When a ship rolls among irregular waves, the effective coefficient of resistance which is given in the form
α
c=α+4/3β/
Tcθ
0varies according to the relative angle θ
0 and the period 2
Tc of the resultant rolling composed of free and forced motions. Hence the component free and forced rollings have variable amplitudes in each swing, different from those when they take place independently of each other. Taking account of this fact there was proposed a new method of calculating the so-called criterion amplitude, in which the coefficients of resistance α and β were assumed to be constant. For four actual ships the criterion amplitudes were calculated for various values of period ratio
Ts/
Tw and compared with those obtained by Mr. R. E. Froude, showing about 10 per cent. difference for ships of moderate resistance.
Next the practical maximum amplitude θ
fmax which a single wave can give to a ship after an increasing swing was calculated for particular resistance to rolling, assuming the ship to be initially rolling in her natural period to the same amplitude as that of the forced rolling due to the wave under consideration. It was found that for a ship of moderate resistance the value of θ
fmax is nearly expressed by the sum of the forced angle and the free angle after one swing in cases where
Tw/
Ts is less than 0.8 and greater than 1.2, and that the value θ
fmax divided by the maximum effective wave slope becomes greatest when
Tw/
Ts is a little greater than unity according to the degree of resistance.
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