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Using Physics and Engineering Concepts for Building Guitar Family Instruments: An Introductory Guide to Their Practical Application
ISBN
0-9760883-0-4
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 books out the door.
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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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