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Left Brain Lutherie...

Left-Brain Lutherie

Using Physics and Engineering Concepts for Building Guitar Family Instruments:  An Introductory Guide to Their Practical Application

ISBN 0-9760883-0-4

 About this book...PLEASE READ CAREFULLY.

This is not a step-by-step manual for making an ukulele or guitar from beginning to end.  Please don't buy this book if that's the only kind of information that you're looking for.

This book is about trying to understand more about physics and engineering concepts as they are actually applied to instrument building.  If you have already built several instruments and want more consistency, better mechanical stability and a deeper understanding of the effects of string load on your instrument (and many other subjects as well), this is the book for you.

I believe that if you take the time to read and think about the information herein and practice using the spreadsheets to understand more about your wood and building, that you will be considerably more consistent with respect to the type of sound you wish to achieve and the long-term stability of the instrument as well.   

There is a lot to think about in the book and it may take some time to become comfortable with some of the calculations.  In all honesty, it took me a fair amount of time to research and write the book since I am not facile in either physics or mathematics.  Please be patient and take the time to work through the different problems and spreadsheets.  In the end, I'm sure that both improvement and understanding will result.

In the following chapters, I apply introductory physics and technology to instrument making in a manner which can be used and tested by anyone with a knowledge of high school mathematics, a home computer and a few easily obtained or constructed instruments.  I show experimental setups in sufficient detail so that those reading this book can duplicate and extend these studies.  These setups are as simple as possible while maintaining an adequate level of accuracy and precision for the experiment at hand.  For example, the top deflections studies only require a piece of 2”x4”, a moderately sized piece of plywood for the base, several different sized PVC pipe fittings, an inexpensive dial micrometer, a foot long 1/4” diameter metal rod, some calibrated weights (I used fishing sinkers), small wood scraps and the wooden plates of interest – hardly a room filled with $10,000 worth of science equipment.

 I have tried to make the format of the book practical and readable:  large pages, 24 lb stock paper for durability, relatively large print, a spiral binding so that the book can lie flat on a workbench or beside the computer without effort and a CD containing both spreadsheets for data manipulation / analysis and many color images of physical measurement setups.

You can buy the book directly from me. Beginning January 1st, 2012 the cost of the book is $55. Shipping and handling by US Postal Service Priority Mail shipping anywhere within the USA is an additional $10.00, making the total $65.00.  Global Priority Mail shipping outside the USA will be extra and a function of the appropriate postal rates.  Please contact me for International First Class postage rates before ordering.  The book can also be ordered from  LMII ,  and MIMF .

We accept checks and as of July 18, 2004, we also accept PayPal payments and credit card payments through PayPal. The PayPal "Buy Now" button is only valid for book purchases within the United States.

 

 

As of October 1st, 2010 more than 1100 books out the door.  

Join the other lutherie literati and combine the left and right halves of your brain for instrument making...8)

To contact me by e-mail, please send to:    

 

            aloha,

David "Kawika" Hurd,   Hilo, Hawaii   2010

TABLE OF CONTENTS

Tables  .........................................................................................x

Figures ....................................................................................... xii

List of Principal Symbols............................................................. xviii

Introduction................................................................................. 1

Chapter 1       Nylon String Guitar Family Sizes and Tunings.... 3

A Description of the Nylon String Guitar Family Instruments................................ 3

Common Ukulele Tunings................................................................................... 3

Body Size and Air Resonance - an Introduction................................................... 5

String Tension and Body Size.............................................................................. 5

Chapter 2.      An Overview of Some Building Issues.................. 8

Which of the guitar family instruments do you wish to build?................................. 8

What are the scale length and materials of the strings?.......................................... 8

What are the dimensions and properties of the front, back and sides?................... 8

What type and pattern of braces should the front and back have?........................ 9

Depending on the bracing pattern, how mechanically stiff should the top be?......... 9

Avoiding "dead spots" on the fingerboard............................................................ 10

What are the general dimensions of the neck and fretboard?................................ 10

Is the bridge the right size and in the right place?.................................................. 10

What are  the right combination  of temperature and humidity conditions?............. 11

Chapter 3.      Looking Ahead:  Creating a Top Deflection Model. 12

Chapter 4.      The Top Deflection Model.................................... 14

Calculating String Tension................................................................................... 14

Creating a Model for Estimating Torque on the Bridge......................................... 15

Introduction to the Problem............................................................................. 15

The Gallagher Model........................................................................................ 15

Sample Calculation........................................................................................... 16

The Licis Model................................................................................................. 17

Sample Calculation........................................................................................... 21

Validation of the Bridge Torque Models........................................................... 21

An Additional Downward Force on the Bridge................................................ 24

Top Deflections for Torques, Thickness’, Size and Material Properties................ 25

Description of Methods for Wood Properties Measurements............................... 33

Conditions for measurement for wood properties............................................ 34

Properties to be Measured................................................................................ 34

Choosing Wood for Instrument Building and Property Measurement............. 35

Measuring Density............................................................................................ 36

Static Determination of  Elastic Moduli........................................................... 36

Dynamic Determination of Elastic Moduli....................................................... 40

A Simple Experiment Dealing with the Static Deformation of a Fixed Plate.. 42

Measuring the Average Modulus of Elasticity for a Plate............................... 44

Vertical Compliance versus Lateral Torque Deflections - Validating Eave....... 47

Testing the Model for a Variety of Woods, Thicknesses and Sizes....................... 49

Experiments Relating Samples Having Different Values of Eave...................... 50

Experiments Dealing with Samples Having Different Thicknesses and Radius..... 51

Calculations Involving All the Predictive Variables........................................ 53

Creating a More General Deflection Model......................................................... 55

Beginning of the Braced Disk Discussion......................................................... 55

An Aside Regarding the Display of the Deflection Map................................... 56

Continuation of the Braced Disk Discussion.................................................... 57

Comparison of Torque Curves for Braced and Unbraced Disks..................... 58

Changes in the Model Resulting From Installing a Crossbrace....................... 60

Generating Apparent Thickness and Eh3 Maps................................................ 64

Adjusting the Calculations for Elliptically Shaped Lower Bouts..................... 69

Top Deflection Under String Load From Compliance Measurements............. 70

Chapter 5.      Testing the Models and Suggestions for Building 73

Royal Hawaiian, 4-string soprano ukulele, ca. 1920’s vintage........................ 73

Martin 4-string soprano ukulele, ca 1920’s vintage......................................... 76

Kawika, 4-string tenor ukulele, 1997............................................................... 79

Gibson TU-1, 4-string tenor ukulele, ca 1930’s vintage.................................. 82

Kenny Hill Palo Escrito #3027 Classical Guitar.............................................. 85

Ramirez R31993 Classical Guitar..................................................................... 88

Summary of Guitar Family Examples:  Measured & Calculated Properties... 95

Calculating Midpoint Mechanical Compliance Ranges for a Given Instrument... 96

Choosing Mechanical Compliance Maps for a Given Instrument................... 99

Chapter 6.      Resonance Coupling.............................................. 101

Appreciating and Utilizing the Work of Jurgen Meyer.......................................... 101

A Statement of the Problem............................................................................. 101

Measuring the Helmholz Resonance for Guitar Family Instruments............... 101

Measuring the Top and Back Resonant Frequencies during Construction...... 102

A Listing of the Resonant Frequencies Studied by Meyer................................ 102

Relationships Among the Resonant Frequencies Studied by Meyer................. 104

Using Spreadsheets Based on Meyer's Data........................................................ 108

Forward Modeling -- Trying to make an instrument with a particular resonant frequency ratio        108

Reverse Modeling -- Trying to copy an instrument with a particular set of final resonance ratios      111

An Empirical Approach for “Optimal” Top and Back Coupling............................ 114

The "Problem" of the Bass Response................................................................... 115

Chapter 7.      Calculating Neck Deflection................................. 117

Variables and Equations in the Spreadsheet.................................................... 117

Derivation of the Neck Deflection Equation.................................................... 118

Useful Auxiliary Data and Sample Calculations.............................................. 119

Chapter 8.      A Step-by-Step Approach to Optimizing the Body and Neck for Stability and Tone     123

Discussion......................................................................................................... 124

Chapter 9.      Other Topics in Instrument Building.................... 126

Bridge Size, Placement and Gluing Considerations............................................... 126

General Dimensions of Bridges........................................................................ 126

Thoughts on Bridge Plates................................................................................ 127

Bridge Gluing Considerations.......................................................................... 128

Bridge Gluing Calculations.............................................................................. 129

Temperature and Humidity Considerations.......................................................... 132

Statement of the Problem................................................................................. 132

Effect of Humidity Change on Wood Dimensions............................................ 133

Stresses Created during Dimensional Change of Constrained Wood.............. 136

Discussion of Lutherie Implications.................................................................. 140

Thoughts on Bracing........................................................................................... 141

Effects of Brace Size and Shape on Stiffness.................................................... 141

Composite Braces............................................................................................. 143

Bracing Attached to Top or Back Plate............................................................ 144

String Diameter Variability and Intonation Problems............................................. 146

Problems with Varying String Diameter.......................................................... 146

Measuring Instrument String Compensation......................................................... 151

Introduction and Description of Compensation Jig......................................... 151

Measurements and Discussion.......................................................................... 154

Go-bars--Properties and Applied Forces............................................................ 156

The Go-bar as an Example of Column Buckling.............................................. 156

Testing Wood for Go-bar Use.......................................................................... 157

Sample Calculations Using the Spreadsheet.................................................... 159

After Thoughts…........................................................................ 160

References..................................................................................... 161

Additional Sources of Information............................................. 163

The Internet................................................................................. 163

Periodicals................................................................................... 163

Software Programs Used in this Work...................................... 164

Appendix 1..................................................................................... A

Additional Details of the Static Approach to MOE Determination A

Getting the Experimental Setup Ready............................................................ A

How Big Should the Weight(s) Be?................................................................... C

General Measurement Procedure..................................................................... D

How Accurately Should Each Parameter be Measured?................................. E

What About Cross-grain Measurements?......................................................... F

Appendix 2..................................................................................... G

Additional Details of the Dynamic Approach for MOE Determination         G

Getting the Experimental Setup Ready............................................................ G

Measurements and Calculations....................................................................... I

Appendix 3..................................................................................... O

An Alternative Dynamic Approach for MOE Determination..... O

Appendix 4..................................................................................... Q

Description of Average E Determination for a Simply Supported Plate       Q

Getting the Experimental Setup Ready............................................................ Q

Measurements and Calculations....................................................................... Q

Appendix 5..................................................................................... S

Derivation of Thickness Comparison Formulae........................ S

Derivation of Comparison Formulas............................................................... S

Suggested Top Thicknesses for Nylon Stringed Instruments............................ U

 

 

 



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