Doctors 



(1958), and the final result is 



R = 



Zirpg 



-tt/2 e i 



k cos 



1 - k d. sec 2 0. sech 2 (kd) 



in which 



7 2 



)P (kcos ff.ksin^ + Q (k cos d, k sin &)\ d0 



/ 



and k is the non-zero solution of Eq. (27), that is, of 



(29) 



(30) 



k - k sec ' tanh(kd) = 



(31) 



The lower limit for is taken as 0, , the smallest positive value 

 of satisfying Eq. (31) for a real k . It is given by : 



*i = ° 



= arcc 



for k d>l (subcritical speed) 

 o 



os\k d for k d<l (supercritical speed) 



(32) 



III. 3. Results 



Some results previously published (Figs. 3 to 7) are now 

 presented to show some of the effects of the choice of pressure dis- 

 tribution given by Eq. (5). For this choice, it was shown that 



. . _ iv ' sin(aw) it' sin(bu) 



P(w,u)-p o a . sinh ( ww / 2a ) ' 0. 8 inh( ir u/20) 



and 



Q(w,u) = 

 while the weight supported by the pressure is just 



W = 4 p ab 

 o 



(33) 



(34) 



For convenience the wave resistance is expressed as a dimensionless 

 coefficient : 



46 



