Change the conditions.
See the ship respond.
Two simplified models make invisible forces visible. Try the controls, then read the engineering behind them.
Why some waves cause more rolling
A ship has a natural roll period. In this model it is 12 seconds. Move the wave period towards that value, then compare the response with extra damping.
Paused at peak heel. Select Play motion to animate.
Model assumptions and what the numbers mean
This is the steady response of a linear damped oscillator: amplitude = 0.7 × wave height / √((1 − r²)² + (2ζr)²), with r = natural period / wave period. The illustrative damping ratio ζ changes from 0.12 to 0.35. Added damping represents a stabilizer effect; it does not simulate a particular fin, speed, control system or vessel. The forcing scale is chosen for demonstration. Real seas contain many frequencies, and large-angle roll is nonlinear. These values are not operating limits or predicted cruise comfort.
Read the response as a table
| Wave period | Without extra damping | With extra damping |
|---|
Same ship. Different waterline.
Add cargo, then distribute ballast between the forward and aft tanks. Equal ballast increases draft evenly. Unequal ballast changes trim.
Model assumptions and calculation
A rectangular barge is 200 m long and 32 m wide, with an assumed lightship mass of 18,000 tonnes and seawater density of 1.025 t/m³. Mean draft = total mass / (density × length × beam). Tank centres are 60 m either side of midships. Small-angle trim uses the rectangular waterplane second moment, beam × length³ / 12. This demonstrates longitudinal equilibrium; it does not calculate transverse stability, free-surface effects, strength, load lines or a safe loading condition. Real ship calculations use approved hydrostatic data.
Read the loading condition as a table
Engineering references
The models are original educational demonstrations. For the underlying concepts, see IMO on the role of ballast and the source lists in our roll-stabilization and hull-design guides.