OK, get ready for that math. Here's the equation (www.woodworking.org):
= (L/2)² + H²
H = Height of arc
L = Length of arc
begin calculating the numerator (top number). To figure out
the length of the radius of the circle I need to draw to obtain
the proper arc, I take the length of the arc and divide it
in half (24/2), leaving me with 12". Then, I have to
square that number (12x12), giving me 144. I take the height
of the arc and multiply that by itself (2x2), giving me 4.
I next have to add those two numbers together (144+4) for
a total of 148.
To calculate the denominator (bottom number), I take the height
and multiply it by 2 to get 4.
Finally, I divide the numerator by the denominator to come
up with 37". That's the radius of the circle I can use
to draw the arc that fits the mark perfectly.
I set a trammel compass to 37" and get to work. I carefully
align my work board and a second board that is the same thickness
as the workpiece. I place the pencil point on the maximum
height mark of the project board, and the other point gets
placed exactly 37" from there, perpendicular to the base
of the arc.
Now, simply draw the arc. It will fit exactly.
the trammel to 37".