HYDRODYNAMIC FORCES 



151 



Absolute coefficients of moment 



r'=A r-=ii r=A 



' qbS '"■ qcS ' i/bS 



(rolling) (pitching) (yawing) 



Angle of set of control surface (relative to neutral position), 

 (Indicate surface by projjcr subscript.) 



z = a. complex number 



a = an angle 



a = waterplane area coefficient 



/J = an angle 



/3 = sectional-area coefficient 



7 = length of prismatic section in terms of ship half- 

 length / 



5 = an increment 



5 = logarithmic decrement 



5 = phase angle 



€ = phase angle 



.f = a complex number 



^ = an angle; pitching angle; polar co-ordinate 



K 



nondimensional damping coefficient, equation (32) 

 Haskind's coefficients defined in Section 6.4 



U = total fluid velocity 

 U = velocity vector in body motions 

 f^i.2.3 = velocity components of body motions 



along three a.xes I Haskind, 



t^.t.e = angular velocity components (Section 6.1 



U„ — velocity of a body surface element along 

 normal to itself 

 F = ship speed; velocity of undisturbed water flow 

 X, y, 2 = Cartesian co-ordinate axes 



X, y = real and imaginary parts of a com])lex number z 

 A', y, Z = forces along x, y, ^-axes 



modulus of time-dependent 



K2(d/X)) 

 Kz{L/\)\ 



Ke) 



X = wave length 

 ^, 1] = real and imaginary parts of a complex number 

 ii Vt t - Cartesian co-ordinate system fixed in a ship 

 p = density (in mass units) 

 (f> = angle of roll or list 

 (j) = velocity potential; 

 velocity potential 

 "I", <i>o, $* = time-dependent velocity potentials defined in Sec- 

 tion 6.1 

 1^ = stream fimction 

 CO = circular frequencj- (used for frequency in all cases 



in which no ambiguity is involved) 

 oJe = frequency of wave encounter (used only when dis- 

 tinction from wave frequency is necessary) 

 Wo = natural frequency of an oscillating body 

 12 = total angular velocity in body rotation about three 

 axes (Section 6.11 



