Propeller Excitation and Response of 230000 TDW Tankers 



dC C 



L L 



e 1 1 



C. 



~t + (2n - 1} ( V* - c L ( i " ir } - /ir^- dx (6) 



L a a o ^ NO 



where C , /3. and /3 are obtained from lifting line calculations 

 L, l 



cos Mrp ft 2 n 



1 - 7rn(cot7rn - cot7rn ) 



1 / fix 



n 

 o 



7T/£ 



a =0. 9(1 + 0.8—) .2tt 



o c 



1 Z 



■^ =t^—.( S v(x) . r(p,z) . dp 



NO NO ^i- k=2 



D 



Vc (x) 



u no 



NO ■/ r 



V (x) = induced velocity normal to the chord line 



V (x) 



r cos^(r). sin(jz(-e+5 ) + OO) 9- <Mp¥) cos(^-0+a k ). sin^r) 



47r)(^(r)e-^(p)s^) 2 + r 2 + p 2 - 2rpcos (^-6+^) j 3/2 



V (x) = induced velocity normal to the chord line, due to a vortex 

 of unit strength 



1 



J U N0 

 o 



k 1 dz (x') 



-T- J 4x^' U^s.x') dx- 



V (x) = induced velocity normal to the chord line due to thickness 

 of the other blades 



Z / 2 2 

 2 ,x-x\ y- , nf . sin 2 



7T s ( ) + n + 2n .cos 20i,H ) 



n = 1 s s 



611 



