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5.2 Predictions of Ship Maneuvering Motion
In this paper, the mathematical maneuvering model with roll [10] is following in a method of MMG model for predictions of ship-steering motion. Furthermore, concerning the stationary hydrodynamic forces acting on a ship hull, the component-type mathematical model is adopted as follows.
(m+mx)・du/dt-m(r・v+xG・r2-zG・r・p)
=XH+XP+XR
(m+my)・dv/dt+(m・XG+my・xl)・dr/dt
-(m・zG+my・zl)・dp/dt+m・r・u
=YH+YR
(IZZ+m・x2G+JZZ+my・x2t)・dr/dt
+(m・xG+my・xt)・dv/dt-(m・xG・zG
+my・xt・zt)・dp/dt+m・xG・r・u
=NH+NR
(IXX+m・z2G+JZZ+my・z2t)・dp/dt-(m・zG+my・zt)・dv/dt-(m・zG・xG+my・zt・xt)・dr/dt
-m・zG・r・u
=KH+KR (5)
where XH, YH, NH, and KH are the stationary hydro-dynamic forces acting on a ship hull at midship and water level(see Appendix and replace v with v-zG・p).
Hydrodynamic hull forces (XH, YH, NH, KH);
The component-type mathematical maneuvering model is adopted in this paper as follows.
XH =XI+XLV+XDi+XC+XC*+XF
YH =YI+YLV+YDi+YC
NH =NI+NLV+NDi+NC
KH =KI+KLV+KDi+KC
where
KI=-zI・YI-W・GM・sinφ
KLV=-1/2・dm・YLv
KDi=-dm・YDi
KC=-dm・YC-3/4・n・(IZZ+JZZ)・|P|・P
W :displacement
zI :the vertical position of the added mass mx from water surface.(≈da/2)
φ :heel angle
n :extinction coefficient
Propeller and rudder hydrodynamic forces (XP, XR, YR, NR, KR);
XP=-(1-t)・p・Kt・n2p・D4P
XR=-(1-tR)・FN・sinδ
YR=-(1+aH)・FN・cosδ
NR=-(xR+aH・xH)・YR
KR=-(da-hR/2)・YR (7)
where
FN=1/2・p・fa・AR・U2R・sinαR
UR2={uR・cosδ-(γ0・v+γr・xa・r)・sinδ}2
+{uR・sinδ・+(γ0・v+γr・xa・r)・cosδ}2
αR=tan-1[{uR・sinδ+(γ0・v+γr・xa・r)・cosδ}/{uR・cosδ-(γ0・v+γr・xa・r)・sinδ}]
+(1-η)・(ε・uP)2
ε=(1-wR)/(1-w)
η=(DP/hR)
uP =(1-w)・u
kR ≒0.6
γ0 =0.4〜0.5
γr =0.72〜1.0
T =KT・(J)・p・n2・DP4
J =uP/(nDP)
Fig. 10. |
Estimated and analyzed hydrodynamic forces of the VLCC "Esso Osaka". |
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