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



307 



stant coefficients) can be assumed to hokl for ship 

 motions, l)ut instantaneous values of coefficients, taken 

 as functions of the draft, are to be taken for lien(Ung 

 moment analysis. 



2 Bending Moment Analysis of ships to which the 

 linear theory does not apply is suggested. This includes 

 such forms, for instance, as the yacht discussed by 

 Korvin-Krouk(i\sky and Jacobs (3-1957) and a shallow- 

 draft vessel of Akita and Ochi (3-1955). In this case 

 the varialjility of coefficients must be considered in 

 calculations of motions, as well as bentling stresses, and 

 the proj(>ct involves step-by-stcp numerical integration 

 or the use of an analog computer. 



3 Effect of Attenuation of the Wave Profile as the 

 wave progresses along the shi|) should be in\-<'stigated. 

 In the strip method of calculation, basetl on Korvin- 

 Kroukovsky and Jacobs (3-1957) and Jacobs (1958), 

 this effect is neglected. Therefore, usually it is not ])os- 

 sible to achieve the closing of the fiending-nioment 

 diagram, and calculations are based on the front half of 

 a ship's length. The method of corrt-cting for the wa\'e 

 attentuation can be based on Grim (3-1957(;, second 

 part). In addition to closing of the bending-moment 

 diagram, the impro\-enient can be expected in the e-\'alua- 

 tion of phase relationships. These relationships are 

 sensitive to cross-coupling coefficients which are directly 

 affected bj- the wave attenuation. Stresses are in turn 

 sen.sitive to phase relationships. 



4 Development of the Control Over Ship's Loading 

 is suggesteil in onlcr to a\'oid exccssixc ship stresses. 

 It was shown in Sections 3.1 and 3.2 (MS San Francisco 

 and SS Ocean Vulcan) that bending moment caused liy 

 a ship's loading often doubled the wave-caused moment. 



5 Correlation of the Computed and Measured Bend- 

 ing Moment on ships at sea can be made broadly follow- 

 ing the technique of Schnadel and Admiralty Ship Weld- 

 ing Committee, Sections 3.1 and 3.2. However, con- 

 siderable refinement in the instrumentation and analysis 

 is needed. Continuous and simultaneous recording of all 

 data must be pro\'ided. The method of recording must 

 be co-ordinated with the available methods of analysis 

 so that a larger proportion of the olitained data could be 

 utilized than heretofore has been possible. The instru- 

 mentation should include a shipborne wa\'e-height 

 indicator (at present Tucker's), preferably installed 

 somewhat ahead of the front end of bilge keels in order 

 to reduce the ship's hull interference. The properties 

 of irregular waves must be I'onsidered in reconstruction 

 of wa\'e profiles. The wave height at positions different 

 from the place at which the height is measured conceiv- 

 ably can be evaluated l)y methods of Fuchs (3-1952) 

 and Cote (1-1954). 



The author does not believe that it is practical to use 

 enough pressure gages to evaluate the total hydrody- 

 namic force with sufficient precision. He suggests, 

 therefore, that pressure measurements and their correla- 

 tion with theory be made only on one or two ship sections. 

 Other cf)rrelations would hv limited to ship motions, 

 bending moments and deflections. 



Past experience indicates the difficulty of maintaining 

 at sea the instruments installed at the ship's bottom. 

 Therefore, it is suggested that strain gages at the deck 

 only be used at sea and that their relationship to bending 

 nu)ments l>e established b.y calibration in port. As in the 

 case of pressure gages, one or two ship sections in ac- 

 cessible location (engine room) can be ec^uipped com- 

 pletely with strain gages. 



It is recommended that a suitable towing-tank test be 

 conducted on the model of a ship usetl in sea observa- 

 tions. The data from such an auxiliarj^ project will 

 help in interpretation of the data ol.)t.ained at sea, and 

 also may be used to fill in the missing data, for instance, 

 because of malfunctioning of isolated transducers. 



6 Relationship Between Hogging and Sagging Bend- 

 ing Moments should be investigated further by theoi-y 

 and model tests. The data of Schnadel, Lewis, and (Jchi 

 agree in showing that the sagging moment is larger, but 

 disagree on the relative magnitudes (see the end of 

 Section 4.2). The ratio of the sagging to hogging bend- 

 ing moments dejiends, of course, on tlic tj'pe of ship. 



7 Limiting Value of Bending Moments in head seas 

 should be investigated b,y using nonlinear theorj- and 

 computational procediu'e. The techni(|ue is similar to 

 that indicated in project 2; ship motions and bending 

 moments are to be evaluated employing step-by-step 

 iiitegratiou of the coupled pitch-heave equations of mo- 

 tion with time-dependent coefficients evaluated on 

 tlie basis of instantaneous conditions. A suitable section 

 of a typical long-crested irregular wave pattern is to be 

 chosen and calculations should cover several wave cycles, 

 starting with a quiescent period and running through the 

 group of highest and steepest waves. It is suggested 

 that the investigation lie made in irregular wa\-es, since 

 the phase relationships in a continuous train of regular 

 wa\'es may be different from those in a group of a few 

 high irregiUar waves, and since bending moments are 

 strongly affected bj' phase relationships. Calculations 

 should be repeated for a few sea conditions of increasing 

 .severity in order to establish the relationship among bend- 

 ing moments and statistically defined sea conditions. 

 Once the computational programming is developed, the 

 additional cases can be evaluated on high-speed com- 

 puters with but little additional lalior. 



8 Bending-Moment Measurements on Models should 

 be made under conditions analogous to the ones outlined 

 in project 7. It should be emphasized that project 7 

 has for its aim the detailed explanation of the limiting 

 ship stress conditions; it is not a statistical project. 

 Project 8 has for its first objective the comparison of 

 theoretical (from project 7) and experimental values. 

 However, this project can be continued to the second 

 objective; namely, to establish statisticallj' the fre- 

 ([uency distribution of high bending moments in a 

 sufficiently long typical irregular wave pattern. In a 

 towing tank of limited length, the long irregular sea 

 pattern can be composed of a number of short test riuis 

 in successive sections of a continuous pattern. 



9 Bending-Moment Measurements on Models in 



