LOADS ACTING ON A SHIP AND THE ELASTIC RESPONSE OF A SHIP 



303 



spectrum in various weather coiulitions must be con- 

 sidered as the most important direction of research 

 leading to the rational evaluation of ship stresses. Since 

 apparently iusurni()untal)k' differences of opinion exist 

 between certain cnu'rentlj^ d(jminant research groups, it is 

 suggested that efforts be directed to interest and support 

 additional research groups, not yet associated with one 

 or another of the mutually opposed opinions. The 

 foregoing remarks are made here only as a reminder on 

 the importance of research on conditions of the sea. 

 For a more detailed exposition the reader is referred to 

 Chapter 1. 



8.3 Linear Theories and Model Tests. The linearized 

 ship-motion and shi]i \'ertical beniling-moment theories 

 ill head or following seas appear to be in a reasonably 

 good state. They were formulated in a general form 

 which includes all aspects affecting a ship's beliaxior. 

 Further improvements are necessary, of course. How- 

 ever, they will be directed primarily to the evaluation of 

 various coefficients entering into differential equations 

 of motions. The most important of these are the co- 

 efficients of damping forces, and the acute need of furtlicr 

 research on these was pointed out earlier. 



Towing tank data on ship-model motions in head 

 regular seas appear to be satisfactory and are in reason- 

 ably good agreement with calculated motions at model 

 speeds which are higher than synchronous sjieed. Motlel 

 test data appear to be unreliable for speeds below syn- 

 chronism because of the interference of waves reflected 

 from the towing tank walls, Abkowitz (.3-L956a). The 

 only measurements available to date in a wide maneuver- 

 ing tank, Numata (1957), indicate considerable dif- 

 ferences in model motions from the results obtained in 

 long tanks at and below synchronous speed. Since ships 

 are always operated below synchronous speed in heavy 

 weather, the additional experimental research in wide 

 tanks in the low speed range is necessary. 



Alodel tests in towing tanks have given clear fiuali- 

 tative information on the magnitude of bending moments 

 as functions of encountered waves. This information, 

 in agreement with theory and with meager data obtained 

 at sea, shows that a ship's bending moment is much 

 smaller than is indicated by static calculations. Static 

 calculations exaggerate bending moments even if the 

 Smith effect is taken into account. The inertial forces of 

 ship masses and liydrodyuamic forces resulting from 

 interaction of a ship and waves further reduce bending 

 moments, liationally computed as well as experi- 

 mentally measured bending moments are much smaller 

 than statically computed ones in any given legnlar wave. 

 On the other hanti, indi\-itlual waves in a tyj^ical irreg- 

 ular sea are often much steeper than the 1 :20 wave used 

 in conventional static calculations. As a result, the 

 actual bending moments in irregular sea are of the same 

 order of magnitude as conventionally computed ones in 

 the case of normal cargo ships. 



Nevertheless it is recommended that the research in 

 further development of rational methods of bending- 

 moment calculations be pursued. The research in this 



domain already has indicated that the bending moment 

 experienced by a ship is a relatively small difference of 

 several large static and dynamic components of different 

 signs. It can lie imagined readily that, in an irregular 

 sea, an unfavorable combination of several components 

 may occur from time to time. Unusually high stresses 

 may then result. Such an occasional unfavorable com- 

 bination may explain the recorded occurrence of high 

 stresses under apparently mild-weather conditions, 

 Section ti. 



Quantitatively, significant differences are observed in 

 bending-moment behavior as measured on models by 

 different investigators. These differences are partic- 

 ularly conspicuous in the \'ariation of bending moments 

 with model speed and in the amoimt by which the sagging 

 stresses exceed the hogging ones, l^'urther model re- 

 search in l)ending-moment and shear distribution is, 

 llierefore, recommended. The probability of important 

 wall inteiference in long tanks indicates that research 

 programs in wide tanks are needed. 



8.4 Nonlinear Theories. I^revious remarks on the 

 raticnial theory of ship motions and bending moments 

 were based on a linear theory. The significance of non- 

 linearity in defining ship motions at large amplitudes is 

 uncertain, and carrying out of nonlinear calculations of 

 motions was suggested in Chapter .3. However, effect of 

 nonlinearity on motions is not l)elie\'ed to be important 

 for ships of normal form, and this direction of research 

 can be assigned a lower priority than the calculations 

 and measurements of mean added masses and damping 

 forces. This opinion is based on the fact that ship mo- 

 tions are obtained by double integration of accelerations 

 caused by hydrotlynamic forces. Nonlinearities cause 

 certain short-duration deviations of instantaneous forces 

 from the mean harmonic variation. The effect of these 

 short-duration variations is smoothed out in the process 

 of double integration '■* and the motions are mainly de- 

 fined by the mean energy transfer between a ship and 

 waves. 



A different situation exists in the case of bending 

 moments. The variations of local displacement and 

 hydrodynamic forces are felt instantly by a .ship's struc- 

 ture while inertial forces depend on the ship's motions. 

 The bending moments are caused by the unbalance 

 among hydrodynamic and inertial forces and, therefore, 

 can be expected to be sensit ve to nonlinearities. The 

 increase of sagging liending moments of destroyers with 

 the wave height and a ship's speed (Sato, 1951; Lewis 

 and Dalze'l, 1958) is suspected to be caused by non- 

 linearities resulting from the submersion of a flared bow 

 in waves. The foregoing discussion and the model ex- 

 periments indicate that the motions remain nearly har- 

 monic in regular wa\TS and are not changed appreciably 

 even by slamming. Hence, the instantaneous hydrody- 

 namic forces can be calculated considering the actual 



'* The e.xpressioii "iloulili' integration" sliould not be considered 

 as applicable to calculations but rather as the description of a 

 physical jjrocess in which time is needed for accelerations to develo]) 

 velocities, and for velocities to develop bodj' displacements. 



