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The roll motion spectrum shown in the Figures 6.15 to 6.17 is the response to a particular wave spectrum having specific peak frequency and significant wave heights discussed in section 6.6.3.

The roll motion responses in Figure 6.15, unlike the heave and pitch motions, do not mimic the corresponding wave spectrum. The majority of oscillations are concentrated around the natural roll frequency regardless of the sea conditions. The magnitude of

150 every test condition is different and it is obvious that when the wave peak frequency is getting close to the natural roll frequency, the magnitude is escalated. The effect of higher significant wave height is also apparent on escalation of the magnitude.

Figure ‎6.15 Power spectra density in a following sea at three different peak

frequencies and three different significant wave heights

The top right frame of Figure 6.15 has least energy with reference to its magnitude scale, and it lies in a fact that roll amplitude was negligible at this particular frequency and Hs. Similar patterns are identified with spectral analysis of roll motions in quartering seas depicted in Figure 6.16. At lower frequencies, the model ship is capable of detecting the responses around the roll natural frequency as well as the frequency range swept over the wave spectrum. However, towards the higher frequencies, detection of the frequencies far-off from the roll natural frequency is damped-out.

Figure ‎6.16 Power spectra density in a quartering sea at three different peak

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Figure ‎6.17 Power spectra density in a beam sea at three different peak frequencies

and three different significant wave heights

At the lower peak frequency of the wave spectrum the response of the roll motions are more random (left column), as shown in Figure 6.17. These are the similar conditions illustrated in Figure 6.12. These conditions improve as the peak frequency of the wave grows higher and the encountered wave length is much longer with respect to the ship’s model breadth.

Results of the Tests

6.7

The figures presented in this section correspond to the motion responses of the ship. The x-axis presents the sea conditions (defined as ‘low’, ‘medium’ and ‘high’ for the three different peak frequencies utilised in generating the wave spectrum) and the y-axis is estimated frequency peak in Hz. The results are presented for the three values of HS and these are defined as ‘small’, ‘medium’ and ‘large’ in line with the three different frequencies. The magnitude scales vary for presentation purposes.

The estimated frequency peak of the wave and the three motions considered in this experiment are shown in Figure 6.18. Two sets of plots in following and quartering seas are compared against each other to illustrate the similarities of the motion behaviours. The response of heave and pitch motions are strongly coupled and closely follow the frequency peak of waves in different sea conditions. However, the roll motion maintains the response close to its natural frequency.

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Figure ‎6.18 Comparison of frequency peaks for each sea condition tested in a following

and quartering sea at small, medium and large HS

A similar trend can be observed in all frames of Figure 6.18 as the value of HS is increasing. However, the coupling effect of heave and pitch under low sea conditions is not as strong as in high sea conditions and it appears to be less significant at a medium HS value. The roll response remains pretty constant for every sea condition and HS values tested.

The results are slightly different in beam seas which are shown in Figure 6.19. The heave motions are not coupled with pitch motions anymore and the frequency peaks follow that of the roll motions. There is not a noticeable trend in the frequency peaks of pitch motions.

In the following discussions, the main emphasis is on the effect of the estimated frequency peak and power peak on the motion responses, as well as any other notable trends observed in the response curves.

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Figure ‎6.19 The frequency peaks for each sea condition tested in a beam sea at small,

medium and large HS

6.7.1 Motion Responses in a Following Sea

The energy of the irregular wave has a dissimilar effect on each of the ship’s motions and the impacts vary in different sea conditions. Figure 6.20 shows the energy of waves generated by the wave maker at Newcastle towing tank over a range of peak frequency and significant wave height. The energy diminishes towards the higher frequency over the X-axis and reduces by smaller significant wave heights.

Figure ‎6.20 Wave energy generated by the wave maker at Newcastle towing tank

The variations in heave and pitch magnitudes shown in Figure 6.21 are in line with changes in wave magnitudes. However, roll magnitude does not display a sharp refraction and follows a steady trend with a slight decrease at high frequencies.

154 In medium and large Hs the rate of roll motion response increases at the higher sea state, where the range of wave peak frequencies is closer to the natural roll frequency and it reaches its maximum at the large HS value. It is a clear indication of synchronous rolling. The coupling effects of heave and pitch motions are obvious in all sea conditions and at every HS value tested. Their magnitudes remain high except at high frequencies.

Figure ‎6.21 Comparison of energy magnitudes for each sea condition tested in a

following sea at different HS

The y-axis presents the PSD and the unit is measured as [m2s/rad] for wave and heave motions whilst it is [deg2 s/rad] for pitch and roll motions. The second scale on the right is for the roll and pitch motions.