Wavemaking Resistanae of Ships with Transom Stern 



irU J.B/2 J.ff Jo itU-ksec^e-ijisece) 



p*l /%B/fe ^» ^<D 2« it(x COS ^- y sin 5) 



= dxRe^ dy\ deV dt ^^^^^ . ^ — . + J 



Jn ttUJ„/„ ' J _ J_ t-ksec^0 - iusec e 



■E/2 *^-v *^0 t - ksec - ifi sec 9 



.B/2 ^TT ^00 



= r dxRe^r dyC deC dtr-i+ — '-^>^r^Q — -i 



Jq kTrUJ_g/2 ' J.^ Jq L t-ksec^e- iixsecG J 



^ it(xco8 ^- y 9in9y ^ 

 X e + J 



&/2^ /%X| />ff/2 ^OD 



= - \ dx T^ \ dy , ' ^ ^ + \ T^ dx lim \ dO \ dt 

 • Jq ^J-B/2 V^2+P Jo ^^^ y,-*ooJ.,r/2 Jo 



- iirx cos 9.1. t a\ 



4e sin (tyi sin 6) . - 



sin e(t - ksec^e - ifi sec 6) 





+ J 



(49) 



Note that t= is not a singularity because of the zero of 



sin {t(X| cos 6 - y sin 6)} in the numerator of the real integrand. 



The integrand J is defined as follows: 



J = Re ^ \ dy de \ ^^-^-^^ 2 ^ 



^U J.B/2 J.ir Jq it(t - k sec'^G - iji sec 9) 



= «^wX ^^X'l^J, H^-^^tr 



1 ) , -ity sin 8 , ity sin 3, 



t - ksec^e - i|isec 9 



+ e 



. „ °"x ,, . r'^d9cos9 ikfsec^esin© 



= Re — =7 lim 4Tr\ e 



^^ B^oo Jo Ik sin 



= Zo-^TrAk^U) (50) 



585 



