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INTRODUCTION TO
SONAR TRANSDUCER
DESIGN
JOHN C. COCHRAN
Cover Design: Wiley
Cover Image: © Cover image provided by John C. Cochran
www.wiley.com
COCHRAN
INTRODUCTION
TO
SONAR
TRANSDUCER
DESIGN
A comprehensive introduction to sonar transducer design,
complete with real world examples, step-by-step
instruction, and detailed mathematical review
In Introduction to Sonar Transducer Design, renowned sensor engineer Dr. John C. Cochran
delivers an instructive and comprehensive exploration of the foundations of sonar transducer
design perfect for beginning and experienced professional transducer designers. The book
offers a detailed mathematical review of the subject, as well as
fulsome design examples.
Beginning with a description of acoustic wave propagation, along with a review of

radiation from a variety of sources, the book moves on to discuss equivalent circuit
models that explain wave propagation in solids and liquids. The book reviews examples
of projectors and hydrophones accompanied by complete mathematical solutions. All
included math is developed from first principles to a final solution using an intuitive,
step-by-step approach.
Introduction to Sonar Transducer Design offers professionals and students the analytical
tools and assumptions required for start-to-finish transducer design. It also provides:
•
A thorough introduction to acoustic waves and radiation, including small signals,
linear acoustics, the equations of continuity, motion, the wave equation in a
fluid media, and integral formulations
•
Comprehensive explorations of the elements of transduction, including various
forms of impedance, and mechanical and acoustical equivalent circuits, as well
as their combination
•
Practical discussions of waves in solid media, including homogeneous, isotropic,

elastic, and solid media, piezoelectricity and piezoelectric ceramic materials,
and waves in non-homogeneous, piezoelectric media
•
In-depth examinations of sonar projectors and sonar hydrophones, including the
elements and tools of sonar projector and sonar hydrophone design, as well as
their applications
Perfect for sonar system engineers, particularly those involved in defense, Introduction
to Sonar Transducer Design will also earn a place in the libraries of acoustic, audio,
underwater communication, and naval engineers.
John C. Cochran, PhD, is a former Principal Engineering Fellow in the Advanced
Technology Department of Raytheon Integrated Defense Systems responsible for sonar
system design and operation. He is a subject matter expert in the design and development
of advanced sensors, sensor arrays, and undersea sensing systems.
32.1 mm 178 x 254 mm

Introduction to Sonar Transducer Design

Introduction to Sonar Transducer Design
John C. Cochran
Raytheon Technologies, RI, USA (Retired)

This edition first published 2022
© 2022 John Wiley Sons, Inc.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted,
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permitted by law. Advice on how to obtain permission to reuse material from this title is available at
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The right of John C. Cochran to be identified as the author of this work has been asserted in accordance with law.
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commercial damages, including but not limited to special, incidental, consequential, or other damages.
Library of Congress Cataloging-in-Publication Data applied for:
ISBN: 9781119851059
Cover Design: Wiley
Cover Image: © John C. Cochran
Set in 9.5/12.5pt STIXTwoText by Straive, Pondicherry, India
10 9 8 7 6 5 4 3 2 1

I dedicate this book to those who have always
been there for me: my wife Elizabeth; my
children Laura, Daniel, Sarah, and Rebecca; and
my mom and dad. I love you all.

Contents
Preface xvii
1 Acoustic Waves and Radiation 1
1.1 Small Signals/Linear Acoustics 1
1.1.1 Compressibility 2
1.1.2 Small Signals/Linear Acoustics 2
1.1.3 Relationship Between Acoustic Pressure and Acoustic Density 2
1.1.4 Condensation 2
1.1.5 Time Derivative Using Eulerian and Lagrangian Description 3
1.2 The Equations of Continuity, Motion, and the Wave Equation in a Fluid Media 3
1.2.1 Equation of Continuity in a Single Dimension 3
1.2.2 The Force Equation in a Single Dimension 4
1.2.3 The Wave Equation in a Single Dimension 5
1.2.4 Generalization of the Wave Equation to Three Dimensions 5
1.2.5 Helmholtz Wave Equation 6
1.2.6 Velocity Potential 6
1.3 Plane Waves 7
1.3.1 Harmonic Plane Waves 7
1.3.2 Plane Waves in an Infinite Media 7
1.3.3 Plane Wave Acoustic Intensity 8
1.3.4 Plane Wave Acoustic Impedance 8
1.4 Radiation from Spheres 8
1.4.1 General Solution to Radiation from Spheres 9
1.4.2 Spherical Wave Acoustic Impedance 11
1.4.3 Axis-Symmetric Radiation from a Sphere – the Spherical Source 11
1.4.4 The Simple Spherical Source 12
1.4.5 Source Strength 12
1.4.6 The General Simple Source 13
1.4.7 Acoustic Reciprocity and Reciprocity Factor 13
1.5 Radiation from Sources on a Cylindrical Surface 14
1.5.1 General Solution to Radiation from Cylinders 15
1.5.2 Radiation from an Infinitely Long Cylinder 18
1.5.3 The Simple, Infinitely Long Cylindrical Source 19
1.5.4 Radiation from an Infinitely Long Strip on an Infinitely Long Cylinder 20
1.5.5 Radiation from a Finite Source on a Cylinder with a Periodic z Dependence 21
vii

1.5.6 Radiation from a Finite Source on a Cylinder with a Uniform z Dependence 22
1.5.7 The Simple Cylindrical Source – Radiation from a Finite Length Cylinder in an Infinitely
Long Cylinder Baffle 25
1.6 Integral Formulations 26
1.6.1 The Green’s Function 27
1.6.2 Helmholtz Integral Formulations 28
1.6.3 Far Field Approximation 29
1.6.4 An Application of the Simple Source Integral Formulation – Radiation from a Finite
Cylinder 34
1.7 Linear Apertures 36
1.7.1 Far Field Radiation (Beam) Patterns as a Fourier Transform of the Linear Aperture
Function – the Directivity Function 36
1.7.2 A Simple Rectangular Aperture Function as an Example of a Linear Aperture 38
1.7.3 The Triangular Window Aperture Function as a Linear Aperture 41
1.7.4 The Cosine Window Aperture Function as a Linear Aperture 43
1.7.5 Other Linear Apertures 45
1.7.6 The Far Field Radiation Pattern of a Linear Aperture on a Cylindrical Surface 45
1.8 Planar Apertures 49
1.8.1 The Green’s Function for Radiation from Planar Apertures Located on a Rigid Plane
Baffle 49
1.8.2 Far Field Radiation Patterns as a Fourier Transform of the Planar Aperture Function 50
1.8.3 The Rectangular Piston in an Infinite Plane Baffle 52
1.8.4 The Circular Piston in an Infinite Plane Baffle 54
1.8.5 The Far Field Radiation Pattern of a Circular Annular Ring 59
1.8.6 The Elliptical Piston in an Infinite Plane Baffle 60
1.8.7 Impact of Boundary Impedance on Radiation Patterns from Planar Apertures 60
1.9 Directivity and Directivity Index (DI) 63
1.9.1 Definition of Directivity and Directivity Index (DI) 65
1.9.2 Relationship Between Source Level and Directivity Index 67
1.9.3 The Directivity of Baffled vs. Unbaffled Sources 68
1.9.4 The Directivity Index of a Baffled Circular Piston 68
1.9.5 The Directivity Index of a Baffled Rectangular Piston 70
1.9.6 The Directivity Index of a Line Source 70
1.10 Scattering and Diffraction 72
1.10.1 Scattering and Diffraction from a Rigid Cylinder 72
1.10.1.1 The Incident Wave 72
1.10.1.2 The Scattered Wave 73
1.10.1.3 Matching the Boundary Conditions for the Total Field 73
1.10.1.4 The Scattered Pressure Field in the Far Field 74
1.10.1.5 The Total Pressure Field 74
1.10.1.6 The Average Pressure Exerted on the Cylinder by the Total Pressure Field 74
1.10.2 The Diffraction Constant for a Rigid Cylinder 76
1.10.3 Diffraction Constant for a Strip on a Rigid Cylinder 76
1.10.4 Diffraction of a Cylinder with Variable Boundary Admittance 77
1.10.4.2 The Boundary Admittance 78
viii Contents

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1.10.4.4 Matching the Boundary Conditions 81
1.10.4.5 The Boundary Reflection Coefficient and the Scattered Field 81
1.10.4.6 The Total Field 82
1.10.4.7 The Average Pressure Exerted on the Cylinder With a Variable Boundary
Admittance 82
1.10.4.8 The Diffraction Constant for a Cylinder with Variable Boundary Admittance 82
1.10.4.9 The Total Diffracted Field in the Far Field 83
1.10.4.10 The Total Diffracted Field at the Surface of the Cylinder 83
1.10.5 Scattering and Diffraction from a Rigid Sphere 84
1.10.5.3 Matching the Boundary Conditions for the Total Field 85
1.10.5.4 The Total Pressure Field 85
1.10.5.5 The Scattered Pressure Field in the Far Field 86
1.10.5.6 The Average Pressure Exerted on the Sphere by the Pressure Field 86
1.10.6 The Diffraction Constant for a Rigid Sphere 87
1.10.7 Scattering and Diffraction from a Thin Cylindrical Ring 87
1.11 Radiation Impedance 89
1.11.1 Introduction to Radiation Impedance 89
1.11.2 Units of Acoustic Radiation Impedance 90
1.11.3 What it Means to be ρc Loaded 90
1.11.4 The Relationship Between Resistance and Reactance – The Hilbert Transform 90
1.11.5 The Relationship Between Radiation Resistance, Directivity, and Diffraction
Constant 92
1.11.6 The Radiation Impedance of a Spherical Radiator 94
1.11.7 The Radiation Impedance of a Simple Source Radiator 95
1.11.8 The Radiation Impedance of a Circular Piston Radiator in a Plane Baffle 95
1.11.9 The Radiation Impedance of a Circular Piston Radiator at the End of a Tube 97
1.11.10 The Radiation Impedance of a Rectangular Piston Radiator in a Plane Baffle 98
1.11.11 The Radiation Impedance of an Infinitely Long Strip Radiator in a Plane Baffle 100
1.11.12 The Radiation Impedance of a Circular Annular Piston Radiator in a Plane Baffle 101
1.11.13 The Radiation Impedance of an Elliptical Piston Radiator in a Plane Baffle 103
1.11.14 The Radiation Impedance of an Infinitely Long Cylindrical Radiator 103
1.11.15 The Radiation Impedance of a Finite Cylindrical Radiator 104
1.11.16 Mutual Radiation Impedance 105
1.11.17 The Mutual Radiation Impedance Between Spherical Radiators 106
1.11.18 The Mutual Radiation Impedance Between Two Circular Piston Radiators in a Plane
Baffle 108
1.11.19 The Mutual Radiation Impedance Between Two Square Piston Radiators in a Plane
Baffle 114
1.11.20 The Mutual Radiation Impedance Between a Circular Piston and an Outer Annular
Ring 116
1.11.21 The Mutual Radiation Impedance Between Rectangular or Square Pistons Located on a
Cylindrical Baffle 118
1.11.22 The Mutual Radiation Impedance Between Bands on a Cylindrical Baffle 124
1.12 Transmission Phenomena 125
1.12.1 Reflection and Transmission of Plane Waves with Normal Incidence at a Boundary 126
Contents ix

1.12.2 Reflection and Transmission of Plane Waves Obliquely Incident at a Plane
Boundary 129
1.12.2.1 Snell’s Law 130
1.12.2.2 Reflection and Transmission Factors for Obliquely Incident Plane Waves 131
1.12.2.3 Brewster’s Angle or the Angle of Zero Reflection 131
1.12.2.4 The Critical Angle or the Angle of Complete Reflection 132
1.12.2.5 Evanescent Waves 132
1.13 Absorption and Attenuation of Sound 133
1.13.1 Absorption Phenomena 133
1.13.2 Absorption in Seawater 134
References 135
2 Mechanical/Acoustical Equivalent Circuits 137
2.1 Different Forms of Impedance 138
2.2 Mechanical Equivalent Circuits 139
2.2.1 The Simple Mechanical System 139
2.2.1.1 A Simple Mechanical Oscillator 139
2.2.1.2 Phasor Form of the Solutions to the Equations of Motion 139
2.2.1.3 Damped Oscillations 140
2.2.1.4 Forced Oscillations 141
2.2.1.5 Complete Solution for a Simple Oscillator 142
2.2.1.6 Analogy to Electrical Circuits 142
2.2.1.7 Behavior of the Steady State, Forced, Mechanical Oscillator 143
2.2.1.8 Equivalent Circuit for a Simple Resonator System 144
2.2.2 Introduction to Mobility 145
2.2.2.1 Mechanical Generators 145
2.2.2.2 Combining Impedance and Mobility Elements 145
2.2.2.3 Elements of Mobility and Impedance Analogs 147
2.2.2.4 Examples of Mechanical Systems Described by Mobility Analogs 149
2.2.2.5 An Example of a Gyrator Conversion 150
2.2.2.6 Converting from Mobility to Impedance and Vice Versa 151
2.3 Acoustical Equivalent Circuits 153
2.3.1 Acoustic Circuit Elements 153
2.3.1.1 Acoustic Compliance – the Closed-End Tube 153
2.3.1.2 Acoustic Mass – the Open-Ended Tube 154
2.3.1.3 Acoustic Resistance 156
2.3.1.4 Acoustic Generators 156
2.3.1.5 Pressure Equalization Orifices 156
2.3.1.6 The Thin Acoustic Orifice 159
2.3.1.7 The Narrow Slit 160
2.3.1.8 The Acoustic Mesh or Perforated Sheet 160
2.3.2 Acoustic Equivalent Circuits 161
2.3.2.1 Example of an Acoustic System Described by an Equivalent Circuit 161
2.3.2.2 Another Example of an Acoustic Equivalent Circuit – the Helmholtz Resonator 161
2.4 Combining Mechanical and Acoustical Equivalent Circuits 163
2.5 Introduction to Transduction 165
x Contents

2.5.1 The Transducer as a Two-Port Equivalent Circuit 165
2.5.2 Reciprocal and Anti-Reciprocal Transducers 166
2.5.3 The Electromechanical Coupling Factor 166
2.5.4 Electromechanical Transformation 167
2.5.5 Transmitters 167
2.5.6 Receivers 169
2.5.7 Relationship Between Transmit and Receive Characteristics 170
References 171
3 Waves in Solid Media 173
3.1 Waves in Homogeneous, Isotropic, Elastic, Solid Media 173
3.1.1 The Components of Stress 173
3.1.2 The Equations of Motion 174
3.1.3 The Components of Strain 175
3.1.4 The Relationship Between Stress and Strain – The Constitutive Equations 177
3.1.4.1 Hooke’s Law – Tensor Form 177
3.1.4.2 Hooke’s Law – Matrix Form 179
3.1.4.3 The Differences Between Tensor and Matrix Forms of the Constitutive Equations 180
3.1.4.4 Lame’s Constants 182
3.1.4.5 Stiffness vs. Compliance Matrices 183
3.1.4.6 Modified Constitutive Equations 184
3.1.5 Acoustic Waves in Isotropic Solids 184
3.1.5.1 The Acoustic Wave Equation for Isotropic Solids 184
3.1.5.2 Waves of Dilatation and Distortion 184
3.1.5.3 Acoustic Plane Waves in Isotropic Solids 186
3.1.6 Longitudinal Waves in Bars 186
3.1.6.1 Vibrations in a Bar with Clamped Boundary Conditions 188
3.1.6.2 Vibrations in a Bar with Free Boundary Conditions 189
3.1.6.3 Equivalent Circuit Representation for Longitudinal Vibrations in a Bar with Arbitrary
Boundary Conditions 190
3.1.6.4 A Two-Port Representation of Longitudinal Vibrations Within a Bar 192
3.1.6.5 Impact of Different Load Impedances on the Longitudinal Vibrations Within a Bar 193
3.1.6.6 Equivalent Circuit Representation for a Mass-Loaded Bar with One Free End 194
3.1.6.7 Equivalent Circuit Representation for a Mass-loaded Bar with One End Clamped 196
3.1.6.8 Lumped Parameter Equivalent Circuit for a Longitudinal Resonator 198
3.1.6.9 The Effective Mass of a Spring 200
3.1.7 Equivalent Circuit Representations for Solid Elements 202
3.1.7.1 Longitudinal Vibrations Within a Hollow Cylinder 202
3.1.7.2 Longitudinal Vibrations Within a Conical Section 204
3.1.7.3 Longitudinal Vibrations Within an Exponential Section 206
3.2 Piezo-electricity and Piezo-electric Ceramic Materials 208
3.2.1 The Nature of Piezo-electricity 208
3.2.2 Piezo-electric Ceramic Materials 211
3.2.3 The Piezo-electric Ceramic Constitutive Equations 212
3.2.4 The Meaning of the Piezo-electric Coefficients 214
3.2.5 Piezo-electric, Elastic, and Dielectric Coefficient Nomenclature 215
Contents xi

3.2.6 Piezo-electric Ceramic Material Properties 216
3.2.7 The Electromechanical Coupling Coefficient 219
3.2.8 Further Observations on the Piezo-electric Constitutive Equations 220
3.3 Waves in Non-Homogenous, Piezo-electric Media 222
3.3.1 Vibrations in Rods and Disks 223
3.3.1.1 Constitutive Equations 223
3.3.1.2 Equations of Motion and Strain in Cylindrical Coordinates 224
3.3.1.3 Radial Mode Vibrations in Thin Disks 224
3.3.1.4 Thickness Mode Vibrations in Thin Disks 228
3.3.1.5 The Relationship Between Dielectric Constant and Coupling Factor for Vibrations in
Thin Disks 233
3.3.1.6 Length Longitudinal Mode Vibrations in Long, Thin Rods or Bars 235
3.3.1.7 Radial Mode Vibrations in Long, Thin Rods or Bars 237
3.3.1.8 The Relationship Between Dielectric Constant and Coupling Factor for Vibrations in
Long, Thin Rods 240
3.3.1.9 Frequency Constants for Vibrations in Rods and Disks 241
3.3.2 Vibrations in Piezo-electric Plates and Parallelepipeds 242
3.3.2.1 Equations of Motion and Strain in Rectangular Coordinates 243
3.3.2.2 Length Expander Bar with Electric Field Perpendicular to Width – The 31 Mode
Bar 244
3.3.2.3 Length Expander Bar with Electric Field Parallel to Width – The 33 Mode Bar 248
3.3.2.4 Thickness Mode Vibrations in Thin Piezo-electric Plates with the Electric Field Parallel to
the Thickness 250
3.3.2.5 Coupled Mode Vibrations in Parallelepipeds with One Large Dimension 254
3.3.2.6 Coupled Mode Vibrations in Thin Piezo-electric Plates with the Electric Field
Perpendicular to the Thickness 256
3.3.2.7 Coupled Mode Vibrations in Thin Piezo-electric Plates with the Electric Field Parallel to
the Width 258
3.3.2.8 Coupled Mode Vibrations in Parallelepipeds with Arbitrary Dimensions 259
3.3.3 Vibrations in Piezo-electric Ceramic Cylinders 261
3.3.3.1 Longitudinal Vibrations in Axially Polarized, Piezo-ceramic Cylinders 263
3.3.3.2 Longitudinal Vibrations in Radially Polarized, Piezo-ceramic Cylinders 272
3.3.3.3 Radial Vibrations in Radially Polarized, Piezo-ceramic Cylinders 281
3.3.3.4 Longitudinal Vibrations in Circumferentially Polarized, Segmented, Piezo-ceramic
Cylinders 285
3.3.3.5 Radial Vibrations in Circumferentially Polarized, Segmented, Piezo-ceramic
Cylinders 294
3.3.4 Vibrations in Radially Polarized Spherical Shells 297
3.3.4.1 Boundary Conditions 297
3.3.4.3 The Equations of Motion and Strain 298
3.3.4.4 Kinetic Energy and Equivalent Mass 299
3.3.4.5 Internal Energy 299
3.3.4.6 Electromechanical Coupling Coefficient 300
3.3.4.7 In-Air Resonance Frequency of a Spherical Shell 300
3.3.4.8 Equivalent Circuit Model for a Radially Polarized Spherical Shell 300
References 303
xii Contents

4 Sonar Projectors 305
4.1 Tools for Underwater Sonar Projector Design 305
4.1.1 Assembling Circuit Elements 305
4.1.1.1 Two-Port Representations for Non-Piezoelectric Components 305
4.1.1.2 Series Combination of Two-Port Networks for Non-Piezoelectric Components 307
4.1.1.3 Parallel Combinations of Two-Port Networks for Non-Piezoelectric Components 307
4.1.1.4 Two-Port Representations of Piezoelectric Components 308
4.1.1.5 Cascaded Combinations of Two-Port Networks for Piezoelectric Components 309
4.1.1.6 Ladder Network Analysis 311
4.1.2 How to Specify a Projector 312
4.2 Specific Applications in Underwater Sonar Projector Design 313
4.2.1 Frequency Ranges for Different Types of Projectors 313
4.2.2 Spherical Projectors 314
4.2.2.1 The Lossless, Air-Backed Spherical Projector 314
4.2.2.2 The Lossy, Air-Backed Spherical Projector 320
4.2.2.3 Fluid-Filled Spherical Projectors 321
4.2.3 The Radially Polarized Cylindrical Projector 323
4.2.3.1 The Radially Polarized, Air-Backed Cylindrical Projector 323
4.2.3.2 Prestressing for Increased Power-Handling Capability 328
4.2.3.3 The Radially Polarized, Fluid-Filled Cylindrical Projector 330
4.2.3.4 The Radially Polarized, Squirter Projector 332
4.2.3.5 The Radially Polarized, Free-Flooded Cylindrical Projector 339
4.2.3.6 The Free-Flooded Cylindrical Projector with a Reflector Plate 342
4.2.4 Circumferentially Polarized Cylindrical Projectors – The Barrel Stave Projector 343
4.2.4.1 The Circumferentially Polarized, Air-Backed Cylindrical Projector 343
4.2.4.2 The Circumferentially Polarized, Free-Flooded Cylindrical Projector 346
4.2.4.3 The Circumferentially Polarized Striped Cylindrical Projector 348
4.2.5 The Tonpilz Transducer 352
4.2.5.1 The End Mass-Loaded Tonpilz Transducer 353
4.2.5.2 The Nodally Mounted Tonpilz Transducer 355
4.2.6 The Flexural Disk Transducer 355
4.2.6.1 The Trilaminar Flexural Disk Transducer 357
4.2.6.2 The Bilaminar Flexural Disk Transducer 375
4.2.7 Flat Oval Flextensional Projectors 385
4.2.8 Slotted Cylinder Projectors 387
4.2.8.1 Geometry and Description 388
4.2.8.2 Wall Thickness, Radii, and Taper Factors 390
4.2.8.3 Neutral Axis 391
4.2.8.4 Displacement Profiles 392
4.2.8.5 Stress and Strain in the SCP 397
4.2.8.6 Kinetic Energy and Equivalent Mass 398
4.2.8.7 Constitutive Equations for the Piezoceramic Component 398
4.2.8.8 Voltage Across Electrodes and Dielectric Displacement 398
4.2.8.9 Internal Energy 399
4.2.8.10 Flexural Stiffness 400
4.2.8.11 In-Air Resonance Frequency 400
4.2.8.12 Effective Electromechanical Coupling Factor, keff 401
Contents xiii

4.2.8.13 In-water Performance 401
4.2.8.14 An SCP Example 407
4.2.9 Moving Coil Transducers 407
4.2.10 The Line-in-Cone Transducer 412
4.2.11 Quarter-Wavelength Resonators 415
4.2.12 Disk Projectors 418
4.2.13 The High-Frequency Line Projector 420
4.3 Special Topics in Underwater Sonar Projector Design 422
4.3.1 Techniques for Increasing Bandwidth 422
4.3.1.1 Bandwidth Increases with Coupling 422
4.3.1.2 Mechanical Tuning with Matching Layers 423
4.3.2 Power Limitations in Sonar Projectors 424
4.3.2.1 Electric Field Limitations 424
4.3.2.2 Loss Tangent Limitations 425
4.3.2.3 Stress Limitations 426
4.3.2.4 Thermal Limitations 427
4.3.2.5 Cavitation Limitations 433
References 436
5 Sonar Hydrophones 439
5.1 Elements of Sonar Hydrophone Design 439
5.1.1 An Equivalent Circuit for a Sonar Hydrophone 440
5.1.2 The Importance of the Piezo-Ceramic g Constant 442
5.1.3 An Equivalent Circuit for a Dielectrically Lossy Sonar Hydrophone 442
5.1.4 The Effect of Cable Capacitance 443
5.1.5 Typical Response of a Sonar Hydrophone 444
5.2 Analysis of Noise in Hydrophone/Preamplifier Systems 445
5.2.1 Ambient Noise 445
5.2.2 Types of Equivalent Noise Sources 446
5.2.3 Ambient Noise Coupling into a Sensor 447
5.2.4 Sensor Self-Noise 448
5.2.5 Sensor Signal to Noise Ratio 450
5.2.6 Preamplifier Noise 450
5.2.7 Combined Sensor and Preamp System Noise, the Equivalent Noise Pressure 452
5.2.8 The Equivalent Noise Pressure at Low Frequencies 453
5.2.9 Comparison of Sensor Noise with Ambient Noise Example 455
5.2.10 Hydrophone Figure of Merit 456
5.2.11 The Effect of Cable Capacitance – Insertion Loss 457
5.3 Specific Applications in Underwater Sonar Hydrophone Design 458
5.3.1 Unidirectional Hydrophone 459
5.3.1.2 Equation of Motion and Strain 460
5.3.1.4 Open Circuit Voltage Sensitivity 460
5.3.2 Hydrostatic Hydrophone 461
5.3.3 Spherical Hydrophone 462
xiv Contents

5.3.3.3 The Equations of Motion and Strain 464
5.3.3.4 Stress Profile in a Spherical Hydrophone 464
5.3.3.5 The Open Circuit Sensitivity of the Spherical Hydrophone 465
5.3.3.6 Spherical Hydrophone Depth Limitations 466
5.3.3.7 The Effect of a Fill Fluid on Hydrophone Performance 467
5.3.4 Cylindrical Hydrophones 468
5.3.4.1 The Radially Polarized Cylindrical Hydrophone 470
5.3.4.2 The Circumferentially Polarized Cylindrical Hydrophone 488
5.3.4.3 The Axially Polarized Cylindrical Hydrophone 493
5.3.5 PVDF Polymer Hydrophones 496
References 497
Appendix 499
Index 509
Contents xv

Preface
This text is the result of my efforts over the years to understand the broad subject of underwater
electroacoustic transducer design. To fully understand underwater transducers, one must under-
stand many different aspects of physics, electrical, and mechanical engineering. It is the broad
nature of acoustic transduction that I enjoy very much.
I started working in the underwater transducer business in 1983. I joined a small company
which specialized in the design and manufacture of underwater acoustic transducers. At the time,
I had no idea what a transducer was. I quickly found that you had to be a jack-of-all-trades in
order to be successful at making transducers. The wide range of expertise required to fully under-
stand underwater transducer design was very attractive to me. I was not one to be pigeonholed
into any one particular area of engineering discipline. I embraced the opportunity to be what
I consider a true engineer to be – an individual who employs the basic principles of physics
and chemistry to solve practical problems and who can implement these solutions into a man-
ufacturable product.
Unfortunately, the process of “coming up to speed” in transducer design is made very difficult by
the lack of specific texts that address the subject. There are texts that address the mechanics of
piezo-electric materials and texts on acoustic theory, but there are very few texts that address
the broad range of topics associated with underwater transducer design. As a result, I was con-
stantly bombarded with “rules of thumb” that had their basis in sound physical principles but
for which no one could account. Not being one to accept the “rules of thumb” on faith alone,
I have endeavored to understand the basis for the theories that are applicable to underwater trans-
ducer design. It is these basic principles that I hope to document in this text.
I consider the text to be an introductory text in underwater acoustic transducer design. The text
walks through the development of various theories starting from the first principles. In some cases,
the mathematical development may lead someone to think that I should have jumped to the answer
sooner. However, it is for the beginner in this field that I have written this book. The beginner
should feel that he can follow mathematical development completely. I have put many of the inter-
mediate mathematical steps into this text.
Though written for the beginner in this field, the text is also for the advanced student or practicing
engineer. The mathematical development is fairly thorough and requires some experience with
advanced mathematical functions (such as Bessel’s functions) in order to get the most out of it.
The text is divided into five chapters. The first chapter explores the physics of the acoustic
medium outside of the transducer. Since the purpose of a transducer is to generate sound in the
water, we must understand the parameters that impact the design of the transducer and its ability
to produce acoustic power.
xvii

Chapter two begins the development of transducer theory by developing equivalent circuits for
simple mechanical and acoustical systems. These principles can sometimes be applied to transducer
design but more generally lead to a physical understanding of how a mechanical/acoustical trans-
ducer works.
Chapter three addresses acoustic waves in solids. In this chapter, we specifically develop the the-
ory for sound propagation in solids that will ultimately impact the design of the transducer.
A transducer is a solid device through which acoustic energy flows. We must understand the prop-
agation of acoustic energy in solids in order to design transducers. The chapter starts off with acous-
tic waves in non-piezo-electric solids and then moves into a thorough discussion of waves in piezo-
electric solids. Piezo-electricity is reviewed to the point that it is applicable to transducer design.
Chapter four discusses projectors. This chapter brings together elements from the first three
chapters. Tools and limitations to projector design are reviewed.
Chapter five discusses hydrophones. Sensor self-noise and its impact on system design are thor-
oughly discussed in this chapter.
Enjoy.
John C. Cochran, PhD
xviii Preface

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Title: The Lusitania's Last Voyage
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*** START OF THE PROJECT GUTENBERG EBOOK THE LUSITANIA'S
LAST VOYAGE ***

THE LUSITANIA’S LAST VOYAGE
THE LUSITANIA’S
LAST VOYAGE
Being a Narrative
of the Torpedoing and Sinking
of the R. M. S. Lusitania
by a German Submarine
off the Irish Coast
May 7, 1915
BY
CHARLES E. LAURIAT, Jr.
ONE OF THE SURVIVORS
With Illustrations

BOSTON AND NEW YORK
HOUGHTON MIFFLIN COMPANY
The Riverside Press Cambridge
1915
COPYRIGHT, 1915, BY CHARLES E. LAURIAT, JR.
ALL RIGHTS RESERVED
Published October 1915
Copyright in Great Britain, Ireland,
and British Colonies, and in all
countries under the Convention, by
Charles E. Lauriat, Jr.
TO MY FATHER
WHO TAUGHT ME IN BOYHOOD TO SWIM, AND
TO KNOW NO FEAR OF THE SEA
AND
TO MY MOTHER
WHO FOUNDED THE FAITH THAT
HAS BROUGHT ME

THROUGH ALL THINGS
I DEDICATE THIS
BOOK

Avert Thy gaze, O God, close tight Thine eyes!
Glance down no longer on the ocean foam,
Lest Thou behold such horrors as can turn
Men’s burning hearts to ice, and chill their souls.
Keep Thine heart warm and full of charity
That Thou mayst yet be able to forgive,
And pity feel for those who know not when
To pause in deeds of ruthless sacrifice.
Restrain Thy wrath, and keep Thine hand in check;
Smite not, nor fiercely thrust without the pale
Those who can dare to strew the ocean waste
With fellow creatures, innocent of wrong.
Forget the studied purpose to destroy;
The launching of the missile through the deep;
The shattered hull; the crushed and bleeding forms;
The seething swirl of wreckage, women, men.
Remember that they know not what they do
Who strike in deadly fear and ghastly hate;
Remember that somehow, and at some time,
Each crime exacts its human penalty.
Remember that man’s conscience and man’s mind
Are agents of Thy purpose and Thy plan,
Which work within a deadlier revenge
Than any shrapnel shot or sabre thrust.
Remember that new generations come
Upon whom fall the burden and the curse,
The anguish of old hatreds and past wrongs,
The crushing debt, the struggle and despair.
Restrain, O God, the sweep of this vast hate;
Recall the nations to their sense of shame:
To those in blinding war, to us at peace,
Reveal anew the message of the Christ.
William Lloyd Garrison, Jr.
(Reprinted by permission of the author and of the Boston Transcript)

PART I
6, New Oxford Street, London, W. C.,
May 12, 1915
Our voyage from New York had been uneventful and in fact it was quite
a “Lauriat Crossing”; fine weather, smooth sea, and after the first few hours
of Sunday (May 2) there had been no fog up to Friday morning (May 7),
when it came in for a short time.
The speed of the boat had not been what I had expected it would be, for
after the first full run of 24 hours, in which we covered 501 miles, the run
dropped each day to well below the 500 mark, and the last 24 hours up to
Friday noon (May 7) we made only 462 miles. This was partly accounted for
by the fact that we picked up Greenwich time at Cape Clear and put the
clock ahead 1 hour and 40 minutes.
The reason this small run impressed itself upon my mind was that I
expected that when we sighted the Irish Coast the “Lucy” would show a
burst of “top speed” and that we should go flying up at not less than 25 miles
an hour. The run up to Thursday noon (May 6) had been 484 miles, and so
confident was I that she would put on steam that I bought the high number in
the pool (for Friday), which was 499. It was the only pool I went into and I
couldn’t help it, for the number sold at £3.0.0 and at that price it looked like
a “bargain.”
During the forenoon of Thursday (May 6) we swung out and uncovered
22 lifeboats, 11 on each side, showing Captain Turner’s preparedness
towards emergency. I was keenly interested in all that was done aboard ship
as we approached the Irish Coast, and in fact all through the voyage I kept
my eyes unusually wide open.
At night the shades in the saloon were closely drawn, and I noticed that
my bedroom steward left a note for the night watchman stating just which
ports were open when he (the steward) went off duty.
Friday noon when the run was posted I was surprised, for I certainly
thought that this was the time to put on speed. The sea was smooth as a
pancake, an ideal chance for a dash up the coast. When I heard the fog horn
early Friday morning I turned over and took another snooze, for there was no

use in getting up if it was foggy and disagreeable weather. The fog did not
last long and was nothing more than a morning mist.
I got up at noon and had time for a stroll around the deck before lunch at
1 o’clock. I noticed that we were not going anywhere near top speed and
were following, as I remembered, the usual course up the Irish Coast, that
being about 5 to 7 miles distant. I wondered at our loafing along at this
gentle pace.
When I bought my ticket at the Cunard Office in Boston I asked if we
were to be convoyed through the war zone, and the reply made was, “Oh
yes! every precaution will be taken.”
When we got into Queenstown I found the people furious through the act
itself and disgusted that three torpedo-boat destroyers should have lain at
anchor in Queenstown harbor all the time the Lusitania was coming up the
Irish Coast. Some of the men along the sea front told me that these boats had
been out during the morning, but had come back for “lunch.” They all turned
up after the tragedy, but they could have been used to better advantage
before it.
After lunch I went to my stateroom and put on my sweater under the coat
of the knickerbocker suit that I was wearing and went up on deck for a real
walk. I came up the main companion-way and stepped out on the port side of
the steamer and saw Mr. and Mrs. Elbert Hubbard standing by the rail, a
little for’ard of the entrance. I joined them and was conversing with them
when the torpedo struck the ship. In fact, Mr. Hubbard had just jokingly
remarked that he didn’t believe he would be a welcome traveller to
Germany, owing to the little essay he had written entitled “Who Lifted the
Lid Off Hell.” Mr. Hubbard had not more than finished this remark when the
shock came. This “essay” appeared in the “Philistine” for October, 1914, and
Mr. Hubbard had given me a copy earlier on the voyage. If you want to read
a piece of vitriolic English, I suggest that you send for a copy.
Where I stood on deck the shock of the impact was not severe; it was a
heavy, rather muffled sound, but the good ship trembled for a moment under
the force of the blow; a second explosion quickly followed, but I do not
think it was a second torpedo, for the sound was quite different; it was more
likely a boiler in the engine room.
As I turned to look in the direction of the explosion I saw a shower of
coal and steam and some débris hurled into the air between the second and

third funnels, and then heard the fall of gratings and other wreckage that had
been blown up by the explosion.
Remember that I was standing well for’ard on the port side, and
consequently looked back at the scene of the explosion, at an angle across to
the starboard side; therefore, although the débris showed between the second
and third funnels, I think the blow was delivered practically in line with the
fourth funnel.
I looked immediately at my watch and it was exactly 8 minutes past 9
(A.M.) Boston time, which means 8 minutes past 2 Greenwich time.
I turned to the Hubbards and suggested that they go to their stateroom to
get their life jackets. Their cabin was on deck B, on the port side, at the foot
of the main companion-way, and they had ample time to go there and get
back to the deck; but Mr. Hubbard stayed by the rail affectionately holding
his arm around his wife’s waist and both seemed unable to act.
I went straight down to my stateroom, which, as you will remember, was
the most for’ard one on deck B on the starboard side. The boat had taken a
list to starboard, but it was not acute, and so I had no difficulty in making my
way to and from my cabin. I tied on a life belt, took the others in the room
and my small leather case containing my business papers, and went up on
deck to the port side. I went back to the spot where I had left the Hubbards,
but they had gone, and I never saw them again.
I found those who needed the life belts, put them on, tied them properly,
and then went aft along the port side of the ship, for I was confident that all
hands would naturally rush to the starboard side and so there would be more
opportunity to help along the port side. I turned and walked for’ard toward
the bridge, and Captain Turner and Captain Anderson were both calling in
stentorian tones not to lower away the boats, ordering all passengers and
sailors to get out of them, saying that there was no danger and that the ship
would float. A woman passenger beside me called out to Captain Turner in a
perfectly clear and calm voice, “Captain, what do you wish us to do?” “Stay
right where you are, Madam, she’s all right.” Then the woman asked him,
“Where do you get your information?”—and he replied in rather a severe
and commanding voice, “From the engine room, Madam.” She and I turned
and walked quietly aft and tried to reassure the passengers we met.
As I looked around to see to whom I could be of the greatest help it
seemed to me that about everyone who passed me wearing a life belt had it

on incorrectly. In their hurry they put them on every way except the right
way: one man had his arm through one armhole and his head through the
other; others had them on around the waist and upside down; but very few
had them on correctly. I stopped these people and spoke to them in a calm
voice and persuaded them to let me help them on with the belts, for they
certainly stood no show in the water rigged as they were. At first they
thought I was trying to take their jackets from them, but on reassuring them
they let me straighten them out.
I had been watching carefully the list of the steamer, and by now I was
confident that she wouldn’t float and that the end was coming fast. I
remembered one or two personal things in my stateroom which I very much
wanted, and I figured that I had time to go down and get them. If I didn’t
come through the final plunge, I wanted to feel I had them with me, and if I
did get through, I was just as sure I wanted them, so there didn’t seem
anything to do but to get them, which I did.
There was a companion-way for’ard of the main staircase, about half-way
between it and my stateroom, so I went along the port passage inside of deck
A, down that companion-way, and along the starboard passage to my
stateroom. It was not until I walked along this passage that I realized how
acute was the list of the ship. My stateroom was an inside one without a
porthole, and consequently could be lighted only by electricity. I pressed the
switch, but the light had gone, so I put my hand on a box of matches; for
each night when I retired I placed a box in a particular place, just in case I
needed it. With the aid of these matches I found the little article for which I
was looking, opened my travelling bag, and took out some papers which
included my passport and other envelopes that could easily be slipped into
my inside pocket.
I had kept my drafts on my person, for I figured that there was no use in
giving them to the purser, except as a precaution against theft, and that was
negligible. If what had happened was to happen, I knew there would be no
time to reclaim them from the purser.
I made my way back along the passage, walking in the angle formed by
the floor and the side walls of the staterooms rather than the floor, and went
back up the for’ard companion-way, the same that I came down. Going
along the passage (on deck B) I looked down some of the cross passages that
lead to the staterooms, and at the bottom of the ones I passed I saw that the
portholes were open and that the water could not have been more than a few

feet from them. Here let me state that I consider it most extraordinary that
the portholes on the lower decks should not have been closed and sealed as
we steamed through the war zone. At luncheon the portholes in the dining-
saloon on deck D were open, and so I doubt not that all the others on that
deck were open. I mean those in the staterooms. I cannot speak with
certainty in regard to the portholes on deck E. I believe that the first list the
ship took brought her down to these open ports on the starboard side and that
she sank much more quickly from filling through them.
On my return to the deck I felt that the steamer must make her final
plunge any moment now, and as there was nothing more that could be done
on the port side—for there was no discipline or order with which to do it—I
passed through to the starboard side. Men were striving to lower the boats
and were putting women and children into them, but it seemed to me that it
only added horror to the whole situation to put people into a boat that you
knew never would be cleared and which would go down with the steamer;
better leave them on the deck to let them take their chance at a piece of
wreckage.
True, there was no panic, in the sense that anyone crowded or pushed his
way to the lifeboats, but there was infinite confusion, and there seemed no
one to take command of any one boat.
As I came out on the starboard side, I saw, a little aft of the main
entrance, a lifeboat well filled with people, principally women and children,
that no one had attempted to clear from the davits. The steamer was rapidly
sinking, and I realized that the boat must be cleared at once if the people
were to be saved.
I climbed into the stern of the boat, which was floating flush with the rail
of deck B, so far had the steamer settled, and helped clear the fall. We freed
our end and swung the ropes clear, but we couldn’t make anyone for’ard
understand what to do or how to do it.
I remember looking for’ard and seeing someone, I think it was a steward,
bravely cutting away at the thick ropes with a pocket knife. How I wish he
had had an axe! What would I have given for one real sailor man for’ard; we
could have saved that boatload of people. I started to go for’ard, but it was
impossible to climb through that boatload of people, mixed up as they were
with oars, boat hooks, kegs of water, rope ladders, sails, and God knows
what—everything that seemed to hinder progress to getting for’ard. The
steamer was all the time rapidly settling, and to look at the tremendous

smokestack hanging out over us only added to the terror of the people in the
boat. I certainly did not blame them, for it was a harrowing sight, even to
one as familiar with the ocean as I am. However, I should have gone for’ard
and made the try, except that the stern end of the boat was raised by a small
swell of the ocean and I was impressed by the nearness of the davit by
getting a blow on the back which nearly knocked me overboard.
Then I admit that I saw the hopelessness of ever clearing the for’ard davit
in time to get the boat away, so I stepped out and made a try for it by
swimming. I spoke to several and urged them to come; but truly they were
petrified, and only my training from boyhood up, in the water and under it,
gave me the courage to jump. I swam about 100 feet away from the ship and
then turned around to see if anyone was following to whom I could lend a
hand, and found several who needed encouragement. Also I wanted to see
when the final plunge of the steamer came, that I might be the more ready to
fight against the vortex and tell the others. The Lusitania did not go down
anything like head first: she had, rather, settled along her whole water line.
This convinces me that practically all the ports must have been open, even
those as far down as Deck E. The stern did not rise to anything like a
perpendicular, nor did it rise so high that I could see a single one of the
propellers or even the end of her rudder. Not one of her funnels fell.
The last I saw of the lifeboat out of which I jumped was that she was
being pulled down, bow first, as the tackle had not been freed and the stern
of the boat was rising high in the air. While the people were thrown out, they
were not so violently thrown as those from some of the lifeboats that were
dropped when half lowered into the water.
There was very little vortex; there was rather a shooting out from the ship
instead of a sucking in, after she sank; this I am told was partly caused by
the water rushing into her funnels and being blown out again by explosions
made by the mixing of the cold water of the sea with the steam of the
boilers. I saw an interesting statement in one of the papers, purporting to
have come from Captain Turner, in which he stated that the small amount of
suction was probably due to the fact that the bow of the boat was already
resting on the bottom when the stern went down. This seems quite feasible,
as she sank in about 60 fathoms (360 feet) of water and she was 755 feet
long.
The sea was wonderfully smooth, and it seemed to me that if one could
keep clear of the wreck and pick up a lifeboat, that it could be manned and

that we could go back and get many survivors. I was able to work this out
quite as I planned.
As I waited for the final plunge something caught me on the top of my
head and slipped down to my shoulders, pressing me under the water; I
couldn’t imagine what it was, but on turning to see I found that it was one of
the aërials of the wireless that stretched from topmast to topmast.
The present style of life belt, or rather jacket, is not the old-fashioned
kind filled with hard cork, but a larger and more bulky affair filled with
fibre, and when you have it on you look and feel like a padded football
player, especially around the shoulders. When I shook this wire off my head,
it caught me around the shoulders on the soft pad, and I couldn’t shake it off.
It took me down under the water and turned me upside down. I tell you I
“kicked.” I came up none the worse for my ducking, for it simply reminded
me of one of my various trips down to see “Susy the Mermaid” when I was a
youngster at Camp Asquam and the older boys used to duck us youngsters
anywhere from five to fifteen times a day, according to the unpardonable
sins we were supposed to have committed; and these weren’t mere
“duckings” either. They used to push us under, put their feet on our
shoulders, and then give a good shove, so that we went down anywhere from
six to sixteen feet under water. I hated the duckings at that time, but they
proved mighty good training!
When I came up, after shaking the Marconi wire, the waves bearing the
wreckage and people were upon me. After swimming around and helping
those I could by pushing them pieces of wreckage to which to cling, I saw a
short distance away a collapsible lifeboat floating right side up, swam to it,
and climbed aboard. A seaman quickly followed, and a fine husky chap he
proved to be. I heard my name called, and for the moment I didn’t realize
whether it was a call from Heaven or Hell, but when I turned in the direction
of the voice I found the man to be G——, one of the three men with whom I
had played cards each evening. I pulled him up on the boat, and we three got
out our jackknives and went at a kind of can-opening operation, which was
really the removing of the canvas cover of the boat.
They call that invention a “boat,” but to start with, it is nothing but a
“raft.” Let me try to draw you a word picture and see if you will understand
it.
Suppose you floated a real lifeboat in the water, and at the water line cut
down the sides so that the bottom of the boat that was left floated flush with

the water. Then deck over and make watertight this part of the boat that is
left. This gives you a round bottomed, watertight raft, floating almost flush
with the water.
Take a long piece of about 24-inch high (or wide) canvas that will reach
all around the sides from one end back to the same end. Nail the lower edge
of this canvas to the outside edge of the “raft.” To enable you to raise these
“collapsible” canvas sides and to keep them in place, make a stout rail that
will be curved to the shape of the floor of the “raft” and nail the top edge of
the canvas on to it.
This now “collapsible boat,” with its folding canvas sides, is of course
shallow, and about three or four of them can be nested on the deck of a
steamer in the space occupied by a “real lifeboat.” There is a canvas cover
laced down over the top of these boats, the same as on regular boats.
Before you can do anything with a collapsible lifeboat you must make it a
“real boat” by lifting up its canvas sides and lashing them in place so they
can’t collapse. Until this is done you have nothing but a “raft.” It is almost
impossible to lift the rail into place if there are people hanging on to it, as
that would mean lifting the people as well. Also, you can’t lift the sides,
which automatically raise the cross seats, if there is anyone lying across the
boat, and you can’t get on the “raft” without getting on the seats. We tried to
persuade the people who were hanging on to the rail to take off their hands
and hang on to the life ropes—but that was impossible. Never have I heard a
more distressing cry of despair than when I tried to tell one of them that that
was what we were doing. In their condition I don’t wonder they thought we
were trying to push them off. So we had to take some aboard, those who
were in the most panicky condition, and try to get up the sides with the “raft”
half covered with people.
The seats of these boats are attached to an iron brace which is supposed
to slide on a metal run in the middle of the boat. A wooden brace at either
end is held in place by a pin when the sides are raised to their proper height,
but, as the saying is, “There warn’t no pin” and the wooden brace in my end
of the boat was broken and the metal run for the iron braces of the seats was
so rusted and corroded that it wasn’t a “run;” so there we were, back to a raft
again.
Not an oar in the boat, nor even a stick with which to reach wreckage so
that we could block up the seats. We must get those seats braced up to give
us the protection of the canvas sides, and they mustn’t fall down either,

because then the “boat” became a “raft,” the people became a little more
panicky, and the falling seats hurt and slightly injured the people sitting
between them, for of course we had to seat those too exhausted to pull and
haul on the floor between the seats. We had to have some oars too to make
the boat navigable, so we fished round in the wreckage and were fortunate to
get five oars (one broken, but that served me as a steering oar) and some
blocks. Then with a long heave and a heave all together we raised the blasted
seats as far as possible, but not to their proper height, and jammed the blocks
under them. We were lucky to get blocks that act as supports to a real
lifeboat, which, as you know, have notches cut on the long side. These
blocks are like little steps, so that we were able to shove them under the seats
to the limit.
About the fifth man aboard the boat was a chap named B——; he was a
husky, no mistake. He weighed about 200 pounds and was all good material.
This man G—— was another good one too; he deserved his name. By this
time we must have had fifteen people in our now “non-collapsible boat.” Let
us thank God for the “non.”
I went aft and took the steering oar and my two huskies, B—— and the
sailor man, rowed the heavy sweeps, and G—— stayed for’ard to help the
people in. We headed back into the wreckage and picked up those who
seemed most urgently in need.
I won’t enter into the detail of the condition of the poor souls we got, but
two instances of nerve stand out so clearly in my mind that I must tell them.
Both pertain to women, and never have I seen greater courage and patience
shown by anyone.
I heard a call near my end of the boat and told the boys to back water, and
I reached over and pulled in a woman who I thought at first glance was a
negress; I never believed a white woman could be so black. I learned
afterwards that she and her husband had got into a lifeboat, and while he was
busy helping to clear it she got panic-stricken by the tremendous
overhanging funnels and jumped back on to the steamer without her husband
knowing it. She was aboard when the final plunge came, and the suction
took her part way down one of the funnels, but the thankful explosion blew
her forth, out into clear water, in among the wreckage, where she could hang
on. The clothes were almost blown off the poor woman, and there wasn’t a
white spot on her except her teeth and the whites of her eyes. Marvellous to

say she wasn’t hurt and proved a great help in cheering us all by her bright
talk.
For coolness I think this second case is even more remarkable. We had
about as many in our boat as we ought to take when I heard a woman’s voice
say, in just as natural a tone of voice as you would ask for another slice of
bread and butter, “Won’t you take me next? you know I can’t swim.” When I
looked over into the mass of wreckage from which this voice emanated all I
could see was a woman’s head, with a piece of wreckage under her chin and
with her hair streaming out over other pieces of wreckage. She was so
jammed in she couldn’t even get her arms out, and with it all she had a half
smile on her face and was placidly chewing gum. The last I saw of her when
I helped her off the boat at Queenstown was that she was still chewing that
piece of gum, and I shouldn’t be surprised if she had it yet. Of course, we
couldn’t leave her, and as there was no possible way that I dared try to get
her without going into the water for her, I told her that if she’d keep cool I’d
come after her. To my surprise she said it was not at all necessary, just hand
her an oar and she’d hang on. That is the last thing in the world I should ever
have dared to do, for naturally I thought, in view of the fact that she could
not swim, that as soon as I cleared away the wreckage with an oar she’d get
rattled and sink. After what she had said I got my huskies to back through
the wreckage till my oar would reach to her. Then I placed it as close to her
face as I could and she wriggled around and got her two hands on the oar,
held fast, and we pulled her through.
Then we rowed for the shore. G—— took the for’ard port oar, and
somewhere in the shuffle we had picked up a couple of the stokers, and
while they weren’t very big men they were red-headed cockneys and they
were trumps. Their conversation was something to remember; I shall never
forget it. They two rowed the for’ard starboard oar, B—— rowed the after
port oar, and the sailor man rowed the after starboard oar. Others helped
push on the oars and so we had a good crew. I steered for a lighthouse on the
coast, for I didn’t know whether the Marconi operator had had time to send
out an S. O. S., or if he had, whether or not it had been picked up. It was a
good long row ashore and I knew we could not get there until after dark, and
it was much better to land on a shore, however barren, near a lighthouse than
to land on that part where there might not be an inhabitant for miles; also I
saw the sail of a fisherman between us and the lighthouse, so I had two goals
for which to steer.

The lighthouse for which we were steering was that on the Head of Old
Kinsale. There were already two real lifeboats between us and the shore. We
had stayed around and picked up everyone who seemed to be in the most
helpless condition. Those we were forced to leave were as safe as if we had
overcrowded them into our flimsy craft. The calmness of the sea was the
only thing that enabled us to take on so many, with any degree of safety.
We must have rowed about a quarter of a mile toward shore, when off in
the distance I saw one lone man floating around by himself. He seemed to
prefer his own society to anyone’s else by going off “on his own,” but
apparently he had changed his mind and got lonesome, for he sure did yell.
He looked safe enough, as he had one of the big round white lifebuoys
around his body, under his arms, and he was perfectly safe from sinking. I
was pretty sure that according to the rules of the blessed “Board of Trade”
we had all the people in our boat that our license would allow us to carry.
Still I headed for the chap, for you couldn’t go off and leave that one more
soul floating around. It was lucky we went for him for he was in pretty bad
shape, but recovered all right after we got him ashore. This chap turned out
to be McM——, a fine Canadian fellow and a man of some experience in
shipwreck, for he was on the Republic when she sank.
After rowing about two miles we came up to the fishing smack, and
although they had already taken on two boatloads, they made room for us.
Before anyone left our boat I counted heads and found we had 32 aboard! It
wasn’t just the time to hunt souvenirs, but I took my steersman’s oarlock
with me; it will do for a paper weight.
Aboard the fisherman I witnessed one of the most affecting scenes of all.
It seems that the husband of the temporary negress we picked up was aboard,
and as we approached she recognized him and called to him; but he stood at
the rail with a perfectly blank expression on his face and refused to
recognize his own wife. Not until we were directly alongside and he could
lean over and look the woman squarely in the face did he realize that his
wife had been given back to him.
The old fishermen did everything in their power for us; they pulled up all
the blankets from their bunks, they started the fire and made us tea while tea
lasted, and after that boiled us water. The old ship was positively slippery
with fish scales and the usual dirt of fishermen, but the deck of that boat,
under our feet, felt as good as the front halls of our own homes.

The sight aboard that craft was a pitiful one, for while most of the first
two boatloads of people that got aboard were dry, many of them had in their
excitement removed much of their clothing before getting into the boat and
consequently were, by this time, pretty thoroughly chilled. Those in my boat
were in the saddest condition, for each one had been thoroughly soaked and
some of them had been through terrible experiences. There is practically no
cabin on one of these little fishermen, so all hands had to stay on deck,
except a few that were able to help themselves down into the so-called cabin.
The worst injured of course had to stay on deck. I gave my sweater to a chap
who had on nothing but an undershirt and a pair of trousers, and I loaned my
coat to a woman until we got into Queenstown. There were not nearly
enough blankets aboard for each to have one. There were over 80 people on
that small boat.
After being aboard about an hour we were picked up by the steamer
Flying Fish which had come down from Queenstown. We were made
comfortable on this good old packet. You will remember she is a side-
wheeler and one of the tenders that came out to meet the ocean steamers
before they were not too proud to stop at Queenstown.
The ocean was so calm that when we transferred our passengers to the
Flying Fish we were able to lay the fisherman alongside the steamer and
those who could stepped across. The two boats lay so close and steadily
together that we carried our cripples across in our arms. The smoothness of
the ocean must have been a special dispensation from Heaven.
We were torpedoed at 8 minutes past 2. I went overboard and my watch
stopped at 9:30 Boston time, 2:30 Greenwich. I figure I was in the water
three or four minutes before my watch stopped. I think the sweater which I
had on under my coat and the life belt that I had tied on made it slower work
for the water to get at my watch.
We must have been an hour and a half getting the boat into shape and
picking up the people from the wreckage, and we must have been rowing
two hours before we reached the fishing smack at 6:00.
By 7:00 we were on the Flying Fish, and tied up to the pier in
Queenstown at 9:15, so you see we fared quite well. It was quite ludicrous to
be held up by the patrol boat at the mouth of Queenstown Harbour and to be
asked in formal tones, “What ship is that?” and to hear the captain reply,
“The ship Flying Fish, with survivors of the Lusitania.” Word was
immediately given us to go on.

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Introduction to Sonar Transducer Design John C Cochran

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