would take 140 / 32 = 4.375 or rounding up 5.
This is less than I expected. It's certainly a lower bound because some will be wasted.
Building guides suggest rounding up is sufficient, so 5 would be minimum. I'd feel safer with 6, or maybe 7.
As reality check, try simply multiplying inches:
159 * 131 = 20829
That's more than what I calculated, I must have made some mistake, but still under 5 panels (23040 sq in).
Leftover could be used on front wall. Front wall is 9'6" (114") by 131 which equals 14934 sqin less opening which is 72 * 80 inches which equals 5760. Net size is 9174 sqin, or 63.7 sqft. 2 32sqft panels just barely cover. Front wall needs some additional vibration resistance because a good portion of wall is devoted to french door, and beyond rattling roof the next worst thing is rattling french door.
For just ceiling, I'd need at least 5 panels but 6 would allow better margin. For doing front, 2 panels but 3 with margin. Doing both, 8 panels should provide plenty of margin. So I'll ask for 8.
13' 2.6875"
10' 10.6875"
Round up to nearest inch:
13' 3" or 159 total inches
10' 11" or 131 total inches
Calculate width of 6" rising sides, from 9' walls to 9' 6" center, assuming 5/12 roofing.
6 / (5/12) = 14.4
So, center portion is reduced by 28.8" in width. Since we already rounded up by 0.3", we can take this subtrahend as simply 29":
10' 11" = 131" - 29" = 101"
So the center portion is 159" x 101"
The sides are 14.4 in horizontal width, but we have to include rise, along the 5/12 slope. So we multiply 14.4" by 1 / cos(5/12 * pi / 4) or (the latter being approximately 1.056). (I had to repeate this calculation several times and think a lot, it boggles my mind that the number would be so small.) Thus 14.4 * 1.056 is 15.2064. That just doesn't seem right, that 1" buys us 6" of rise (though it could be true, maybe).
Instead, I'll take a more generous allowance for the rise, and simply add it to the sides, giving 20.4 inches, and then round down to 20 inches
So the ceiling consists of 2 sides 20" by 101", and 1 center portion at 159 x 101".
Total square inches is 16059 + 4040 = 20099 sqin
Total square feet is 20099 / 144 = 139.6 or, rounding up 140.
Each 4x8 panel is 32 sq ft.
If there were no waste (unlikely), it would take 140 / 32 = 4.375 or rounding up 5.
This is less than I expected. It's certainly a lower bound because some will be wasted.
Building guides suggest rounding up is sufficient, so 5 would be minimum. I'd feel safer with 6, or maybe 7.
As reality check, try simply multiplying inches:
159 * 131 = 20829
That's more than what I calculated, I must have made some mistake, but still under 5 panels (23040 sq in).
Leftover could be used on front wall. Front wall is 9'6" (114") by 131 which equals 14934 sqin less opening which is 72 * 80 inches which equals 5760. Net size is 9174 sqin, or 63.7 sqft. 2 32sqft panels just barely cover. Front wall needs some additional vibration resistance because a good portion of wall is devoted to french door, and beyond rattling roof the next worst thing is rattling french door.
For just ceiling, I'd need at least 5 panels but 6 would allow better margin. For doing front, 2 panels but 3 with margin. Doing both, 8 panels should provide plenty of margin. So I'll ask for 8.
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