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The radius of curvature of a circle, or an arc of a circle is the same as the radius of the circle.For a curve (other than a circle) the radius of curvature at a given point is obtained by finding a circular arc that best fits the curve around that point. The radius of that arc is the radius of curvature for the curve at that point.The radius of curvature for a straight line is infinite.
See the following link.
Radius of curvature divided by tube diameter. To get the radius of curvature, imaging the bend in the tube is a segment of a circle, the radius of curvature is the radius of that circle.
The french curve is a set of segments of Euler spirals, also known as clothoids. The curvature of a clothoid varies linearly along its length. If you start at the least curved end of one of the segments (curvature closest to zero) there will be a declining radius of curvature as you go until you reach the end of that segment. The french curve set has several segments with different rates of curvature change.
Usually a straight line that touches a curve at one point. At the point of contact, the tangent is perpendicular to the radius of curvature.