HYDRODYNAMIC FORCES 



141 



cn_ 



2.0 



Fig. 35 Towing-tank record of slamming of a model of T2-SE-A1 tanker in irregular head 



waves (from E. V Lewis, 1954) 



duration as well. A studj' of the data .';ho\vs that reduc- 

 tion of the.se extremely high pressure.'? occurs \'ery rapidly. 

 For e.xample, at a time 0.0001 sec later than that which 

 produced a maximum pressure of 1450 psi for Station .3, 

 the pressure has dropped to approximately half of its 

 original \-alue, and at a time lapse of 0,0004 .sec, it had 

 experienced an 84 percent decrease. Figure ....-' 

 shows further that this high pressure is restricted to an 

 extremely small area of the ship's bottom. Therefore, 

 due to the extreme localization and rapid reduction of 

 these large pressures, they contribute but little to the 

 total impact load which tiie ship recei\'es." 



The work of Bledsoe is \-aluable in demonstrating 

 quantitatively the significance of ship fullness in the 

 slamming process. The calculations were based, how- 

 ever, on the assumption of artificial apjjroach con- 

 ditions, and the absolute values of pressure do not corre- 

 spond to the operating conditions of a ship. Among 

 other things, the assumed ship draft was less than 20 per 

 cent of the normal ship draft. 



The high pressures computed theoretically probabl\' 

 would not occur in a physical experiment. In the first 

 place they result from the expanding-plate theory, •\\'ith- 

 out consideration of the spray-root properties. Con- 

 sideration of these would result in a somewhat lower and 

 more diffused, although still narrow, jjeak. Further- 

 more, the theory is based on a ciuasi-static consideration ; 

 i.e., the water flow at each in,stant is taken to be identical 

 with the steady state flow. It was explained in Section 

 3.12 that the added mass deri\'ed from the water flow at 

 the free surface is not a fixed property of the body form 

 but depends on the past history of the fluid motion. 



The impact theory resulting from this assumption has 

 been shown by experiments with seaplane bottoms to give 



good results for deadri.ses of the order of 20 deg. There 

 is some suspicion that the theory partially breaks down 

 at deadrises below 8 deg. Exact experimental veri- 

 fication is extremely difficult because of the narrowness 

 of the pressure peak and the rapidity ^\•ith which it 

 moves pa.st a pressure gage. Greenspon (lO.jG) gave the 

 results of pressure measurements on a Coast Guard Cut- 

 ter operating in a rough sea with the specific intention of 

 developing strong slamming. Peak pressures up to 295 

 psi were recorded, while the mean pressiu'e o\'er the area 

 of a bottom plate l3et\\-een structural supports was of 

 the order of 100 psi. 



It should be mentioned that, in addition to strong dis- 

 tinct slams, a series of almost continuous impacts of 

 lesser magnitude also can be felt. Like slams these oc- 

 cur freriuently on typical cargo ships in shallow-draft 

 condition, and may maintain a ship in an almost con- 

 tinuous state of vibration. For fast .ships, such as de- 

 stroyers, they may occur at normal draft. 



7.5 Impact on Wavy Water Surface. Available theo- 

 retical methods of e\aluating slamming pressures fail in 

 the case of impact of a flat plate on smooth water. In 

 such case they yield infinite pressures. Such an impact, 

 however, would be rare at sea. Usually the sea consists 

 of many different wa^-es, ranging from the smallest (rip- 

 ples) to the largest, corresponding to the wind and swell 

 conditions. While the conditions conducive to slamming 

 are determined by the larger wave components, the actual 

 impact takes place on a surface covered with ripples and 

 small, sharp-crested wa\'es. These waves ha\'e a large 

 cushioning effect, reducing both the local pressures and 

 the total slamming load. Some idea of the latter effect 

 may be obtained by recollecting that in M. A. Todd's 

 (1955) experiments the penetration of the water surface 



