Radius from Chord and Sagitta
Radius from Chord and Sagitta
\[r = \frac{h}{2} + \frac{c^2}{8h}\]
Variables
r = radius (m)
h = sagitta height (m)
c = chord length (m)
Description
What is this formula?
This formula calculates the radius of a circle from the chord length and the sagitta height of a circular segment.
When to use it
Use this formula when the chord and sagitta of a circular arc are known and the radius of the original circle needs to be determined.
Example
If the chord length is 8 m and the sagitta is 1 m:
r = (1/2) + (8²/(8×1)) = 8.5 m
Applications
- Civil engineering
- Arch and bridge construction
- Mechanical fabrication
- Reverse geometry calculations
- CAD and technical drafting
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