Prediction of Ship Slamming at Sea 



were many cases during the tests in which no appreciable impact pressure was 

 imparted to the ship bottom even though the forefoot emerged from the water 

 surface. It was found that a certain magnitude of relative velocity between wave 

 and ship bow (hereafter referred to as the threshold velocity) was required to 

 induce slamming. 



The threshold velocity is a critical relative velocity between ship bow and 

 waves below which slamming does not occur. Although little information is 

 available concerning the magnitude of the threshold velocity associated with 

 slamming, the magnitude was evaluated from various available sources [3-5], 

 and the results are tabulated in Table 1. For convenience, the values have been 

 converted to those for a 520-ft ship for comparison with the MARINER. As can 

 be seen in the table, the values have been obtained for various test conditions. 

 Nevertheless, the magnitudes of the threshold velocity are nearly constant with 

 an average of 12 ft/sec. To determine the threshold velocity for the cargo ves- 

 sels (U- and V-Form) listed in Table 1, ship speed was increased until the ship 

 started to slam in the given regular waves (x/L = 1, h/k = 1/30). The speeds 

 for which slamming first appeared were 10.4 and 11.9 knots for the U- and 

 "V-Form, respectively. The relative velocities evaluated for these speeds were 

 taken as the threshold velocities. For higher ship speeds slamming was severe, 

 and hence the relative velocities between wave and the ship bow for these speeds 

 could not be considered as the threshold velocity. Note that the threshold ve- 

 locity is the minimum velocity which causes slamming. 



In regular wave tests conducted on a high speed craft listed in the table, an 

 immersion sensing element was fixed to the model at Station 2. Hence, the rel- 

 ative motion between wave and the bow was directly measured, and the relative 

 velocity was obtained by differentiation. 



It is of great interest to mention that the magnitude of the threshold velocity 

 evaluated from the MARINER tests in irregular waves is very close to that 

 evaluated for other types of vessels tested in regular waves. For evaluation of 

 the threshold velocity for the MARINER the data obtained in a severe Sea State 7 

 at a ship speed of 10 knots were analyzed [4]. Since the wave measuring device 

 was located 9.83 feet (410 feet full scale) ahead of the model in these tests, one 

 assumption was introduced in the analysis. That is, waves measured at the lo- 

 cation of the wave probe would maintain their form until they reached the ship 

 bow. With this assumption, the magnitude of relative velocity at the instant the 

 ship slammed was evaluated from simultaneous records of pressure, ship mo- 

 tion, bow vertical acceleration and wave. Figure 1 shows the relationship be- 

 tween relative velocity and impact pressure measured at 0.10 L aft of the for- 

 ward perpendicular. As can be seen in the figure, no impact pressure is 

 observed for a relative velocity less than 12 ft/sec. On the basis of the above 

 finding, it is considered appropriate to take 12 ft/sec as the threshold velocity 

 associated with slamming for a 520-ft ship. The reader's attention is called to 

 the fact that this magnitude of threshold velocity cannot be used universally. 

 For a ship of different length, the above given value should be modified accord- 

 ing to the Froude scaling law. 



547 



