284 



THEORY OF SEAKEEPING 



80 



Conventionally Calculated ' 



Bending Moment for L/20 Regular Wave 



GO 



80 



Conventionallv Calculated 



Bending Moment for L/20 Regular Wave 



Bending Moment Amplitudes 

 in Regular L/20 Heod Seas 

 I Lw/L=1.00 I 



I u Li 



50 



40 



30 ^ 



20 § 

 o 



10^ 



ol 



10 _a.' 



O 



u 



20 ^ 



D- 



30 '^ 



40 

 50 



5 10 15 



Ship Speed, Knots 



J I I 



20 



1 



2 3 



Vm Ft/Sec 



Fig. 34 Bending moment amplitudes in regular L 20 head 

 seas; L^./L = 1.00 (from Lewis and Dalzell, 1957) 



casioiially it was claimed that the prior emersion of the 

 bow is not necessary in order to produce a slam. It 

 appears that any wave shock applied at the bow and 

 severe enough to excite hull vibration has been described 

 as a slam. The subject is apparentlj- confused because 

 too many events are included in one concept of excessive 

 generality. In order to clarify the issue it is necessary 

 to decomp(jse this broad concept into several more 

 narrowly defined ones. In Section 2-7 attention was 

 called to the distinction between high local pressure 

 and the large total force at a lower mean pressure. The 

 first causes damage to the bottom plating in the early 

 stages of an impact and the second causes vibration of a 

 ship and affects bending moments occurring in the later 

 stages of impact. In the present section the distinction 

 between the nature of slamming of slow ships and of 

 high-speed ships also will be introduced. In addition, 

 the relationship between hydrodynamic loads in slam- 

 ming and the bending stress in a ship will be considered. 

 5.1 Slamming of Slow Ships. The term "slow ship" 

 means here the usual type of a cargo ship which is char- 

 acterized by rather full lines, a relatively broad bottom 

 area at the bow, and a very small deadrise. These ships 



are known to slam frequently in head seas when in light- 

 draft condition. In the Admiralty Ship Welding Com- 

 mittee Report No. 8 (on SS Ocean Vulcan), a statement 

 is made that the ship slammed during one out of three 

 days in open ocean under light load conditions. There 

 exists a large literature on the bottom-plating damage 

 by slamming but too little emphasis has been placed on 

 the speed loss resulting from the necessit}^ to guard 

 against slamming. 



In cargo ships, the impact of the water on the ship's 

 bottom is the most conspicuous part of the slamming. 

 Because of the .small deadrise, the water-impact pressures 

 are very high and freciuently cause damage to the bottom 

 plating. Also, because of a small deadrise, a large area 

 of the bottom is wetted in an extremely short interval of 

 time. A large total force is generated almost instantly 

 and is felt as a sharp shock. When the edge of the 

 wetted bottom area reaches the turn of the bilge, local 

 pressures and the total pressure force diminish rapidly. 

 This follows from Wagner's theory of impact which 

 was outlined in Section 2-7.1. It was shown that pres- 

 sures vary inversely as the square of the deadrise-angle 

 tangent. They are very high when the angle is small 

 and they diminish rapidly as the angle increases at the 

 bilges. 



The experimental data for a complete investigation of 

 slamming events are very meager. The towing-tank 

 experiments of Szebehely and Lum (3-1955), E. V. 

 Lewis (1954), and Akita and Ochi (3-1955) established 

 that slamming occurs when a ship is heaved up and is in 

 a nearly level attitude. At this time the bow has nearly 

 maximum downward velocity. In a cargo ship, the 

 prior emergence of the bow is a necessary prereciuisite to 

 slamming. However, these experimenters provided 

 no data for making a detailed analysis of the slamming 

 process. 



Attention should be called to the fact that the most 

 conspicuous result of the slamming, the hull vibration, 

 has not been reproduced correctlj- on models. On a 

 ship, the slamming vibrations at a two-node frequency 

 are often felt for 60 cycles or over 30 sec. An example of 

 such a vibration following a slam is shown in Fig. 37. 

 In model experiments on the other hand the vibrations 

 are extinguished very quickly. Typical examples are 

 shown in Fig. 2-36 and in Fig. 41. Ttiese were taken 

 from the work of Akita and Ochi (1955) and Ochi 

 (1956a) which was done with large-size models built of 

 brass sheets. The model construction was generally 

 similar to the one normally used in ships. A plaasible 

 explanation may lie in the higher frequency of a model 

 vibration as compared to a full-size ship. Lockwood 

 Taylor (1930) showed that the damping of ship vibra- 

 tions is caused almost entirely by the hysteresis of the 

 structure, that it is very small at a usual two-node fre- 

 quency of ships' vibration, and that it increases rapidly 

 with the increase of the frequency.-' 



2' Also see Section 5.53. 



