146 



THEORY OF SEAKEEPING 



(6) The use of curved lines in conjunction with dead- 

 wood (or skegs) which are common in the stern portions 

 of ships. 



(c) The use of curved Hues in conjunction with pro- 

 peller-shaft bossings which are common in multi-screw 

 ships. 



It is belie\-ed that these recommended evaluations can 

 be accomplished by electric analog}^ methods (Section 

 3.11; Koch, 1933). 



2 Analytical Research for Evaluation of Added 

 Masses and Damping in heaving oscillations of cylin- 

 drical bodies (F. M. Lewis' Sections), floating on the 

 free water surface, is recommended for the full range of 

 frequencies. This would be an extension of Ursell's 

 (1949&) work on heaving oscillations of a circular cylinder 

 (Section 3.12). 



3 Analytical Investigation of Added Masses for .ship 

 sections the sides of which are inclined is also required. 

 These inclinations are particularly prominent in the 

 stern section of most ships, and are also present to a 

 smaller degree in the bow sections of V-form ships. They 

 are present throughout the length of sailing yachts. 

 This project involves (.see Sectiou 3.12 for details) 

 water-surface penetration at moderate vertical velocities 

 (not permitting neglect of the gravity forces), the con- 

 junction of a deep draft and inclined sides, and move- 

 ments both into and out of water. 



4 Analytical Investigation of a Three-Dimensional 

 Correction to the two-dimen.sionally evaluated added 

 masses in heaving and pitching oscillation of ships is 

 advisable. Section 3.13. The correction is required at 

 individual strips (sections of a ship's length) for u.se in 

 the computation of bending moments. For the com- 

 panion project on damping forces see item 17. 



5 Experimental Measurements of Added Masses 

 (Section 3.15) for prisms and cj'linders of various cross 

 sections are needed, The objective of the tests is experi- 

 mental verification of the theoretical research listed 

 under items 1(a), (6), and (c), 2 and 3. The test bodies 

 must span the experimental tanks. Tests preferably 

 should be conducted in long towing tanks and particular 

 care must be taken to eliminate reflected waves from the 

 tank ends. Proper control and reporting of oscillation 

 frequencies should be provided. Inertia! forces and 

 damping forces should be recorded as 180 and 90 deg 

 out-of-phase components of the total hydrodynamic 

 force. 



6 Experimental Measurements of the Forces and 

 Moments Exerted by Waves on ship models are needed. 

 Section 3.14-4. Tests at low model speeds should be 

 conducted in wide tanks in order to avoid contamination 

 by reflected waves. Different model forms should be 

 used and waves of different lengths, from 0.75 to 2 times 

 the model lengths, are suggested. Amplitudes of forces 

 and moments and phase lags should be measured. Wave 

 profiles at the model (but not distorted by it) should be 

 recorded simultaneously. Inertial (acceleration) and 

 velocity-proportional forces .should be computed as in- 



phase (0 or 180 deg) and 90 deg out-of-phase com- 

 ponents of the total force or moment. 



7 The Distribution of Hydrodynamic Wave-Caused 

 Forces along the .ship length should be determined. This 

 can be done cither by using a segmented ship model or 

 by measuring the pressure distribution over the hull. 

 The last method calls for a very large number of pressure 

 probes if the pressure integration is to be reliable. The 

 method can be made practical, however, if properly 

 supplemented by theoretical considerations. Theory can 

 be used to indicate all details of the pressure distribution. 

 A relatively small number of pressure probes can then 

 show the difference between theoretical and measured 

 (or measurable) values. 



8 Theoretical Evaluation of Sectional Damping 

 Forces Appears to be the Most Pressing Need in the 

 theory of heaving and pitching motions and in the 

 rational evaluation of ship bending moments, Section 

 3.2. A critical review of Grim's (1953) work is sug- 

 gested, since this study is the most ad\'anced in this field 

 yet appears to fail in indirect experimental verification. 

 Section 3.21. In particular, it is desirable to assess 

 the deviations from true physical conditions in settmg 

 up a mathematical model and if possible to reduce these 

 deviations. Attention should be concentrated on the 

 range of oscillation frequencies of practical interest in 

 ship i^roblems. 



9 Alternate Evaluation of Sectional Damping Forces 

 should be undertaken making use of the flow evaluation 

 method given bj' Ur.sell (1949a). 



10 Alternate Evaluation of Sectional Damping Forces 

 and Their Distribution Along the Ship Length on the 

 basis of the work of Haskind (1946) and Hanaoka 

 (1957) is also advisable. 



11 Theoretical Evaluation of Mean Values of Non- 

 linear Sectional Damping (with respect to draft changes. 

 Section 3.22) can probably be obtained relatively easily 

 by a suitable extension of the Holstein-Havelock source 

 method. 



12 Three-Dimensional Damping Considering Non- 

 linear Sectional Contributions (Section 3.22, la.st para- 

 graph) can probabl.v be attacked successfully by extend- 

 ing the Holstein-Havelock source method. The evalua- 

 tion of three-dimensional effects by Havelock and 

 \'ossers, based on the theory of infinitesimal displace- 

 ments, failed to impro\'e the agreement between com- 

 puted and experimental damping forces, Section 3.21. 

 Since the damping intensity is indicated by the energy 

 carried by waves at infinity, and since the amplitudes of 

 these waves are governed by wave interference patterns, 

 it is suspected that periodicallj^ changing drafts at the 

 ship ends may be the most important a.spect of three- 

 dimen.sional effect. 



13 Theoretical Investigation of Damping in Heaving 

 of Sections With Inclined Sides is a companion project 

 to No. 3 on added masses. The problem is outlined in 

 Section 3.12. In regard to damping the problem is 

 further characterized bj' the fact that water particles at 



