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



259 



Fig. 1 (top) and Fig. 2 (bottom) Experimental towing tank 



calculations and experimental data for amidships of Model 172 3 



(destroyer). 5.71-ft model at 5 fps; wave length = model 



length; wave height = ' /,, model length 



Force component 

 caused by 



' displacement = pgB{z + ^6) 



I velocity = [N(^) - Vpd(Shh)/d^] 



{z + ^6 - Yd) (4) 

 (acceleration = iii(z + ^d) + 



Next, the forces exerted by waves on a restrained ship 

 will be considered. The sectional force due to wave 

 action, (dF/d^)^ is given directly by equation (25) of 

 Appendix C. It may be convenient to separate the 

 first term of A'l coefficient from the others and to write 

 the force in the form of two components: 



(dF/d^U = pgBlh^m-''- 



. 27r.r\ 

 ni 



{dF/diU 



(5) 



remaining terms of equation (25) of Appen- 

 dix C 



The first of these components is simply the change of 

 the displacement caused by the wave rise as it is used 

 in conventional static calculations. This force (with 

 sign changed) can be added to the first of ecjuations 

 (4) in order to get the total force due to the change of dis- 

 placement. The remaining part of the first term of 

 efjuation (25) of Appendix C represents the Smith 

 effect modified by a ship's interference with waves. 

 The second term of eciuation (25) is a further correction 

 for a ship's speed. 



Efiuation (25) of Appendix C was derived from the 



potential solution which does not account for the dissi- 

 pation of energy in the form of surface waves. The 

 force ('(iniponent caused by the vertical water motion in 

 waves, /v-V({), must be added, therefore, to the force 

 resulting from ship motions, (z -\- (6 — T6).V({), in 

 equation (4). In the analysis of ship motions in Appen- 

 dix C, the force i'y,N{^) was neglected becau.se it bccauK^ 

 insignificant after integration with respect to ship's 

 length. However, it gives a significant contrilnition to 

 the loading of a ship's section, f/^, and should be included 

 in the analysis of bending moments. 



As an example, the results of bending-moment cal- 

 culations are shown in Table 2 and Figs. I and 2. ' The.se 

 data refer to the model 1723 (destroyer, the body plan of 

 which is shown in Fig. 31 and the particulars are given 

 in Table (3). The data on motions of this model in waves 

 were given liy Korvin-Krouko\'sky and Jacobs (3-l!)57). 



Fig. 2 shows an excellent agreement between expei'i- 

 mental and calculated bending moments. Talile 2 

 shows in detail the conditions existing at a particular 

 instant indicated by the tlouble circles in l-'igs. 1 and 2. 

 This instant corresponds to the hogging condition with 

 the l)ending moment nearly at its maximum. The 

 data at the bottom of the table indicate the tlynamic 

 conditions exi.sting at this instant. The wave crest is 

 amidships but at the same time the pitch angle is at its 

 maximum as this is indicated by 6 = and by the high 

 value of the pitching acceleration, 6. The small value 

 of the phase lag between heaving and pitching, 55 deg, 

 brings about simultaneously high values of heaving and 

 pitching accelerations. This brings about, in turn, a 

 large inertial force due to ship's masses and the added 

 water ma.s.ses. At station 5 for instance, the inertial 

 forces, 2.00 -|- 1.12, are greater than the displacement 

 force of —2.81 lb. Most of the remaining force of 

 — 0.51 lb is the result of the velocity-dependent (tlanip- 

 ing) foi'ce computed on the basis of iV(^). Table 2 

 demonstrates that the net loading at any ship section is a 

 relatively small difference between several large com- 

 ponents f)f different signs. The final shear distril)ution 

 and the bending moment are therefore very sensitive to 

 the accuracy of calculation of the iiidi\-idual com- 

 ponents. 



The large part played by inertial and by velocity- 

 dependent forces also indicates the sensiti\'ity of the 

 loading curve and of bending-moment cur\-es to phase 

 relationships. 



For an additional example of bending-moment cal- 

 culations, the reader is referred to Section 4.12. In this 

 section T-2 tanker model data are analyzed. A more 

 complete description of the procedures outlined in the 

 foregoing and in the T-2 tanker analysis will be found in 

 Jacobs (1!).58). 



2.2 Nonlinear Theory. The destroyer model in low 

 waves, (X//i = 48), cited in the foregoing exani])le, aj)- 

 pears to be amenable to t)oth motion and bending- 



■' This material is takon from an uiipulilished work of Winnifred 

 R. Jacobs (1!)57) of the Davidson Lalioratory, Stevens Institute 

 of Technology. 



