Angle of repose
Granular piles on a coarse grid relax by toppling excess height to neighbors until local slopes fall below μ = tan α, the angle of repose for a Coulomb-style friction cartoon. Each column stores continuous height; one grain is a unit increment. Relaxation is iterative, similar to cellular automaton sandpile rules used in hazard and animation demos. The green dashed line is a geometric guide for the chosen μ, not a measured output from a continuum PDE.
Who it's for: Introductory friction, geomorphology intuition, and discrete avalanche models.
Key terms
- Angle of repose
- Sandpile
- Coulomb friction
- Avalanche
- Lattice model
How it works
Discrete sandpile on a 1D lattice: each column stores height. After a grain lands, sand avalanches until no neighbor exceeds μ = tan α (angle of repose). The green dashed line shows the ideal slope for the current μ.
Frequently asked questions
- Is this BCRE or Saint-Venant shallow granular flow?
- No. It is a minimal 1D lattice toy for slope thresholds, not a continuum PDE solver.
- Why 1D columns instead of a 2D heap?
- A 1D slice keeps the control simple while still showing relaxation to a slope threshold; extend mentally to axisymmetric heaps.
More from Classical Mechanics
Other simulators in this category — or see all 84.
Cart & Inverted Pendulum
Horizontal force on a cart with a hinged rod: coupled (M+m)ẍ and mL²θ̈ integrated for manual balancing.
Woodpecker Toy
Stick–slip sleeve on a rod: static hold, spring loading, then kinetic slip — a qualitative hop cycle.
Vortex Ring (Smoke Ring)
Self-propelling toroidal vortex shown as a 2D cross-section: counter-rotating Lamb–Oseen pair drifts at V_self ≈ Γ/(4πa).
Rayleigh–Taylor Instability
Heavy fluid above light: Fourier modes grow as exp(σt) with σ = √(A g k); mushrooming fingers reach down.
Faraday Waves
Vertical parametric drive of a thin liquid layer: Mathieu sub-harmonic instability locks stripes, squares or hexagons.
Airfoil Streamlines (Joukowski)
Potential flow over a Joukowski airfoil: stream-function bands with the Kutta condition fixing circulation.