The ellipse is a geometrical entity that does not permit calculation of the perimeter very easily, as with a circle. To calculate the perimeter, one must:
Write the elliptical equation:
Solve Eq 1 for y in terms of x:
Use arclength formula to calculate length for positive portion of Eq 2 and multiply by 2 to account for the negative half of Eq 2:
Using Eq 3 and 4, and a = 7/16 and b = 49/128, we obtain for the perimeter of the inner ellipse for the disk:
Arclength’ = Perimeterellipse = Pe = 2.579952 . 2.58 inches
Use this perimeter (circumference in terms of a circle) to calculate the radius, R, of the circle:
solving Eq 5 for R:
Ri = 0.41062 inches
For aid in drawing, R can be approximated as Ri = 105/256, introducing an error of only 0.11%. This R is the radius of the inner ring of the circle, the outer ring can be found by adding a wall thickness of 1/32 giving Ro = 113/256 .
or you can do it the easy way and give me the dimensions of your ellipse, and I'll calculate the perimeter for you on the cad system...
Mike...
The quality is remembered long after the price is forgotten, so build your teardrop with the best materials...