Yamazaki 



H ,„ = (-1)'' iH , „ - H . „ H . 



k'Hk ^ ' k'zHk -i X K ' xHk -\ ^ k' 



B^i "^ ''"^ 3t?j 



'k 'yHk 



3zjj(T7^,u) 

 ^K 'R - ^K ' zR " -y- — ^ "kxR 



B^j LxHKm 3^^ 



^LHKm " ("!)" ^LzHkih ~ :^ r \xHKm ;i^ ^LyHKm ' ^LRm" \zRm' 



3z^(t7j,u) 



3 _/_1\K-lp _ "^ p _ p 



LHKnm ~ ^ ^> '^LzHKnm -, y LxHunm -, LyHKnm' 



" ^ 1 '1 



= Pt 



LRnm LzRnm 7 , , -. LxRnm ' . 



TR " ~ ~TZ TT" TxR 



i (^i)^u 



7 i 





p _ ,_1XK-Ip _ O^^l' '1^ p _ °^^ '^^ p 



^THKm " '^ •^-' TzHKm -^ ;, '^TxHKm p, TyHKm ' 



p - p i4(:v^p '-/ "^ ■ 



^TRm ~ ^TzRm y , . -, "TxUm ' 



"K'Pmn = ^K-xPrnn " ( ^/^') ^k ' 0Pmn • ^LPmn = ^LxPmn " ( ^/'= ) ^L9Pmn ' 



PlPh = PlxPh- (--^Z^) PlSPh ' KTPn= KxxPn- (^/^) ^TePn ' PtP= ^TxP- (^/^ Pj^P • (101) 



By solving simultaneously Eqs. (98), (99) and (100) we get the solutions m*^ (^i-^i), 

 SRmC^i-'-' )> ^^^ gn(^'V). Substituting Eqs. (97), etc., and these solutions into the 

 expressions from Eqs. (82) through (86) we can obtain the forces and moments 

 acting on the hull, rudder, and propeller. Of course the steady components, i.e., 

 the values for m = O, correspond to the mean values, and the unsteady compo- 

 nents, i.e., the values for m ;^ o, represent the vibrating parts. 



Finally, let us consider the velocity induced by 4>p^ . Letting cp = 9(^')(vi - v' ), 

 0pj defined in Eq. (74) is rewritten as 



Sb k ' =1 " ^ ' 



52 



