SCHRIFTENREIHE SCHIFFBAU Festschrift anlässlich des 100 ...

another energy component which is added to the A15-contribution representing direct heeling
moments introduced by beam wave components (Aext). Then the mean, speed independent,
limiting wave height is calculated by:
A0
{ ( ) = 0}
!
H H | A A + A
H := ∈ −
[10]
40min
15diff
To account for the dependency between limiting wave height and the encounter frequency
the function f is determined by regression from simulated results. For this purpose the mean
limiting wave height from the simulations over all speeds is calculated. Then, the difference
between the actual limiting wave height at a certain speed and the mean value is determined.
Fig. 10 shows the results for all cases in our database. Although the results are scattered
significantly the 1:1 and 2:1 resonance conditions are clearly imprinted in the data set. The
regression function, shown in Fig. 10 as green curve is calculated with the following
approach:
f 0 ( ωe
/ ωs
, Ci
)
( 2.8, C ) + C ω
⎧
f ( ωe
/ ωs
, Ci
) = ⎨
⎩ f 0 i 9 ⋅
for
e / ωs
ωe
/ ωs
< 2.8
for ωe
/ ωs
≥ 2.8
[11]
The function f0 is a combination of three sine-functions and reads as follows:
f
0
Fig. 10: Frequency dependency of the limiting wave
( ωe
/ ωs
, Ci
) = C1
⋅ sin(
2πωe
/ ωs
− C2
⋅ π / 2)
C3
⋅ sin(
πωe
/ ωs
− C4
⋅ π / 2)
C5
⋅ sin(
C6πωe
/ ωs
− C7
⋅ π / 2)
+ C8
The regression coefficients C1 through C11 are determined at the following values:
ext
[12]
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