Details

Inside a bend, the spheres arrange themselves so as to minimize the compression ratio; they are all either in contact with the outer wall of the tube or in a zigzag pattern parallel to the axis of curvature along the tube centerline.

If the spheres are centered in the tube, the angular separation between successive spheres is

.

When the spheres are all flush with the outer wall of the tubing, the angle is

,

and the compression ratio is

.

For the zigzag pattern, the angle is

,

and the compression ratio is

.

The transition point occurs when

.