Compression Ratio of Spheres in a Curved Tube

bend radius to sphere radius b/s

5

tube radius to sphere radius t/s

1

sphere opacity

0.5

wall opacity

0.5

This Demonstration determines the optimal packing for spheres in a curved tube. Spheres of radius

s

are packed in a tube of radius

t

, where

t≥s

, with a

°

180

bend of radius

b

. We seek the minimum value of the compression ratio. For small ratios

t/s

, the spheres are in contact with the outside wall. For larger

t/s

, optimal compression is attained by arranging the spheres in a zigzag pattern parallel to the axis of curvature along the tube centerline.