A Vortex Theory for the Maneuvering Ship 



Figure 4 



Figure 5 



A vortex of the f^ -family is lying on a closed contour made itself of two 

 arcs; one is P'm'P starting from P' on the port side of (2g j, and going to P, on 

 the starboard side oi d^^. m' is on the upper side s' of s, the other arc is 

 made of the streamline of the relative motion starting from P and going to the 

 infinity downstream, and of the similar streamline starting from P' , but de- 

 scribed in the opposite direction. The intensity of the filament vortex above is 



A vortex of the fg-family is similar to the previous one; but the arc Pm p' 

 has to be substituted for P'm'P, m" being on the lower side s" of s; moreover 

 the streamlines starting from P and P' are described from P' to the infinity 

 downstream, and from the infinity downstream to P. The intensity of the fila- 

 ment vortex is dy^ . 



The intensity of the free vortex resulting from the addition ( fp) + (fo^ is 



dFp = d7^ -dy^' along P co P' . (18) 



The arcs P'm'P and Pm'P' are orthogonal to the contribution of w^ in the 

 total relative velocity on s . 



829 



