Math CentralQuandaries & Queries


Question from Craige:

I need to calculate the bending radius of 2" wide steel to achieve given inside and outside arc lengths


The relationship involving the arc length a the radius of the circle r and the angle θ measured in radians is

a = r θ.

I let the inside radius be r, the length of the inside arc be a1 and the length of the outside arc be a2. Then for the inside arc

a1 = r θ

and for the outside arc

a2 = (r + 2) θ.

Since the angle θ is the same for both arcs

a1/r = a2/(r + 2)

Solving for r gives

r = 2a1/(a2 - a1)


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