257 



+ M. 



2lu + u,;3^+v^^— . 



3v 3u 

 s . s 



■ 3w 3u 



(75) 



where V^ denotes the flow field surrounded by the 

 survey surfaces, and 



.(e) = V 



^^^y^A^ 



V \ 2 /^^ \ 2 



+ 2 



' 3w 3 V \ 2 / 3w 8u ^^ 2 

 V 3y 3z / \ 3x Sz 

 3u 8v N 2 



v3y 3x 



(76) 



By using (74) and (75) , the effective horsepower, 

 EHP, can be expressed as follows: 



EHP = J dV $g(e) + — J 

 Vf S, 



dS(u|+v|+w|) (U+Ug) 



FIGURE 5. Survey surfaces. 



DHP = dV $ (e) 



J sp 



Vf 



dS 



U+u 



sp 



sp 



sp 



(U+u ) 

 sp 



up^g 



dz5^ + J dS Us(ps-po) 



-b 



dS ) (PO-Pgp) (U+Ugp) 



- u. 



dS 



3u / 3v 3u 



1 s , s , s 



2us ^ + '^c \ ^^ + ^^ 



^ 3x s V 3x 3y 



3 u / 3 V 3 u 



2(U+u )^+v (_^ + -^ 

 spdx sp\dX oy 



3w 3u 



I s , s 



= \3x 3z 



(77) 



3w 



sp V dx 



(79) 



The first term on the right side expresses heat 

 energy, the second term expresses the increase of 

 kinetic energy, the third term expresses the in- 

 crease of potential energy, and the fourth and fifth 

 terms express work toward the outside of V^. This 

 equation, (77) gives the work, EHP, transmitted 

 to the fluid through the hull when the hull is 

 towed in still water. 



Next, the self-propulsion condition can be 

 considered in the same manner as the towed condition. 

 The equation for the balance of forces is as follows: 



where 



j> (e) = y 

 sp e 



u \ 2 / dv \ 2 /dw \ 2 

 ^^^) -^(^) -^^-^ 



u 3v \ 2 /3v 3w \ 2 



3y 3x 

 3w 3u \ 2 

 X 3z 



3z 3y 



(80) 



Then, using (78) and (79) , we can get the following 

 equation: 



AR 



dS 



PO -p +2p 

 " sp 6 



sp 



I u (U+u ) 

 f sp sp 



DHP + UAR 



dV $ (e) 



sp 



P^g 



dz C^ 



sp 



(78) 



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

 sp sp sp sp 



where the subscript sp denotes the self-propulsion 

 condition and AR represents the skin friction 

 correction which is used for the ordinary propulsion 

 test at the towing tank. When the energy balance 

 is considered, we can get the following equation: 



up^g 



2 J 'sp 

 -b 



dz C + dS u (p -p ) 



sp sp 



