Ogitvie 



nonhomogeneous part depends on 4>o. which we have not obtained 

 explicitly. (The right-hand side of (2-46) finally has an effect.) 

 Also, spanwise effects occur in the body boundary condition, (2-47), 

 for the first time. Therefore I shall put this problem to rest at this 

 point. Table 2-2 shows the sequence of steps that we have followed 

 in this problem. 



TABLE 2-2 

 HIGH- ASPECT -RATIO WING -- SUMMARY 



Terms 



Far-Field Near-Field 

 Expansion Expansion 



Quantity Determined 

 by Matching 



<j>0= Ux 



*. $. 



4>o+ <(>| + <|>2 



1 Condition at infinity for 

 4>Q problem 



2 Vorticity, ^1(2), in far 

 field 



3 Downwash velocity (condi- 

 tion at infinity for $1 

 problem) 



4 Correction to vorticity in 

 far field; densities of 

 vertical, horizontal 

 dlpoles in far field 



One point in particular should be noted: The near-field 

 problem was not linearized. If one can predict the flow around the 

 two-dimensional fornns which appear in the near -field problem, one 

 is not limited to consideration of, say, thin wings. All that is 

 necessary is that the spanwise length be much greater than the 

 dimensions in the two-dimensional problems and that there be gradual 

 change in the body and flow geometry in the spanwise direction. 

 Needless to say, the latter condition is usually violated at the wing 

 tips, and so the analysis breaks down there. It may be hoped that 

 the prediction of important physical quantities is not affected too 

 seriously thereby, but higher and higher approximations certainly 

 cannot be found until the extra singularities at the tips are removed 

 somehow. 



708 



