273 



V,/(V, + W) = U /(U + W") 

 A A a xe xe a 



(12) 



following from the equality of forces on the pro- 

 peller blade section. 



However, another approach to the problem of 

 experimental determination of the effective wake 

 is also possible based on the data analysis of 

 measured flow velocities and total head pressure 

 immediately ahead of the propeller and behind it. 

 In this case, measurements are taken only with the 

 propeller in operation behind the hull. 



As is known, the circumferential induced velocity 

 at propeller section, Wq , in "open water" is pro- 

 portional to the jump in the total head at the pro- 

 peller disk 



puTW (ce) = H2(Te) - Hi(Te) 



(13) 



It can be shown that this relationship is also 

 valid for the propeller behind the hull, if the 

 variation of the circumferential induced velocity 

 of the hull wake, U9, is negligible within the axial 

 length of the propeller or between the sections 

 where measurements are taken. In this case total 

 head pressures at sections 1 and 2 (see Figure 10) , 

 ahead of the propeller and behind it are, respec- 

 tively, equal to 



Hide) 



f[<"x.)^ 



61 xr 



hzCtS) = p2 + J [("x2^^ "" '"ei ■*■ " 



where 



+ (W,2 +^2''l 



62' 



(14) 



FIGURE 10. Circumferential distribution of velocity 

 components in way of propeller (r = 0.590). 



^1 



X2 



^1 



xej 



U 



+ W 



xe2 a2 

 W„ and W 



= axial flow velocity at 



section 1 

 = axial flow velocity at 



section 2 

 = propeller induced velocity 



components at respective 



sections 



U (X ) = U (X ) + — - 

 xo xe 2 



U - U 



^2 ^1 



U + xAX, 



Xj AX 1 



(18) 



Theoretical investigation results of propeller in- 

 duced velocities and test data make it possible to 

 linearly approximate component variations of the 

 induced velocity, W^{x) , within the limits of the 

 propeller axial length. It is believed that the 

 axial component variation of the wake in this re- 

 gion is small and also obeys the linear law. 



With the above assumptions, in order to determine 

 the design effective velocity, U^g , at section Xq 

 where the condition 



Wa(^o) + -Y 



(15) 



is observed, we obtain the following set of equa- 

 tions : 



tgBi = 



U (X„) + W /2 

 xe a„ 



UT - w„/2 + U. 



tgBi 



(16) 



(17) 



where 



Ax 



hydrodynamic flow angle of a propeller 



blade section 



distance between sections 1 and 2 



AXi = X 



Xi 



distance between section 1 

 and the point of calculation 



In propeller theory it is generally taken that the 

 above condition is met at the propeller disk plane 

 corresponding to the midspan section of the blade, 

 and, in the case of blade rake, corresponding to 

 the midsection of the blade at a relative radius, 

 T = 0.7. 



However the calculation results of variations in 

 the anomalous induced velocity, ^(^(X) , of the pro- 

 peller with the finite axial length indicate that 

 in fact the point must be found upstream of the pro- 

 peller disc plane. 



This conclusion is confirmed by the experimental 

 investigation results of the propeller velocity field 

 in open water. Taking account of these data it is 

 more reasonable to assume the point of calculation, 

 corresponding to condition (15) , to be on the lead- 

 ing edge of the blade. 



