255 



150 nun 100 



N=5 , Lo', 



-"•1 L„' only 



To only 



elliptic 



' h-' 



200mm 150 100 50 



1-326.6 



200imii 150 100 50 

 1-279.91 



// lOOtm 150 100 50 



200mm 150 100 50 



200 mm 150 100 50 



Jtl. 



Cy ,z) = coordinat:e of a point on hull surface U(ship speed) = 2 .OSm/sec 



P" 1 



{y,z)= coordinate of a point on hull surface U(ship speed)=l. 27m/sec 



FIGURE 3. Numerical calculation of pressure change on a hull. 



calculations of pressures and velocities induced by 

 the hull and propeller. Generally, the calculations 

 of induced pressure require less time in comparison 

 with the calculations of induced velocity. Thus, 

 when the present method is used, the time required 

 for numerical calculations can be reduced to a 

 practical value. This method can also be applied 

 for the calculation of propeller-induced surface 

 forces [ishida, (1975)]. 



It is anticipated that the results derived by 

 this method may be worse as the calculation point 

 moves closer to the stern, because, in this method, 

 the assumption of a thin hull is used, propeller 

 boundary conditions are simplified, and the rudder 

 is disregarded. When the actual experimental values 

 are examined, it seems that the anticipation may be 

 correct. However, it is more appropriate to con- 

 sider that the majority of the error is due to the 

 fact that the flow field around the hull is assumed 

 to be inviscid. 



should be effectively recovered. This is due to 

 the fact that the balance of force is a basic prin- 

 ciple of analysis in the method, in which the balance 

 of energy is not given sufficient consideration, 

 and further, because almost no information on the 

 flow field can be given. To cover the fault of the 

 self-propulsion test method, a knowledge of the 

 overall flow field is necessary and the distribution 

 of energy in the flow must be found. In the vicinity 

 of the propeller, however, the flow field is so 

 complicated that experimental measurement and 

 theoretical analysis are difficult. Hence, we might 

 consider, as a practical approximation, an attempt 

 to estimate wake energy recovery by a propeller 

 through an analysis of the wake at a position far 

 from the propeller. 



In the next section, the phenomena of the inter- 

 action in a distant wake are analyzed by the use 

 of Oseen's approximation to determine under what 



4. 



WAKE ENERGY RECOVERY BY A PROPELLER 



TABLE 2 Thrust Deduction Fraction 



A towed hull pulls still water forward, but when 

 the hull is self-propelled, the propeller acceler- 

 ates this forward flow toward the back, and thus, 

 the propeller recovers wake energy. Hence, it is 

 important for the improvement of propulsion effi- 

 ciency of a ship to know how the wake energy can be 

 recovered effectively. The present, self-propulsion 

 test method can give information for the wake energy 

 recovery as a propulsion factor. This method is, 

 however, insufficient to tell us how wake energy 



SHIP 



.166 

 .201 



.140 

 .160 



.109 

 .200 



tp is obtained from pressure measurement 

 tp* is calculated by present method. 



