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Computing average radii for ellipse and comparing to a circle of same circumference

Posted: Sun Apr 12, 2020 11:11 am
by dbhguru
HI Ents,

When we wrap a Tape around a trunk, we get the diameter of a circle that has the same circumference as the tape wrap. If perimeter of the trunk does to represent the circumference of a circle, i.e. the trunk isn't circular, what can we say about the diameter from the Tape? Some people think of it as a kind of average diameter. If we were to take caliper measurements of the trunk, working our way around it and averaging the measurements, we'd get an average diameter. How would this compare to the result obtained from using the DTape? The actual average would be smaller than the DTape result for non-circular trunks. But how much smaller? We usually can't say unless the trunk shape follows a predictable path. That is the case for elliptical trunks.

The attachment allows the user to compute an average radius for an ellipse given major and minor axes, with comparison to the circle. If you read the explanation, you can skip all the calculation columns.