The clear advantage of "V" sections established several times can be explained 

 by 1) the increase of k z and Kl // which vary roughly as a following some approximate 

 calculations, and by 2) the decrease of the exciting functions E z , Ey. On the other 

 hand, differences in natural periods T z , T^ may be unimportant. 



2. L — const., B zz const., J v zz const., aH zz const. 



We discuss this somewhat artificial assumption since it has been tested using 3 wall- 

 sided, flat-bottomed models with a zz 0.533, %, 0.8 to check Haskind's damping 

 formulas [65]. See Fig. 6. Models with higher a (larger A w and still larger I y ) 

 experience much less motion at A* =z 0.815 as well as A* zz 1.33. 



The explanation again is obvious, exciting functions and damping working in 

 the same direction. 



Natural periods disclose a somewhat erratic behavior which seems to be of no 

 great moment; unfortunately, however, nothing has been said about the wetness of 

 models. 



Slamming, which will undoubtedly affect the very shallow full models, limits 

 the practical applicability of results beyond the statements made with respect to damp- 

 ing and exciting forces. 



3. Affine distortions of the set of lines, first so that L zz const.; BH zz const. 

 An increase of B and, therefore, decrease in H leads to a slight reduction in natural 

 periods, but the most important change is the strong increase in damping coefficients. 



The exciting forces are slightly increased due to a smaller Smith effect, but 

 decreased due to a larger relative-motion (diffraction) effect, the net balance probably 

 being close to zero. Thus, motions are reduced; however, the advantage may be 

 destroyed by adverse impact effects. 



4. Affine distortions of lines, with variation of length, such that LB zz const., 

 H zz const. Let us consider two cases for which L is increased by decrease in beam 

 L/B being strongly increased: 



4a. J y — constant. 



Again, this artificial case is considered because systematic experiments have 

 been made on damping properties of three affine models C 3 , C„, C 1 with LB ratios 

 5, 7.5, 10. 



Heaving periods T z are not too much affected by the variations (decrease in 

 added mass), pitching periods vary approximately as -\JI y where I y is the moment of 

 inertia of the waterline. 



Keeping A zz const such that A 3 * = 1.15, A 2 * = 0.94, A x * zz 0.815. z m * 

 and xp m * decrease heavily with increased length because of the decline of the exciting 

 functions Z:(A*). Beside, an increase in phase lag indicates stronger damping in pitch 

 for C 2 and C x . See Fig. 7a. 



Fig. 7b shows a more interesting comparison at a constant A* = 1.33. 



The reduction of pitching motion for the longer models is due to an increase in 

 the dimensionless damping coefficient in agreement with theory. 



The heaving diagram cannot be satisfactorily explained by present theoretical 

 reasoning. 



Jy 



4b. /„ variable, — ^ constant. 

 l y 

 Natural periods are slightly reduced. 



As under 4a. the dimensionless heave damping may be reduced and the same 

 applies now to pitching although the absolute damping coefficient increases strongly 

 with length. 



The advantage of the form variation under consideration consists in the fact 

 that, keeping the speed of advance constant, resonance for a longer ship occurs almost 

 in the same seaway since Ty remains almost constant. This means a reduction in \ R * 

 and thus amplitude ratios z m *, <//,„*. 



