We manufacture circular things that have parallel lines across them, evenly spaced. Someone drew a picture here https://i.stack.imgur.com/3LPtM.png though we don't have a chord through the center.
How to sum the lengths of all the parallel chords given radius and the fixed perpendicular distance between chords?
Presently, I use the chord formula based upon perpendicular distance from center: $2({\sqrt(r^2-h^2)}$, h is perpendicular distance from center
In Excel, I have cell for r and cells for h and enough cells containing the chord formula, and finally the sum.
How to get the sum of all these chords given r, h?
Additional point: We do not ever have a chord passing through the center. In other words, there are always and even number of chords. This defines the position of the first chord.
Example:
r = 30 (it's meters, by the way, these things are huge)
h = 1
So the first chord from center is $h/2 = 0.5$ perpendicularly from center. Its length is: $2({\sqrt(30^2-0.5^2)} = 29.17$
The next chord is h further away from center, ie $0.5 + h = 1.5$ Its length: $2({\sqrt(30^2-1.5^2)} = 28.95$
Follow up question: what is the Excel formula (if it even possible with normal Excel formulas)?
Thanks so much for reading even if you do not reply!
Wish I could add tags: sum parallel chords, but not allowed.
Questions here that sound similar but do not fit:
Sum and average length of chords
https://www.desmos.com/calculator/lejeoyuo81which can compute summations directly. – mrtechtroid Jan 17 '23 at 09:07