Slender Body Theory for an Oscillating Ship 



In order to obtain the three dimensional and forward speed effects the 

 terms originating from (3.2) must be added to (3.12). A comparison of these 

 results with Gerritsma's experimental data show a qualitative agreement. The 

 influence of forward speed, as expressed in (3.2), involves F(^, l,). This func- 

 tion assumes positive values at the bow, negative values at the stern. The 

 deviations from the midship behaviour in Gerritsma's results show the same 

 character. 



For the case II the coefficients can be obtained by computation of the re- 

 sults of section 4. If the forward speed is zero M and N become: 



f d^i [ f^(^i,^i)d^i f F(^,0 lny(7,j-f)2 + (^j+0 



c(0 





^'^L C' 



j^ I b(^,)d^i j b(^) {Ho(^J^i-fl) + Yo(#J^i-^|)} 



d^ 



(5.5) 



e'^L 



1 1 



I b(^i)d^, I b(0 Jo(^L 1^1-^1 )d^ 



(5.6) 



Here b(^) is the beam at the point ^. 



The damping coefficient and the part of the added mass that depends on the 

 frequency is calculated and represented in the graph below. For b(x) is taken 



b(x) = 2 cos -^ X and e - 0.2 • 



^2 



-0.004 - 



-0.008 - 



-0.012- 



0.016 



0.012 



0,008 



0.004 





