Wavemaking Resistance of Ships with Transom Stern 



that is on the free surface, at the stern, and perpendicular to the 

 ship centerplane. In the previous section it is known that the transom 

 stern can be represented by a sink line at the stern, it is therefore 

 natural to deduce that the sink could contribute in cancelling stern 

 waves [ 1] . Since a moving point sink produces negative cosine regular 

 waves behind, the proper main hull should have a hull shape that 

 produces positive cosine stern waves. To investigate the best shape 

 of transom sterns, in a simple way, we have chosen two simple bare- 

 hull forms, represented in the Michell sense by the following equa- 

 tions: 



y\=Tt\^- ^°^ (27ix)[, in H '^ " <9) 



^^ ^ ".< z < 



1 < X < 

 H 



and 



7R « - 1 < X < U 



y2= -ip(x +x2), in ^ (10) 



-^<z<0 



where L, B, , and H are the ship length, the beam, and the draft, 

 respectively; (x,y,z) is the right-hand rectangular cartesian co- 

 ordinate system with the origin on the free surface; the x axis is 

 in the direction of the uniform flow velocity at infinity; and the z 

 axis is vertically upward. The hull in Eq. (9) produces the favorable 

 stern waves for the transom stern but has cusps in both ends and is 

 Ccilled a cusped cosine ship here. The hull in Eq. (10) is rather a 

 common parabolic hull form, not particularly favorable for the tran- 

 sonn stern. The corresponding source distributions by the Michell 

 approximation are 



cr, =-|gJ sin(2Trx) (11) 



in 



D (y = 0, - 1 <x< 0, - H/L < z < 0) (12) 



and 



^2= -^^^ "^^^)' ^" ^ <^3) 



The theory of superposition can be allowed in the sense of the Michell 

 ships. For convenience, we set 



577 



