obtain the total effect. The procedure can be considerably simplified if the ship form is 

 replaced by one of constant section whose shape and dimensions are the mean of those 

 corresponding to the individual ship sections. Such a form will have a waterline beam equal 



to the average waterline beam of the ship (C^B), and a mean section draft equal to the average 

 section draft of the ship (C^H). 



Using the relations given in Reference 10, it can easily be shown that, for the form of 

 constant sections, the dimensionless damping coefficient k can be written as 



e~2'?sin2 ^ 

 where 



[1] 



and 



V = Al [2] 



•'o 

 The magnification factor is related to the damping coefficient by the expression 



^, =[(1-A2j2+k2 A2j-y= [5] 



In Figure 17, the magnification factors obtained from the constant section approximation 

 are compared with the results obtained from more rigorous calculation methods, and with the 

 results obtained from experimental heave damping measurements given in References 11 and 12. 

 The curves indicate that, at least for this case, the results of the approximate method compare 

 favorably with experimental measurements. 



Magnification factors for resonant conditions were calculated for the five models, and 

 for a number of actual ships ranging from tankers to destroyers and from 100-ft yachts to 

 1000-ft carriers. The results for A = 1.0 are plotted against mean beam-draft ratios in 

 Figure 18. All of the spots can be represented by a single faired curve which indicates that 

 the heave magnification approximation depends only on the mean beam-draft ratio. Similar 

 curves are obtained for other tuning factors. 



Following the notation of Reference 10, the relationship between the magnification 

 factor and the heave parameter can be written, for uncoupled motion, as 



1-3 



