Transmitting Force through a Tube Filled with Spheres and Spacers

This Demonstration examines a model for force transmitted through a cylindrical tube filled with an arrangement of spheres and cylindrical spacers. We consider the densest packing of spheres with unit diameter in a linear tubing of inner diameter .
Force transmission is opposed by friction proportional to contact force between the tube and spheres.

SNAPSHOTS

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DETAILS

When , the spheres are packed in a straight line. The line joining the centers zigzags as the tube diameter increases until , at which point the spheres are stacked in two columns.
For only spheres, the angle between the axis of the channel and center to center of spheres is:
.
For spheres and spacers, the angle between the axis of the channel and center to center of spheres is:
.
The center-to-center distance of the two spheres is:
.
The compression ratio is:
.
The force input-output model is represented by the equations:
,
.
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