Linearized Potential Flow Theory for ACVs in a Seaway 



and 

 ( 



- I 



2 2 



(x 1 + z' ) dm = I , , 



y y 



where I •„• is the moment of inertia of the ACV in pitch about a late- 

 ral axis through o' . 



When these results are used, the i and k integrals in the 

 above expression vanish (a result not unexpected) and after simplifi- 

 cation the final result for the pitching moment is 



where 



M„ = Id - mh, 

 R G 



1 = 1+ mh 



y y g 



(x cos 9 + (g - z) sin 



is the moment of inertia of the ACV about a lateral axis through the 

 C. G. 



j 

 This expression may be linearized for small values of 9 

 and introducing the perturbation expansions for x , z and 9 , the 

 final result is 



M = - 5meh 9 - flmgh 9 - 6/3mgh 6 



+ « e < mh (ax - q 6 ) - <* I 9 



) G V 001 S 00l' 001 



+ 8a> 



> 1<Tt | mh G ^ ( *101 " £ 001 W - g ^10l]- "XoiJ 



;1<7t | mh G [ 



+ Bate { mh„ <r (x^ , , - z nn , , _) - gL,, 



M | G v Oil 001 010' 5 011 



icrt 



" ate mh o » ( *ooi "no + S ioi 'oio + £ on *ioo> 



'"oiij 



I 



- 5 « e mh Q - z^ 0^ 



/?2 i<rt 

 - P a e 



mh G * 2 »011 *010 



(IV. 2) 



209 



