Sphere Packing — Random Close Packing & Jamming

Identical spheres poured randomly and settled reach φ_RCP ≈ 0.637 (Bernal 1960). At this density, each sphere is mechanically trapped ("jammed").

φ = (N·(4π/3)r³) / V

Below φ_RCP: fluid-like, spheres rattle. Above: rigid, force chains percolate. The jamming transition is a geometric phase transition.

Crystal FCC/HCP reaches φ_FCC = π/(3√2) ≈ 0.7405 (Kepler conjecture, proved Hales 1998).

φ_RCP ≈ 0.637
φ_FCC = π/3√2 ≈ 0.7405

Particle count N: 80 Gravity g: 0.5 Restitution e: 0.3

φ = 0.000
Status: settling

Packing fraction φ

0RCP 0.637FCC 0.74