THEORY OF SEAKEEPING 



Chapter 2 



HYDRODYNAMIC FORCES 



1 Introduction 



1.1 Forces Acting on a Body Oscillating in a Fluid 



1.2 Order of Exposition 



3.1 



3 

 3 

 3 

 3 

 3 

 3 

 3 

 3, 

 3 



3 



3 



3 



3 



3.3 



Estimates of Hydrodynamic Forces and Mo- 

 ments by Comparison With Ellipsoids 



Evaluation of Forces in Heaving and Pitching 

 by Strip Theory 



Inertial Forces Acting on a Body Oscillating in 

 Smooth Water: 



11 Conformal transformations 



12 Effect of the free water surface 



13 Three-dimensional effects 



14 Inertial forces caused by waves 



.15 Experiment data on inertial forces 



151 Deeplj' submerged ])risms and cylinders 



152 Prisms oscillating on the water surface 



153 Ship forms oscillating on the water surface. . . 



154 Restrained ship forms and other bodies sub- 



jected to wave action 



Damping Forces 



.21 JOxjjerimental verification of the sectional 

 damping coefficients 



22 Nonlinear effects in evaluating mean damping 



23 Three-dimensional eh'ects 



24 S])eed elfect on damping 



Integration With Resjiect to Length 



114 

 115 

 115 

 115 



116 



117 

 118 



119 

 122 

 122 

 123 

 124 



Forces in Lateral Motion 124 



5 Forces and Moments in Rolling . 



5.1 Restoring Moment 



5.2 Inertial Moments 



5.3 Damping Moments 



125 

 126 

 126 

 127 



7.3 



7.4 

 7.5 

 7.6 



8 

 8.1 



8.2 

 8.3 

 8.4 



31 Linear apiiroximation 127 



32 Empirical data on damping in roll 128 



33 Theoretical knowledge of damping in roll. . . . 129 



34 Effects of viscosity and frequency 130 



Direct Three-Dimensional Solution Including 



Wave Making 130 



Statement of the Problem 130 



Evaluation of the Velocity Potential 131 



Experimental Verification 133 



Computations of Haskind 134 



Concluding Remarks 135 



Forces Caused by Slamming 136 



E\])anding Plate Theory in Landing Impact of 



Seaplanes 136 



Spray Root Theory 137 



Adaptation of Seaplane Impact Theories to Ship 



Slamming 138 



Calcvdated Slamming Pressures 140 



Impact on Wavy Water Surface 141 



Forces Generated by a Bow Flare 142 



Concluding Remarks and General Research 



Suggestions 143 



E-xperimental Research: 8.11 Methods of test- 

 ing 143 



.12 Prismatic models 144 



.13 Complete ship models 144 



Theoretical Research 144 



Measurements on Full-Size Ships 145 



Slamming Pressures and Forces .... 145 



Condensed List of Suggested Research Topics 145 



Nomenclature 150 



Chapter 3 



SHIP MOTIONS 



1 Introduction 152 



2 Ship Motions in Long-Crested Harmonic Waves 152 



2.1 Ship Motions in the Plane of Synnnetry: 2.11 



Linear theor,\' of coupled pitching and heaving 153 



2.12 Comparison of computed and observed shij) 



model motions 155 



2.13 Variable coefficients and non-linearities 157 



2.14 Significant characteristics of ship motions; 



significance of pha,se relationships 158 



2.2 Rolling, Heaving, and Side Swaj- 158 



2.21 Deviations from Froude's assumptions 159 



2.22 Xonlinearities in rolling in side waves 160 



2.3 Six-Component Shi]) Motions in Waves: 2.31 



Motions with rudder fixed 162 



2.32 A degree of freedom addeil liy the use of a 



rudder 163 



2.33 Approximations based on a limited number of 



degrees of freedom 164 



3 Ship Motions in Irregular Seas 166 



ii.l Probabilistic X'crsus Deterministic Methods... . 166 



3.2 A Deterministic Method for Studying Ship Mo- 



tions in Irregular Seas 167 



3.3 Shi]) Motion Studies Based on Linear Superjjosi- 



tion 168 



3.4 Statistical Methods for Stud>-ing Motions in Ir- 



regular Waves 1 69 



3.5 Analysis of Ship Motions Data — Single Param- 



eter 172 



3.6 Cross-Spectrum Analysis 173 



3.61 Covariance-digital method 175 



3.61 Analog methods 176 



3.7 Rolling of Ships in Natural Irregular Waves. . . 176 

 3.71 Wink of V'ozncssensky and Firsoff 178 



4 Model Tests in Waves 178 



4.1 Towing Tanks and Equiijment 179 



4.2 Tanks for Tests in Obliiiue Waves 179 



4.3 Wave Generation 179 



4.4 The Nature of Activity in Towing Tank Testing 



in Oblique Seas 1 80 



4.41 Tests of practical nature: conditions of simi- 

 larity ISO 



