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AUTHOR'S BIOGRAPHY
KARASUNO, KEIICHI, Prof. of Hokkaido University (1982- ), Assistant Prof. of Kobe University of Mercantile Marine (1969-1982), Dr. of Engineering (University of Osaka, 1972). He has been engaged in investigations on hydrodynamic forces, motion and control systems in ship maneuvering.
OKANO, SEIJI, Student of the doctor course of Hokkaido University, Graduated in the master course of Hokkaido University (2002).
MIYOSHI, JUN, Student of the doctor course of Hokkaido University, Graduated in the master course of Hokkaido University (2001).
MAEKAWA, KAZUYOSHI, Assistant Prof. of Graduate School of Fisheries Sciences, Hokkaido University, Japan. He received his B.Eng. and M.Eng. degrees in Naval Architecture from Kyushu University, Japan, in 1991 and 1993, respectively. He has engaged in investigations on ship hydrodynamics and maneuverability.
APPENDIX
The total steady hydrodynamic forces on a ship hull XH, YH,and NH are described as follows.
XH =XI+XLv+XDi+XC+X*c+XF
YH =YI+YLv+YDi+YC
NH =NI+NLv+NDi+NC
After each of the following terms, we list the expressions used in the model:
xf =-xa=Lpp/2
x'f =-x'a=xf/Lpp=-xa/Lpp=0.5
dm=(df+da)/2, t=da-df
xt=-1/6・t/dm・Lpp
A.1 Ideal fluid's force due to the stream.
XI =1/2・p・L2pp・dm・m'y'(v・r+ xf・r2)
YI =-1/2・p・L2pp・dm・m'x・r・u
NI =-1/2・p・L2pp・dm・(m'y-m'x)・v・u
-1/2・p・L2pp・dm・m'y・xt・r・u (A1)
A.2 Viscous lift due to the stream by Kutta's Condition.
XLv= 1/2・p・Lpp・dm
・[{df/dm・C'Lf・cosβ・(v+Cev・xf・r)・(v+xf・r)
+da/dm・C'La・cosβ・(v+Cev・xa・r)・(v+xa・r)}
+dm/dm・αL・{df/dm・C'Lf・cosβ・Cev・xf・r
+da/dm・C'La・cosβ・Cev・xa・r}・v]
YLV=-1/2・p・Lpp・dm
・[{df/dm・C'Lf・cosβ・(v+Cev・xf・r)・u
+da/dm・C'La・cosβ・(v+Cev・xa・r)・u}
+dm/dm・αL・{df/dm・C'Lf・cosβ・Cev・xf・r
+da/dm・C'La・cosβ・Cev・xa・r}・u]
NLv=-1/2・p・L2pp・dm
・{x'f・df/dm・C'Lf・cosβ・(v+Cev・xf・r)・u
+x'a・da/dm・C'La・cosβ・(v+Cev・xa・r)・u} (A2)
A.3 Cross flow lift/drag due to the interaction between cross flow vortex wake and bound vortices.
XC=-1/2・p・Lpp・dm・CDLm・C'c
・[{m'y・(v・r+xt・r2)・Lpp・(1-|cosβ|)
+df/dm・C'Lf・cosβ
・(v+Cev・xf・r)・(v+xf・r)
+da/dm・C'La・cosβ
・(v+Cev・xa・r)・(v+xa・r)}
+dm/dm・αL・{df/dm・C'Lf・cosβ・Cev・xf・r
+da/dm・C'La・cosβ・Cev・xa・r}・v]
Yc=-1/2・p・Lpp・dm・CDLc・C'c2
・∫d/dm・(v+x・r)2・(1+p・cos2βx)
・(-sinβx)・dx'
-1/2・P・Lpp・dm・αc・CDLc・C'c2
・2・dm/Lpp/2・(Lpp・r)2
・∫(d/dm)2・(1-|cosβx|)2
・sgn(v+x・r)・dx'
NC=-1/2・p・L2pp・dm・CDLc・C'c2
・∫d/dm・(v+x・r)2・(1+p・cos2βx)
・(-sinβx)・x'・dx'
-1/2・p・L2pp・dm・αc・CDLC・C'c2
・2・dm/Lpp/2・(Lpp・r)2
・∫(d/dm)2・(1-|cosβx|)2
・sgn(v+x・r)・x'・dx'
X*C=1/2・p・Lpp・dm
・{df/dm・CLASf
・(1-|cosβf|)・(v+xf・r)2
-da/dm・CLASa
・(1-|cosβa|)・(v+xa・r)2} (A3)
A.4 Induced drag due to the interaction between the trailing and bound vortices.
XDi =-1/2・p・Lpp・dm
・[df/dm・{m'y・(v+xf・r)
+C'Lf・cosβ・(v+Cev・xf・r)・cosβf
・{CDLf・(Lpp/2/dm)
・{Csv・m'y・(v+Cevc・xf・r)
+C'Lf・cosβ・(v+Cev'xf・r)}
+CDLfc・C'c・|cosβf|・(v+Cevc・xf・r)}
+da/dm・{-m'y・(v+xa・r)
+C'La・cosβ・(v+Cev・xa・r)}・cosβa
・{CDLf・(Lpp/2/dm)
・{-Csv・m'y・(v+Cevc・xa・r)
+C'La・cosβ・(v+Cev・xa・r)}
-CDLfc・C'C・|cosβa|・(v+Cevc・xa・r)}
+dm/dm・{-2・m'y・xf・r
+αL・(df/dm・C'Lf・cosβ・Cev・xf・r
+da/dm・C'La・cosβ・Cev・xa・r)}
・cosβ・Cevc
・{CDLf・(Lpp/2/dm)・{-2・Csv・m'y・xf・r
+αL・(df/dm・C'Lf・cosβ・Cev・xf・r
+da/dm・C'La・cosβ・Cev・xa・r)}
-CDLfc・2・C'c・|cosβ|・xf・r}
YDi =-1/2・p・Lpp・dm
・[df/dm・{m'y・(v+xf・r)
+C'Lf・cosβ・(v+Cev・xf・r)}・(-sinβf)
・{CDLf・(Lpp/2/dm)
・{Csv・m'y・(v+Cevc・xf・r)
+C'Lf・cosβ・(v+Cev・xf・r)}
+CDLfC・C'c・|cosβf|・(v+ Cevc・xf・r)}
+da/dm・{-m'y・(v+xa・r)
+C'La・cosβ・(v+Cev・xa・r)}・(-sinβa)
・{CDLf・(Lpp/2/dm)
・{-Csv・m'y・(v+Cevc・xa・r)+C'La・cosβ・(v+Cev・xa・r)}
-CDLfc・C'c・|cosβa|・(v+Cevc・xa・r)}
+dm/dm・{-2・m'y・xf・r
+aL・(df/dm・C'Lf・cosβ・Cev・xf・r
+da/dm・C'La・cosβ・Cev・xa・r)}
・(-sinβ)・Cevc
・{CDLf・(Lpp/2/dm)・{-2・Csv・m' y・xf・r
+αL・(df/dm・C'Lf・cosβ・Cev・xf・r
+da/dm・CLa・cosβ・Cev・xf・r)}
-CDLfc・2・C'c・|cosβ|・xf・r}]
NDi =-1/2・p・L2pp・dm
・[x'f・df/dm・{m'y・(v+xf・r)
+C'Lf・cosβ・(v+Cev・xf・r)}・(-sinβf)
・{CDLf・(Lpp/2/dm)
・{Csv・m'y・(v+Cevc・xf・r)
+C'Lf・cosβ・(v+Cev・xf・r)}
+CDLfc・C'c・|cosβf|・(v+Cevc・xf・r)}
+x'a・da/dm・{-m'y・(v+xa・r)
+C'La・cosβ・(v+Cev・xa・r)}・(-sinβa)
・{CDLf・(Lpp/2/dm)
・{-Csv・m'y・(v+Cevc・xa・r)
+C'La・cosβ・(v+Cev・xa・r)}
-CDLfc・C'c・|cosβa|・(v+Cevc・xa・r)}] (A4)
A.5 Frictional resistance
XF =-1/2・p・Lpp・dm・C'F・|u|・u (A5)
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