Eq. 11.55, and Eg. 11.59 as 
H\(@) = spy(@)/S, ,(@) 
H(@1,@2) = = 
Sy n(® Sqn(@2) Sy? mm (@1—@2,@1 + @2) 
as a special case of Eq. 11.60. Therefore, 
Sdy (20, 0) if SDyy(2w, 0) 
Hx(@,-@) = (Qw.0) 
syn(w)) ‘ Sean 
SD yn (@1—@2,01 +2) Spy (W1—-2,01 + @2) 
(11.61) 
(11.62) 
(11.63) 
Dalzell performed a series of tests in a towing tank on resistance increase on en- 
countering head waves, with sea states A, B, and C, where the significant wave heights 
are in the ratio of 1:2:4. The results were analyzed and the applicability of these theories 
was made clear. 
Figure 11.3 shows the linear frequency response function [H,(w) = G(o) in 
Dalzell’s expression] obtained by Eq. 11.61 in real and imaginary parts, and Fig. 11.4 
shows the impulse response function A(T) that is the Fourier transform of H(@) in the 
discrete form L,, 
iy{( = Le d(- KAD}, 
At being the sampling time interval. 
oO 
0.1 02 03 04 05 06 07 08 09 10 I. 1.2 13 
\ | 7 
r —— a 2 
POINT ESTIMATES FROM 
CROSS SPECTRUM ANALYSES 
O SEA.STATE A 
+ SEA STATE B 
& SEA STATE C 
TRANSFORM OF 
DISCRETE LINEAR KERNEL 
oO 
0.2 03\0.4 9.5 06 0.7 08 0.9 1.0 1.1 
| | S—OeH—4 
12 13 
\ 
InlG(o )) 
oO 
Fig. 11.3. Linear resistance frequency response. (From Dalzell.°°) 
309 
(11.64) 
