Illusions of Curvature

One often attempts to assess the radius of curvature of an object by eye.  This leads to huge degrees of error. 

Fig. 65 – A curvature illusion.  All three curves have the same radius of curvature. 

In the above figure, all three arcs have the same radius of curvature, though it does not appear to be the case.  They are all parts of the same circle.  Yet it appears as if the smallest arc is much “flatter” than the rest, or that its radius of curvature is larger. 

The estimation of the curvature of an arc is determined by the fraction of the whole circle visible to the observer.  As the arc gets smaller, one tends to guess at a radius which is larger.