Brard 



When the rudder is made of two parts symmetrical with respect to the 

 (x, y) -planes, the term in ^a are vanishing, but not those in ^^^. In this case, 

 one has: 



^A = -2/^^aU'c 



1+2^ 



U/., 



^A " 2' 

 Z. = 



4 ^ 



^A= i^-ALU^'=.,x2(^)^,xCA^ 



t *- J 1, — o -^ 



M3') 



1 + 2 



,u/., 



iU/,, \u 



Mlt)^/A 



-E ^kA^okCt') -AJI^; 



AY. = as above , 



A£a = , 



A}I^ = as above 



M4') 



Of course, this simplification is impossible in the case of such appendages 

 as sails. 



11.3. Some Comments About the Previous Formulae 



1*) At the beginning of a maneuvering, the delay in the growth of the 

 circulation around the body increases the efficiency of the rudder and diving 

 planes. 



2*) c^^ and c^^ have been taken >0 when, in a steady motion, the 

 torque about the axis tends to bring back the rudder or the diving plane to zero 

 angle. 



878 



