Ship Form of Minimum Wave Resistance 



0.4 



ygE 



Figure 13 



of the bottom. Then the system of sources is the combination of a discrete 

 source at the forward end of the bottom and a discrete sink at the after end to- 

 gether with the horizontal distribution. The source and the sink form the so- 

 called Rankine ovoid, and the resulting shape is the combination of a submerged 

 ovoid and a surface piercing hull. At a lower Froude number, the surface 

 piercing part is much greater than the submerged part, so that the former can 

 be regarded as the main hull, while the latter forms bulbs on both sides. At 

 higher Froude numbers on the other hand, the submerged part becomes the 

 main hull, while the upper part is like the super -structure or bridge of a half 

 submerged submarine. Such a type of ship as this may be called a semi- 

 submerged ship which has been discussed from time to time [17]. If the strength 

 of the submerged source at the point •>i=-l, z = f , is designated by m^t and an 

 equal sink is placed at the point x = -l, z = f , the wave resistance when com- 

 bined with the horizontal source distribution given by Eq. (68) becomes 



/•7T/2 / \ 



64 TTpy^ m^ exp i-y^ — sec ^e\ 



tt" - y " sec 



sin'^ (7 sec 6) sec^^'dt 



(75) 



Write the area of the midsection of the Rankine ovoid as A^ and that of the 

 bridge by A^ , Then there is approximate relations due to a linearized theory 

 such as 



477^ 



and m, 



UAi 



Si 



(76) 



1043 



