Secondly, the wave height of even 2[m] (corresponding to the unity wave amplitude) is essential. The wave height of 4[m] is absolutely 'destructive' for the turning manoeuvre the surge velocity vx goes below zero (for such a reason, Fig. 9 does not contain the drift angle β in that case). A very interesting issue is that the yaw velocity ωz, is very resistant to the wave second order impact, also in situations of higher wave heights. Notwithstanding some oscillations, the yaw velocity is generally like in calm water  even large alterations in drift angle (contributing also to hull and rudder forces) do not have a higher impact here.
Fig.7 Turning tracks in waves
Fig.8 Surge velocity during turning in waves
Fig.9 Drift angle during turning in waves
Fig.10 Sway velocity during tunring in waves
Fig.11 Yaw velocity during turning in waves
Though the model presented above is not extremely accurate (it reflects in a certain way the status of the ship manoeuvring hydrodynamics science) as relying still upon not fully validated assumptions (hypotheses), it seems to have enough properties to test the wave impact within the stated research objectives.
3. FINAL REMARKS
The regular waves, though justified from a theoretical point of view (being simple to investigate analytically and/or experimentally and enabling gathering input data for irregular wave case) are not however representative for simulating the ship manoeuvring behaviour in waves, at least with regard to the wave second order forces. Two major motives lie under such a conclusion.
The first one is that the ship manoeuvring motion is very sensitive on small wave amplitudes of order even 1[m] if associated with low wave/ship length ratios (λ/L less than e.g. 0.6). Depending of course upon the sea spectrum parameters (significant wave height and modal frequency) and additionally upon the spectrum discretisation while transforming it into harmonic (regular) components, those wave amplitudes and lengths are sometimes hardly to be achieved in, a realworld. A short wave/ship length ratio could be easier reached in a seaway by very long ships. Though the ship analysed in the paper belongs to somewhat shorter ones, and due to her freeboard 〜2[m] (as a rough criterion of manoeuvring motion sensitivity upon the wave amplitude) being subject already to small wave amplitudes, it could be considered a bit not illustrative in realworld conditions. However, a quite similar and true response seems to be experienced if the ship and the wave height are proportionally scaled up to higher dimensions  the case of e.g. a big tanker is obtained.
The second aspect concerns the wave to wind dependence. This relationship (actually there are many formulas more or less widely adopted) exists only in relation to irregular waves e.g. the wind velocity 15[m/s] produces a fully developed random waves of the significant wave height ca. 5 [m]. Thus to have an adequate simulation under combined wind and wave conditions, the only accepted is the ship manoeuvring in irregular waves like in e.g. [13]. However, the readytouse formulations (strictly lookup tables) by [13] for second order forces are of no advantage as they are computed for one particular sea spectrum. The latter is strongly linked to the wave significant height, which in turn is affected by the wind velocity.
The wave first or second order forces and the frequency dependence of added masses and hull derivatives are not the only aspect of the wave action. Of some importance appears the propeller, wake, and rudder performance in waves (as usual with any interactions) a great progress has been made here so far. Moreover, a higher interest is returning lately with reference to modelling the wave forces in restricted waterways (including the bank proximity) e.g. [32].
SYMBOLS
AR rudder area 
m66 yaw added inertia 
B  ship beam 
Mz yaw moment 
cB block coeff. 
n propeller revs 
cD rudder drag coeff. 
P/D pitch ratio 
cL rudder lift coeff. 
vPS slipstream velocity 
cm m22
corrective ratio 
vx surge velocity 
cTh thrust load coeff. 
vy sway velocity 
D propeller drameter 
α rudder incidence angle 
FDR rudder drag force 
β ship drift angle 
FnL Froude number 
βR rudder local drift angle 
FLR rudder lift force 
γWV wave direction 
Fx surge force 
γWVrel wave incidence angle 
Fy sway force 
δ rudder angle 
g gravity acceleration 
ζo wave amplitude 
h wave height 
λ wave length 
H ship height 
λR rudder aspect ratio 
Jz inertia moment 
ρ water density 
k11 m11
ratio 
Ψ ship course 
k22 m22
ratio 
ω wave frequency 
L ship length 
ωE wave encountered freq. 
m ship mass 
ωz yaw velocity 
m11 surge added mass 
Ωm modified relative yaw velocity 
m22 sway added mass 

subscripts: 
'H' hull, 'P'propeller, 'R'rudder 
'WD'wind, 'WV' wave 
'WV1'(wave) first order excitations 
'WV2'(wave) second order excitations 
'FK'(wave) FroudeKrylov component 
'D'(wave) diffraction component 

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AUTHOR'S BIOGRAPHY
Jaroslaw Artysznk, Ph.D. in sea navigation, Assistant Professor at Szczecin Maritime University (Poland), Faculty of Navigation. Multiyear service at sea on big tankers (chief officer rank). Educational experience: lectures and simulator training on ship manoeuvring and handling. Scientific interest: ship manoeuvring mathematical model identification and ship manoeuvring simulation.
