HYDRODYNAMIC FORCES 



139 



Experimental motion study, 1.2 lb towing force 

 Regular seas: X = 5 ft, \/h = 16.7 Natural periods: (T„)n 0.65 sec; (T„); = 0.70 sec 

 Ballast condition: A = 38.19 1b Gyradius: 1.394 ft 



Fig. 33 Towing tank record of slamming of a model of liberty ship in steep regular waves (from Szebehely and Lum, 1955) 



to be read in the order of numlier.s just ahox-c pilchinj;; 

 trace. The slam occurs at the instaut 4 at wliich the pitch 

 angle is barely below level ; i.e. , the downward bow \'clocity 

 is nearly at its highest \'alue. Heaving is on the decrease, 

 but is still high. Maximum pitching ^-clocity is combined 

 with the downward heaving velocity to give a high tlown- 

 ward velocity at the bow. In this case a large metal model 

 was used, nevertheless the vibrations after slamming de- 

 cayed rapidly. On a full-size ship they last longer, so 

 that nearly the full value of stress due to slamming is 

 superposed on the primary bending stress. On a small 

 wooden model used by Lewis (1954), on the other hand, 

 the vibrations were cjuickly extinguished. 



The work of Szebehely and Lum (1955) and Akita and 

 Ochi (1955) point.s up the intentional artificiality of the 

 test conditions and calculations used by 'SI. A. Todd 

 (1954). One can consider Todd's work as compo.sed of 

 two parts: (a) Use of Wagner's (19;51) method in evalu- 

 ating hydrodynamic forces for a given vertical \elocity 



of a body; and (6) u.se of the methods employed by .Mayo 

 (1945), Benscotter (1947) anil Alilwitzki (1948) in for- 

 mulating the ecjuation of motion for a falling body de- 

 celerated by water forces. Li the latter sense the ex- 

 perimental conditions were analogous to a seaplane land- 

 ing in that the entire kinetic energy of the falling body 

 was absorbed by the hydrodynamic forces generated in 

 the process of the impact. H(nve\'er, although the slam- 

 ming force in waves is large, its duration is so short that 

 a negligible amount of kinetic energy is absorbed, and 

 the pitching and hea\'ing motions continue es.sentially as 

 if the slam did not occur. ( )nly part {a) of M. A. Todd's 

 work should be used in an analysis of slamming in waves. 

 Since the bottom area affected by slamming pressures 

 will be more limited than in still water becau.se of the 

 curvature of the wa\'e profile, fewer hull stations will ha\-e 

 to be analyzed. Thus, the problem of expressing the 

 forces occurring in slamming is basically simpler than in 

 the artificial case of slamming due to pure pitching in 



