The Physics and Technology of Tennis
By Howard Brody, Rod Cross & Crawford Lindsey
Table of Contents
Preface
PART 1: RACQUETS
1 Choosing A Racquet
Rod Cross
- Choosing a Racquet
- How Does It Feel?
- Grip Size
- Racquet Weight and Power
- Sweetspots
- Balance Point and Swingweight
- Headsize
- Frame Stiffness
- String Type and Diameter
- String Tension
2 Racquet Materials
Crawford Lindsey
- Graphite
- Modulus and Strength
- Making High Modulus Carbon
- Making a Racquet
- Racquet Lay-up
- Titanium
- Piezoelectric Materials
3 Weight, Balance & Swingweight
Crawford Lindsey & Howard Brody
- Force, Mass and Inertia
- Weight
- Balance Point
- Pickup Weight
- What Balance Point Means to Tennis Players
- Customizing the Balance Point
- Swingweight
- What Swingweight Means to the Player
- Customizing Swingweight
- The Relationship of Weight, Balance and Swingweight
- Is It the Weight of the Swing, or the Swing of the Weight?
- As Weight Goes Down, Balance Goes Up
4 Racquet Stability
Crawford Lindsey & Howard Brody
- Weight In Past Racquet Developments
- Stability By Weight Polarization
- What, How, When, Where and Why of Polarization
- Twistweight: The Stability of the Racquet Against Twisting
- Interpreting the Stability Table
5 Measuring Swingweights
Rod Cross & Crawford Lindsey
- Measuring Swingweight
- Measuring Twistweight
- Measuring Recoilweight
6 Sweetspots
Howard Brody, Rod Cross, & Crawford Lindsey
- The Center of Percussion
- The Node
- The Power of the Tennis Racquet: COR and ACOR
- The Deadspot
7 Introduction To Shock & Vibration
Howard Brody & Crawford Lindsey
- Introduction
- What Is Vibration?
- Bending Shapes (Modes)
- Amplitude of Vibration and the Node
- Frequency
- Stiffness
- Dampening
- Injury
- What Is Shock and What Is Its Relation to Vibration?
- Lessons From Vibrations
- How Does Shock Absorption Work?
- Conclusion
8 Racquet Vibration Theory
Rod Cross
- Frame Bending and Vibrations
- Vibration Shapes
- Racquet Motion During Impact
- Vibration Frequency
- Vibration Modes of a Rod or Beam
- Impact with a Beam or Racquet
- Bounce Speed Off a Vibration Node
9 Racquet Feel
Rod Cross
- Effects of String Tension on Jarring
- Simple Stiffness and Vibration Experiments
- Measurements of Shock and Vibration
- Vibration Frequency and Amplitude
- Vibration Frequency of a Racquet
- Sweetspot Softness and Feel
- Sweetspot Size
- Shock and Feel
- Recoil Speed of the Handle
- Impact Duration, Force, and Feel
- Effect of Frame and String Stiffness on Frame Vibrations
- String Vibrations
- Measurements of the Force on the Hand
- String Vibrations and Feel
10 Force and Momentum
Crawford Lindsey
- Introduction
- Newton's First Law of Tennis
- Newton's Second Law of Tennis
- Newton's Third Law of Tennis
- Momentum
- Impulse = Change in Momentum Theorem
- Law of Conservation of Racquet and Ball Momentum
- Conclusion
11 Energy and Coefficient of Restitution
Crawford Lindsey
- Introduction
- Kinetic Energy
- Law of Conservation of Racquet and Ball Energy
- Difference between Racquet Energy and Momentum
- Energy Return and Coefficient of Restitution (COR)
- Final Ball and Racquet Velocities -- The Hard Way
- How To Use the Speed Equations
- Apparent Coefficient of Restitution (ACOR)
- Final Ball Speed Formulas -- The Easy Way
- Conclusion
12 Collisions
Rod Cross
- Effect of Racquet Mass on Serve Speed
- Elastic Energy Stored During a Collision
- Calculation of the COR
- Rotation
- Relation Between Angular Speed and Actual Speed
- Moment of Inertia
- Angular Momentum
- Collisions Involving Rotation of the Racquet
- Effective Racquet Mass
- Estimating the ACOR from the Effective Racquet Mass
- Axis of Rotation of a Racquet
- Notes
- Appendix
- Formula for Effective Racquet Mass for Impact Along Center Line
- Formula for Effective Racquet Mass for Impact Anywhere
13 Tennis Springs
Rod Cross
- Stiff Springs and Soft Springs
- Springs in Series or Parallel
- Potential Energy
- Potential Energy Stored in a Mass
- Potential Energy Stored in a Spring
- The Tennis Ball As a Spring
- Strings
- How the Elastic Energy Is Shared
- Effect of String Tension on Ball Speed
- Sideways Stiffness of a Single Stretched String
- Impact of a Ball on a Stretched String
14 Racquet Power
Rod Cross
- Summary
- Introduction
- Factors Affecting Power
- Physics of Power
- Maximum Possible Racquet Power
- Estimating Racquet Power
- Moving Racquet vs Free Racquet at Rest
- Effects of Frame Stiffness on Racquet Power
15 Determining On Court Ball Speed
Howard Brody
- Measuring Serve Speeds
- Measuring Groundstroke Speeds
16 Customizing Racquets
Rod Cross
- Introduction
- Balance Point
- Swingweight
- Racquet Power
- Rotation About the Long Axis
- Shifting the Sweetspots
- Summary
PART 2: STROKES
17 Racquet Technology and Strokes
Howard Brody
- Traditional Racquets
- Modern Racquets
- Classic Strokes
- New Strokes
- Sweetspots
- Stability
- Power
- Court Surfaces and Strokes
- 'Bring Back the Wood Racquet'
18 Impact Location
Howard Brody
- Where on the Racquet Head Should You Hit the Ball?
- Transverse Direction
- Conclusion
19 Improving Your Serve
Howard Brody
- Introduction
- Vertical Angular Acceptance (Window)
- Ball Speed
- Impact Height
- Topspin
- Higher Ball Toss
- Location on Court
- Racquet Parameters
- Summary
20 Serve Speed
Rod Cross & Howard Brody
- Serve Speed vs Racquet Speed
- Serve Speed Formulas
- Impact Duration
- Arm Rotation
- Serve Speed Strategy
- Case Study 1: Second Serve Speed
- Case Study 2: Serve Speed
- Summary
21 Receiving Serve
Howard Brody
22 Strokes and Spin
Howard Brody
- Topspin vs Backspin
- Watch That Spin
- Slicing the Slice
- The Approach Shot -- Why Keep It Low and Deep?
23 The Drop Shot
Howard Brody
- Hitting a Drop Shot
- Returning a Drop Shot
24 Time and Strokes
Howard Brody
25 Error Reduction
Howard Brody
- Lateral Errors
- Errors of Depth
- Equipment and Error Reduction
PART 3: STRINGS
26 Overview of Strings
Howard Brody
- Introduction
- Air Resistance
- The String Plane Deformation
- The Ping of the String
- Dwell Time
- Power
- The Feel of the Strings
- Elasticity
- Gauge
- Wear and Breakage
- String Patterns
- Control
- Rebound Angle
- Grommets
27 String Chemistry
Crawford Lindsey
- Polymers
- Bonding
- Bonding on a Chain
- Bonding Between Polymer Chains
- String Materials
- Copolymers
- Polymers Are Silly
- Conclusion
28 String Materials
Crawford Lindsey
- What Materials?
- What Is Strength?
- What Is Stiffness?
- Tension and Stretch
- Strength and Stiffness by Weight
- Conclusion
29 String Construction
Crawford Lindsey
- Core Principles
- Natural Gut Construction and Play
- Wraps: To Serve and Protect
- Twists, Angles and Fiber Counts
- Resin: The Glue that Bonds
- Coatings: Slip Sliding Away
- How Are Strings Different?
- Why the Cost Differences?
30 String Properties
Rod Cross & Crawford Lindsey
- Dynamic Stiffness -- It Determines Almost Everything
- Impact Force and Duration -- It's What You Feel
- Calculations
- Do Strings Ever Lose Power or Resilience?
- Player Perceptions of Power
31 Power and Strings Part 1
Crawford Lindsey
- String Tension and Power
- String Length and Power
- String Gauge and Power
32 Power and Strings Part 2
Rod Cross
- Serve Speed
- Typical ACOR Values
- Increasing Power by Increasing Bounce
- Increasing Bounce Speed by Lowering Tension
- Stored Energy vs Lost Energy in Strings and Balls
- What if the Ball and Strings Are Equally Stiff?
- Effect of Lowering Tension on Stored Energy and Power
- How Does This Affect the Serve Speed?
- Energy Calculations
33 String Tension
Crawford Lindsey
- What Is Tension?
- String Tension Is a Moving Target
- Where Does It Go and by How Much?
- Why Does It Go?
- Tension Loss While Stringing
- Tension Loss and Pre-stretching
- Time: Every Second Counts
- Consistency and Attention to Detail
- Pull Angle and Tension
- Tension Head Location and Final Tension
- Temperature and Tension
- Conclusion
34 Measuring String Tension
Rod Cross
- Racquet Diagnostic Machines
- The Stringmeter
- The ERT700
- Artificial Tension Calibration
- Four Reasons for Tension Loss During Stringing
- String Tension: Can Players Tell the Difference?
- Determining Actual Stringbed Tension: Method 1
- Determining Actual Stringbed Tension: Method 2
- Determining Tension in Each String
- Comparing Pull Tension, ERT, Pacific RA, and Calculations
- Comparing the Stringmeter with Calculations
- Where To Go From Here?
- The Stringmeter Revisited
- Conclusion
35 String Gauges
Rod Cross
- Summary
- Introduction
- Controlled Experiment
- Conclusions
PART4: BALLS AND COURTS
36 The Tennis Ball
Howard Brody
- Pressurized and Pressureless Balls
- High Altitude Balls
- Big Balls
- Air Resistance and the Big Ball
37 Ball Testing for Bounce
Rod Cross
- Compression Test
- Slow vs Fast Compression
- Bounce of Spinning Ball
38 The Bounce of the Ball
Howard Brody
- Vertical Velocity
- Horizontal Velocity
- Fast Courts -- Slow Courts
39 Ball Spin and Bounce Off the Court
Rod Cross
- Summary
- Introduction
- Ball Spin
- Friction Force
- Rolling
- Spaghetti Strings
- Ball Speed and COR
- Horizontal Speed of a Court
- Measurements of Court Speed
- Measurements of Court Speed on Different Surfaces
- Measurements of Ball Spin
- Measurements of Vertical Speed (COR)
- Measurements of Court Speed on Actual Courts
- Measurements of the Coefficient of Friction
40 Ball Bite and Bounce
Rod Cross
- Introduction
- Apparatus
- Friction Force Results
- Explanation of Friction Force Results
- Slamming on the Brakes
- Perception of Court Speed
41 Ball Spin and Bounce Off A Racquet
Rod Cross
- Introduction
- Bounce Basics
- Topspin or Backspin Into the Strings?
- Ball Speed, Spin and Angle Measurements
- How To Calculate the Bounce Off a Moving Racquet
- Example of Bounce Calculation
- Serving with Topspin
42 Ball Trajectories
Rod Cross
- Introduction
- Examples of Ball Trajectories
- Drag Force
- Magnus Force
- Serve Trajectories
- Appendix 1: Trajectory Equations
- Appendix 2: Simple Ball Speed Measurement
APPENDICES
Appendix A: Glossary
Appendix B: Units and Conversions
Appendix C: Equipment Rules
Appendix D: The Mathematics of Ball Bounce
- Brody's Bounce Model
- Case Where Ball Slides Throughout the Bounce
- Case Where Ball Rolls
Appendix E: Tennis Court Dimensions
Appendix F: References
- Aerodynamics
- Ball Bounce
- Biomechanics
- General Interest
- Measurements
- Racquets
- Related Sports
- Statistics
- Strings
- Strokes
- Sweetspots
- Tennis Courts
Index
About the Authors
| Chapters | 42 |
| Sections | 4 |
| Pages | 450 |
| Illustrations | 310 |
| Glossary | Yes |
| Index | Yes |
| References | Yes |
| Appendices | 6 |
| Cover | Paperback |
| Size | 8.5 × 11 |
| ISBN | 0-9722759-0-8 |