256 



L ship 

 Y- l-61.3 I mm 



T ship 



50 ■ 



150 imr 100 

 Cy,z)= coordinate of a point on hull surface U{ship speed)=2.05m/sec 



200 mm 150 100 50 



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



FIGURE 4. Comparison between calculated and experimental value. 



conditions the wake energy is effectively recovered 

 by the propeller. 



Fundamental Equation 



In this section, we assume that a ship is stationary 

 in a uniform flow of speed U. We proceed to examine 

 the balances of force and energy between the ship 

 and the flow field. 



Now, for the surfaces where force and energy are 

 surveyed, we define six rectangular cross-sections 

 in addition to the hull and propeller surfaces. 

 These six rectangular cross-sections are indicated 

 in Figure 5. Two vertical planes are in right angle 

 to the direction of the uniform flow at the front 

 and rear of the hull. The free surface and the 

 bottom of the water are held between the two vertical 

 planes, and two more vertical planes are parallel 

 to the uniform flow at infinite distances to the 

 right and left of the hull. Further for simplicity, 

 we assume that the flow field is independent of 

 time even if a propeller exists and a coefficient 

 of diffusion, y^ , due to viscosity or turbulent 

 flow is constant. Moreover, notations used here 

 have the same meaning as those in Section 3. 



At first, let us examine the input and output 

 of momentum at the individual surveyed surface in 

 the towed condition. Then, as a result, the total 

 resistance, R , can be given by the integration on 

 the rectangular cross section, S , in the rear of 

 the hull as follows: ^ 



3u 



ds[po-p +2y — -^- p u (U+u ) 

 s e dx f s s 



1 r 2 



Pfg 



"-b 



+ 2 Pf9 / dz 5s , 



(74) 



where u, v, and w represent x-, y- , and z-components 

 of disturbance velocity and b represents the half 

 width of S at the free surface. Further, po repre- 

 sents the pressure at x = -°°. Moreover, when the 

 energy balance is examined, kinetic energy lost 

 when the uniform flow passes along the hull must 

 be equal to the sum of the energy dissipated to the 

 outside through the surveyed surfaces by heat and 

 work. Thus, we can obtain the equation as follows: 



+ v^ + w^) ] (U + u ) 

 s s s 



ds[U^ - (U+Uc 



dV $ (e) - 



dS <(po-p) (U+u 



