Ogilvie 



DISTANCE FROM LEADING EDGE, FT 



/' /■ 



BODY LOCATION 



^^ 



0.20 



_ -0.20 



FIRST-ORDER THEORY 

 SECOND- ORDER THEORY 

 THIRD- ORDER THEORY 

 EXPERIMENT 



FROUDE NUMBER =0.79i£. = t/b = 0.30 

 (FROM SALVESEN (1969)) 



Fig. (5-7). Third-Order Effect on Wave Length 



Section 1.3. If one did ncft allow for a variation in either K or U, 

 the third approximation would not be valid at infinity, and so one 

 would have great difficulty in predicting wave resistance, since that 

 quantity depends explicitly on the wave height at infinity. 



Figure (5-7) is taken from Salvesen [ 1969] . It shows very 

 clearly the change in wave length that arises in the third-order 

 solution. In fact, it appears in this case that the change of wave 

 length is practically the only third-order effect. This figure also 

 speaks well for Salvesen's experimental technique ! 



5.4. Submerged Body at Low Speed 



Salvesen [ 1969] computed the wave height behind a hydrofoil 

 up to the third approximation, as already mentioned in Section 5.3. 

 Although his third approximation Is not really consistent, he gives 

 what appear to be sufficient arguments to demonstrate that the con- 

 sistent result would not be much different from the results presented 

 In his paper. Figure (5-8), from Salvesen [ 1969] , presents the wave- 

 height computations In a way that shows the relative Importance of the 

 first-, second-, and third-order term. Let the wave amplitude be 

 expressed by the series: 



H ~ H, + H-, + H,. 



/here H^^i = o(Hn) as t -^ 0. 



792 



