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



269 



Table 4 Factors Involved in Bending Moments of Ships or Ship Models in Waves (from E. V. Lev/is, 1954) 



Conv. 

 static 



-Calculations • 



Ocean 

 Modif. Vulcan 

 conv. analysis (9) 



Restrained 

 model, 

 Speed 



-Experiments- 



Wave forces in undisturbed waves:" 



1 Buoyancy — Hydrostatic 



(a) Hull assumed level X 



(b) Hull at correct pitched and heaved 



position; Kriloff (17) 



2 Pressure distribution in wave; Smith 



effect (13) 



Interaction between hull and wave: 



3 Modification of pressures by presence 



of hull or by vertical motion in 

 pitch and heave relative to undis- 

 turbed wave; damping (9, 24, 26). . . . 



4 Modification of pressures in wave by 



vertical accelerations of hull and of 

 wave particles; virtual mass (9, 29, 

 31) 



5 Modification of wave profile by pres- 



ence of hull — hence pressures and 

 velocities. Reflection, Kreitner 

 (30). (Mainly due directly to for- 

 ward speed ) , 



Effects of motion on virtual weights: 

 \'ertical accelerations; KrilofT (17) 



Miscellaneous effects: 



7 Effect of natural period of hull vibra- 



tion (28) 



8 Effect of eccentricity of compressive 



forces (9) 



9 Direct effect of speed in modifying 



pressures (33) and causing dy- 

 namic lift 



X 



X 



X 



X 



X 



(partial) 



X 



(partial) 



X 



X 



X 



X 

 (partial) 



X 



(partial) 



X 



(minor) 



X 



(minor) 



X 



-Free Model 



Moving 

 (and 

 ship) 



Speed 



X 



X 



X 



X 



(minor) 



X"- 

 (minor) 



X 



(minor) 



X 



X 



X 



X 



X 



X 



X 



Ship 

 pressure 

 integra- 

 tion 



(9) 



X 



X 



X 



X 



X 



NoTK Ittms :(. 4. and are affected indirectly by changes in phase relationships and in the tuning; factor (ratio of natural period to [)eri*td 

 of encounter) in pitch and heave. 

 " I'roude- Kriluff hypothesis 

 *• At speed, phase relationships in this case are such that model acceleratii)ns do not affect tnaximum bending; moments. 



discussion of the origin and cau.ses of ship bending mo- 

 ment. This discussion represents in fact a qualitative 

 analysis. Of particular interest is Table 4 which hsts 

 various causes contributing to bending moments and 

 shows to what extent they are incorporated in various 

 analyses and tests. 



An attempt at a quantitative analysis also was made 

 and the results are shown in Fig. 18. The calculations 

 were based on the observed wave profile at the model's 

 side and on measured accelerations. The statically 

 computed buoyancy was not in balance with the hull 

 weights which were reduced by model accelerations. 

 Since the method of accounting for various water-flow 

 effects was not available, the buoyancy curve was ad- 

 justed by judgement so as to provide the necessary 

 balance. Quoting from E. V. Lewis: "In order to indi- 



cate the order of magnitude of the dynamic effects, which 

 have not been accounted for, a hj'pothetical curve of 

 effective buoyancy has been drawn in Fig. 18.'^ This 

 ciu've would bring about a balance between virtual weight 

 and buoyancy and at the same time would give equal 

 forebody and afterbody bending moments of 13.0 Ib- 

 in., as measured with the model in the position shown. 

 It is clear that dynamic effects are of appreciable mag- 

 nitude and therefore that their investigation is of con- 

 siderable importance. " 



A complete quantitative analysis of bending moments 

 in regular waves was made later by Jacobs (1958). 

 The analysis followed the pattern outlined in Section 2 

 of this chapter. Comparison of the e.xperimental and 

 calculated bending moments is shown in Fig. 19 for 



1' The figure number of the iiresent monograph is substituted. 



