Radius of an arc
Formulas for determining the radius of an arc, or "eyebrow"
I would like to know the formula for determining the radius of an arc, or "eyebrow", in cabinetmakers terms. I know it starts with a line connecting two points of the arc and the amount of "rise" within that segment.
I looked for this formula for a long time and found it in a book called "Pocket Ref" by Thomas J. Glover.
Here is the formula if the line connecting the to points is "A" and the distance from a to the edge of the circle is b (at a 90 degree angle to a)
then (^2 equals "squared"):
or half a squared plus b squared divided by 2 times b.
I think the degrees are (atan(a/2)/(r-b))*2
I just draw the horizontal line and then the rise from the midpoint, create a 3 point arc, then ask ACAD what the radius is.
Here is another way:
Square 1/2 of span.
Divide by rise.
Divide by 2.
Rise squared plus half the width squared divided by twice the rise.
The comments below were added after this Forum discussion was archived as a Knowledge Base article (add your comment).
Comment from contributor A:
C= chord length
M= distance from chord to edge of circle
C squared divided by 8M + M/2 = R
Comment from contributor B:
To calculate radius of a circle where:
r = radius and is unknown
C = chord length (a line the crosses any two points on a circle)
B = length of perpendicular line from midpoint of chord to edge of circle
r=((4*Bsquared + Csquared)/8B)
Would you like to add information to this article?
Interested in writing or submitting an article?
Have a question about this article?
Have you reviewed the related Knowledge Base areas below?
KnowledgeBase: Architectural Millwork
KnowledgeBase: Architectural Millwork: Custom Millwork
KnowledgeBase: Business: Project Management
KnowledgeBase: Furniture: Custom Furniture
KnowledgeBase: Solid Wood Machining
KnowledgeBase: Woodworking Miscellaneous
KnowledgeBase: Woodworking Miscellaneous: Bending Wood
KnowledgeBase: Knowledge Base
All rights reserved. No part of this publication may be reproduced in
any manner without permission of the Editor.
Review WOODWEB's Copyright Policy.
The editors, writers, and staff at WOODWEB try to promote safe practices.
What is safe for one woodworker under certain conditions may not be safe
for others in different circumstances. Readers should undertake the use
of materials and methods discussed at WOODWEB after considerate evaluation,
and at their own risk.
335 Bedell Road
Montrose, PA 18801
Copyright © 1996-2017 - WOODWEB ® Inc.