Math for a given Radius and width to fin
I just thought this might be interesting to some here.
I’m framing an addition on my friends house and he has three 8′ wide by 8′ high garage doors that have an arch on top and I called the garage door company yesterday and asked them what the radius was for their doors and they told me 12’6″.
Now I know all I have to do is snap a 8′ line on the floor and pull the 12′ 6″ from each end of the 8′ wide opening until they cross each other and then mark that and tack a nail there. Then I can make the radius and see what the height is above the center of the 8′ opening.
For me, I would just want to figure out what the height is to actually mark that on the sheet of plywood that I will be using. Knowing the height makes it easier prepping the plywood when I sheath the openings, I can mark the height to set the plywood.
I was just curious of the math evolved to figure out the height being that we already know the width and the radius but not the height.
For my 8′ wide door and a 12′ 6″ radius I can do this with Construction Master:
12′ 6″ [Diag]
48†[Rise]
[Run] = 142.1126â€
12’ 6†– 142.1126†= 7.887369†or 7-7/8†(Height)
Or you can do this:
C² – A² = B²
12’ 6†² – 48†² = 142.1126â€
12’6†– 142.1126†= 7.887369†or 7-7/8â€
You can check it out to see if it works by knowing the width and height and figuring out the radius.
8’ wide and 7.887369†height.
One way to figure a radius:
(½ width² / height) + (height / 2) = Radius.
48² / 7.887369 = 292.1126 = 7.887369 = 300 / 2= 150†or 12’ 6†(Radius)
Or another way:
(Width² / 8) / (height) + (½ height) = Radius
96² / 8 = 1152 / 7.887369 =146.0563 + 3.943685 = 150†or 12’6†(Radius)
Another way:
96†[Run]
7.887369†[Rise]
[Conv] [Diag] = 150†or 12’6†(Radius)
Replies
Yeah, I came up with 7 7/8".
I cheated - autocad gave me 7.8885"
you gave away my secret too. Autocad it is.