Vortex Theory for Bodtes Moving tn Water 
where 6p is the pressure difference between the two sides of the 
wing. The difficulties due to the singularity of the kernel have been 
overcome by the authors who obtained a very good agreement between 
calculated and measured values of 46 p for harmonic motions. 
PROPELLER THEORY 
The determination of the steady and unsteady forces acting 
on a propeller is a problem of importance (efficiency, risk of cavita- 
tion, vibrations, noise, etc...). We just mention it for it is beyond 
the purpose of the present paper. 
SHIP MANEUVERABILITY THEORY 
A first step in the mathematical maneuverability theory con- 
sists of the determination of the bound vortices when the relative mo- 
tion is steady. This problem has been considered by P. Casal in his 
Thesis dissertation fora shipata constant drift angle in the horizontal 
plane and for a ship in a forced turning motion in the same plane(1), 
Several drastic simplifications were made : 
(i) The waves generated by the ship are neglected. Thus one 
deals with the Zero-Froude-number approximation. 
(ii) The ship is assumed to be infinitely thin ; the heel angle is 
ignored. 
(iii) The free vortex sheets are attached to the hull along the keel 
and its mirror image with respect to the plane of the free 
surface at rest. 
(iv) The free vortex filaments start in the direction of the bis- 
sectrix of the angle between the local velocity of the body on 
the keel and the keel line. 
In fact, because of the errors due to the first three assump- 
tions, the fourth one is essentially used for the determination of the 
(1) Casal's Thesis was written 20 years ago when the author was 
staying as scientist at the Bassin d'Essais des Carénes (Report Bas- 
sin d'Essais des Carénes - 1951) and published much later [9] . 
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