Davis and Oates 

 ^L) = -0(,^ + (v + X(L)^- 2(L)^- Vw^^^) Sin r^L) -(w- X(L)^+ y(L)^- ^w^ ^ ) ) ''°' ^(D 



(80) 



^R) = %^^^ - (v + X(g)0- 2(R)0- v^^^ J sin r^j^^ + (w- X(R)e+ y^^^c^- w^^^ J cos r^^^ 



(81) 



It will be seen from the foregoing that it is convenient to produce the net 

 angle of attack normal to the foil element. Cl^ can be obtained for vertical 

 forces or for forces normal to the foil. It is logical therefore to derive the lift 

 normal to an element and to then resolve this into vertical and horizontal com- 

 ponents to produce the lift and side forces respectively. In this manner any di- 

 hedral angle (r) and roll angle (0) can be taken into account in the computation 

 of forces 



Derivation of Moments 



The moments about the craft centre of gravity are dependent upon the foil 

 element loading distribution and thus the centre of pressure location relative to 

 the e.g. For a surface piercing foil the loading varies with immersion depth 

 and therefore spanwise c.p. has to be derived as a function of the foil immersion 

 depth (h). A linear variation with h is usually sufficiently accurate. Chordwise 

 c.p. movement is usually a negligible percentage of the distance from the foil 

 element c.p. to the craft e.g. and can be assumed fixed at say the foil quarter 

 chord position. 



REGULAR AND RANDOM SEAWAY CALCULATIONS 



Regular Seas 



Simulated regular seas are an important aid to hydrofoil craft design. They 

 are easy to produce and much useful data can be obtained. For example, mag- 

 nification factors can be determined for a realistic range of amplitude for each 

 significant frequency as shown in Figs. 3 to 6. 



The regular seas to be simulated are usually decided by the frequency of 

 encounter range which gives a significant energy input to the craft (Figs. 9 and 

 11). Once the frequency of encounter is known then it is a simple process to 

 derive the other parameters that are necessary for the sinusoidal wave simula- 

 tion. The pertinent expressions for gravity waves are as given below. 



Frequency of Encounter 



co' = 277f' (rad/sec) (1) 



= CO + — co^ (rad/sec). (2) 



g 



630 



