Slow Drag in a Granular Medium

We have studied the drag force acting on an object moving with low velocity through a granular medium. Although the drag force is a dynamic quantity, its behavior in this regime is dominated by the inhomogeneous distribution of stress in static granular media. We find experimentally that the drag force on a vertical cylinder is linearly dependent on the cylinder diameter, quadratically dependent on the depth of insertion, and independent of velocity. An accompanying analytical calculation based on the static distribution of forces arrives at the same result, demonstrating that the local theory of stress propagation in static granular media can be used to predict this bulk dynamic property.