In the general case of two convex bodies, the effective radius can be expressed as follows
where R and R" are the principal radii of curvature for the surfaces i' = 1 and 2, evaluated at points of closest approach distance, and &phi; is the angle between the planes spanned by the circles with smaller curvature radii. When the bodies are non-spherical around the position of closest approach, a torque between the two bodies develops and is given by
where 
The above expressions for two spheres are recovered by setting R = R" = R. The torque vanishes in this case.
The expression for two perpendicularly crossing cylinders is obtained from R = R and R"' &rarr; &infin;. In this case, torque will tend to orient the cylinders perpendicularly for repulsive forces.
For attractive forces, the torque will tend to align them.
These general formulas have been used to evaluate approximate interaction forces between ellipsoids.