.-w/wtt»w»n>«^uvwTro»u«^T«vwvxwru>nDoun« 



- 1 sin k(x - x ,)]{ 



+ 2iti (cos a* + i sin ctj){e ° °l + l [coa k (x - x o 1 + i) 



- i sin k (x - x C j +1 >] 



- e ° * ^J+l^cos k (x - x 0j ) - 1 sin k^x - x Qj )]} (70) 



the new variable and notation are given in Figure 8. The details for derivation 

 of Equation (70) are given by References 3 and 12. 



The numerical procedure for determining o^ and T is as follows: First, we 

 evaluate the normal derivative of the two-dimensional Green function which 

 enables us to solve Equation (62) for a,. Next, we calculate the normal 

 velocities at segssenta due to a unit vortex located at the center of the 

 section. To eliminate these normal velocities, we distribute O, at each segment 

 of ths section and determine o" 3 with Equation (23). He finally solve for the 

 vortex strength T in Equation (21) using the Kutta condition. 



The computational procedure of forces and moments is as follows: The forces 

 and moments of the bare hull are first computed. This means it is assumed no 

 interference of control planes to the bare hull. To include the interference 

 effect of the bare hull to the control planes, the flow velocity, U, in Figure 2 

 is different from U in Figure 1. A control plane is cut at three different 

 spanwise locations. At the leading edge of each location (or section), U io 

 computed. This velocity is different from the steady forward speedy U, in 

 Figure 1. Two-dimensional forces and moments are computed at each section; and 

 these: are sunused along the spsnwise direction. Finally, these summed forces and 

 moments are added to those of the bare hull. 



22 



