A New Appraisal of Strip Theory 



In the column headed "Coefficient" are the coefficients of the linear terms 

 of each of the motion variables. On the left side of this column, the coefficients 

 are merely expressed arbitrarily as letters in alphabetical sequence. On the 

 right-hand side of this column, the coefficients are expressed in the nomencla- 

 ture of Bulletin 1-5 of The Society of Naval Architects and Marine Engineers, 

 which system is developed with reference to axes fixed in the ship, which pro- 

 vides the advantage of centerline plane symmetry in any hydrodynamic calcula- 

 tions. The appearance of double terms in the right-hand part of the column, 

 arises from the rigorous treatment of transferring from axes oriented in the 

 ship to axes (specifically heave) oriented relative to fixed space. The linear 

 coefficients in this form are valid independent of any method one wishes to de- 

 termine them — whether theoretically by strip theory, slender body theory, thin 

 ship theory or by model experiments. 



Under the column designated "New Approach" is listed the formulation for 

 calculating these coefficients by a "pure strip theory" — i.e., each section 

 treated as a cylindrical section and completely independent of the shape of other 

 ship sections. Since the terms are calculated by integrals over the various ship 

 sections, in a geometry fixed in the ship, the forward speed effect on some of 

 the coefficients very neatly falls in place, such as in the terms 



- u^ Z^ = u^ I /i(x) dx 



since by strip method 



- z. 



J /i(x) dx , 

 -"oZw = u„|N(x)dx 



since by strip method 



-Z^ ^ J N(x)dx. 



In the column headed "Korvin-Kroukovsky Approach" are listed formula- 

 tions as attributed to the strip theory of Korvin-Kroukovsky. Perhaps a great 

 deal of difficulty and confusion results from semantics in that what is often re- 

 ferred to as Korvin-Kroukovsky strip theory is in reality not a pure strip theory, 

 but a rather crude slender body theory which takes into account three- 

 dimensional effects in a rather rough way. Nevertheless, because of the physi- 

 cal realities of the situation, any method of calculation of the coefficients should 

 be consistent with the terms listed in the right-hand side of the coefficient col- 

 umn. Hence, the Korvin-Kroukovsky terms given below in the coefficient e(a^) 

 should reduce to -u z. (or u j /4x) dx) 



2"oJ ^''^ "^^ "*" "° J dx ^^^ ''dx - u^J /x(x) dx 



361 



