## Historical perspective Raholas criterion

Rahola (1939) analysed statistically accidents caused by defects in stability and included the results in recommendations for 'safe stability'. These recommendations are based on the criterion of a degree of dynamic stability up to 40° angle of heel. The dynamic stability can be represented by the area below the stability moment curve, i.e. as the integral of the stability moment over the range of inclination (Fig. A.1). (This quantity equals the mechanical work done, or energy used, in heeling the ship.) If the righting arm h is considered instead of the stability moment MSt, the area below the righting arm curve represents the dynamical lever e. This distance e is identical with the increase in the vertical distance between form and mass centres of gravity in heeled positions (Fig. A.2). e can be found by numerically evaluating the righting arm curve.

Rahola's investigation resulted in the standard requirements:

righting lever for 20° heel: h20° > 0.14 m righting lever for 30° heel: h30° > 0.20 m heel angle of maximum righting lever: 0max > 35°

Other righting levers are seen as equivalent if

for 0max > 40°, where 0max is the upper limit of integration (Fig. A.3).

Rahola's criterion disregards important characteristics (e.g. seakeeping behaviour) and was derived for small cargo ships, especially coasters of a type which prevailed in the 1930s in the Baltic Sea. Nevertheless, Rahola's criterion became and still is widely popular with statutory bodies. The Germanischer

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