286 



THEORY OF SEAKEEPING 



100 



80 



SO 



40 



Trends of Bending Moments m Irregular 



Seas with Speed 



(Sea Corresponding to that Generated by 



Approximately a 30 Knot Wind of 17 Hours Duration) 



The Highest Value 

 Measured — ^ 



7^ 



ConventiongllY 



Calculated Static Moment * 



c 20' 



__ 



-ts.5 * 



+-f 



.-o-K 



^^ 



y 



Average o-f 10 % 

 Highest lagging Momen+s 



CD O 



40 



rAverage Hogging Monnen+ 



i_.J_._.L_ ^ 



Seraqe c 



-Average of 10% Highest Hogging Moments 



go I Convent ipnglly 



80 



zf 



..o— -o 



Calculated Static Moment • 



-\ 



-+-. 



The Highest Value 

 Measured 



60 

 50 



40 



30 



n 



20 2 

 y: 



io| 

 -(- 



1^ 



10 



I/) 



20 CO 

 3,0 

 40 

 50 



2 3 4 



V^^ C Ft/Sec) 



5 10 15 20 25 



Ship Speed : Knots 

 5tatic Calculation tor L/20 Regular Wave 



Fig. 36 Trends of bending moments in irregular seas with 

 speed (from Lewis and Dalzell, 1958) 



5.3 Observations on a Destroyer. Fig. 40, taken 

 from Wariisiiick and St. Denis (11)57), shows a sample of 

 a record taken on a destroyer at sea. A brief description 

 of instrumentation was given in Section 3-5.16, and in 

 Figs. 3-49. Wave conditions were outlined in Section 4.5 

 of the present Chapter. The recorded data are given 

 by diagrams in the middle column of Fig. 40, and the 

 photographs in the right and left-hand columns, respec- 

 tively, correspond to various instants during the recorded 

 period. 



The time scale in seconds is given along the lower edge 

 of Fig. 40. It is measured from an arbitrar_y instant. 

 The numbers just above the time scale designate the 

 film frame numbers. The broken vertical lines, cor- 

 responding to the instants the photographs were taken, 

 are drawn through all sections of diagrams. 



The short horizontal stretches found between 7 and 

 8.5 sec on four upper pressure curves of Fig. 40, corres- 

 pond to the atmospheric pressure and show that these 

 gages emerged from the water. The instant of slam is 



shown by a short vertical rise of pressure curves at the 

 scale time of 8.5 sec. This instantaneous rise on the 

 time scale of this diagram corresponds to the very rapid 

 occurrence of pressure pulse on the USCGC Unimak. 

 In the present case this pressure pulse at 8.5 sec reaches 

 only a small pressure of 8 to 10 psi. 



The lines of the particular destroyer, to which these 

 data apply, are not available. However, typical de- 

 stroyer lines such as are shown in Figs. 27 and 31 can be 

 assimied. These bod,y plans show a sharp V-form with a 

 large deadrise angle for the first 60 to 80 ft of the ship's 

 length from the bow. With such a large deadrise angle, 

 only small impact pressures can be expected on the basis 

 of Wagner's theory. Quahtatively this is in agreement 

 with 8 to 10 psi shown bj' the rise of the vertical line at 

 8.5 sec in Fig. 40. 



Reference to the curve of pitching angles on the upper 

 part of Fig. 40 shows that at the instant of slam (at 

 8.5 sec) the ship was on an even keel. This feature is in 

 agreement with towing-tank tests of E. V. Lewis (1954), 

 Szebehely and Lum (3-1955), and Akita and Ochi 

 (3-1955). The data on these were given by Figs. 2-34, 

 35 and 36. In these figures the instants of slams were 

 shown by the readings of accelerometers at the bows. 



In the present case, however, the shock at the first 

 instant of slamming, at 8.5 sec, is mild as compared to the 

 final development of the impact force later, and the ac- 

 celerometer records are more difficult to interpret. 



On the records of the USCGC Unimak, the pressure 

 pulse was of very short duration. In the case of the 

 destroyer, shown in Fig. 40, the drop of the pressure 

 following the pressure pulse is absent and, instead, the 

 pressure rises relatively slowly with time and reaches the 

 maximum value in about 1 sec after initial impact; i.e., 

 at the time scale of 9.5 sec. Reference to the pitching 

 curve shows that at this instant the ship's bow is in its 

 lowest position. This is confirmed by the photograph, 

 No. 24, which corresponds to an instant at 10 sec. 



It appears that with the sharp V-bottom sections of a 

 destroyer, the bottom impact plays a relatively small 

 part in a slamming process and that maximimi water 

 pressure is associated with the full immersion of the bow. 

 The pressure, however, is only partly hydrostatic and 

 contains a large dynamic component. The peak pressure 

 at Frame 195 is shown in Fig. 40 to be 27 psi. Assuming 

 a height of the stem of 33 ft, the hydrostatic pressure at 

 full submersion would be expected to reach only 16.5 psi. 

 There is therefore an added dynamic increment of 10.5 

 psi. Wagner's theory, outlined in Section 2-7.1, indi- 

 cates that there must necessarily occur an increase of 

 local water pressure as the water le\'cl rises to the flare 

 at the deck. The references cited in connection with 

 Sections 2-7.1 and 7.2 show, moreover, that a significant 

 pressure increase o\'er the entire periphery of a sub- 

 merged body occurs simultaneously with the sharp rise 

 of the local pressure at the water level and the formation 

 of the spray. The submersion of the bou' and the dy- 

 namic effect of the boio flare appear, therefore, to be the 

 major causes of "slams" in ships of a destroyer type. 



