Evaluation of Motions of Marine Craft in Irregular Seas 



V - I ■'7o I ^° ^ ( ~>~ '^ ■*" '^^* 



Let us now make a coordinate transformation to a moving (x, z) reference 

 frame, free to translate with forward speed u of the body but constrained in 

 pitch, heave, and surge. 



^ = Ut + X 



C - z . 



Suppose we locate a wave probe at some prescribed distance x^ with respect to 

 an origin corresponding to the midship station of the moving reference. Further- 

 more, if the particle displacement at some reference depth z^ below the calm 

 water datum is required, then an attenuation factor e'^^"/') ^o must be applied 

 to the surface wave. The resulting equation for the wave encountered by a point 

 on the body at depth z^ can be obtained as 



T7(x„,z^,t) = \7]J e ■ e . 



The real part notation has been left out temporarily without obscuring the issue. 

 Making use of two well-known wave relations 



and 



-=r- = -T- (c - U cos y) = OJ ± — U 



where y is the heading angle. Then restricting this to head (+) and following 

 (-) seas in the ± designation, the wave number may be expressed as 



277 OJ^ 



}y g C + U 



Substituting this back in the equation for 77, 



^C'<r,'Z„,t) 



j2 



— (■ X + i z 'j 

 t ^ o o ^ 



When compared to the above equation, the authors' corresponding version 

 of the wave as denoted by their Eq. (13), lacks the subscript e in the driving 

 frequency for the general case. Hence, the results can only be valid for the 

 special case of beam seas or for zero speed- of- advance. This omission was 

 evident in many of the ensuing equations. The error can be easily remedied by 

 inserting the subscript e for all frequencies identified with the system 



501 



