138 



THEORY OF SEAKEEPING 



0.2 0.3 



t "in Seconds 



Fig. 32 Theoretical and experimental linear acceleration 



curves for 7.8-ft model of M/S San Francisco when rotating 



about a fixed point (from M. A. Todd, 1954) 



of the mathematical analysis and omission of intermedi- 

 ate steps in the development. It has lieen presented in 

 English and expanded by Pier.son and Le.shno^•er (1948) 

 and J. 1). Pier.son (ID.'iO." ID.")! ). 



7.3 Adaptation of Seaplane Impact Theories to Ship 

 Slamming. Seaplane impact theories ha\'e been adapted 

 to the pi'oblems of ship slamming; by 8zel:)ehely (lU.j'2, 

 1954), Szebehely, Todd and JAim (1954) and Szebehely 

 and Todd (1955). An extensive bibliogra])hy on slam- 

 ming was prepared by Szebehely (1954). 



The problem of slamming can be divided into two dis- 

 tinct parts; i.e., the study of ship motions leading to 

 slamming, and the generation of pressure.s and forces in 

 the process of slamming. Both are treated by Szebehely 

 and Todd (1955), but only pressures and forces will be 

 treated in this chapter, while motions will be dealt with 

 in the next one. 



Neither the mathematical theories nor the experi- 

 mental data were adecjuate at the time to permit Szebe- 

 hely to correlate actual ship slamming in wa\'es with 

 theory. Therefore, it was necessary to devise artificial 

 experiments which would be amenable to mathematical 

 analysis. The first of these by Szebehely and Brooks 

 (1952) consisted of dropping a ship model onto water, 

 while maintaining it in a horizontal position. The 

 second, a more realistic one, was de\'ised and analyzed 

 bv M. A. Todd (1954). The experiments were per- 

 formed on a model of the MS San Francisco (7.8 ft long 

 BP, 12.9 in. beam.) Tests were made at several drafts 

 and were correlated with calculations at a very shallow 

 draft of 1.09 in. The model was pivoted at a point 2.o ft 

 aft of amidships. The experiment was performed in 

 smooth water by lifting the bow until a 12.2-deg angle of 

 trim was obtained and then letting it drop freely onto 

 the water. Accelerations were read from an accelerom- 

 eter placed 10.5 in. aft of the forward perpendicular at 

 the model bottom. Ecjuations of model motion were de- 

 veloped using Wagner's principle of series expansion to 

 define the hull cross sections and the resultant pressures 



and torccs. Excellent agreement between experiment 

 and calculaticjns was secured as shown in Pig. 32. 



In view of the success of this correlation, a series of 

 theoretical computations of slamming pressures was made 

 by Bledsoe (1956) for the David Taylor Model Basin 

 Series 60 hulls in order to establish the effect of ship full- 

 ness, or block coefficient, on slamming pressures. The 

 results of the calculations agree with practical ship ob- 

 servations in that, other conditions t)eing e([ual, slamming 

 pressures increa.se rapidly with ship fullness. 



While these artificial experiments were necessary for 

 verification of the ship-slamming theory, other experi- 

 ments wei'e necessary in order to investigate the natural 

 conditions under which slamming occurs. Szebehely 

 and Lum (1955) attacked this problem by testing a 

 model of the Liberty Ship in head seas. Kent (1949) pre- 

 viously had concluded that slamming does not occur in 

 regular seas and that it was necessary to create a com- 

 plex sea containing several wave lengths in order to make 

 the model slam. Since facilities were not j'et available 

 for making reproducible irregular seas, Szebehely and 

 Lum obtained slamming in regular wa^'es by using steep 

 regidar waA'es with a length-to-height ratio of 16.7. 



Results of two tests with towing forces of 1.2 and 0.8 

 lb are gi\'en in Pigs. 33 and 34. The most important ob- 

 servation is that slamming, indicated by the disturbance 

 of the acceleration curve, occurs at the instant when the 

 descending bow position is nearly level. Also, the curves 

 of displacements or velocities are not sensibly affected 

 by the occiu'rence of slamming. This is important since 

 it permits definition of the conditions leading to the 

 slam by means of ship-motion calciUations made without 

 regard to the slam itself. The severity of slamming de- 

 pends on the relati\-e vertical \'elocity of a ship's bow with 

 respect to the wave surface, which, in turn, depends on 

 the phase relationship between the wave and ship-bow 

 motions. At the lower speed resulting from the 0.8-lb 

 towing weight in Pig. 34, the wave vertical velocity at 

 the instant of slamming is either nil or slightly downward ; 

 i.e., deductive from the bow A'elocity. The resultant 

 slams arc \'ery light. When speed is increased by using 

 a 1.2-lb towing weight as shown in Pig. 33, the phase 

 relationships change so that at the instant of slam an 

 appreciable upward velocity of the wave surface is added 

 to the high downward ^-elocity of the .ship bow. 



These two tests bring out clearly the fact, well known 

 in practice, that slamming can generally be eased by a 

 reduction of speed. While the tests were made in ab- 

 normally' high regular waves, the results appear to agree 

 qualitati\'ely with actual obser\'ations in a complex .sea, 

 as well as with E. V. Lewis' (1954) towing-tank tests in 

 irregular waves shown in Pig. 35. 



The results of Szebehely and Lum (1955) have been 

 confirmed by tests made by Akita and Ochi (1955). In 

 the latter case, sustained and .sex'ere slanuning was ob- 

 tained in regular waves in a towing tank by using a flat- 

 bottomed shij) model with full ends in plan view at an 

 extremely shallow draft. An example of the test re- 

 sults is given in Pig. 36 where the sequence of events is 



