Figure 7. 



(a) (b) 



Dimensionless amplitude of pitch, heave, and motion of the stem for models of differing 



length and waterline moments of inertia. V = constant, J v = constant, 

 (a) X = constant. (b) X* = constant. 



5. A length increase with LH — constant and low, B == const., while the 

 longitudinal mass distribution remains affine, involves 



1 . a moderate decrease in T z and Ty, and 



2. a slight increase in dimensionless damping Kz and k^. 



Resonance occurs at somewhat lower wave length A, and \ R * is still further 

 decreased as compared with 4. 



The discussion can be, obviously, conducted in such a way that the advantages 

 of lengthening with respect to higher speeds of advance are demonstrated. 



6. Finally, it can be considered as well established that the bulb has no detri- 

 mental effect on motion performance [66], [31], [61]. 



These findings throw some light on the merits of the analysis by E. Lewis based 

 on the parameter D/L 3 . Although effects are lumped together which follow different 

 laws corresponding to B/L, H/L, a and 8 variations, the overwhelming importance of 

 the length dimension is clearly borne out by plotting results versus Taylor's parameter. 

 To this extent, E. Lewis' synopsis, intended to cover the whole range of normal ship 

 types, is justified. On the other hand, investigations on the sea performance of a given 

 type require a more detailed approach. 



We have seen that a ship with normal proportions and mass distribution will 

 meet resonance in the hove-to conditions at \ R * well below unity. 



At finite speeds the supercritical range is extended to larger \ R *. Theory and 

 experiment show that absolute motions can be small in the supercritical range; phase 

 relationship and accelerations require a special investigation. When sufficient power 



89 



