Dynamics of Hydrofoils as Applied to Naval Propellers 



These simple relations represent the cavitation index, which appears in the 

 "incipient cavitation diagrams" referred to before, in a precise, analytical way. 

 At the same time, this analytical solution amplifies and corrects the meaning of 

 the cavitation charts both in that it includes the possibility of realizing lift par- 

 tially by camber and partially by incidence, and in that the evaluation of the lift 

 coefficient produced by camber takes into adequate account the influence of the 

 thickness. 



The same relations show the convenience of realizing a certain amount of 

 lift, that is, 10%, as suggested previously, by incidence, and the remaining 

 amount by camber. Introducing these percentages into the above relations, and 

 also eventually neglecting the term K^ t„/c which causes small differences to 

 arise for thicknesses less than 0.05, the same relations can be further simpli- 

 fied; the first, for instance, becomes: 



, ■ ^ = fl+ 1.132 -^+0.238 Ci^j - 1 ."■ " 



The analytical layout also offers the advantage of a direct determination of 

 the minimum chord length required to avoid cavitation, without iterative proc- 

 esses and without further readings of the "charts." U it is desired, the strength 

 requirements may also be introduced directly by means of a specified series of 

 the products t^^ c for each section, or by means of the appropriate values for 

 the root section. 



All this clearly facilitates the preparation of electronic computer programs. 



2.3 Chordwise Load and Pressure Distribution 



An ideal foil, such as that shown in Fig. 8, without thickness and incidence 

 and cambered according to the mean line a = l, has a uniform load distribution 

 all along the chord, a constant negative pressure coefficient on the suction side 



Ap, .' N 



- — = 0.5 c^, + (0.25 c^,)2 ■ \ ' ; 

 and a constant positive pressure coefficient on the face ' ' 



-^= 0.5 C^, - (0.25 C^,)2 "• i 



However, when the foil considered is no longer ideal, but thick, the chord- 

 wise load distribution still remains more or less constant, but the pressure dis- 

 tribution changes considerably. 



Figure 9 shows the pressure distribution on both sides of a section foil at 

 shock free entry conditions, with mean line a = l, thickness ratio 0.18, and cam- 

 ber ratio 0.05515. This figure clearly reveals that at least from a theoretical 

 point of view and as far as cavitation is concerned it is advisable to load the ex- 

 tremities of an actual section foil more heavily, when hydrodynamically possi- 

 ble. In the inlet area this loading is achieved precisely by realizing a given part 



1031 



