Stone-skipping Simulation

Model and simulate the motion of a skipping stone.

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Question

What launch and impact conditions make a stone skip repeatedly across water?

The MATLAB force model produces a shallow sequence of skips whose height and spacing decrease as fluid drag removes speed.
The MATLAB force model produces a shallow sequence of skips whose height and spacing decrease as fluid drag removes speed.

Goals

  • Build a motion model with gravity in air and fluid forces during water contact.
  • Simulate the trajectory and measure how launch conditions change the number of skips.

Method

Integrate one motion model that changes its forces as the stone enters and leaves the water.

  • Represent the stone as a shallow tilted segment with mass, length, position, and velocity.
  • Apply gravity above the surface; during partial immersion, compute lift and drag from speed, submerged length, and the two fluid coefficients.
  • Advance the state in short Euler steps, record each water contact, and compare trajectories for different launches.

Paper and MATLAB model

Paper

The physics of stone skipping

Lyderic Bocquet · arXiv:physics/0210015

Read on arXiv ↗

A simplified physical model for water impact, repeated bounces, and the conditions behind a successful throw.

MATLAB code StoneSkipping.m

The original Euler-step simulation behind this project, with clarified comments and unchanged equations.

Download .m ↓ 
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Try an example

Stone Skipping

Source code ↗ Open full screen ↗

A simple old-style game based on the attached MATLAB model, with gravity in air and speed-dependent lift and drag during water contact.

Controls: Press Enter or click to begin. Drag backward from the stone and release; Enter uses the MATLAB default shot. Use Space to pause, R to reset, or Esc for the title.