The Society of Naval Architects of Japan
60TH ANNIVERSARY SERIES
VOLUME 2
ADVANCES IN CALCULATION
OF
WAVE-MAKING RESISTANCE OF SHIPS
By
Takao
I N U IHajime
MARUO%uith the collaboration of
Masatoshi
BESSHOTatsuro
HANAOKAToshio
HiSHiDATatsuo
JINNAKATetsuo
NiSHiYAMAYoshiyuki
YAMAMOTOThe Society of Naval Architects of Japan
Tokyo, 1957
C O N T E N T S
PREFACE
t
Part I Non-Uniform Motion
Modem Developments of the Theory of Wave-Making
Resistance i n the Non-Uniform Motion
By H a j i m e MARUO, Yokohama National University
Introduction ^^^^ Chapter 1 Basic Formulae , g
§ 1 A fluid motion caused by a body moving under the surface of water !'.' 3 Chapter 2 Periodic Motion
§ 2 An oscillating body in a rectilinear motion
§3 Damping of ship's rolling due to wave-making , §4 Ship's oscillation among waves
§5 Resistance of a ship in a seaway Chapter 3 Non-Periodic Motion
§ 6 Resistance in the accelerated motion § 7 Finite depth of water
Chapter 4 Conclusions
§8 The future aspects in the theory of wave resistance in non-uniform motion Figm-es 1~17 .. 11 .. 11 .. 20 .. 28 .. 39 .. 51 .. 51 .. 60 .. 67 . . 67 73-82
Part I I Uniform Motion
Wave Pattems and Ship Waves
By Tatsuo J i N N A K A , Ktjushu University § 1 Introduction
§ 2 Expressions for wave elevation
§8 Numerical evaluation of local disturbances § 4 Numerical evaluation of regular free waves
§5 Comparison with the results by the 'stationary phase' method
§6 Exact calculations for wave profiles on the actually curved sides of ships'
Introduction
Study on Submerged Hydrofoils
i i CONTENTS
Page
§ 1 Methods of analysis • 96 §2 Approximate solution for submerged hydrofoils of the plate section 96 §3 Exact solution for submerged hydrofoils of the plate section 99 §4 Approximate solution for feubmerged hydrofoils of an arbitrary section 103
§5 Exact solution for submerged hydrofoils of an arbitrary section. 106 § 6 Fh-st approximation to submerged hydrofoils of the profile form satisfying the
prescribed pressure distribution 109 § 7 Second approximation • • UO
§ 8 Characteristics of submerged hydrofoils among stationary waves 112 Chapter 2 Theory of Submerged Hydrofoils with Finite Span (Three-Dimensional
Problem) , • 116
§9 Induced velocity 116 §10 Hydrodynamic characteristics US
§11 Optimum distribution of circulation 120 §12 Effect of dihedral angle on the characteristics of submerged hydrofoils .: 122
§13 Conclusions 126 Figures 1-31 128-134
On the Wave Resistance Theory of a Submerged Body
By Masatoshi B E S S H O , Defence Academy
Introduction 1^5 Chapter 1 Higher Approximation to the Wave-Making Resistance of a Submerged
Body (Three-Dimensional Problem) 136 §1 Expressions for the wave-making resistance of a submerged spheroid 136
§2 Numerical evaluation for a submerged sphere.; 141 § 3 Numerical evaluation for a submerged spheroid and its comparison with model
basin experiments 145 §4 General expressions for the wave-making resistance of a submerged body of
an arbitrary form • • • • • 1^4 Chapter 2 Effects of Finite Amplitude on the Wave-Making Resistance (Two-Dimen¬
sional Problem) 159
§5 The wave-making resistance of a submerged circular cylinder- 159
§ 6 Conclusions • 16'''
Figures 1-12 169-172
Study on Wave-Making Resistance of Ships
By Takao INUI, University of Tokyo
Chapter 1 Introduction l ' ^ ^ §1 Historical review 1'''4 §2 Outline of the methods applied 181
Chapter 2 The Boundary Condition on the Surface of Ships 185 § 3 Wave-making resistance of ships with finite breadth (Case of infinite draught) 186
§ 4 Wave-making resistance of ships with finite breadth (Case of finite draught).. 192
§5 Preliminary examination by model basin experiments 195 Chapter 3 Simplified Method of Calculations for Wave-Making Resistance 197
§ 6 Asymptotic expansions of the resistance integrals 197
CONTENTS i i i
Page
Chapter 4 Wave-Making Resistance in Viscous Fluid 205 §8 Consideration of the effects of viscosity 205 §9 Consideration of the effects of hull's self-interference 209
§ 10 Consideration of the effects of finite amplitude 213 Chapter 5 Measurement of Total Resistance vi^ith Floating Models 215
§11 Horizontal towing guide 216 §12 Tui-bulence stimulation 219 §13 Experimental results 222 Chapter 6 Measurement of Viscous Form Resistance with Submerged Double Models 222
§ 14 Resistance-dynamometer for a submerged body 223
§15 Experimental results 224 Chapter 7 Detection of Wave Profiles along the Sides, and in the Rear of Models .. 227
§ 16" Equipment used for recording wave profiles 228
§17 Methods and results of experiments 229
§ 18 Effect of draught 232 Chapter 8 Photographic Observations 232
§19 Minute observation of flow separation and wave-making at the stez-n 233 § 20 Bird's-eye view observation of the total wave systems in the rear »f models 234
Chapter 9 Comparison between Theory and Experiment 235
§21 Comparison in wave-making resistance 235
§22 Comparison in wave profiles 240 Chapter 10 Wave-Making Resistance in Shallow Water 242
§ 23 Wave-making resistance in the unrestricted shallow water 242 §24 Wave-making resistance in the restricted shallow water 243 §25 Measurement of total resistance in a shallow water model basin 244
§26 Comparison between theory and experiment (Practical application—1) 246
Chapter 11 Applications in Hull Design .- 249 § 27 Waterline forms and optimum Froude number (Practical application—-2) . . . . 250
§28 Analysis of the results of resistance experiment on various hull forms
(Practical application—3) 252 §29 The effect of hull surface roughness upon wave-making resistance (Practical
application—4) 252 Chapter 12 Conclusions 254
§30 Summary . ' 254
§31 The future aspects 256 Tables 1-37... 260-288 Figures 1-104 289-355