How does a ship move in waves? When a ship is hit by waves, the incident wave is scattered by the hull (the diffraction wave), and the hull's own motions (sway, heave and roll) generate outgoing waves (the radiation waves). The resulting pressures act on the hull as forces. A ship's seakeeping performance is evaluated by solving this coupling between hydrodynamic forces and motions.

The interactive teaching tool below uses a 2-D Boundary Element Method (BEM, Green-function method) to compute the ship motions and the wave field in real time, right in your browser. Change the hull section or the wave conditions and watch how the waves and motions respond.

What is happening

• The incident wave meets the hull; part of it is reflected (back to the right) and part is transmitted (through to the left).
• The hull oscillates under the wave forces, and those motions in turn radiate waves.
• In linear theory energy is conserved, so the transmission and reflection coefficients satisfy |T|² + |R|² = 1. The tool's "accuracy check" shows whether such physical identities hold.

Try it

• Hull shape: drag the control points in the section editor, or use the presets and sliders (beam-draft ratio, area coefficient).
• Wave conditions: change the nondimensional wavenumber and the wave amplitude. The amplitude is restricted to the small range where linear theory is valid.
• Display: toggle the incident, diffraction and radiation waves to study each contribution.