Fig. 4 The kinds of cross sections for the models (or floating bodies) studied in this paper: (a) rectangular section for Model 1(a) and Model 1(b); (b) Lewis section for Model 2(a) and Model 2(b).

　

Table 1 The principal particulars for the four models (length L = 0.6 m) with d_f = 0.004 m and b_f = 0.02 m.

　

* For the immersed part.

　

3.1 Influence of Oscillating Frequencies ω_w on the Coefficients C_v and C_p

For the cases of β = B/d = 0.95 fin length l_f = L = 0.6 m and fin angles θ_f = 30⁰, 60⁰ and 90⁰, the curves of C_v vs. ω_w and those of curves of C_p vs. ω_w for the Models 2(b) (i.e., the Lewis form with area coefficient σ = 0.785 at draft d = 0.084m, as shown in Fig. 4(b)) obtained from the present experimental method are shown in Fig. 5. Where both C_v and C_p are the sectional added mass coefficients, but the former is obtained from the heave-motion tests and the latter from the pitch-motion tests, while ω_w is the oscillating frequency of the floating body with fins.

From Fig. 5, one finds that all the curves for C_v vs. ω_w and C_p vs. ω_w in the range of ω_w = 10〜40 rad/sec, take the form

C_x = C_o + C₁ω_w + C₂ω_w² + C₃ω_w³ + C₄ω_w⁴ (12)

where C_i (i = 0〜4) are coefficients of curve fitting and the subscript X = V, P. In other words, either C_v or Cp may be obtained from a polynomial of ω_w with the power of four.

For example, the curve of C_v vs. ω_w at fin angle θ_f = 90⁰

as shown in Fig. 5 may be represented by

C_v = 2.17542 - 7.31116ω_w² + 3.80484ω_w² - 8.86969ω_w³ + 7.72327ω_w⁴ (13)

　

Fig. 5 The relationship between the oscillating frequency ω_w and the sectional added mass coefficients C_v and C_p at fin angles θ_f = 30⁰ , 60⁰ and 9⁰ for Model 2(b).

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