3.2 Influence of Fin Length lf on the Coefficients Cv and Cp
For the cases of fin angle θf = 60o, Fig. 6(a) shows the relationship between the oscillating frequency ωw and the added mass coefficient Cv for Model 1(a) and (b) (i.e., rectangular cross section with area coefficient σ = 1.0) with fin length lf = 0.5L = 0.3 m and lf = L = 0.6 m, while Fig. 6(b) shows the relationship between the oscillating frequency ωw and the added mass coefficients and Cp for Model 2(a) and (b) (i.e., Lewis section with area coefficient σ = 0.785 at draft d = 0.084 m) with fin length lf = 0.5L = 0.3 m and lf = L = 0.6 m. For convenience of comparison, the curves representing the relationships between ωw and Cv (and Cp) for the floating bodies without fin (with fin lengths lf = 0) are also shown in Figs. 6(a) and (b), respectively. Comparing with the model without fin (i.e., lf = 0), from Fig. 6(a) one sees that the values of Cv for Model 1(a) (with lf = 0.5L) and those for Model 1(b) (with lf = L) increase about 36% and 61%, respectively. From Fig. 6(b), one sees that the influence of fin length lf on the values of Cv for the Models 2(a) and 2(b) (with Lewis sections) is similar to that for the Models 1 (a) and 1(b) (with rectangular sections). It is seen (Fig. 6(b)) that the values of Cv for Model 2(a) (with lf = 0.5L) and those for Model 2(b) (with lf = L) are greater than the values of Cv for the model without fin about 36% and 64%, respectively. However, the influence of fin length lf on the values of Cp are much smaller than that on the values of Cv. From Fig. 6(b) one sees that the values of Cp for Model 2(a) (with lf = 0.5L) and those for Model 2(b) (with lf = L) are only greater than the values of Cp for the model without fin about 18% and 25% respectively. In other words, the influence of fin length lf on the heave motion is much than that on the pitch motion for the floating bodies with Lewis sections. It is noted that all the foregoing and the subsequent percentages (%) are determined with respect to the corresponding values of Cv (and/or Cp) for the associated floating bodies (or models) "without" fins (i.e., lf = θf = 0).
3.3 Influence of Fin Angle θf on the Coefficients Cv and Cp
For the cases of fin length lf= 0.5L =0.3 m and beam/draft ratio β = b/d = 0.95, the influence of fin angle θf on the added mass coefficients Cv and Cp are shown in Fig. 7(a) for Model 1(a) (with rectangular cross sections) and in Fig. 7(b) for Model 2(a) (with Lewis-form sections). The solid curve shown m Fig. 7(a) is for the floating body "without" fin (i.e.. lf = θf = 0). From Fig. 7(a) one sees that the values of Cv for Model 1(a) with fin angle θf = 30o and those with fin angle θf = 90o are respectively larger than the values of Cv for Model 1(a) without fin about 30% and 38%. The influence of fin angle θf on the values of Cv for Model 2(a) (with Lewis-form sections) is similar to that for Model 1(a) (with rectangular cross sections), but, for Model 2(a), the influence of fin angle θf on the values of added mass coefficients obtained from pitch-motion tests, Cp, is much smaller than the influence of fin angleθf on the those obtained from heave-motion tests, Cv as one may see from Fig. 7(b). It is seen that the values of Cp for Model 2(a) with fin angle θf = 30o and those with fin angle θf = 90o are respectively larger than the values of Cp for Model 2(a) without fin about 12% and 20%.
