How To Calculate Segmented Radius For Building Arches
Calculating the Radius of Segmented Arches: The Magic Arch Formula
The video demonstrates a formula, referred to as the "magic arch formula," for calculating the radius of segmented arches. This formula is explained through three practical examples.
Example 1
The first example involves a 3-foot wide opening. Half the width is calculated as 18 inches, which is then converted to 1.5 feet. A height of 1 foot is added, resulting in a total of 2.5 feet.
The magic arch formula is: height squared + (half width squared) / (height x 2)
Following this formula:
The height squared is calculated as 12 x 12 = 144.
The half width squared is calculated as 1.5 x 1.5 = 2.25.
These two numbers are added together, resulting in 146.25.
Finally, this number is divided by the height times two (2.5 x 2 = 5), yielding 29.25.
It is suggested that reversing the numbers (dividing 5 by 146.25) might be easier on a calculator. This calculation gives 19.5 inches, which is the radius of the arch.
Example 2
The second example uses a 49-inch opening. Half the width is found to be 24.5 inches. In this case, 3 inches are subtracted from the height to get a measurement of 6 inches for the arch itself.
Using the same formula:
The height squared is calculated as 6 x 6 = 36.
The half width squared is calculated as 24.5 x 24.5 = 600.25
These two numbers are added together, resulting in 636.25
This number is then divided by the height times two (6 x 2 = 12), giving 53.02 inches
An additional 3 inches are added to this number to account for the space needed to construct the arch using plywood and two-by-fours. The final radius is therefore 56.02 inches
Example 3
The third example involves a 9-foot wide opening and a 7-foot, 5-inch tall opening. Half the width is determined to be 54 inches, and 5 inches are subtracted from the height, leaving 14 inches for the arch.
Again, applying the formula:
The height squared is calculated as 14 x 14 = 196
The half width squared is calculated as 54 x 54 = 2916
These two numbers are added together to get 3112
Finally, this number is divided by the height times two (14 x 2 = 28) which results in 111.14 inches
Conclusion:
The video concludes by emphasizing the usefulness of the magic arch formula as a tool for calculating the radius of segmented arches. Back To Arch Framing
