# Compression Ratio of Spheres in a Curved Tube

Compression Ratio of Spheres in a Curved Tube

This Demonstration determines the optimal packing for spheres in a curved tube. Spheres of radius are packed in a tube of radius , where , with a bend of radius . We seek the minimum value of the compression ratio. For small ratios , the spheres are in contact with the outside wall. For larger , optimal compression is attained by arranging the spheres in a zigzag pattern parallel to the axis of curvature along the tube centerline.

s

t

t≥s

°

180

b

t/s

t/s