Subject: Radius of an arch
Name: Kelly
Who are you: Other

OK,

I looked this one up on your site and I can't seem to arrive at the correct answer. From a wrong headed attempt before consulting your site I was able to make an arch .391" high on a length 17.375" long. I am trying to achieve an arc height of .375 on the length of 17.375. So, using the information I reviewed on your site I believe the formula is:

R= (4x height squared + length/2 squared)/4 over 8/h

Thus:
(4 X .375= 1.50 X 1.50 = 2.25 + 8.6875 X 8.6875)/4 divided by 8/h or 77.72/4 = 19.43 this result is divided by 8 X .375 or 19.43/3= 6.48.

A 6.48 radius does not produce an arc 3/8" high 17 3/8" long. My errant attempt to produce this arc radius resulting in a 7/16" high arc was 80 3/32 long. What am I doing wrong? No laughing!

Thanks,

Kelly

Hi Kelly,

In an answer to a question asked by Stace I used this diagram

And developed the expression

In your situation h = 3/8 inches and c = 17 3/8 inches, thus I get

r = [0.375² + (17.375/2)²]/(2 0.375)
= [0.1406 + 75.4727]/0.750
= 100.82 inches

Penny