Quarter Circle Arc Ellipse Approximation

In manufacturing and design it is often easier to create ellipse approximations rather than true ellipses. Several methods of creating pseudo-ellipses use circular arcs.

For example, two pairs of quarter circle arcs can be used to make a figure that looks very much like a true ellipse. The size difference between the arcs determines the shape's eccentricity.

 

Denote the length of the half-major axis by a, the half-minor axis by b, the longer arc radius by r₂, and the shorter arc radius by r₁. If you know both a and b, then you can determine r₂ and r₁.

Likewise, if you know r₂ and r₁, you can solve for a and b. All of the necessary formulas are given below, or you can use the convenient calculator above.

Calculating r₂ and r₁ from a and b

Given dimensions a and b, where a ≥ b and a ≤ (1+√2)b, you can find the values of r₂ and r₁ as well as the perimeter and area with the equations

Calculating a and b from r₂ and r₁

Given r₂ and r₁, you can find the values of a and b as well as the perimeter and area with the equations

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