Figure 11.6 shows an example of the three—dimensional plot of the modulus of a 
cross bispectrum of wave—wave resistance Spyy(W -@2). Fig. 11.7 shows the plot of the 
real part of the same cross bispectrum. 
|Cp(Q4, 22)I 
Fig. 11.6. lsometric plot of modulus of wave—wave resistance cross bispectrum, 
sea state B, Fn = 0.15. 
(From Dalzell.55) 
The axis (2, 025 used here is Q) = w;—W 2, Q2 =w, +>. Figure 11.8 shows an 
example of the real part of H2(w , 2) obtained by Eq. 11.62, and Fig. 11.9 shows the 
second order impulse response function h2(T1,T2) in discrete form Q jk as 
h2(T1,T2) > Oj 6, —jAt) 6 2 — kAt) (11.65) 
in the form of weighting functions. These values were obtained from the data in sea state 
A. Using these weighting functions L; (Fig. 11.4) and Q;, (Fig. 11.9), obtained from the 
test data for sea state A, the added resistance was calculated by 
P 
Ue P 
Day= Y Lin-j+ Y YL O«gen-jn-wH (11.66) 
j=-m Ui=—P = =P 
for sea states B and C, where the discrete readings 7(n —j),7(n — k) of the time history of 
wave height 7(t) for sea states B and C were used. The added resistance thus calculated 
was compared with the real time history of added resistance in sea states B and C. The 
results for sea state C are shown in Fig. 11.10 as an example. The agreement of this com- 
puted time history with the actually observed time history is surprisingly good. Here, two 
digital filters, as shown in Fig. 11.11, were used to get rid of the effect of the finite length 
of the digitized impulse response functions. 
311 
