GM from Rolling Period
Estimate effective GM from an observed natural rolling period using the Weiss/IMO formula - no inclining test required.
Estimated GM
2.548m
Formula, assumptions, and limits
$$GM = \frac{4 \pi^2 (C \cdot B)^2}{g \cdot T^2}$$
Time an unforced full roll cycle (port-starboard-port = one period) at least five times and average. Accurate ±10 % for small heels. Not a substitute for the inclining experiment in the lightship condition.
Symbol legend
| Symbol | Meaning | Unit | Source |
|---|---|---|---|
| $B$ | Ship beam at waterline | m | ship particulars |
| $T$ | Natural rolling period | s | timed observation |
| $C$ | Empirical roll factor (≈0.373) | - | IMO Res A.749(18) |
| $g$ | Gravitational acceleration | m/s² | 9.81 |
| $GM$ | Metacentric height | m | result |
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