156 



THEORY OF SEAKEEPING 



225^ 



180 



135 



I- 90 



45 



— o o— ExperimGn + 



--•- -•-- Coupled Mo+ion 



—n □ — Uncoupled Motion 



2.00 



Fig. 3(c) Comparison of computed and observed motion 

 amplitudes and phases of Series 60, 0.60-block-coefficient 

 model: a wave amplitude, Z,, amplitude of heaving motion, B^ 

 amplitude of pitching angle, a maximum wave slope, 5 phase 

 lag of heaving after pitching motions (from Gerritsma, 1958) 



ZZ5 



■' 180 



35 



90 



45 







E xperlment 

 ' Coupled Motion 

 Uncoupled Motion 



2.00 



Fig. 3 {d) Comparison of computed and observed motion am- 

 plitudes and phases of Series 60, 0.60-block-coefficient model: 

 a wave amplitude, Z„ amplitude of heaving motion, 9.i amplitude 

 of pitching angle, a maximum wave slope, h phase lag of heaving 

 after pitching motions (from Gerritsma, 1958) 



motions and the phase lags of these motions. The phase 

 lags in particular have been found sensitive to computa- 

 tional errors 



It appears that the destroyer form most closely ap- 

 proximates the theoretical linearizing assumptions and 

 there is good agreement between computed and meas- 

 ured data. The agreement is generally satisfactory also 

 in the case of the series 60 model, shown on Fig. 2. In 

 this case, however, a well-defined discrepancy is observed 

 in the amplitude of heaving in the vicinity of synchro- 

 nism. Subsequently, Gerritsma's (1957c and d, 1958; 

 see Section 2-3.21) experiments indicated that the dis- 

 crepancy was caused by underestimating the damping in 

 the heaving motion. It was stated in Chapter 2 that the 

 development of more reliable methods of estimating 

 damping is the most important need in the prediction of 

 ship motions. 



Fig. 2 shows a comparison of the motions of the series 

 60, 0.60 block coefficient model as computed by strip 



theory and as measured in a towing tank. Gerritsma 

 (1958) repeated tests of this model and made motion 

 calculations indicated by equations (2), (4) and (5), 

 using his experimentally determined coefficients. He 

 also made alternate calculations, in which the cross- 

 coupling terms were neglected. The comparison of the 

 measured motions, the motions calculated by equations 

 (2), and those calculated without the cross-coupling terms 

 is shown in Figs. 3(o.), (6), (c), and (rf). A good agree- 

 ment is demonstrated between motions as measured and 

 as calculated with coupling effects. Neglect of coupling 

 results in severe discrepancies in heaving amplitudes and 

 in phase relationships. At low Froude numbers, Ger- 

 ritsma's tests confirmed Fay's (1958) theoretical conclu- 

 sion that, through the couplmg, pitching strongly affects 

 heaving but heaving has a small effect on pitching. At 

 the higher Froude numbers, however, both heaving and 

 pitching are affected. In particular, Fig. 3(d) clearly 



