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

The Physics and Technology of Tennis ISBN 0972275908, 0-9722759-0-8
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Book Specifications
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