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There is no such expression. The normal to a surface, at a given point is the radius of curvature of the surface, at that point.
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.
It is the distance from the centre to all points on the surface of a sphere with a radius of 1 foot.
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.
Because, to allow for the curvature of the spherical surface, each angle must be slightly larger than its plane-surface equivalent.