268 



THEORY OF SEAKEEPING 



Hog 



Wave 



Restraining 

 Mamen+ 



Wave Velocities 



Restrained Model 

 Model Held Rigid by Attachment ot Afterbody +o Carriage. 

 Vertical Velocity and Acceleration ot Model are Zero. 

 Vertical Velocities ot Wave Particles are as shown, 



Acting in the Direction to Increase the Bending Moments. 



Wave 



Wave Velocities 



Model Velocities 



Wave Velocities 



Wove Velocities 



Free Mode! 

 Model Free to Heave, Pitch, and Surge. 



Model is Practically Horizontal at Maximum Kog and Sag. 

 Vertical Velocities ot Model and Wave areas shown, 



Tending to Compensate one another. 

 Vertical Accelerations ot Model are near Zero (Velocities Maximum). 



Fig. 13 Diagram comparing dynamic effects on restrained and free models at zero speed (from E. V. Lewis, 1954) 



effect was later traced to a defect in instrumentation 

 and doe.s not represent true ship conditions. 



Fig. 15 shows the relative ship-wave positions at 

 several consecutive instances and at three ship speeds 

 in regular head wa\-es. Readings of the corresponding 

 bending-moment diagrams are to be taken at vertical 

 lines passing through the instantaneous bow positions. 

 Only the first diagram, at zero ship's speed, represents 

 the practical ship conditions. The lower two diagrams 

 correspond to speeds of 14.5 and 26.6 knots, which are 

 not attainable in the indicated wave size, and represent 

 artificial laboratory conditions. 



Fig. 16 shows the bending moments which occurred in 

 irregular sea tests. A paper b,v St. Denis and Pierson, 

 on ship's behavior in irregular seas, appeared in 1953. 

 Lewis' (1954) paper was the first in which the irregular- 

 wave theory was applied to ship motions and to bending 

 moments in connection with towing-tank tests. An 

 irregular operation of the wa^'emaker paddle had been 

 devised and it has produced the complex long-crested 

 waves. These were found by analysis to possess the 

 statistical characteristics of the irregular ocean waves. 

 The average height of irregular waves was about 85 per 

 cent of the "standard," L/20, wave and the highest 

 waves, therefore, considerably exceeded the height of the 

 standard wave. This led, of course, to higher peak 



bending moments as this is shown by dots in Fig. 16. 

 The bending moments in irregular seas ha^'e now reached 

 those obtained from a static calculation with Smith 

 correction (in regular waves), but still remained well 

 below the conventional static method. There was no 

 significant variation of bending moments with speed. 



Ship positions at peak sagging and hogging conditions 

 and at maximum slamming are shown in Fig. 17. This 

 figure brings out ^'i^'idly the severity of the model test 

 conditions. It represents, of course, an exaggeration as 

 far as an actual ship is concerned. No captain will or 

 can operate a T-2 tanker at 14.5 knots in head seas in 

 which the average wave height is 12 ft and the mean of 

 10 per cent highest waves reaches 25 ft. As a residt of 

 this exaggeration the slamming was encountered under 

 full-load conditions, while on cargo ships at sea the 

 slamming of fully loaded ships is rare and becomes fre- 

 ciuent only in light conditions. 



4.12. Analysis of E. V. Lewis' bending-moment data. 

 At the time E. V. Lewis' tests were starteti, the rational 

 approach outlined in Section 2 of this chapter was not 

 yet available.'^ It had become available later and was 

 applied to the T-2 tanker data by W. R. Jacobs (1958). 

 In his 1954 paper, however, Lewis gave an extensive 



" The early theoretical work of Kriloff and of Horn and meas- 

 urements at sea by Schnadel appear to have been forgotten. 



