Science of the Golf Swing

Copyright © 2019 by Michael Jacobs All Rights Reserved. This book or any portion thereof may not be reproduced or used in any manner whatsoever without the express written permission of the publisher, except for the use of brief quotations in a review.

Printed in the United States of America First Printing, 2019 ISBN 9781797556338 RSB Golf Inc. 105 Clancy Road Manorville, NY 11949 www.jacobs3d.com

CONTENTS FOREWORD, by Dr. Steven Nesbit................................................................................................................................9 INTRODUCTION: Science of the Golf Swing........................................................................................................11 CHAPTER 1: Kinematic and Kinetic Classroom...............................................................................................17 CHAPTER 2: The Hub Path.............................................................................................................................................147 CHAPTER 3: Resistance......................................................................................................................................................181 CHAPTER 4: The Lesson Tee..........................................................................................................................................273 Lesson 1: Lesson 2: Lesson 3: Lesson 4: Lesson 5: Lesson 6: Lesson 7: Lesson 8: Lesson 9: Lesson 10: Lesson 11: Lesson 12: Lesson 13:

Grip Alignment ................................................................................................................274 Grip Placement ...............................................................................................................274 Body Segments ..............................................................................................................277 Spine .......................................................................................................................................279 Segment One ...................................................................................................................281 Backswing Blueprints ................................................................................................283 Radius of Curvature ....................................................................................................286 Backswing First Half ...................................................................................................288 Backswing Second Half...........................................................................................290 Late Backswing ..............................................................................................................297 Transition .............................................................................................................................302 To Last Parallel ...............................................................................................................308 To Impact onto the Finish .......................................................................................324

AFTERWORD, by Brian Manzella...................................................................................................................................331 ACKNOWLEDGMENTS...............................................................................................................................333

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FOREWORD

BY DR. STEVEN NESBIT

Michael Jacobs has created the most impressive golf science book I have ever read—and I have read them all. This amazing book successfully bridges the huge and empty expanse between the physics that describe the golf swing and the practical applications that serve to benefit all those who play and teach. Mike really digs deep into the fundamentals and nuances of the swing. There is considerable new information that is not only useful for describing the swing, but that actually matters to the mechanics of the swing. This is very dense material. The physics are presented and their relevance to the golfer explained, and, most importantly, Mike offers the application of these physics to the golf swing in a way I particularly value—with a wealth of examples that demonstrate the good, the bad, and the variety. You may just see pieces of yourself in these pages!

Mike’s straightforward language and excellent graphics make understanding this material inevitable, and the reading and studying both enlightening and enjoyable. From this information and understanding, the direct application to your own swing mechanics becomes almost intuitive.

This has been an extremely rewarding journey with my friend Michael Jacobs and his Jacobs 3D project. It has been so much fun to dive deep into the raw material of a golf swing and decipher the

intricate motions and transfer of driving forces and energy that occur. It’s fun because the work has been professionally challenging, and rewarding because it has opened the doors to so many other avenues of golf research and application.

One of the highlights of doing research with Mike is seeing how it plays out in practical application. There’s a real symbiosis at play from our collaborations.

In all my years of modeling, measuring, and analyzing golf swings, I get asked the same question repeatedly: “What is the one thing that is most important to know about the golf swing?”

I can say with absolute certainty: There is not just one thing. There are many things one should know and understand.

This book will help you on that quest to learn those things that matter. But get outside academia and it’s easy to see how someone could be buried in all of this available information. That’s why Mike’s part in this is so important, in fact the most important—and why he’s a recognized and exceptional golf scientist and instructor. Mike has proven he can translate this information in a way that’s useful to his students—and to the world of golf.

This book does not rely on clever analogies.

Using analogies to help teach golf students is commonplace, and it has been for years. However, the golfer and teacher are burdened with

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useful but limiting “analogies” such as “the swing is a wheel,” or “turn in a barrel,” for communicating swing concepts and improving techniques through non-technical means. The information in this book replaces analogies with facts and concepts that need no interpretation to directly and effectively understand and apply to the swing.

This book shows teachers and players from the novice to the professional the scientific underpinnings of the swing—and it offers a fascinating preview of the work Mike and I are doing revealing exactly how the body works in producing the unique swing characteristics that each one of us possesses. The Science of the Golf Swing— and, before it, The Elements of the Swing—get anybody willing to put in some time and thought the ability to understand this amazingly useful viewpoint of the golf swing. It opens so many doors. I am confident if you put in the time and

Foreword

effort into learning and applying the information in this book you will become a better and more knowledgeable golfer and teacher.

It is clear to me why Mike is one of the best golf teachers in America. Let him teach you through his unique approach that combines golf science, extensive experience, and practical examples. I’m excited for you to read The Science of the Swing, and I’m looking forward to what comes next with my friend Michael Jacobs.

Once again, this is truly an amazing book!

Dr. Steven Nesbit Department of Mechanical Engineering Lafayette College Easton, Pa.

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INTRODUCTION To say the release of the “fundamentals” book in 2016 broke ground in the world of golf would be an understatement.

It was fantastic to hear from thousands of golfers about how the analysis in the book helped them see their own swings in a completely different way—and how seeing the physics of the swing influenced the way they thought about making changes and improvements. The highlight has been seeing the excitement the book has created about the prospect of solving all the questions about the movement of the club that have never been within the grasp of a golfer before now. As I always say to Dr. Steven Nesbit—my friend and collaborator—we are ending the search for the perfect swing.

There was also plenty of back-and-forth about the relative merits of “engineering-based” golf instruction vs. the “old school” style of teaching— and even about the relative merits of what Dr. Nesbit and I have put together in this program.

I can break down the vast majority of the feedback I’ve gotten about the book and Jacobs 3D into four basic categories, or questions. I want to start off this “master” sequel to the original Elements book by talking about this feedback and giving some background about how this project came to be—and what the goals for it (and this book) are.

Does Golf Have to Be Complicated?

Some of the loudest commentary came from the group of golfers that believe a golf swing is a simple movement closer to an art than a science.

They see graphs and data and hear some of the terminology thrown around at the top level of these discussions and come to the conclusion that average players couldn’t possibly understand or need that level of detail.

It’s a ball and a stick, they say. Making it more complicated just locks people up. They can’t see the forest for the trees. To be honest, they are in the vast majority—and there is a place for that.

But for those who have golf in their blood and spent a lifetime trying to master the swing, the journey that I am going to lay out through this book (and the ones to come) will be fascinating.

Dr. Nesbit and I are revealing the unconstrained truth about the physics of golf club and human body movement.

Golf has had centuries of kinematic diagnoses—descriptions and analysis of two-dimensional movement—without any insight about what actually caused the motion. Kinetics is the branch of dynamics where the explanation of movement is answered using classic Newtonian physics.

Kinetics cause the kinematics (force and torque

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cause the movement), and there are certain kinematics that are very informative once the kinetic is revealed.

This is where one of the most common misconceptions about the “science of golf”—at least how I’ve learned it and now teach with it every day—comes from. There is a massive difference between becoming an expert in the fine details behind the physics of the golf motion and becoming an expert at applying the principles into a golf swing. You can be an expert in the field of golf science and be a terrible golfer. And you can have no knowledge of how the golf swing really works and still be an effective player or coach. You can also know a lot of the scientific information we’re going to talk about in this book and yet talk about the golf swing in a language that is recognizable to anybody.

Golfers come in the same kinds of categories.

You can be a player who wants to know all of the details, like Tiger Woods or Bryson DeChambeau.

You can also be a player who wants to keep the game as instinctive as possible, like Fred Couples or John Daly.

This might shock you to hear from a supposed “science guy” like me, but I think all of that is great. It’s great that some instructors get fantastic results because of the quality of their psychology, and their instincts about making swing changes to help a player. It’s also great that some players want to know how all the knobs and dials work, while other ones want to hear it as simply as possible.

The world is filled with all different kinds of people, and all different kinds of learners. If you’re going to be in the business of teaching anything—whether it’s hitting a golf ball or third grade—you’re going to reach more people if you can adapt your approach to fit a learner’s personality and learning style.

So, does that mean golf instruction has to necessarily be complicated? Yes and no.

When you take your car to a mechanic to get a specific problem fixed, the problem could be a simple one—and the mechanic could be somebody with lots of experience fixing that particular problem. The problem could also be complicated

Introduction

and hidden deep down in the bowels of the car.

Developing a complete understanding of how the club moves and the body works takes time and study—and it’s not always easy sledding.

This is the point where some of the criticism of “modern” golf swing analytics starts to go off the rails. Let’s say you’ve spent a ton of time and effort to learn all of this “under the hood” stuff, and you’ve also trained for hundreds of hours on how the physics of the swing translates from player to player. I’m not sure where the idea comes from that this level of expertise means a teacher who has that expertise is going to bury a player in pile of jargon—or get them lost in a sea of complicated technical points and swing thoughts that make the swing worse, not better.

Are there teachers who do a bad job integrating technology into their instruction? Sure.

There are also teachers who don’t use any technology, and roll out the same three or four instruction points they’ve been using for 25 years, regardless of the student and regardless of the problem. There are also scientists who do over simplify their research studies and derive the wrong conclusions.

My answer to those kinds of challenges is always the same. The true kinetics of the movement of the club had never been properly studied and explained. We have seen simplified models, but it wasn’t until Dr. Nesbit came along in 1988 that we got the entire story. And even that was delayed. After he did his contractual work with the USGA, he wrote some research papers of discovery that set the tone for golf science in the new millennium. Although Dr. Nesbit built the physics model, there was no golf professional to assist him with the explanation of what it means to a golfer. Over the years I have been able to supply him with that and the desire for him to learn what it means to golf has been awesome to witness.

We’ve uncovered details within his models of the physics that were even news to him. In our meetings he always says, I just supplied the physics and never delved deep into the nuances of its application. This is what makes him a true scien-

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tist; He is opened minded and explores all of my conclusions and inquires.

Of all the golf science available, Dr. Nesbit’s interpretation of the physics is unparalleled and my studies with him have given me more information on which to base my opinions. I think of it as being a writer who has access to two alphabets. I can work with a student like one of my top junior players from China, who does not speak English, and get across important instruction points without using any words at all. And if one of my technologically advanced teaching friends or data-junkie students comes by and wants to dive deep, we can do that, too.

It’s great to have choices.

Introduction

golfers over the years, and it has prevented tens of thousands more from reaching their full potential.

By the time I got to Methodist University in North Carolina, I knew my future wasn’t as a player, but as a teacher. And I knew I wanted to be a teacher who could help players unravel the mystery of the swing. While in the Professional Golf Management program at Methodist, I dove deeply into Homer Kelley’s Golfing Machine, along with Search for the Perfect Swing from Cochran and Stobbs. My favorite college course was Jerry Hogge’s Science of the Swing class, where we devoured Search for the Perfect Swing with a professor from the physics department. Dr. Singh probably doesn’t remember me, but he was so influential in setting me out on this mission. He and I would go through Jorgenson’s Physics of Golf after every class, and the seeds were planted that would eventually bud at Lafayette College with Dr. Nesbit many years later.

Why Are You Doing This?

From the time I started in this business, 21 years ago as a 19-year-old on a summer internship on Long Island, I’ve always been driven by one thing. I never wanted to be in a position where a student asked me a question and I didn’t have the answer. I wanted to know.

I had also gone through a lot of frustration with my own game over the years. As a kid, I was the athlete who could pick up any sport right away. I played baseball, basketball and football, and when I got hooked on golf, I thought it was just a matter of putting in the time to practice and I’d be really good.

It didn’t quite work out that way. I devoured every golf book I could find, and I wired my parents’ VCR up to record every PGA Tour event, so I could watch the tour players swing. I researched who the best teacher in my area was, and I took lessons religiously. But all the information I got— from television, the magazines, my teacher—conflicted with itself, and worse yet, it didn’t help me get any better. In fact, I started getting worse. To give just one example, the first thing I learned at junior golf camp was that you could never have enough forward shaft lean. Tell that to a kid who was as determined as I was and you’re going to get somebody who sets the record for alpha torque.

That lag conversation has destroyed thousands of

What is the One Thing Everybody Wants to Know?

Interestingly enough, this process of answering questions and identifying new problems has inspired one very common question from players and teachers. I get at least one every day in an email or on the discussion forum at my website.

Everybody wants to know what the single best way to swing is.

Because my Jacobs 3D software produces something called the “hub path optimization”— the ideal path your hands should take through the swing—a lot of people think that means they can skip all the preliminaries and just get right to that.

Here’s my swing, they say. Tell me what I should do. Or, they figure that there must be an optimum “swing model” that everybody should be copying, like Ben Hogan’s swing.

There are all kinds of good-looking swings out there, and lots and lots of ugly ones. Some of those beautiful swings produce great shots, and some of those ugly ones do, too. That’s an extension of the fundamentally fascinating point Dr.

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Nesbit has made time and time again during the time we’ve spent together.

So many people want to hear that there’s one optimum way to swing the club. But there are lots and lots of efficient ways to do it. There are reasons why relatively small players can sometimes produce lots of clubhead speed, and why some giant people can’t swing very fast at all.

Golf swings are like songs. All different kinds produce happiness. Lots of different kinds “work.”

Where the skill of the instructor (and, by extension, the player) comes in is understanding how the sum of a swings parts work together with the physical realities of the player making the swing. There is no perfect swing, but there’s an efficient one for you. If you come into this book (or the previous one) looking for the single answer for every swing—the “how”—you’re probably going to be disappointed. The how is good to know, and there’ll be time to talk about that down the road, but the much more important and interesting question is the “why.”

Take your time and work through the information in this book and you’ll discover the definitive “why” behind the way the club moves. When you know the why, the how will be very obvious!

How Do You Know Your Stuff is Right?

The history of research into the golf swing is actually pretty simplified. Through the years many players, teachers and scientists have worked to accumulate as much data as possible about the swing—from the still footage models of David Williams, to Giedon Aeril’s Biomechanics all the way up through Jacobs 3D today.

But the vast majority of the research that has been done on the golf swing has been simplified. This is because until the 1990’s, it was way too difficult to model the entire three-dimensional phenomenon of the golf swing. So many researchers were constraining their models to two dimensions—a planar model—with the assumption that the path of the hands was circular enough to constrain the mathematics to a constant radius circle.

Introduction

When you look at a swing in a picture sequence or on video, you’re seeing a “flat” image in 2D. It limits most research to measuring the location of the club and the body during various parts of the swing and trying to establish relationships from there. Most scientific models—even the ones you see from other respected golf scientists—either project the swing into 2D or still follow the same re-creation of the 2D mathematics of yesteryear.

The golf swing has a bunch of moving parts, and it happens on all kinds of changing planes of motion and ever changing radii in movement paths made by players of all different shapes and sizes. With so many variables, the natural tendency is to simplify the analysis by removing variables to make the math easier. Dr. Nesbit didn’t apply any constraints to his mathematics, and here we sit with an explanation of the golf swing that was never thought to be possible.

The engine behind Jacobs 3D—and the books you’ve been reading—is the most advanced three dimensional sports movement algorithm in the world. Dr. Nesbit has built upon his work for the USGA building the predictive model they use to test drivers for rules compliance to create a system that not only shows the forces and torques at work on the golf club during a swing, but how the various segments of the body contribute to producing movement. (The body element is the absolute cutting edge in swing analysis, and “Alpha Man,” as we call him, is going to be the hero in the next series of books and research publications that we produce in the future.)

Could somebody argue that Dr. Nesbit’s convention of applying Newtonian physics to the golf swing isn’t correct, or that the practical application side of it that I’ve created isn’t as useful as some other form of analysis? Sure they could. I welcome the discussion.

Dr. Nesbit’s research goes beyond golf and his distinguished career and body of work is by far the most referenced by other golf researchers.

And over the last two years, the research we’ve been doing using Jacobs 3D will be the basis of the next generation of peer-reviewed scholarly

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papers Dr. Nesbit will be publishing.

Top-shelf academic credentials are nice, but plenty of people want to see proof out in the real world. They want to see players using this information to play better. It happens every day on my lesson tee, for the professionals, top amateurs, firemen and accountants who come for lessons.

I am excited to share with you some of the results of all that study. My friend Matthew Rudy (the ghosting editor of this book) always teased me about how annoyed I got at his efforts to make the material in the first Elements book simple and relatable for most players. Looking back, I have to agree that there was a need for a foundational book introducing everyone to the terminology and underpinnings of an unconstrained convention. I’m a collector of golf history, and on the shelves of my office are books written by the giants of golf—from Willie Park Jr., Sir Walter Simpson, Horace Hutchinson, James Taylor, Bobby Jones, Abe Mitchell, Sam Snead and hundreds more.

I have been driven by all of their hard work and passion to try to keep moving the ball—to do my part to solve the search for a perfect golf swing. I hope this book helps you make your own leap.

Michael Jacobs Top 50 Best Golf Teachers in America -Golf Digest Top 100 Teachers in America -Golf Magazine

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Introduction

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CHAPTER

ONE

KINEMATIC AND KINETIC CLASSROOM In the elementary edition of this series, we started the book with a simple anecdote about a NASCAR race that illustrates the difference between what you can see with your eyes and what is actually happening behind the scenes. That same racing analogy is a good one to start off the master edition of this project. When you watch cars speeding around a big oval track, you see some of them going faster, some slower and some coming into the pits for more fuel or different tires. In a crash, cars start bouncing off each other (and the walls), and they come to a stop—usually after sliding and rotating around.

What you see with your eyes—the changing position of the cars relative to each other and relative to the track—are kinematics. You’re seeing the end result of the forces and torques at work within the engines of the cars - the kinetics.

In the world of golf swings, you can watch somebody move the club (or see a photo or video of a swing on TV, the Internet or Golf Digest article) and see that swings kinematics, or physical movement. Maybe a player lifts his or her hands

high in the air in the backswing, or makes a larger hip turn toward the target on the downswing relative to some other player. But seeing a swings physical properties doesn’t give you the full picture about how that player creates forces and torques in his or her swing—or how close that player is to optimizing those forces. A photograph of Rickie Fowler’s setup or top-of-the-backswing position doesn’t reveal why a 5-foot-8, 150-pound player can hit the ball farther than somebody 6-foot-4 and 240 pounds.

Plenty of good analysts can pick up on some of the things a player like Fowler does to produce so much speed at his size—and some can take the next step and use the art of teaching to deliver the right bites of information and advice about the how and why of Fowler’s swing in a way that applies to the golfer in front of them.

Still, the vast majority of that analysis is happening in the kinematic world— just the movement of the club and body—not the kinetics, or what is actually producing that motion.

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The first chapter of the elementary edition gave a thorough introduction to the core components of this kinetic classroom— Force, Torque, Rotations: alpha, beta, and gamma. Taken together these elements describe the different kinds of forces and torques at work on the club during a swing.

The first book was designed to provide an introduction to alpha, beta and gamma (along with other elements of the swing, like the hub path and relative swing plane), so that swing enthusiasts could see the framework that underpins the Jacobs 3D convention and get used to thinking about swings in this new language.

Here, we’re going to go deeper into these elements and discuss how they actually work together to produce productive (and not-so-productive) swings. After a few months of studying the elementary edition of this book, you know the basics. Now, it’s time to dive into the entire Jacobs 3D and Dr. Steven Nesbit Convention.

Chapter One

measured. At the heart of the convention Steve first developed for his golf projects—and greatly expanded to create Jacobs 3D—was his background in robotics. Now, almost 30 years later, we’ve developed software that not only examines what the club’s experience is during a swing, but also offers a full analysis of 17 body segments and how they contribute to the production of forces and torques in the swing. (You’ll be seeing and hearing plenty about Alpha Man in the future.)

Words like force, torque, alpha, beta, gamma, angular response, moment of inertia, center of mass, quivers—just to name a few—have become staples in the vocabulary of swing kinetics since the Fundamental edition was published. Here, I’m going to expand on some of these terms and use them to explain the equations of motion as it relates to the golf club’s movement.

Let’s start by setting the atmosphere for the dynamic equations of motion. We’ll begin with what’s called an “inertial reference frame.”

The Framework FIGURE 1

The “origin story” behind the force analysis program I created with Dr. Nesbit has been welltold, but I’ll start with a brief summary if this is new to you—because it’s important to understand where Jacobs 3D came from to see why it’s so effective at helping us understand what’s really happening in the swing.

In the early 1990s, Steve designed a convention to thoroughly analyze the inputs and loads applied to the golf club by a player—a story he reminisced about in the foreword of the first Elements book. Through the course of three decades of research and study, he has both uncovered previously unexplored branches of mechanics that explain many of the nuances you find in various golf swings and he has transformed how the USGA approaches regulating the sport. In the early 1990s at the USGA, Steve helped them determine what part of driving distance was being provided by the player and what part was coming from the club itself—and helped the association come up with a standard by which drivers are

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An inertial reference frame is a fixed location from where we can watch the club move through three-dimensional space. The inertial frame in a 3D analysis is defined by the X, Y and Z coordinates. In Fig. 1, notice how the X, Y and Z coordinates are fixed to the ground. (You can also see how my Jacobs 3D logo was derived—inspired by this set of coordinates.)

Chapter One

Mass: Amount of matter in an object, and a measure of its inertia.

Inertia: Tendency of an object to resist acceleration (a change of state in its motion).

Mass is often confused with weight, but those two things aren’t the same. Mass is measured in kilograms, while weight is measured in newtons because the force of gravity is involved. If you and I are standing on Earth, our mass is the same as it would be if we were standing on Mars—but our weight would be different in each place because of the change in the force of gravity.

“We adopt the philosophy that somewhere there is a universe coordinate system to which everything we discuss can be referenced. We will describe all positions and orientations with respect to the universe coordinate system or with respect to other Cartesian coordinate systems which are or could be defined relative to the universe system.”

Center of mass: The point in a body or system of bodies at which the whole mass can be considered as concentrated.

John J. Craig - Intro to Robotics (1955) Once we have our universe set, we can start to build the golf club model. Let’s first examine the properties of the golf club.

FIGURE 2

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Identifying and understanding where the center of mass of club is and how it responds is a fundamental part of club kinetics. Throughout this book, you’ll see the center of mass of the golf club depicted by an orange ball. To get a quick understanding of where it is, hold your finger out and balance the club so that it doesn’t fall one way or the other (figure 2). Because there is a considerable amount of mass in the clubhead, the actual center of mass of the entire club is NOT on the club. The center of mass is in space on that vertical line down from the balance point of the shaft. Fig. 2 displays the approximate mass center of the club and the human body in a standard anatomical position.

Chapter One

can yaw (alpha), pitch (beta) and roll (gamma).

One of the most powerful visual reminders of these planes of rotation comes from using a model airplane. I have a foam one I use when students and other teachers come to the studio for golf lessons. In Figs. 4 and 5, you can see the alpha, beta and gamma axes and how they would correspond to the way an airplane would move in the air.

Alpha

Gamma

FIGURE 3

Beta

Once you locate the club’s mass center, you will need to take yet another coordinate system and embed it directly into that mass center. In order to differentiate between this new coordinate system and the inertial frame, a lower case x, y, and z is used to depict the coordinates in the mass center frame. Since in our convention we replace the x, y, and z with alpha, beta, and gamma we will embed a lowercase a, b, and g into the mass center (figure 3).

The three planes of rotation of the club are defined using the a-b-g coordinate system embedded into the mass center of the club. The club

When the airplane is yawing from side to side (about the red axis), it is moving in alpha rotation.

If you’re flying and the pilot stays at the same altitude but turns the plane left or right, you’re experiencing that alpha rotation. If the plane changes pitch by nosing up or nosing down, you’re experiencing beta rotation (about the blue axis).

Gamma rotation (about the green axis) on a plane wouldn’t be so fun, but it would look like the plane is twisting in a barrel roll or corkscrew— like something out of the Blue Angels.

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FIGURE 4

FIGURE 5

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FIGURE 6

“The translational motion of a body is defined in terms of the acceleration of the body’s mass center, which is measured from an inertial XYZ reference. The equation of translational motion for the body can be written as F=ma.”

Chapter One

Hibbeler Dynamics (2016)

In the previous books, videos and presentations I’ve shared on kinetics, I’ve used something called the sum of the forces. That means I’ve only shown illustrations of the overall force applied by the golfer at the grip point (figure 6). It’s easily shown by the classic F=ma equation, and the examples that reinforce how the overall sum of the forces quiver grows in magnitude and direction.

But when you’re trying to explain or engineer a swing change, there is so much more information beyond just the sum of the forces.

You can break down the sum into its individual components so you can truly dissect what kinds of actions each player is imposing on the club.

If you’ve come to work with me over the years, you’ve seen the result of this information. A truly unconstrained club has six degrees of freedom in which it can move— three dimensions of linear movement (through force) and three dimensions of rotation (through torque and angular response from the force).

One of the most interesting things I learned over the years of diving into the quantitative side of the swing with Dr. Nesbit is the use of specific words and symbols in the nomenclature of engineers when they’re writing equations. The symbols can be intimidating, but with a little bit of study, they’ll become a natural interpretive language for you—and a language that can answer a lot of questions. The symbol ∑ means “sum.”

Equations of Linear Motion

∑Fx = m(aG )x ∑Fy = m(aG )y ∑Fz = m(aG )z

The sum of the Forces = mass x acceleration It means that all three dimensions of force applied to the club from the golfer are summed together in one total force. That’s as far as we went in the Fundamental edition, and it was a good introduction to the world of club kinetics.

Now, you’re ready to take the next step.

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Chapter One

FIGURE 8

FIGURE 7

Let’s break the sum of the forces down into our convention of components. Remember the embedded coordinate system I described earlier?

It’s set in the center of mass of the club, with the alpha, beta and gamma coordinates, shown here in Fig. 7. Now look at Fig. 8, imagine the golfer has grasped the center of mass of the club and is getting ready to force it in the different alpha, beta and gamma directions. If we held the mass center only, the club would just linearly respond.

Because we hold it at a distance from the mass center we get more than just a linear response.

FIGURE 9

“Once the forces are resolved they can be transformed to other more relevant coordinate systems like alpha, beta and gamma of the club or normal, tangential, bi-normal of the hub path.”

Dr. Steven Nesbit

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Chapter One

Alpha force

is the component of the force that accelerates the mass center in the alpha direction. (Fig. 10)

Beta force is the component of the force that accelerates the mass center in the beta direction. (Fig. 11)

Gamma force

is the component of the force that accelerates the mass center in the gamma direction. (Fig. 12) Those three equations can be merged into ∑Forces=ma

FIGURE 10

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FIGURE 11

FIGURE 12

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Let’s stop for a second and talk about how those forces actually relate to a real swing. Not only do they translate the club’s mass center from the start of the backswing to the finish, they also influence the rotation of the club. Because you hold the club at the handle—which is a distance away from the mass center—forcing the club linearly translates the mass center, but also produces a leveraging action, which in turn produces rotation.

The rotation created from the forcing action of the player is something engineers call a “moment.” This moment or angular response (as we call it) has a very specific meaning to us, and we need to keep it separate if we’re going to truly explain the actions of a golfer.

Let’s compare another real-world example of a “moment” created by forcing an object at a distance from its mass center.

How about a refrigerator?

FIGURE 13

Chapter One

Picture a person getting ready to push (or force) a refrigerator. In Fig. 14, you can see the orange ball, which marks the refrigerator’s approximate mass center. If you push the fridge directly in line with the mass center, it will only linearly translate. Just like in the traditional {F=ma equation, you’ve supplied enough force to the refrigerator to overcome its mass, and because the force was in line with the mass center, the response was only linear acceleration. It slid across the floor.

(Let’s keep friction out of this discussion) So what if we take the example from Fig. 14 and apply it to a golfer? It would be the equivalent of forcing the club all the way down by the mass center—something no player does. In a golf swing, we hold the club at a distance from the mass center, which means we must adjust our refrigerator example accordingly.

In Fig. 15, you’re now pushing the refrigerator at a distance from the mass center. Now that the force is trying to linearly accelerate the fridge from this distance, the force will produce some of that linear acceleration, but it will also bleed into some angular response. Fig. 14 would represent beta force that produced a beta linear acceleration. Fig. 15 would be beta force that linearly accelerated the fridge, but also alpha rotated it because of the distance of that force from the mass center.

If you look at the fridge on the floor in Fig. 15, you can see that the alpha-beta-gamma coordinate system rotated 90 degrees from where it started. (Again, we are keeping friction out of this discussion) Why is this important for golf?

This is where the rubber meets the road in our analysis. The action of the pusher in both Fig. 14 and 15 is identical! The person only feels that they have pushed the fridge, the way the fridge responded was very different.

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FIGURE 14

FIGURE 15

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Chapter One

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For the past seven years, I’ve been refining my explanations of the way the club rotates in the swing, and with Dr. Nesbit’s help, I think we’ve designed the best explanation to date. Any golfer can intuitively apply what we’re about to discuss.

Dr. Nesbit has written the most influential papers in the history of golf science, and while some are the exact same kinetics as the Jacobs 3D convention (like the Work and Power paper), the 2D papers are simplified kinetics. The 2009 Hub Path Optimization paper (which is in 2D) is not for a kinetic analysis, but to validate certain hypotheses. In fact, a 2D analysis is a different branch of dynamics than a 3D analysis. They are not comparable, but are almost always lumped together by other golf researchers to date. I continue to find it fascinating that golfdom mostly believes 2D and 3D dynamics are the same study.

They are not.

Alpha-beta-gamma “space” is what the golf world is familiar with so far. To set the space frame, you need to choose a general position in SPACE FIGURE 1

Chapter One

the golf swing for the a, b, and g axes to be orientated. In our Jacobs 3D convention we use the impact position (Space Fig. 1). Historically, Dr. Nesbit has used both the impact position and the address position throughout his published works.

Once the general position is set, the space frame is frozen solid.

Space Fig. 2 has this frozen a-b-g fixed impact frame along with the translating and rotating club near the top of this player’s backswing. This rotational procedure allows us to identify general angular changes of the club throughout the swing.

It is very difficult to show the 3D rotations of the golf club in 2D imagery. Even if you have a background in 3D dynamics it can be very difficult to wrap your head around all the six degrees of freedom that the club is experiencing. Because golf analytics have historically been picture and video based, the fundamental space frame at least gives you an introductory framework for the rotational movement of the golf club.

SPACE FIGURE 2

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When a golfer sets himself or herself at address, he or she has eye focus and gaze directed at the ball. Through the capacity of the cervical spine, the player can contort their body throughout the swing while letting the neck rotate relative to the turning torso. Because of this, Dr. Nesbit thought it is best to describe the rotation of the club from that “fixed” space frame so the player can relate to how much they have angularly displaced the club. (Angular displacement is part of the equation for angular work which we’ll discuss in a separate publication work and energy.)

But there’s a difference between the ability to explain space rotations from a fixed reference point and the player’s actual instantaneous kinetics. Keep that in mind as we push onwards.

Chapter One

Most swing enthusiasts who read the Fundamental book are well versed in the alpha-beta-gamma rotations from the space reference.

But what you are going to learn now is the fact that the only kinetics that you can relate with the space frame are the kinetics of the takeaway and down near impact. Why is that? That’s when the alpha-beta-gamma axes of the club line up to the eventual impact frame coordinates.

Before we get deeper into this kinetic discussion, let’s take an in-depth look at these alpha, beta and gamma planes of motion from the frozen impact frame. Figures 16-35 are a collection of Jacobs 3D graphics which display the impact planes from all different viewpoints.

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FIGURE 16 Reference system colors, alpha red, beta blue, and gamma black

FIGURE 17 - The Above-view of Fig. 16

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FIGURE 18 - Alpha Beta Gamma Coordinates (Down-the-line-view)

FIGURE 19 - Alpha Plane (Face-on-view)

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FIGURE 20 - Alpha Plane (From-target-view)

FIGURE 21 - Alpha Plane (Above-view)

32

FIGURE 22 - Alpha Plane (Down-the-line-view)

FIGURE 23 - Beta Plane (Above-view)

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FIGURE 24 - Beta Plane (Down-the-line-view)

FIGURE 25 - Beta Plane (From-target-view)

34

FIGURE 26 - Beta Plane (Behind-the-golfer-view)

FIGURE 27 - Gamma Plane (Face-on-view)

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FIGURE 28 - Gamma Plane (From-target-view)

FIGURE 29 - Gamma Plane (Above-view)

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FIGURE 30 - Gamma Plane (Down-the-line-view)

FIGURE 31 - Gamma Plane (Behind-the-golfer-view)

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FIGURE 32 - All Three Planes (Face-on-view)

FIGURE 33 All Three Planes (From-target-view)

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FIGURE 34 - All Three Planes (Above-view)

FIGURE 35 All Three Planes (Down-the-line-view)

39

Figs. 36-39 are illustrations using the tabletop analogy that will probably be familiar to you from the previous book and my presentations.

FIGURE 36

FIGURE 37

40

FIGURE 38

FIGURE 39

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The alpha, beta and gamma planes of motion from the fixed space frame are very important and something that you should continue to study.

Space Fig. 3 is a look at the rotations from the fixed impact frame in conjunction with the airplane analogy. The images of the golfer at the bottom of Fig. 3 are directly from the Fundamental Elements book. Take note how the yellow arrows for alpha and beta are fixed and translate with the club, but they do rotate with it.

Chapter One

In the Fundamental book there were several sets of golfer-applied torques, and all of them were from the alpha, beta, and gamma user frame and are equal to the space frame when the quote below is understood. As you now enter the Jacobs 3D user frame, there will be times when it can get complex. Whenever you need extra help, you can revert to the space impact frame to assist in comprehension.

SPACE FIGURE 3

“The x, y, z axes may be chosen such that the axes only translate relative to the inertial frame. At first glance this seems like a simplification but the body may have a rotation w about these axes and therefore the moments and products of inertia of the body would have to be expressed as functions of time- not easy!

So this choice has little value.

Peter Schiavone Hibbeler Dynamics 12th Edition

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Alpha Beta Gamma User Frame The a-b-g axes: “Can be chosen such that they are fixed in and move with the body.

The moments and products of inertia of the body relative to these axes will then be constant during the motion.”

Hibbeler Dynamics (2016) “A moving coordinate system is defined with the Z direction along the length of the shaft, the X direction perpendicular to the shaft and parallel to the club face, and the Y direction perpendicular to the shaft and the club face.”

Dr. Steven Nesbit (Describing the club model of alpha,

beta, and gamma in his 2010 paper)

43

FIGURE 40 - Top of Backswing - user frame

FIGURE 41 - Mid Backswing - user frame

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Moment of Inertia

that works on its own and is a useful metric to analyze what the golfer as a “complete system” is overcoming.

The moment of inertia is very dependent on which point you choose to analyze, too. Some players like to choke down on the grip. Those players have decreased their distance from the mass center, and by doing so they have reduced the resistance to twisting. This is why the club feels easier to swing when you grip lower and lower on the handle. Try the experiment in Figs.

42 and 43. Grab a club as you normally would, at the handle, and hold it out in front of you. Waggle it side to side a few times. Take note of how the club is resisting your waggling action. Once you get a feel for the moment of inertia at that point, now grip down on the shaft very close to where the center of mass of the club is. From that point waggle the club side to side the same way you did prior when you were holding at the grip point.

When you get this close to the center of mass of the club, the rotational resistance will be at its minimum. As your grip point moves farther away

Just like the discussion of the linear properties of the club that began with mass, we start our rotational kinetics with the concept that the club will resist what we try to input to make it rotate.

In the fundamental book, we supplied the most basic equation for torque:

Chapter One

Torque = Inertia X Angular Acceleration

The golf swing is in no way that simple, as we continue in this chapter you will see just how indepth the sum of the moments equations can be.

But you can start with that basic equation and see how important the I term (inertia) is.

When you want to actively twist the club with an alpha, beta or gamma torque, you have to overcome the club’s moment of inertia—resistance to twisting—to get an angular acceleration.

How do we quantify moment of inertia? A couple of different ways. We analyze the static properties of the club itself, and also use a separate quantity FIGURE 42

FIGURE 43

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from the center of mass, the resistance exponentially grows in magnitude. So distance matters!

As we’ve just seen, the moment of inertia is “point dependent,” which means you have to select exactly where you want to analyze. I’ll take you through the process I went through to learn MOI principles from Dr. Nesbit. We are going to start with our point of interest at the grip. This will give us the moment of inertia of the static properties of the whole club. We are going to suspend the club in an inertia pendulum so you can see what the process looks like.

In Figs. 45-47, I have created some illustrations of what the club would be experiencing in this inertia pendulum. Even though the alpha and beta pivot points are the same distance from the mass center, they align differently with the properties of the clubhead.

What we’ve just defined are the alpha-beta-gamma moments of inertia defined by the grip as the selected pivot point. We’re going to call this “static inertia,” or i-static. When you use this static measurement procedure, suspending the club in a pendulum, you’re only getting the rotational

Chapter One

FIGURE 44 Equations of Rotational Motion

∑ M x = Ix wx - ( Iy - Iz )wy wz ∑ M y = Iy wy - ( Iz - Ix )wz wx ∑ M z = Iz wz - ( Ix - Iy )wx wy resistance information for when the club is actually rotating around that point.

When you analyze how the club rotates in a swing, it’s also very important to find the instantaneous point the club is pivoting around during its trip. The club only pivots around that inertia pendulum grip point for the briefest of moments in the swing. In fact, there are times when the club pivots around a point that isn’t even on the club!

I’ll show you how this works—and why it matters.

FIGURE 45 MOMENT OF INERTIA ALPHA

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Chapter One

FIGURE 46 MOMENT OF INERTIA BETA has the same distance from the pivot point as MOI alpha, but they have different directions relative to the clubhead.

FIGURE 47 MOMENT OF INERTIA GAMMA is unique because rotational resistance is much lower than alpha and beta.

Because the rolling action of the club is a twist about the club’s axis, the distance from the mass center is very small.

This makes the club very responsive to gamma torque.

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Chapter One

Here we will define our kinetic directions that were derived in the same way that Dr. Nesbit constructed his 3-dimensional papers. Post computation, the directions are chosen to facilitate the presentation of the results to the golfing world.

If the club is being forced in a curvilinear manner (which it almost always is), the gamma force will grow exponentially as the centripetal acceleration increases. Because of this increase you’d expect to see the direction of the gamma force be negative. A positive gamma force would push the club in a straight line. We’ll talk much more about this but for now the important point to understand is that gamma forcing has very little to do with angular response. Now that we’ve defined gamma force directions, let’s talk about alpha and beta forces.

Fig. 49 shows the alpha force directions using the airplane prop from earlier in the chapter. A positive alpha force will always lift the tail of the airplane on the club upward. The upward force on the tail will make the nose point down and create an angular response that makes the club rotate away from you in a somersault move. This action and response is defined in Figs. 50 and 51.

The force and the angular response—the moment—will always be positive alpha force = positive beta angular response regardless of where

the club is during the swing . It’s also true that a negative alpha force will always create a negative beta angular response, regardless of where it happens in the swing. So pushing the tail of the plane down will make the nose point up, and create a back-flipping rotation of the club towards the golfer. You can start to see the implications of this information—and how it starts to separate good golfers from ones who struggle.

By definition, beta force linearly accelerates the mass center along the alpha plane, as you can see in Fig. 53.

Fig. 54 shows beta force in the positive and negative directions. Regardless of the club’s position during the swing, positive and negative beta forcing actions stay relative to the embedded coordinate system in the mass center of the club. I kept the airplane as a reference to help illustrate this.

Fig. 55 shows the alpha moments from the different beta force directions, while Fig. 56 shows the alpha plane of motion once again as a pure table top.

FIGURE 48

48

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FIGURE 49

49

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FIGURE 50

50

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FIGURE 51 Positive alpha force induces a positive beta rotation Negative alpha force induces a negative beta rotation

51

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Chapter One

FIGURE 52 Positive beta: A somersault rotation of the club at every instant during the golf swing.

Negative beta: A back-flipping rotation of the club at every instant in time.

52

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FIGURE 53

53

Chapter One

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FIGURE 54

54

Chapter One

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FIGURE 55

55

Chapter One

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Chapter One

FIGURE 56

As you probably know, the next generation of Jacobs 3D software features Alpha Man—which shows what each individual body segment contributes to producing force and torque on the club. It’s a whole new world—and one that will produce its own book in the near future. For now, I want to give you a sneak peak at some of Alpha Man images that reinforce what we’ve been discussing here.

In Figs. 57-59, you can see all 17 segments of Alpha Man with their respective alpha-beta-gamma coordinates (Yes, Alpha Man has a record number of analytics—enough to make your head swim!). Notice how the alpha-beta-gamma forces are being applied to the grip by the player during various points in the swing.

After covering three of the external movers that influence the club (or any other rigid body), you can see how the force components linearly accelerate the mass center in a given direction but also can induce rotation if they are at a distance from the mass center. Alpha force induces a beta rotation, beta force induces an alpha rotation and gamma force is along the long axis of the club and any achieved rotations are very small.

Along with the forces and angular responses,

the golfer also has the ability to create three other external movers to produce acceleration. These three external inputs come from torque. In our convention, torque is the external input from the player’s wrists and hands twisting on the club, separate from angular response created from the player’s force. It’s critical to differentiate between the torque applied by the golfer and the angular response created by the force.

Dr. Nesbit categorized and defined the two rotational producers in his 2005 Work and Power Paper for the academic world. We’re defining it for the golfing world in this book. The refrigerator example is a good place to begin to understand what I mean by the specific action of the person.

Even without an intentional torquing action on the fridge, it rotated 90 degrees from a pure force.

Any torquing action on the refrigerator (or a golf club, for that matter) would be a completely different input.

Since we’re trying to uncover every specific external input applied by the golfer, we have to split hairs between angular response and applied torque. Let’s take a look at alpha, beta and gamma torque on the grip, and then we’ll summarize the six dynamic equations of golf motion.

56

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FIGURE 57

57

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FIGURE 58

58

Chapter One

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FIGURE 59

59

Chapter One

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Chapter One

FIGURE 60 - Alpha Torque - The torquing action applied by the golfer in the alpha plane of motion

60

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Chapter One

FIGURE 61 - Beta Torque - The torquing action applied by the golfer in the beta plane of motion

61

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Chapter One

FIGURE 62 - Gamma Torque - The torquing action applied by the golfer in the gamma plane of motion

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Chapter One

Fig. 63 demonstrates the gamma plane of motion, while Fig. 64 shows a real-life example of a gamma torquing action. Chalking a pool cue is a twisting action about the long axis of the stick, and is a great analogy to understand gamma in golf.

FIGURE 63

FIGURE 64

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FIGURE 65

Jacobs 3D Parameter—Swing Angles Swing angles are defined as the alphabeta-gamma coordinates’ angular displacement from the space fixed frame. How do we find a swing angle? You don’t need a fancy 3D system to get a decent look. What you have to do first is identify your space fixed frame with a simple video recording of the swing and a line-drawing app. For this exercise, we’ll use impact (Fig. 65).

Next, locate the top of the backswing and use a protractor to calculate how much the player has rotated the club about the fixed alpha angle. The changes in alpha angle throughout the backswing and downswing are commonly called the Alpha Clock (Fig 66).

The player here has rotated the club approximately 250 degrees around the alpha clock. The only kinematic that we’re interested in right now is the rotation about the alpha axes.

In Fig. 67, you see a golfer who has almost rotated the club 270 degrees around the Alpha clock at the top of the swing. A 270-degree rotation from the space reference frame would be the classic parallel to the ground length backswing.

With the alpha swing dial on this figure, you can see just how much angular displacement the golfer performed regardless of linear translation.

To stress the importance of angular vs linear displacement in relation to swing angles, Fig. 68 shows a crude example of a golfer who performed a backswing by linearly translating the center of mass only to the same top of the backswing position as the other figures. This would be an alpha angular displacement of zero, and you can see he had to detach his arms to achieve this. I think you get the point that this just doesn’t work. The changing alpha angle throughout the backswing and downswing is one of the dominant swinging actions of the golfer. We will need to add the kinetic analysis to figure out the external forces that actually drive this alpha swing angle. It’s the marriage of the kinematics and the kinetics that tell the entire story.

FIGURE 66

FIGURE 67

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FIGURE 68

Chapter One

FIGURE 69

Fig. 69 is the same player’s movement relative to the alpha clock. Backswing rotation is in the negative direction, and downswing rotation is in the positive direction in our Jacobs 3D convention. It is very difficult to decipher the beta swing angle with the use of 2D video or photography. The beta swing angle is defined as the beta rotation of the club from the space fixed frame, and, naturally, gamma is the gamma rotation from the same frame. The gamma swing angle is much easier to spot with a video camera and is extremely important and something we will dig deeper into.

Figs. 70-72 show this same golfer’s actual Jacobs 3D swing angles graph from the start of the backswing to impact.

Now let’s take a look at some of the practicalities of how this works in a swing—and what we should expect to see in various golfers.

65

FIGURE 70

Alpha Swing Angle Subject Golf Swing--7 Iron

150 100

Angle (deg)

50 0 -50

-100 -150 -200 -250 -300 -1.2

-1

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FIGURE 71

Beta Swing Angle Subject Golf Swing--7 Iron

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FIGURE 72

Gamma Swing Angle Subject Golf Swing--7 Iron

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Time (Sec)

Alpha Swing Angle The amount of rotation from the space fixed alpha frame is an indicator of several phenomena that we can expect to see in a golf swing. Once I have an idea of the player’s alpha angle (which, with some practice, you can learn to estimate visually), I can predict quite a few outcomes. If a golfer struggles with flexibility, he or she is going to lack the ability to significantly alpha rotate the club. You will generally see a full swing alpha backswing angle of 200-230 degrees for folks who have a tough time getting enough backswing length. Fig. 73 is a quick alpha angle chart that you can use for reference.

Figs. 74 and 75 are of two very good players at the top of their backswings. The rotation of the club around the alpha clock between these players is sizable. I placed an arrow on each image with a target showing the force capabilities of each player. A shorter alpha clock backswing will reduce the ability to apply a negative alpha

-0.4

-0.2

0

force which rotates the club into a more lagging position. There are a host of practical golf swing discussions that arise from this topic. We will be examining them for years to come, but for now, grasping the basic concept is useful.

Studying the angular movement of a golf club, or any rigid body, starts with “position.” Once we have a clearly defined position (which our coordinate systems allow us to figure out) we can start to analyze changes in position relative to time. This change in angular position divided by time would give us the angular velocity of the club at any instant. If we’re interested in more derivations of time we could go onto angular acceleration and angular jerk—both of which are covered in the Jacobs 3D software. It’s important to remember that these are the kinematic traits of a swing—and there are six possible external inputs that create these kinematics.

67

FIGURE 73

FIGURE 74

FIGURE 75

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Chapter One

FIGURE 76

Let’s take a look at a few swings using the lens of Jacobs 3D, and test out the physics you’ve just learned. Once you’re comfortable with these elements, you can look at the larger catalog of swing reports throughout this book. You’ll see lots of different swings, made with different clubs.

We’ll begin every Jacobs 3D report sheet with a sequence of the golf swing from face on and down the line.

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Chapter One

FIGURE 77

Our first subject is a Tour winner who is now preparing for a run on the PGA Champions Tour.

Here are the metrics from his shot with a 6-iron.

•Path: 3.5 degrees inside out •AOA: 3.5 degrees down •Face: 2 degrees closed •Clubhead speed: 86 mph •Distance: 168 yards

70

| FIGURE 78

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Chapter One

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Chapter One

Jacobs 3D Report Tutorial for 30 parameters that deal with this chapter: Plotting the path of the hub (blue stars), clubhead (black dots), and the shaft (cyan lines)

FIGURE 79 - Full Rendering of Golf Swing

72

Backswing | Chapter One Mike Meehan--6 Iron 2/7 FIGURE 80 - Backswing

Duration of Backswing (sec) 0.756

500 1000

500

0

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73

Y (mm)

ration of downswing (sec) and te 328 2.3 |

FIGURE 81 - Downswing

74

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Chapter One

FIGURE 82 - Follow-Through

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FIGURE 83 - Backswing with Time stamp

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FIGURE 84 - Downswing with Time stamp

Negative number = time to impact Impact time is Zero

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Chapter One

Hub Path Mike Meehan--6 Iron 2/7

FIGURE 85 - Hub Path - Face-on-view

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Blue circles - Hub path Cyan lines - Shafts Multicolored dots - Center of Mass

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FIGURE 86 - Hub Path - Down-the-line-view

Hub Path Mike Meehan--6 Iron 2/7

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FIGURE 87 - Sum of the Forces Face-on-view - Downswing to Finish

1

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Black Dots - Clubhead Path Cyan Lines - Club Shafts Colored Dots - Center of Mass from frame prior to club shaft Blue Stars - Hub Path Colored Arrows coming from the hub - Force Quiver Force Quiver is showing the direction and magnitude of the ∑F

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FIGURE 88 - ∑F Quivers spaced out to every 5 club shafts

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Linear Force Quadrant 1 |

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FIGURE 89 - ∑F Quivers 1st phase of downswing

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FIGURE 90 - ∑F Quivers 2nd phase of downswing

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FIGURE 91 - ∑F Quivers 3rd phase of downswing

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FIGURE 92 - ∑F Quivers 4th phase of downswing

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FIGURE 93 - ∑F Quivers Backswing

86

Chapter One

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Chapter One

FIGURE 94 - Alpha Force Quiver Backswing

Quiver Color Code - Magnitude and Direction Red - Negative Green - Positive

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FIGURE 95 - Beta Force Quiver Backswing

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FIGURE 96 - Gamma Force Quiver Backswing

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FIGURE 97 - Alpha Force Quiver Downswing

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FIGURE 98 - Beta Force Quiver Downswing

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FIGURE 99 - Gamma Force Quiver Downswing

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FIGURE 100 - Alpha Beta and Gamma forces quivers downswing together

Quiver Color Code - Magnitude and Direction Green - Negative Gamma Force Yellow - Negative Beta Force Blue - Positive Beta Force Red - Positive Alpha Force Magenta - Negative Alpha Force

93

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FIGURE 101 - ∑F Quiver transposed from the grip point to the center of mass for a visual experience

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FIGURE 102 - A-B-G Swing Angles

Swing Angles Mike Meehan--6 Iron 2/7 Alpha Beta Gamma

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Chapter One

FIGURE 103 - A-B-G Sum of the Moments Entire Swing

Sum of the Moments Mike Meehan--6 Iron 2/7

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Alpha Beta Gamma

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Chapter One

FIGURE 104 - A-B-G Sum of the Moments Downswing

Sum of the Moments Downswing Mike Meehan--6 Iron 2/7

30

Alpha Beta Gamma

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Mike Meehan--6 Iron 2/7 |

Chapter One

FIGURE 105 - Alpha Torque Quiver Backswing

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Mike Meehan--6 Iron 2/7 |

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FIGURE 106 - Beta Torque Quiver Backswing

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FIGURE 107 - Gamma Torque Quiver Backswing

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FIGURE 108 - Alpha Torque Quiver Downswing

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FIGURE 109 - Beta Torque Quiver Downswing

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FIGURE 110 - Gamma Torque Quiver Downswing

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FIGURE 111 - Torque Graph Downswing

Torque Downswing Mike Meehan--6 Iron 2/7

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Alpha Beta Gamma

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FIGURE 112 - Alpha Torque Graph Downswing

Alpha Torque Downswing Mike Meehan--6 Iron 2/7

50 Alpha

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FIGURE 113 - Full Rendering of Golf Swing

The 34 graphs that came just before this represent everything we covered in this chapter.

Once you understand how these reports work, you’ll really be able to see which elements of the swing make sense and which can be improved— and more importantly, you’ll be able to see what kind of information applies to you and how you can use that information.

To finish up this chapter, let’s take a look at one more sequence. Figs. 113-115 are just the movement of the club for one of the dominant LPGA players of the last 15 years. By leaving out the avatar of a player’s body, you can focus just on what the club is doing.

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FIGURE 114 - Backswing

Driver Shot Path: 0 degrees AOA: 3 degrees up Face: 1 degree open Clubhead speed: 103 mph Shot Distance: 247 yards

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FIGURE 115 - Downswing

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FIGURE 116 - Full Rendering of Golf Swing

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FIGURE 120 - Backswing with Time stamp

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Hub Path Nick Price--Driver FIGURE 122 - Hub Path - Face-on-view

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FIGURE 123 - Hub Path Down-the-line-view

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FIGURE 138 - ∑F Quiver transposed from the grip point to the center of mass for a visual experience

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FIGURE 139 - A-B-G Swing Angles

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FIGURE 141- A-B-G Sum of the Moments Downswing

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FIGURE 148 - Torque Graph Downswing

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FIGURE 149- Alpha Torque Graph Downswing

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Figures 150abc show the alpha, beta, and gamma force directions at the bottom of this player’s swing. (These are common kinetics with a 7-iron). Notice how the negative beta force line (force across the shaft) starts to lessen just before impact. Every player will do this at a different time and when this takes place it’s a master manipulator of the golfer’s alpha torque.

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FIGURE 150c

Chapter 4 will marry the kinetics with the practical side of golf teaching.

You made it through the toughest part. Congratulations! Now that you’ve spent some time in the kinetic classroom, let’s go “outside” and look at the rest of the golf swing story.

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TWO The Hub Path

There’s an ocean of analysis about what a player should be doing with his or her body to make a golf club hit the ball in the most effective way.

Thousands of hours of video, hundreds of books, and millions of words exchanged between golfers in classrooms, on a lesson tee and over the web.

You can find theories about what the spine should do, how weight needs to shift, how to use the hands, what the chest and hips do, and a million other combinations that make up the potential movement patterns of a golf swing. But if you’re looking for a “signature” of an individual golf swing—the movement that helps identify what’s happening (and what isn’t), that signature comes in the form of the hub path, or the route the point where the hands link to the club takes through the swing.

In the Fundamental book we demonstrated how the path that the grip takes is incredibly important, because it’s the “result” of how you impose all of the forces and torques in the golf swing onto the club.

It’s a reaction to how you’re applying your kinetics to make the club do what you expect it to do.

This is a big deal, obviously, and it’s a subject that golf researchers have been investigating for decades—long before any of us had the ability to use modern measurement technology and advances in scientific study to really look in three dimensions.

When Alistair Cochran and John Stobbs produced The Search for the Perfect Swing in 1969, they wanted to reveal a mechanical model of what was happening in a golf swing. That wasn’t so different than what David Williams did with the Science of the Golf Swing in the 1960s, Gideon Ariel did in the 1980’s, or Dr. Theodore Jorgensen did with Physics of Golf in the 1990s.

But a lot of these efforts had a “simplification” in common. They relied on the concept that the shape of the hand path through the swing was close enough to circular that it could be modeled as a circle. That meant that the radius of that circle stayed the same in their golf swing modeling.

Dr. Nesbit changed everything when he presented Fig. 1 at the World Scientific Golf Convention.

Now, with thousands of swings measured on the Jacobs 3D software—Dr. Nesbit continues to show

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that the shape of that hub path is anything but a constant circle. In fact, the subtle changes in that curve are the reason swings do what they do. The ever-changing radius—and how and when it changes—reveals the strengths of someone’s swing but also their weakness. Fig. 2 is a fully rendered swing with the true shape of the hub path. For comparison, I placed a perfect red circle in the middle of the hub path to show just how non-circular it is. Fig. 3 shows a constant radius simplification graphic compared to what really happened in the golf swing.

Basically, those changes in radius are the swing.

Dr. Nesbit started his research on the hub path decades ago, and his first papers on the subject examined the basics of this changing radius phenomenon. As the years went on, he started writing papers reflecting his research on how the hub path could be “optimized” for various sports, like softball and golf. Over the years, he proved that by simply changing the hub path you could optimize a motion for force, torque, or speed. He then went on to do studies where he was able to determine what kinds

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of capabilities various players had and how much force and torque they could produce given their physical makeup.

FIGURE 1

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FIGURE 3

One of the decisions Steve made about how he used the hub path information made a huge difference in how we look at swings. He took what the club was experiencing—the forces and torques applied to it in the alpha-beta-gamma embedded coordinates you learned about in Chapter 1—and transformed them into a hub path-based coordinate system. By transposing the forces from the club to the hub path, he hoped that would help explain what the golfer was experiencing—and ultimately help a player better control their inputs. He actually

got this idea from his work on the baseball swing. In baseball, the bat drops so much at the beginning of the swing that Steve believed examining just the experience of the bat wouldn’t give all the information needed to help the batter actually understand what he or she was doing. Now, the hitter could understand how changes in the shape of the path could change where and how far the ball went. Let’s take a look at the forces transposed to the hub path, and what information that provides.

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The translational motion of a golf club is defined in terms of the acceleration of the club’s mass center measured from the inertial reference frame (defined in Chapter 1, Fig. 1).

Once the forces are resolved in the inertial frame, they can then be applied to other more relevant coordinate systems like the alpha-beta-gamma coordinates from chapter one or this hub path coordinate system we are introducing here.

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The hub path coordinate system can be broken down into three components: Tangential: The force along the hub path that speeds it up Normal: The force perpendicular to the hub path that changes the direction Bi-normal: The force that moves in and out of plane Translated into regular terminology, tangential force is the player’s effort to speed up, normal force is the effort to change direction, and bi-normal is the effort to move out of the plane. Fig. 5 and 6 show two different golf swings, with their force components at the hub path. The force quivers display both direction and magnitude.

FIGURE 4 - The Hub Path Coordinate System

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FIGURE 5 - 7-iron, PGA Champions player

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FIGURE 6 - Driver, mini-tour player

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It’s important to note that the forces along the hub path do not align with the alpha-beta-gamma forces on the club. When looking at the true kinetic experience of the golf club, you would use the coordinate system on the club we talked about in Chapter 1. With this second set of coordinates, we can look at the hub forces and examine what makes them speed up, what makes them move in and out of the plane, and what changes direction. From my own personal experience, I have had more success teaching with the club embedded coordinate system. As time goes on you can decide for yourself

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which is more informative. The total magnitude of force is obviously the same but the components will have different values. In future swing reports both coordinate systems will be published now that they have been defined.

Figs. 7 and 8 show the hub path direction compared to the alpha plane at impact. You can clearly see that the direction that the hub path is taking doesn’t align with the alpha-beta-gamma coordinate system embedded into the center of mass.

FIGURE 7

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FIGURE 8 - Down-the-line-view - This player’s 7-iron swing has the Alpha Plane a few degrees to the right at impact (an inside out swing direction yet the hub path curves to the left)

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Hub Path Center of Curvature By looking at how and when the hub path curves—and what the center of curvature is during that movement—you can learn amazing things about swings. It shows you why swings work well and why they don’t. And it shows why some of the “looks” teachers and players have been worried about for decades really don’t matter when it comes to producing a “better” swing.

Let’s start by defining what the center of curvature is. As the hub moves along its curved path, you can draw a perpendicular line from each point on the curve inward. There will reach a point where each one of those lines intersects. That intersection point is the center of curvature at that moment in time. By not only mapping out the radius of curvature of the hub path but also then tracing another path of the movement of the actual center curvature, we can learn a lot about how a golfer is interacting with the golf club. For simplicity’s sake, the center of curvature is the point at which a certain thing is curving around at a given point in time. Fig. 9 shows three examples of how to find the center of curvature.

Image A, B and C show three different samples of center of curvature locations. Image A is most representative of a golf swing hub path with an ever-changing curve. To locate the center of curvature you must first find the tangent and normal component of the curve at every instant in time (the blue arrow is tangent to the curve and the red arrow is normal to the curve). The point at which the three lines intersect is the center of curvature at that moment in time. You would perform the same procedure for finding the center of curvature of the path of any curve. In Chapter 3 we will add the center of curvature of the clubhead and overall club to the story. Image B shows a perfectly straight set of railroad tracks. The tracks would have zero curvature, because none of the lines you drew perpendicular to the path would ever intersect. Image C is of a perfect circle. In the case of circular motion, the radius of curvature is always the same length—making the center of curvature the center of the circle.

How does all this relate to a golf swing analysis?

Chapter Two

We now know that the player’s link to the club—the hub—is changing its curve throughout the entire swing. And when you compare the center of curvature of this hub path with the center of curvature of the overall club itself and the center of curvature of the clubhead, how those elements interact together tell the story of the shape of your golf swing.

Let’s map out the center of curvature of some hub paths and then we’ll look at the interaction with the other center of curvatures in Chapter 3.

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FIGURE 9

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The viewpoint of the hub path in Fig. 10 was captured from up high, so that we’re looking down at the hub. The red curve is the backswing hub path and the green curve is the downswing hub path. You can use the same procedure described in Fig. 9 to render a hub path center of curvature. The black lines are the radius of curvature for three points along the hub path and they intersect at the red dot on the golfer’s chest. That red dot is the center of curvature of the hub path at that instant in time. If we used this procedure for the entire duration of the swing, the radius of curvature would be ever changing and the red dots representing the center of curvature would be moving all around. We would then start to look at the movement of the center of curvature path throughout the swing to draw conclusions about the curving changes of the hub and what that means in conjunction with the golfer’s reaction to their kinetic inputs into the club.

So what does a 3D graphic of the entire trace of a center of curvature look like? In Jacobs 3D, we mathematically render the center of curvature trace on the backswing and downswing. Over the next few pages you will see our center of curvature plots and I want you to notice three things:

FIGURE 10

1. How the trace moves in three dimensions, especially in transition 2. The time in the swings where the trace gets wider and when it gets smaller 3. How the trace is unique to each individual.

You are about to go through a catalog of hub path center of curvature traces for the same two players we used for the hub path force components earlier in this chapter. Here is a fresh look at their downswings again in Figs. 11 and 12.

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FIGURE 11

FIGURE 12

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HUB PATH CENTER OF CURVATURE CATALOG FIGURE 13A - Subject Golf Swing - 7-iron backswing

FIGURE 13B - Web.com Tour Player - Driver backswing

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Even if you don’t have your own hub path curvature to study, you can compare and contrast the results from known swings and see some fascinating things that should influence the way you think about the shape of your swing.

A few years ago I asked Dr. Nesbit if he could devise a way for me to be able to look at a graphic and get an instantaneous impression of the radius changes during the swing. He thought about it for a while—and like he usually does—he produced another gem, the Hub Illustrator. It’s something we covered briefly in the Fundamentals book, but we’ll talk about in much more depth here. The Hub Il-

Chapter Two

lustrator has a color code on its path. When the hub path is colored green, it means the radius is getting bigger at that instant and the curve is widening. No matter how big or small the widening is, the color will change. This visual color change gives me instantaneous feedback on a golf swing—which I can use to make decisions on the lesson tee. And if the hub path changes color to red, the radius is shrinking and the path is starting to curve more. Here are the Hub Illustrators from the same two players:

FIGURE 38 - Hub Illustrator - 7-iron

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FIGURE 39 - Web.com Tour Player Driver

You can look at trends in this data and start to see why some kinds of swings don’t produce very good shots. For example, a lot of bad swings show a tendency for the hub curve to widen in the latter stages of the downswing—usually because a player is trying to lag the head too much or because of a misunderstanding of how to generate speed. Instead of shortening the radius down at the bottom of the swing they’re pushing the handle forward for too long toward the target—with less of a curve in the hub path—because driving the handle forward and down feels powerful.

In Fig. 38, this 7-iron swing has a great color scheme. The hub path is colored green early in the downswing and then turns red all the way to impact.

That initial green hub path proves that the player is generating lag early in the downswing, and then he curves the hub path more all the way to impact.

That initial green proves that the players is generating lag in the first third of the downswing followed by red which means that the curve is shrinking in the last two-thirds. This gradual shortening of the

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Why does this matter so much?

Many players focus a tremendous amount of time on lifting weights and getting stronger in an effort to produce more clubhead speed. Fitness can help a certain amount, but muscle power is only

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hub radius is allowing a smooth outward movement of the club.

In contrast, the Web.com tour player’s driver swing makes five distinct changes in the widening and shortening of his hub curvature. At the very start of the downswing, you see a red hub path— which turns quickly green for a short duration before turning red again. In the final third of the downswing, you see the hub path turn back to green and back to red again before impact. This player is shortening, widening, shortening and widening again before finally shortening for a third time. With all those changes of the radius of curvature in a .25 second downswing, you can imagine what kind of inconsistency there is in his driving game.

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going to get you so much speed. A faster speed gain comes from changing your hub path to something more optimal. That’s something within the scope of any player without lifting a single weight, and it represents a massive amount of “energy transfer.”

Players who extract the most energy from their bodies do it by moving the hub wide early followed by curving it until impact. They’re cracking the whip down near the ball, so to speak. There’s a huge advantage to curving the hub more and at the right time to make the clubhead move out in a consistent, more powerful way.

We’ll talk more about how to do this over the next chapters. We’re also not done with center of curvatures. In Chapter 3, we’ll cover the two other curvatures of interest that I mentioned earlier in this chapter. The curvature of the overall club and the curvature of the clubhead will be instrumental in understanding how the golfer interacts with the club.

Hub Quiver In addition to tracking the change in hub path curvature, it’s also valuable to create a visual experience of the changing directions of the hub path

Chapter Two

as well. This is where we turn to the “hub quiver” as Dr. Nesbit likes to call it. Once we’ve mapped out a golfer’s hub path, we take every three points along the path and create a plane based on those three instantaneous points. Once we have a plane, we then place a quiver normal to that instantaneous plane so that we can see the direction it is pointing.

We do this for the entire swing, and each quiver has the same length—so when we see changes in the appearance of the hub quiver travel we know that they are purely directional changes.

Fig. 40 is a hub quiver rendering of a tour player’s 7-iron downswing. This quiver trace is one of the best that we have ever seen, See how the quivers travel in a very smooth cylindrical way? This implies that the golfer’s joints are centrated throughout his body—which means he’s moving with peak efficiency. (We can learn more about this—and prove that point—with the Alpha Man body software, but more on that later.)

Figs. 41 - 44 are hub quiver traces of 7-iron swings from a variety of players. You can really see how the hub path is each player’s individual “swing signature” because of the variability.

FIGURE 40 - Downswing

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FIGURE 42 - Hub Quiver Downswing Side-view

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FIGURE 43 - Hub Quiver Downswing Side-view

FIGURE 44 - Hub Quiver Downswing Side-view

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We use this same procedure for the clubhead path, and by tracing out the directional changes through the use of quivers we can compare changes in hub path direction vs changes in clubhead path direction. In Jacobs 3D swing reports, you will always see both the hub and clubhead quivers.

Fig. 45 is a tour player’s clubhead path quiver. The differential between the hub path quiver and the clubhead quiver is something we defined in the Fundamental book, the Relative Swing Plane (RSP).

Fig. 46 is the RSP of the subject’s 7-iron swing used throughout this chapter. The RSP proves that a golf swing is anything but constrained.

I want cover two more hub path analytics before we move to Chapter 3: Compactness ratio and the hub path optimizer.

Chapter Two

Dr. Nesbit doesn’t play golf, but he likes to watch it on TV. I can remember a conversation he and I had about how swings are analyzed during the telecasts, and he was curious to hear more about commentators referring to swings as “compact.”

With his engineering mind, he immediately tried to find a way to define “compactness” in mechanical terms. This curiosity gave birth to the Jacobs 3D parameter we call the “flyswatter”—which includes the golfer’s compactness ratio.

What does that mean?

Fig. 47 is a Jacobs 3D rendering of a mini-tour player’s downswing. The downswing is rendered in 3D—but squashed, as if it was hit by a flyswatter.

FIGURE 45 - Clubhead Quiver Downswing Side-view

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Fig. 48 shows the result of the transformation— which leaves us with a 3D phenomenon flattened to a 2D image. When you look at the difference from the Side-view in both figures, you can immediately see the difference between a two-dimensional and three-dimensional analysis.

Once the graph has been “swatted,” Dr. Nesbit derives the volume of the hub path and clubhead path into a ratio. The “Compactness Ratio” is shown in Figs. 48 and 49. Conclusions and findings from this parameter will be published in future books and journals.

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It’s obvious from all the discussion in this chapter that the hub path has had an important role in Dr. Nesbit’s work over the last 30 years. He has published a ton of research describing the importance of the hub path, and dedicated several papers to just the hub path’s role in kinetic and kinematic transfers to the golf club. One of his greatest achievements has been the optimization algorithm he created to find the hub path shape that would work best for each individual golf swing. In future publications we will explore the optimizer in more depth.

Fly Swatter with Compactness Ratio Mike Meehan--6 Iron 2/7

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CHAPTER

THREE RESISTANCE

It isn’t any surprise golf enthusiasts have been drawing lines on videos and still photographs for 125 years to try to organize swings into coherent patterns—both to understand what’s going on and to try to guide a player into what he or she should be doing in the swing. Part of what makes studying swing kinetics so fascinating is that it reveals what is below the surface of what we see with our eyes.

As we’ve talked about before, the movements you see when you watch a swing live or on video are the results of the forces and torques at work behind the scenes, so to speak.

Forces and torques are what you input and experience, while the movements you see are the result. But you can’t leave out the one other part of Newton’s equation—which is the resistance. Not only are there resistances in all of the force and torque equations of motion, they are also what the golfer is feeling during the swing. Resistance (along with human emotions and nerves) is what makes consistency and “feel” so hard to pin down for even some of the greatest players in the world.

When you input force and torque to a rigid body (in our case a golf club), something always inhibits the resulting movement. These “blocks” to movement are what make it hard to consistently repeat results and recreate feels. Your swing feels different from week to week and year to year because of the way you interpret and respond to the resistances of the club—which go beyond just it’s static properties. When you can understand all of the resistances that exist in your swing (and every swing!), you’re on the right track to adjust your motor movements to account for them.

Let’s start with Newton’s Second Law—both linear and rotational.

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FIGURE 1

Golf science hasn’t produced much literature examining the loads and resistances a player has to overcome during the swing. Usually, it just gets mentioned with the equations and labeled in a free body diagram. Without Dr. Nesbit, I don’t think it would even have been discussed or quantified up to this point. What we’ve discovered about resistance is going to transform conventional understanding of the golf swing. In this chapter, you’re going to learn about all the hidden blocks that are keeping you from doing what you want (and what you think you’re doing) with the club.

Rotational Resistance You’ve probably heard or read me and Dr. Nesbit use the term “rotational resistance” when talking about the swing. Basically, it means the golf club’s instantaneous moment of inertia (MOI).

MOI a key part of club manufacturing, clubheads for example that have a high moment of inertia resist much more to being twisted from an off-center strike. On a driver, it means the head won’t twist as much and send the ball off line as readily as one that had a lower MOI would.

Just like that clubhead has a moment of inertia, the entire club does, too. Back in Chapter 1, we discussed the inertia pendulum in all three directions (alpha, beta and gamma). We talked in regard to the MOI about the mass center (where the club has the

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least amount of rotational resistance) and the point at the grip which is at a distance from the mass center. You performed the experiment where you waggled the club at two different points, at the grip and at the mass center, remember?

Now, repeat that experiment (it’s Fig. 42 and 43 if you need reference), paying close attention to the angular response you get as a result of your waggle.

When you hold the club at the mass center, you get much more of a rotational response than when you waggle at the top of the grip.

What does this mean?

The mass moment of inertia is dependent upon which point you choose, and is expressed as: Ip = Ig + md² In English, it means that the inertia about any point is equal to the inertia about the mass center plus the mass of the club, times the distance that selected point is from the mass center, squared.

All other things being equal, the farther you get from the mass center, angular response from your applied torque will exponentially reduce.

Does a golf club rotate around the mass center or the grip point the entire swing?

No. Other than at the top of the swing you basically have to let go of the club to get it to rotate around its own mass center. And if you tried to rotate the club around the grip point the entire swing, it would look like something out of a sci-fi movie.

Dr. Nesbit figured out that although the golfer is trying to impose his or her will at the grip point by applying their external forces there, the instantaneous point for mass moment of inertia is very rarely at that same point on the handle. Knowing where that instantaneous point actually is located would provide so much information on what resistance the golfer as a “complete system” is trying to overcome.

We measure it in Jacobs 3D, and call it the rotational resistance ratio.

In simple terms, it shows when the club is most responsive to twisting, and when it is not.

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Great players throughout history have had more lag early in their downswing in comparison to lesser players. Those players can turn their bodies faster, hit it farther and make it look way more effortless.

It turns out that they’re able to do this (and look like this) because they have configured the movement path of the club in such a way that they’re rotating the club early in the downswing very close to its mass center.

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This does some major things: • It lowers the rotational resistance of the entire system, and lets the player turn his or her body faster. Picture a figure skater, and how he or she spins faster when the arms get closer to the body. Just by spreading the arms out, the rotational speed goes down.

A golf swing works the same way!

• It delays the outward movement of the club to a point where the energy transfer is more efficient and beneficial to clubhead speed.

FIGURE 2

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In this professional player’s downswing, the avatars represent different times in the swing separated by yellow and blue colors. If you look closely at the initial downswing, the yellow and blue clubs are curving around a point very close to the club’s mass center. The center of curvature of the club is

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mapped out in the Jacobs 3D images and shows the exact mathematical location of the center of curvature at each instant in time. The black dots are the path of the clubhead, the blue is the hub path, and the red is the path of the center of curvature. As the golfer begins to let the club swing out, the red

FIGURE 3

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curve moves further away from the black dots. This is a clear increase in the radius of curvature of the club. Note how early in the downswing the red trace is very flat and fairly consistent in its distance from the black curve. This is the SECRET to delaying the outward movement of the club and keeping a

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lower rotational resistance (lag). As the golfer comes into impact, the radius of curvature of the hub path shrinks and that of the club’s expands. This interaction of curvature is the SECRET to swing efficiency.

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Hub, Club and Club Head Radius of Curvature Downswing Rickie Fowler--Driver Hub Path Club Head Club

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Does this mean that the old cliché “hold the lag” path radius before impact. This proves the player is transferring energy from body to club, and by the really is a good thing to do? Depends on what you timing of the curve change alone, we can infer a lot think lag is, and how it is created. I think lag comes of information. This chapter is dedicated to definin two layers. The traditional early-downswing lag ing and identifying these principles. (In chapter 4, I comes from the kinetics of alpha force and beta will give examples of how to use this information to torque. The second layer of lag comes from beta improve your golf swing.) force and alpha torque. You’re basically driving the club in different planes of motion with six different kinetic inputs that are separate equations, yet they share the same terms!

As the downswing progresses it is beneficial to allow the club to move out away from the body.

The Club Illustrator gives a quick snapshot of When this move out happens, the radius of curthe instantaneous changes in the radius of curvature vature will increase but the timing of this is wildly of the overall golf club. The green curve is the clubdifferent subject to subject. Take a look back at the head, the blue is the hub path and the shaft colors graph in Fig. 4. The hub path radius of curvature change as the radius of curvature of the overall club and the club radius of curvature are interacting with changes. A black colored shaft indicates the radius each other at .035 seconds before impact. That pat- of curvature is decreasing. A magenta colored shaft tern of curvature is something that we have found to Illustrator means that the radius of curvature is increasing.

Club be very beneficial for golfers. The radius of curRickie Fowler--Driver vature of the club grows to be bigger than the hub

The Club Illustrator

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The center of curvatures we have covered so far tie in closely with the rotational resistance experienced by the golfer. Fig. 6 is a rotational resistance graph from Jacobs 3D of the same golfer we have been dissecting in this chapter.

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On the left side of the graph, you’ll see a numbered ratio of 0-3. This ratio is a metric that Dr. Nesbit created to provide a snapshot of the dynamic moment of inertia that the golfer is experiencing (the I about p from the moment of inertia equation.)

FIGURE 6

Ratio definitions: Zero = Inertia about the mass center (the lowest rotational resistance possible) .1 - .9 = I about P distance is less than the grip point but greater than the mass center 1.0 = Inertia about the grip point (as displayed in the inertia pendulum) Above 1 = I about P distance is greater than the grip point 2.0 = Two times the distance of the grip point 2.5 = Two and a half times the distance of the grip point 3.0 = Three times the distance of the grip point

At the bottom of the graph, you can see the ratio is displayed over time. The realities of what you experience at every instant in time is something that we will continue to dissect throughout this book.

I Static vs I Dynamic Two terms we often use in Jacobs 3D are called I static and I dynamic. Let’s define them here so that you can become accustomed to using them as well.

I static = I about P at the grip point as defined in chapter 1 I dynamic = The instantaneous I about P

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FIGURE 7 - Inertia Ratio

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Clubhead Center of Curvature

The Head Illustrator

As with the hub and club, we also organize the path of the clubhead the exact same way. The radius of curvature changes within the head path give us clues about how the golfer is interacting with the different sections of the club. When we analyze the curvature of the clubhead path, we use the same methodology as with the hub and club curvity. How the different segments of the club interact at different times during the swing for players of various skill levels has been fascinating to see. We’ll be talking more about it more in the chapters and publications to come.

The Head Illustrator showboats the instantaneous change in the radius of curvature of the clubhead path. The blue curve is the hub path, the black lines are the club shaft, and the path of the clubhead changes color in conjunction with a change in radius. A red colored clubhead indicates the path is increasing its curve and the green colored clubhead means that it is decreasing in curvature. A decrease in curvature indicates that the clubhead is moving outward—which is beneficial to clubhead speed.

Now that these have been defined, we can start to analyze the results.

FIGURE 8

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Radius Ratio One thing that I have learned from my time with Dr. Nesbit is that he comes up with some great ways to study the interaction between certain quantities.

Since the hub path radius of curvature is our bedrock analytic and the one that the golfer has the most control over, Steve designed the radius ratio to show the change in the relationship between the radius of the overall club and clubhead relative to the hub.

The increase or decrease of the lines in the graph are their relative changes to the hub path radius. As the clubhead radius of curvature (green) grows or shrinks relative to the hub radius, so does

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the slope in the graph. And as the club radius of curvature (blue) grows or shrinks relative to the hub radius of curvature, so does the slope in the graph.

The ratio displays how many times larger the radius is of the club or head relative to the hub. So if the ratio of the clubhead is at 3, that means that it is three times larger than the hub radius at that moment in time. The unit of measurement that we use for the radii is in millimeters.

As you start to collect Jacobs 3D swing reports, you can draw all kinds of conclusions from each curvature metric. To show you how unconstrained golf swings can be, look at the differences in figures 9a, 9b, 9c and 9d.

FIGURE 9a - Driver Swing - Player we have been studying in this chapter

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FIGURE 9b - Iron swing of a college player

FIGURE 9c - Iron swing of a PGA Tour player

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FIGURE 9d - Driver swing of a PGA Tour player

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G-Load You’ve probably heard some “old school” instruction based on the concept of feeling a light or heavy club during the swing. We know from our study of the equations of motion that the mass of the golf club is the total amount of matter that makes up the club. The mass of the club is obviously a known quantity—and it is not that heavy at all. A kilogram is equivalent to 2.2 pounds. The mass of a golf club is generally around 400-500 grams, so it is essentially a half kilo. This means you are swinging a one-pound golf club that is between 36-45 inches long depending on the selected club.

That doesn’t sound like much at all.

So why do so many golfers get hurt and tired playing golf? Golfers are notorious for getting debilitating back injuries and nasty wrist and hand damage. Why? There are several reasons why, but one that has never been discussed is something we call the g-load.

G-force is a measurement of the type of acceleration that causes a perception of weight. The g-force should not be considered as a fundamental type of force but one that is directly related to the acceleration of the golf club’s mass center.

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Everybody talks about accelerating the club to hit it far, and you certainly have to do that. But most people only think about the acceleration of the mass center toward the target on the downswing.

The fact that the club moves on a curved path — and that there is a strong acceleration back toward the center of curvature that is responsible for changing the direction of the club—often gets overlooked. And as that acceleration increases, it gets more difficult to change radius of curvature.

This “centripetal acceleration” is magnified by the velocity of the club squared.

2 Centripetal Acceleration = V / R The larger the centripetal acceleration, the more force is needed by the golfer to redirect the club’s curve. You can clearly see it on tour players who are jumping up off their feet coming into impact.

Over the years, Dr. Nesbit and I have talked a lot about how the club effectively gets “heavier” down at the bottom of the swing. This is why you see such high interaction forces with the ground from the best players near the bottom of the swing. They’re recruiting their hip joints to bear this g-load.

FIGURE 10

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Figure 11 and figure 12 are the g-loads of two different players. One is from a club professional with whom I work, and the other is a very well known PGA Tour player. The club professional is hitting a 7-iron and the tour player is hitting a driver. On the left side of the graphs, you will see the “G Load of the Club”—which is the effective weight of the club at every instant in time. The club professional’s 7-iron surged up to 58 pounds right before contact while the tour player’s driver went to 117 pounds.

This is a significant load and requires some rigorous activity at the last instant of the swing before the impact. This is the time in the swing where we often see players lose their balance, extend their bodies, twist the spine, etc. The quick surge in effective weight will break down the body if it is misaligned.

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Many players pull through with a chicken wing of the lead arm in an effort to move the heavier club through with an already compromised body. Chapter 4 will cover a lot of ways that I help players handle the G Load through their body joints and segments.

Figure 12B is another sample. This time another club pro is hitting the same 7-iron as the subject in figure 11, but applying a g-load of 73 pounds before impact. This proves that even though the same golf club was used for both of these players, the effective weight of the club was clearly not identical. This proves that we all accelerate the club differently— and by acceleration we are also talking a lot about directional change.

FIGURE 11

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Let’s go back to our four golfers that we looked at in the first two chapters and add everything that we have discussed thus far to their Jacobs 3D swing report.

Enjoy the study!

TOUR WINNER PLAYER FROM CHAPTER ONE - 6-IRON SWING

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CHAPTER

FOUR THE LESSON TEE

By now, you’ve learned all about how the club moves in six degrees of freedom within six dynamic equations of motion. But when you start to examine the kinetic inputs, you’ll notice something that helps explain why so many people struggle with this game.

The golf swing doesn’t align well with how the joints of the body want to work. It’s why the transition at the top is so difficult to master, and why it’s so hard to swing the same way hole after hole, day after day.

Every player’s body also has its various constraints.

Your shoulders, hips, elbows and knees all have different degrees of freedom, and they are constrained compared to the degrees of freedom the golf club has. And that’s before you even get into the complexities of how the human brain and nervous system work.

It’s a hard game!

In this chapter, I’m going to take you through 13 lessons that use the concepts we’ve been examining in this book—uncovered by both the research Dr. Nesbit and I have done and my more than 20 years of teaching—to make the elusive process of improving a little easier to undertake. Lessons one to seven

will get you ready to make a golf swing, while lessons eight through 13 will explain a prototypical golf swing in unabridged kinetic language as opposed to everyday lesson dialect.

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I tell my students every day that the goal is to get just a little bit better during this lesson or the next practice session. By concentrating on one new movement or combination of small movements—or one concept from these lessons—you’ll improve the whole, bit by bit.

Here, you’re going to get a catalog of concepts I use every day, all based on the alpha-beta-gamma user frame. Use it as a buffet, and pick and choose what works for you.

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FIGURE 1

Lesson #1 Grip Alignment We’ve all heard the cliché that good golf begins with a good grip. And now that you know just how much is going on with the club in multiple directions—from g-load, magnitudes of force and torque, rotational resistance, etc.—it’s easy to see how important it is to have a mechanically sound hold on the handle as you try to make a swing.

Since the alpha-beta-gamma user frame represents kinetics applied to the handle of the club, it makes sense to have a grip alignment that matches up with that frame. This means that when you flex and extend your wrists it should predominantly generate an alpha rotation of the club. Radial and ulna deviation of the wrists, beta rotation of the club, and pronation and supination a gamma rotation.

The closer you can get to these alignments, the easier it will be to manage the rotation of the club.

Most players align their grip in a way that if they flex and extend their wrists it creates a combination of alpha and beta rotations. That’s fine, but it does require that you know what it will allow you to do in your swing—and what it will prevent you from doing.

This might be a new concept for anybody who hasn’t come and taken a lesson from me, but I’m convinced that over time, it will become the standard way we define “weak,” “strong,” and “neutral grips,’” by how they work relative to the user frame.

Lesson #2 GRIP PLACEMENt The top hand is in a powerful position on the club—where it plays a large role in the beta rotation inputs. The position of the top thumb is a source of the positive beta torque which offsets the negative alpha force during the latter stages of the backswing.

I always recommend that my players try to make their thumb print as big as possible when they place the top hand on the grip. I always use the analogy of placing the left thumb on the grip just as if you were getting a fingerprint taken (assuming you’re a righty golfer...switch it for the left handers out there).

When the curve changes at the bottom of the swing and the g-load is increasing, how you hold the grip will either help you or prevent you from consistently managing the heavier perception of weight.

If you’ve followed my instruction tips in the media, you probably saw an article I wrote for Golf Digest in 2015, which included an image where I was holding a suitcase in my left hand. The “ulna deviation” of the top hand when grabbing the club or suitcase is an important fundamental. In Fig. 2 there is a demonstration of the difference between ulna and radial deviation. By ulna deviating, you can get the handle straighter across the hand—which is desirable. Fig. 3 is an excerpt of my suitcase article, and a great primer on setting your grip.

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Lesson 3 Body Segments Golf instruction is dominated by advice about body movements, and that probably makes sense given that approximately 74-83% of all the energy created during a golf swing goes into just moving the segments of the body.

But within all that instruction, you won’t find any commentary categorizing those body movements

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into ‘’absolute” and “relative” subdivisions. That’s something common to the fields of robotics and dynamics, and we do it in Jacobs 3D because it helps provide both a local and system wide perspective for what you’re trying to do. “Absolute movement” would be the changes in position of the body segments to the universe frame. So when someone says, “I turned my chest 45 degrees,” that’s almost always based on the “universe” perspective. Absolute movement is something that you can readily see as a golf swing observer—and before reading this

FIGURE 1 - Jacobs 3D Alpha Man Segments

FIGURE 1a - Dr. Nesbit’s Original Full Body Model

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book, it probably accounted for the vast majority of your swing study.

“Relative movement” is the differentiation between segments. So if we were to say the chest turned 45 degrees in this scenario, we’d be talking about relative to its proximal segment. Since we’re at the point in this textbook where I am going to include some body movements in conjunction with the kinematics and kinetics of the club, I want to make sure that you understand our approach to analyzing body categories of movement.

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Fig. 1 is an image of Alpha Man with the segments and joints that make up our full body model.

The red dots indicate the segment joints, while the black shapes represent the actual segments themselves. Fig. 2 is sneak peek of Alpha Man in the address position with the mass centers of all 17 segments. All 17 segments have received the same treatment you’ve seen on the club, with an embedded alpha, beta, and gamma axes in each mass center.

FIGURE 2

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Lesson 4 Spine When you hear the topic “posture” mentioned in golf context, it’s usually in reference to the angles established between the back, hips and head and how those relationships relate to the swing method of choice.

For me, posture starts with the spine, and it’s a fascinating study. As I’m writing this chapter, Dr. Nesbit is finishing up a paper we did on the effects of the golf swing on the spine. We performed the study here at my studio on Long Island, and then took an in-depth look at how the spine handles the loads of a golf swing. What does a neutral, healthy

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spine look like? If the spine deviates from neutral will that change the swing?

Those answers and more are coming from the academic side as we continue to use Jacobs 3D for research and development.

Because the spine is so important both in the swing and for overall health and functionality, we start from the spine outwards in our assessment of a player. Fig. 1 is a healthy human spine. Notice three curves—one at the bottom called the lumbar, one in the thoracic that curves in a different direction, and finally the curve up by the neck which is called the cervical spine and is similar in shape to the curve at the bottom.

Now picture a Slinky toy. There’s no way for that Slinky to stand up on its own without any type of supporting structure.

FIGURE 1

Slinky Toy

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I want you to envision your spine in the same way—picture your spine being held up by a support system to keep it in a neutral posture. You’ll have to recruit different parts of the body in order to keep the spine neutral and in good working order. I’ve seen a lot of trees get planted here at my home club over the years, and they’ve always been put up with support wires to help stabilize them until the roots take hold.

Just think back to the g-load for a second, and the perception of the effective weight that will be experienced by the golfer. If the spine needs support just to allow us to stand up and walk, it sure needs the support under the extreme loads of a golf swing. There will be some degree of flexion and extension of the spine in a golf swing but the closer we come to a neutral spine the less likely we are to get injured or leak power.

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Lesson 5 Segment one The main area of structure for the spine is segment one of Alpha Man. Essentially, it’s the section from the pelvis to the ribcage highlighted green in Fig. 1.

FIGURE 1

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It’s quite common for golfers to think of their stability and reinforcement as coming solely from the ground. Ground reaction forces have become a very popular field of study in the world of golf, as it is very easy to get your hands on a force plate or pressure mat. The ability to transmit energy throughout the body is the ultimate goal of “stability.” Transmission of energy throughout the links of the body requires soundness in the junction between the upper and lower body segments. For now, we will call this junction the “lumbar segment” because that is the term Dr. Nesbit used in his original papers. When the new full body publications are released the body segments may or may not be renamed.

When a player is preparing to set their overall body position at address, the way they hinge the hips and maintain the lumbar segment is the most important element in establishing posture. I ask my students to find the top of their pelvis—the crest— with the pinky and the bottom of the rib cage with the thumbs (Fig. 2).

FIGURE 2

This area serves as a buttress for movement and is a key structural zone that allows the rotational power from the hip joints to move up through the body links and ultimately out to the club.

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FIGURE 3

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Once they lock the lumbar segment together (Fig. 3) I have them focus in on where the hip joints are, so they can align their thighs (femurs) accordingly (Fig. 4). Once we have a good identification of where the hip joints are and the lumbar segment is locked, we can then train a hip-hinge type movement where the hip joints rotate the body into a golf position with a supporting knee flexion. The spine is then as neutral as possible (Fig. 5).

You can train these movements daily—even if you don’t use a club. The better you get at it, the more efficient your swing and health will be.

FIGURE 5

FIGURE 4

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Lesson 6 Backswing blueprints Failing to apply enough positive alpha force in the early backswing is a very common swing flaw (Fig. 1).

It happens so often for a variety of reasons:

• Golfers have been told to stay “connected” with their arms and body

• They’ve been told to take it away “low and slow”

• The length of the radius of curvature of the club in the takeaway

• Lack of mechanical energy—no motion at the startup to transfer

• Trying to swing to the inside on the downswing perpetuates a backswing that feels like it should go to the inside

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In my opinion, the lack of understanding about alpha force is the number one reason why coming “over the top” or coming in “steep” is thought of as an epidemic.

Before we discuss some of the ways to improve your takeaway, we should briefly touch on the shoulder joints—which are a very important piece of the puzzle. Fig. 2 is an x-ray of a healthy human shoulder joint. The shoulder is an amazing (but fragile) joint with a host of muscles involved in its intricate movements. In my opinion, shoulder and hip joint movements are what separate the good player from the less-skilled one. The shoulder joints do not align well with the alpha, beta, and gamma rotations of the club, which makes the golf swing even more challenging.

• Working on a “one-piece takeaway”

FIGURE 1

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FIGURE 2

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either gets dragged back by way of the large body segments or rotated quickly by the elbows and wrists with very little work coming from the bigger body segments. Both of these scenarios aren’t ideal for the shoulder joint, and they create varying levels of the beta force and alpha torque inputs during the takeaway. The dominant yawing inputs (beta force and alpha torque) compromise the shoulder joints and require the golfer to recruit other segments of the body—mostly, the spine—to drive the swing in the beta plane of motion. That’s a good recipe for a sore back in the short term and surgery in the long term.

I realize some of this is hard to process the first time through, but go back and pick your way through again slowly, because it’s the gold at the bottom of the river. Once you can pick it out, you can be golf swing “rich.”

Rotations of the shoulder joint are going to be one of the main ways by which you can improve the movement of the center of mass of the golf club.

When Alpha Man is published you will have the alpha beta and gamma of every joint of the body and its direct influence on the alpha, beta and gamma kinetics of the golf club. Joint torque is what creates the mechanical work inside the body and rotates the segments relative to each other. Since the shoulder joints are such important segments to improving the club kinetics we should look at their basic motions in Fig. 3.

Basic Shoulder Joint Motions: Flexion/Extension Abduction/Adduction Internal/External Rotations For bonus points, try to figure out which of these rotations would produce alpha, beta and gamma yaw, pitch and roll.

Once you can understand and coordinate the motions of the shoulder joint, you can begin to blend them with the rest of the body segments on the backswing and downswing. I usually see either too much “body” on the takeaway or too much wrists and elbows. What I mean by that is the club

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FIGURE 3

285

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Lesson 7 Radius of Curvature Now that you’re reaching for the Tylenol bottle (or bottle of Scotch), hang in there just a little longer with me. We’re getting to some of the real mechanical secrets of the swing.

I touched on takeaway flaws—too much body or too much elbows and wrists—earlier, and now we’re going to continue on that topic and tie it all together

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in the next few lessons.

Fig. 1 represents the center of curvature of the overall club on the backswing superimposed as best as possible over the golfer’s avatar. The golf club begins curving immediately on the takeaway, but the radius of curvature is above the hands during the start up. The two most common flaws are taking it back with too much body by dragging the club with a strong positive beta force (a lagging clubhead takeaway, Fig. 2) OR shrinking the radius immediately by driving the club with the wrists and elbows and not

FIGURE 1

286

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enough body (Fig. 3).

It’s a mistake to name the immediate reduction in radius as “picking the club up too quick”—which in my opinion is really just a pitching motion to the club—when in fact there is also a negative beta force banking the club around the body in a lot of these flawed backswings.

So what is the best way to take the club back?

Obviously, the answer is it depends as there are so many variables and individual traits of each golfer and swing. As my friend Dr. Ryan McGinnis said,

FIGURE 2

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“The kinetic drivers will be as different as all golf swings look. No two being identical.”

Players and teachers often ask me if there is a template of what the best players do. It’s different from player to player, but we can find just enough commonalities to at least give you a blueprint.

Essentially I am going to explain and demonstrate a golf swing that has the most efficient blend of linear and angular movements.

In Lesson 8 and 9, let’s bring the club toward the top with a prototype backswing.

FIGURE 3

287

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Lesson 8 Backswing First Half You can avoid a lot of swing sins if you can get off to a good start. Fig. 1 is the avatar of one of my students. We spent a lot of time on that takeaway movement you see in the Fig. 1, with our main focus being the blending of alpha, beta and gamma drivers of the club.

From takeaway to first parallel, the best players are applying enough alpha force so that the center of mass of the club is as high as their hands. When looking down the target line at first parallel, I like to see enough alpha force applied so that the shaft and the center of mass are hidden by the clubhead. Let’s put the airplane back on the club and take a look at how the player managed the yaw pitch and roll of the club (Fig. 2).

You can see how smoothly the alpha, beta and gamma coordinates both linearly and angularly

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changed position. The alpha, beta and gamma frame is in a location I believe is the best way to accommodate the shoulder joints (Fig. 3).

It was quite popular in golf teaching to try to get a player to have the clubface tilted down at this first parallel position. “Get the clubhead on the same angle as your spine” was and is a very popular tip.

You will see a lot of great players do that, but I think you have to monitor the shoulder joints closely. I do see a lot of good players who are trying to execute this backswing idea and they end up with their alpha, beta and gamma frame tilted too much toward the ground—and then the rear shoulder starts to get compromised. With the alpha, beta and gamma frame rotating uniformly, I have found that the player can manage the complicated actions of the shoulder joint much more efficiently. You can obviously pose this takeaway position and not make favorable body movements and pay the price for it later in the swing. Blending body segments with the driving action at the club is what makes the science

FIGURE 1

288

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of the golf swing so fascinating. There are a multitude of body segment combinations that will make someone a successful golfer and they will be included in future publications.

One of the most interesting things that I have witnessed over the years is the improvement in body segment movement from just a change in a player’s intent. For example, when someone understands that they want to apply a negative alpha force in the second half of the backswing, they will start to change their body motions not only at that moment but also in the portions of the swing that lead up to it and follow.

FIGURE 2

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“A change in kinetic intent will immediately change a golf swing.”

FIGURE 3

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Lesson 9 Backswing Second Half First parallel in the backswing is where the alpha user plane is at the side of the golfer (Fig. 1). This means that the alpha torque and beta force actions will make the club move in front or behind the golfer, while the beta torque and alpha force actions will make the club pitch up and down.

This next stage up to the top of the backswing has very distinct actions in the beta plane of motion.

The negative gamma force continues to curve the club, while the alpha force component will start to switch to negative—which means that this is the time of the swing where the club gets driven toward our shoulder and onto the other side of our hub path.

Great players are able to keep their beta angular velocity stable with a positive beta torque. The balancing act between the angular response and the torque gives the golfer the best chance of an efficient transition.

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I know that this explanation is extremely complex but if you want the truth about what is happening this is it!

In Fig. 2 the green arrows are the gamma force, red arrows the alpha force, the big blue arrows are the response, while the small blue arrows on the golfer’s hands are the beta torque. These are the main drivers of mid to late backswing and are fairly predictable subject to subject.

What is extremely variable is the third dimension of this discussion and that is what is happening in the alpha plane of motion. Beta force and alpha torque are going to be the drivers that YAW the club either in front or behind the golfer.

There will be some players who have a negative beta force as they work their way to the top, and there will be players who have a positive beta force.

When the club is curled all the way around near the top of the backswing, it’s very difficult to apply a lot of beta force as the club is positioned up above the shoulders.

FIGURE 1

290

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FIGURE 2

291

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Fig. 3 shows the direction and magnitude of each component of force in the second half of this player’s backswing. The magnitudes of force are changing and the instantaneous values of each component can be anywhere in those numerical ranges. The graph in Fig. 4 is the magnitude of the sum of all these components.

FIGURE 3

292

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FIGURE 4

Linear Force Magnitude Subject Golf Swing--7 Iron 80 70 60

N

50 40 30 20 10

-0.5

-0.45

-0.4

-0.35

-0.3

Time (sec)

-0.25

FIGURE 5

Negative beta force can be hard to envision at the top of the swing so it helps to revert back to the fundamental space frame and perform a negative beta force. The amount that this player is applying is very small. You will notice that the clubhead and mass center look to be slightly forward of the hands at the top of the backswing (Fig. 5). We know the negative beta force was slightly accelerating the mass center in that direction but the rotational position of the club indicates that this golfer applied a positive alpha torque with enough of a magnitude to overcome the slight negative alpha response from the beta force and had enough of a magnitude to positively alpha rotate the club. Figs. 6 and 7 are the alpha sum of the moments and the alpha torque, both of which prove what we see in the kinematics.

293

-0.2

-0.15

FIGURE 6

FIGURE 7

294

|

The negative alpha force in conjunction with the negative gamma force drive the club up to the top of the swing, and as the golfer begins the transition, they maintain these force directions—which is why the sum of the forces quiver you have been accustomed to seeing is pointing up and away from the golfer (Fig. 8).

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The overall sum quiver should point up, away, and slightly forward of the mass center at the top.

Fig. 9 is a close up of the summed quiver, I added a long white shadow to the quiver to show the line of action proving the 3 components listed are summed together (the viewpoint of Fig. 9 is looking down the line).

For this player we can add these three components of force into a summed quiver: Negative Alpha Force Negative Gamma Force Negative Beta Force

FIGURE 8

295

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FIGURE 9

296

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Lesson 10 Late Backswing Let’s take Lesson 9 and add a contrasting subject’s swing. This is what’s happening when the golfer is applying a positive beta force in the second half of the backswing. As I mentioned in the last lesson, the largest variability among subjects will be the kinetics in the alpha plane of motion.

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Fig. 1 shows a 3-handicap player finishing his backswing. I took his force quiver and superimposed it over the avatar for that instant in time.

Based on the summed force quiver, the golfer is clearly trying to force the center of mass behind him for the downswing. Fig. 2 is a graph of his beta force near the end of the backswing. You can see how this player continues to apply this force in the positive direction.

FIGURE 1

297

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When you compare this to the other player from Lesson 9 it is evident that they have to be applying different kinetic inputs (Fig. 3).

Look at all the positions of the club in Fig. 3, and how their axes would be twisted in different directions. The alpha, beta, and gamma planes of motion would be completely different for these two players.

The one thing that jumps out to most golfers is the difference in wrist positions. Most instructors would put their effort into trying to change the golfer’s wrist action—which could work only if it changes the beta linear acceleration of the mass center and the applied alpha torque.

This positive beta force at the top portion of the

backswing will make the club accelerate behind the player, producing a very different look to the initial stages of the downswing. Now look at how the clubhead path is buried well behind the hub in Fig. 4. There are a lot of golfers who are intentionally trying to make this happen, and they need to realize that you will have to apply more negative beta force later on to recover if you overdo the positive stuff early. By definition this extra negative beta force needed to recover will make the club negatively alpha respond and delay the player’s release even more. Late positive alpha torque will be needed to overcome this obstacle.

FIGURE 2

Alpha-Beta-Gamma Forces 3 Handicap--Iron 8 6 4 2

N

0 -2 -4 -6 -8 -10 -12 -0.31

Alpha Beta Gamma

-0.3

-0.29

-0.28

-0.27

-0.26

Time (sec) 298

-0.25

-0.24

FIGURE 3

Downswing 3 Handicap--Iron

2000 FIGURE 4

1500 1000 500 0

-500 2000

1000 0

299

|

Alpha Torque and Alpha Sum of the Moments Integrated with beta force is alpha torque and these items with all of their angular responses will combine for the alpha sum of the moments. In Fig. 5 you will see this golfer’s alpha torque. You can see that he is applying a very slight negative alpha torque during this interval and towards the -0.23 mark he starts to apply a positive alpha torque.

A negative alpha torque will make the club want to rotate even more behind the player but just a couple of N m is not going to do much.

If you go back to your space frame for a sec-

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ond, we know that a positive beta force produces a positive alpha rotation. So even though this club is curled all the way around at the top of the backswing, we know from what we’ve already examined that the a-b-g axes “can be chosen such that they are fixed in and move with the body. (When it gets confusing, revert back to the space frame and rehearse the kinetic to help your comprehension.)

The positive beta force near the end of the backswing generated a positive alpha response which is greater than the negative alpha torque for this section of the swing. Therefore we should expect to see a very small positive Alpha Sum of the Moments in Fig. 6.

FIGURE 5

Alpha Torque 3 Handicap--Iron 0

Alpha

-1

N-m

-2 -3 -4 -5 -0.33 -0.32 -0.31 -0.3 -0.29 -0.28 -0.27 -0.26 -0.25 -0.24

Time (sec)

300

|

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FIGURE 6

4 3.5

Sum of the Moments 3 Handicap--Iron Alpha Beta Gamma

3

N-m

2.5 2

1.5 1 0.5 -0.31

-0.3

-0.29

-0.28

-0.27

Time (sec)

301

-0.26

-0.25

-0.24

|

Lesson 11 Transition They say the Kentucky Derby is the most exciting and fastest two minutes in sports. A golfer’s downswing is roughly .25 seconds, and is just as exciting as the run for the roses. There are so many kinetic and kinematic interchanges in that quarter of a second, and they explain why the golf swing is so difficult to master. Over the years, golfers have become familiar with the kinematic descriptions of the swing. Heck, you can buy a system like GEARS and see every movement of the golfer and club at 360 frames per second times eight cameras for a whopping 2,880 capture frames per second. The kinematic portrait of a golf swing is easy to find in books, online, or even at your local sporting goods store in the launch monitor bay. But what you are about to read is an all new way of looking under the hood so to speak, with unconstrained 3D dynamics.

What is happening in the downswing?

First we must define exactly what the “downswing” is. In Jacobs 3D we define the exact time of the downswing as the change in direction of the hub from the upswing to downswing. This distinct definition is extremely important because the vast majority of the golf world chooses the golf club change of direction as the start of the downswing. If you use this typical definition, the hands will have already traveled down before the club is reversed and you can confuse yourself on what is happening at the intersection of the backswing and downswing.

Since things are changing direction rapidly let’s go through each kinetic driver individually.

Beta Plane of Motion Kinetic Drivers Alpha Force and Beta Torque From the previous lessons we know that the golfer is applying a negative alpha force, a negative gamma force and a positive beta torque (Fig. 1). We know from Lesson 9 that this player was applying

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FIGURE 1

a greater magnitude of alpha force than gamma force and that is why the red arrow is slightly bigger than the green one. If we were to create a resultant arrow between these two components of force, it would be tilted up and away (like it has in hundreds of the graphs that have been presented in Jacobs 3D presentations over the years).

As we learned in Lesson 9, there would be a third force component as well, and that beta force (if present) would make the resultant arrow either tilt more in front of the player or more behind. The negative alpha force is at a distance from the mass center and therefore induces a negative beta angular response—which will require the player to balance it out with a positive beta torque (blue arrow in Fig. 1) if the goal is to stop the club from over-rotating or lagging too much. This “over-lagging” can be demonstrated by swinging a chain. A chain is unresponsive to applied torque, which means that all it can do is angularly respond to the direction

302

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you force it. Swinging a chain or a rope is a popular golf exercise, but I’m sorry to prick the bubble that comes with it. That move requires a wildly different hub path to make it look like a golf swing. That’s why I only ever recommend it as something you’re doing to work out, not work on your swing.

As the golfer transitions from backswing to downswing the hands start to lower as the kinetics continue in the same directions. This action is the secret to lag. So a negative alpha force, negative gamma force, very small to no gamma torque, positive beta torque to halt the sag, beta force to push it either in front or more behind you along with combinations of alpha torque. Those are essentially the transitional kinetics in conjunction with the hands being brought down by the body links to form a hub path shape.

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Let’s look at some graphs of these metrics from the same player we have been using.

Fig. 2 shows the actual force components and their magnitudes during this portion of the swing.

You can see the red alpha force line is negative 11.5 newtons as the graph begins and then starts to lessen and approach zero by -0.15 seconds to impact.

Fig. 3 is a time stamp of the downswing so you can see where the club is at in these landmark places.

As expected the negative gamma force continually grows during this phase on its way to over 230 newtons before impact.

The negative beta force is linearly driving the mass center toward the forward side of the player, as we saw in Lesson 9. The slope of the beta force graph will work its way toward positive by -0.19 seconds. This indicates that the player is now be-

FIGURE 2

Alpha-Beta-Gamma Forces Downswing Subject Golf Swing--7 Iron 60 40 20 0

N

-20 -40 -60 -80 -100 -120 -140

Alpha Beta Gamma

-0.28 -0.26 -0.24 -0.22 -0.2 -0.18 -0.16 -0.14 -0.12 -0.1

Time (sec)

303

|

ginning to force the club more behind him. Fig. 4 is the avatar of this player showing this beta force directional change. (As a reminder this is the same 7-iron swing of the tour player from Chapter 2, and all of his other kinematics and kinetics are splashed throughout this book) Fig. 5 shows the components of torque. A positive beta torque was applied, which proves he was trying to balance out the angular response from the

Chapter Four

alpha force. If you look at the sum of the moments graph in Fig. 6, note how the beta sum is a very slight negative which means that the golfer is balancing the torque and the angular response. Just after the -0.2 mark it will start to drop some more. At that point there is still a negative alpha force being applied which has a magnitude of about half of what it did earlier in this phase. The positive beta torque has subsided more than half of its original value, this

FIGURE 3

304

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means we should see a wee bit more lag.

Finally, in the alpha plane of motion, we know that this player forced the club towards the front of him followed by forcing it more behind him. The negative beta force is tiny at the start of the graph in Fig. 2, and it creates a very small amount of negative alpha response (by definition). Fig. 5 shows the golfer applying a small amount of positive alpha torque that provides us with a sum of the moments

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alpha between 1 and 3 N m until it starts to spike up after -0.19. This confirms the images in Fig. 8 that there is very little angular behavior of the club in the alpha plane of motion in these early stages and since they are slightly positive the club will be staying very close to in-line with the hands. Gamma torque is very minimal as you can see in the green line on the torque graph back in Fig. 5.

FIGURE 4

305

FIGURE 5

20 15 10

Torque Downswing Subject Golf Swing--7 Iron Alpha Beta Gamma

5

N-m

0 -5

-10 -15 -20 -25 -30 -0.28 -0.26 -0.24 -0.22

-0.2

-0.18 -0.16 -0.14 -0.12

Time (sec)

FIGURE 6

Sum of the Moments Downswing Subject Golf Swing--7 Iron Alpha Beta Gamma

12 10 8

N-m

6 4 2 0 -2 -4 -6 -0.28 -0.26 -0.24 -0.22

-0.2

-0.18 -0.16 -0.14 -0.12

Time (sec)

306

FIGURE 7

FIGURE 8

307

|

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Lesson 12 To Last Parallel After transition, the body links are aligned to start to force the golf club down and towards the other side of the hub path. Let’s take a look at the kinetic drivers for this phase and bring the swing to .05 seconds before impact.

FIGURE 1

Alpha-Beta-Gamma Forces Downswing Subject Golf Swing--7 Iron 50

N

0

-50

-100

-150

Alpha Beta Gamma

-0.25

-0.2

-0.15

Time (sec)

308

-0.1

-0.05

|

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Negative alpha force changes over to positive at -0.15 seconds before impact and then ramps up towards its maximum in the next tenth of a second.

Fig. 1 are the alpha beta gamma forces while Fig. 2 shows the avatar at the exact time of this alpha force switch over.

FIGURE 2

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|

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At -0.15, the alpha force crosses zero while the beta torque has already gone negative and is at a magnitude of -9.5 N m. This means that at the exact interchange between negative and positive alpha force, this player is applying a small torque to help delay (lag) the outward movement of the club (Fig. 3).

FIGURE 3

310

|

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As the downswing progresses, this golfer surges his positive alpha force—reaching 54.5 newtons by -.05 seconds before impact. A culmination of movements throughout the body linkage participates with the arms in this alpha force boost (Fig. 4).

FIGURE 4

311

|

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If we replace the club with an airplane once again, a positive alpha force will pull upwards on the tail of the plane regardless of how it is oriented. This is the same exact way you should envision applying your positive alpha force to the club (Fig. 5).

FIGURE 5

312

|

The spike in positive alpha force is going to create a positive beta angular moment. The club will react with an angular response that wants to line up with this component of force but you can clearly see in Fig. 4 that this did not happen. This player applied a negative beta torque in order to get that behavior you see from the club. Fig. 6 is a nice visual showing you how the airplane would want to line up with this positive component of alpha force.

Since the plane (or club) is in this angular position, it means that a negative beta torque was applied.

Before we look at the magnitude of the beta torque

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I want to point out a very important concept. The movement of the club is three-dimensional, with the equations of motion sharing terms in all of the different directions. It will never perfectly align with what you would expect it to do in 2D, 1D or on a back of a napkin mathematical calculation.

Effects in other directions will have an impact in all dimensions.

For example, what you are about to see happening in the alpha plane of motion is going to strongly affect this golfer’s kinetic abilities in the beta plane of motion.

FIGURE 6

313

|

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At -0.05 seconds, this player is applying -46 N m of beta torque while the positive response from the force is just a few less N m giving us a sum of slightly negative. As I said the actions in the other directions do make the links of our body change positions and affect what can be done in any plane of motion.

Fig. 7 is his downswing torque graph, which we’ll use as a reference for the rest of this chapter.

Before we analyze the alpha and gamma directions of this portion of the swing, let’s revisit one of

FIGURE 7

Torque Downswing Subject Golf Swing--7 Iron

50 Alpha Beta Gamma

40 30 20

N-m

10 0

-10 -20 -30 -40 -50

-0.3

-0.25

-0.2

-0.15

Time (sec)

314

-0.1

-0.05

0

|

my more favorite instructional analogies. In April of 2016, Golf Digest published a two-page article where I introduced the “fishing rod” drill. Let’s go into more detail on that very drill, because it is designed exactly for what we just covered.

The left side of Fig. 8 shows the end of a backswing fishing cast. Since we have never actually measured a fishing cast we will just infer some arrows to show the components of force (the arrows are not of any scale or actual meaning other than to illustrate the concepts). Just like a golf club, we would expect the pullback to have a component of alpha force and gamma force that is curving it up to the top. There would be a third component of force (beta) that would be driving the rod either in front or behind the fisherman (for the sake of this example, we will stay with just the alpha and gamma components).

As the fisherman commences the forward cast,

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the path of the handle is moving wide while preserving the negative alpha force component. This will delay the outward movement, essentially lagging the rod.

As the forward cast heats up, we will examine Fig. 9, which has the rest of the journey of the rod with just the alpha force component displayed. You will see that the alpha force has to switch ends from negative to positive just like in a golf swing—and at similar times too!

We know from our golf study that a torque in the opposite direction of the angular response will be necessary to control the downward pitch of the rod. So a fisherman will apply a negative beta torque to control the acceleration of the pitch down of the rod. I always tell my students to envision a fisherman pulling the rod UP and IN at the end of the cast and applying a torque back toward them at the handle to control the pitch. (Fig. 10.)

FIGURE 8

315

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FIGURE 9

FIGURE 10

316

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The gamma force and gamma torque components are displayed in Figs. 11 and 12. When you choose to dig deeper, you can go back to Chapters 2 and 3 and marry this player’s gamma force to his center of curvatures.

The gamma force is continuing to ramp up as the centripetal acceleration increases. The g-load, direction changes etc are all starting to make things interesting and the effects will be showing up

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throughout the body of the golfer.

It is clear in the gamma torque graph that a positive (green quiver) torque is being applied through this phase of the swing. We can predict that to be the case in almost all subjects.

The actions that take place in the alpha plane are one of the most fascinating parts of the kinetic study. The beta force and alpha torque components are going to drive the club either back out in front

FIGURE 11

317

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of the player or work in such a way that they get stuck behind. Driving the club in front of you too early will require you to have to drive it back behind through impact creating the classic over-the-top, outside-in, chicken wing. Driving the club too far behind you will get it stuck behind and create the need for a late, desperate wrap-around move to get it somewhat out in front of you.

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This textbook is landing in early 2019, and right now it is a very popular fad to keep the club behind you on the downswing for as long as possible, and then have it whip around at the bottom. I think that fad will die out when the kinetics are better understood within the convention Dr. Nesbit and I have created.

FIGURE 12

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A positive beta force in this phase of the swing will drive the club more behind you and a negative force more in front of you. Fig. 13 is at the time in the swing when the beta force passed through zero.

Looking back at Fig. 1, you can see that the beta force slope crosses to negative very close to the -.09 time frame.

This means that in the next phase of the downswing, this player is going to drive that club to the

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other side of him via a forcing kinetic. A negative beta force is going to induce a negative alpha angular response, therefore the action in the alpha plane of motion will now make the club want to yaw back behind you even though you are trying to drive it forward. If you DO NOT positively alpha torque at this time, the club will get stuck well back behind you. This negative beta force will bank around and reach its negative peak just before impact. At the

FIGURE 13

319

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FIGURE 14

320

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FIGURE 15

Alpha Torque Downswing Subject Golf Swing--7 Iron Alpha

25

N-m

20

15

X: -0.09195 Y: 11.08

10

5 -0.16

-0.14

-0.12

-0.1

Time (sec)

321

-0.08

-0.06

-0.04

|

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FIGURE 16

m

m

322

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FIGURE 17

Sum of the Moments Alpha Subject Golf Swing--7 Iron Alpha

16 14

X: -0.09195 Y: 11.38

12

N-m

10 8 6 4

X: -0.05028 Y: 1.361

2 0 -2 -0.7

-0.6

-0.5

-0.4

-0.3

Time (sec)

323

-0.2

-0.1

0

|

time frame of -.05 seconds which is where this phase ends the negative beta force is -19 newtons.

Fig. 14 shows the superimposed avatars of this -.09 to -.05 interval. During this time, the negative beta force will grow to -19 newtons but at the start of this interval the alpha angular response from the force is zero. Fig. 15 is the alpha torque over the entire downswing. At -.09 seconds the alpha torque is a positive 11 N m, which means that he is trying to yaw the golf club out in front of him. Fig. 16 shows you the positive alpha torque and effort direction.

Fig. 17 is the alpha sum of the moments, which has started its descent toward 1.3 N m at the end of this interval. Essentially, the negative beta force is start-

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ing its rise, which is beginning to create a negative alpha angular response. The angular response from the force along with the torque requirements in the other directions are going to force (no pun intended) the alpha sum of the moments to drop.

Lesson 13 To Impact onto the Finish We will now analyze what is happening from -.05 seconds to the finish, and we will start with the alpha components. Figs. 1 - 5 show the timing of peak negative beta force, which is -0.01 seconds

FIGURE 1

Alpha-Beta-Gamma Forces Downswing Subject Golf Swing--7 Iron 20 0 -20

N

-40

X: -0.01139 Y: -68.69

-60 -80

-100 -120 -140 -160

Alpha Beta Gamma

-0.18 -0.16 -0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02

Time (sec)

324

|

before impact. Fig. 1 is the graph and Figs. 2-5 are the avatar from all different viewpoints.

That is a high level of negative beta force late in the swing, and there are two main reasons for this. This player swings inside out, requiring more negative beta force to bank the club around, and he also has a good amount of forward lean on the shaft at impact.

If you look back to Lesson 12, you will see the alpha torque graph and notice that once the negative beta force peaks and starts to lessen, so does FIGURE 2

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the alpha torque. The changes in alpha torque are very stable—the wrists can only provide so much power, so there will not be massive fluctuations in alpha torque. We will generally see an alpha torque peak of 40-50 N m during the downswing, while at impact a value of approximately 20-35 N m is common.

The sum of the moments alpha drops to -3 N m at impact for this player. A negative sum at impact is extremely common and very predictable, but the journey is completely different player to player. The

FIGURE 3

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kinetic combinations are infinite, yet so much of golf science just looks at the net sum and arrives at oversimplified conclusions of “how” it happened.

From impact to the finish you will see all different kinds of beta force and alpha torque combinations. Because impact is so violent, we stop a lot of our graphs at that time. The kinetics of the follow-through will be a lot like the ones on the backswing in regard to the gamma and alpha forces driving the club up to the finish.

Chapter Four

Positive alpha force going into impact reached its peak at -.03 seconds before impact and then dropped 33 newtons rapidly by time of impact. The gamma force climbed over 200 newtons, and all of these high kinetic interchanges prove that a lot of effort is going into directional changes and trajectory control. Gamma torque went negative before impact, which is extremely common especially on an iron. Beta torque started to ease up as the alpha force magnitude started to drop.

FIGURE 4

FIGURE 5

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Chapter Four

Figs. 7 and 8 are the sum of the forces from the Face-on-view and the Down-the-line-view.

(Take note of the slope of the hub path in the Follow-Through as the body starts to rise.)

As you can see, there is a universe of analysis available to anybody who wants to put in the study time. We’re just getting started producing content like books, video series and seminars to help explore all the possibilities for players and teachers.

FIGURE 6

Sum of the Moments Downswing Subject Golf Swing--7 Iron 2 X: -0.03639 Y: -0.02962

1 0

Alpha Beta Gamma

-1

N-m

-2 X: 0 Y: -3.861

-3 -4 -5 -6 -7 -0.08

-0.07

-0.06

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-0.03

Time (sec)

327

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-0.01

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Chapter Four

FIGURE 7

Linear Force Applied to Grip Point 5 Subject Golf Swing--7 Iron 3500 3000 2500

Z (mm)

2000 1500 1000 500 0 -500 2000 1500 1000

3000 2000 1000

500

0

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Y (mm)

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0 -1000

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Chapter Four

FIGURE 8

Linear Force Applied to Grip Point 5 Subject Golf Swing--7 Iron

2500 2000

Z (mm)

1500 1000 500 0

2000

1500

1000

500

X (mm)

329

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-500

-1000 0 1000

Y (mm)

The principles of Work and Power will be covered in their own publication.

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AFTERWORD

BY BRIAN MANZELLA

I have listened to explanations of what is happening in the golf swing for nearly half a century.

Some folks use a lot of detail and some use less, but in my opinion, the vast majority miss the mark by a large margin. Wouldn’t be great if someone made an analysis and you could find out exactly what happened in the golf swing?

When Dr. Steven Nesbit used his knowledge of rigid body dynamics and robotics to solve this mystery for the United States Golf Association back in the 1990s, it was done for the purpose of applying the answers to equipment standards. That project was the foundation of Dr. Nesbit’s published papers on the golf swing. One of those papers, Work and Power Analysis of the Golf Swing, is one of the main reasons I was part of a group of golf professionals that traveled visit Nesbit in 2010.

We were looking for those answers.

Another golf teacher in the group was my dear friend Michael Jacobs. We were both long time students of renowned instructor Ben Doyle. Ben had told me about this “up-and-comer from Long Island” for several years before we finally met, six years earlier.

Michael and I had very similar backgrounds.

We grew up playing public golf courses, knew we

wanted to teach golf for a living before we graduated from college, and found the book The Golfing Machine in our search for answers about how the swing really works. We got along famously and started doing golf schools together in 2006.

I’ll never forget the day we went to see “Dr. Steve” for the first time. When Mike and I got in the car on Long Island with two other pros for the three-hour trip, I opened an email from Golf Magazine that informed me that I had finally been named to their Top 100 Teachers in America list after many years of trying hard to hone my craft and be recognized for it at the national level.

At the meeting, we all sat at a long table and Dr. Steve used an overhead projector and a blackboard to explain concepts to us. One of those explanations stuck with me. It was Nesbit’s simple explanation of the force the golfer applied to the club. Dr. Steve explained that the golfer essentially pulled the club more or less along the path of the hands early in the downswing and then more and more inside that path of the hands, and then finally a right angles or “normal” to that path—right back at the golfer—by impact. And I knew even before his explanation was complete that I had inadvertently tried to get a lot of students to do something very different. And obvi-

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ously very wrong. If “normal” was where I needed to get my students and myself to wind up at impact, then I needed to create a different set of conditions at nearly every point along the way so we all could “go normal.” Not long after that, “going normal” became the first catch phrase of the modern era of science-based golf instruction. And the first set of “science-y” words that many golf teaching professionals ever heard of or learned were the “alphabeta-gamma” terms from Nesbit’s Work and Power.

But poring over the graphs in that Dr. Steve research paper was never going to be enough to really understand the detail inside the Nesbit analysis. The next step was more examination and Michael Jacobs had the gumption to begin to making this study his mission.

Years later after finally looking at good raw 3D data from Mike’s new optical capture system— Nesbit told Michael that he could put “something” together to compute the forces and torques we had been studying.

Six months later, Dr. Nesbit emailed Mike and told him, “Your program is ready.” I went on the trip to pick up the program and on the ride back we were filled with anticipation for what was to come.

We got back to Mike’s place off the Long Island Expressway and ran inside to run a swing. As luck would have it, the first one we did was that of long drive phenom Jamie Sadlowski.

Mike pulled up the graphs for Sadlowski’s forces and torques, picked up a club and worked his way into Jamie’s extreme top of the backswing position.

Looking at the readouts on a big monitor, he started to try to duplicate what the graphs said the long driver did in transition. Two seconds into Michael following the force and torque directions, I could clearly see—and he could easily feel—that he was replicating the exact movements of the longest hitter in golf.

It was a moment I’ll never forget. It was the real deal, and we now had the tools to find out the secrets of the golf swing that have eluded golfers, teachers and theorists over the centuries. A little more than four years have passed since that day.

We have taught across the USA and in quite a few countries around the world with the findings we’ve

Afterword

discovered with Jacobs 3D. We’ve vastly improved our teaching and our own golf games. The software and the math that makes it go has been a constant source of interest in the golf instruction world.

As Director of Instruction for Jacobs 3D, I’ve improved my understanding of the material and how I use it in lessons by leaps and bounds. And, in my opinion, Michael Jacobs has become the world’s foremost authority on the subject of golfer applied club kinetics. The cherry on top of the cake is Michael’s business collaboration with Dr. Nesbit has resulted in Steve building the keys to another research tool—Alpha Man—which computes the forces and torques of the whole body.

I wrote that one day Mike’s Elements of the Swing book would “be talked about... as one that changed the game of instruction.” It is my view that The Science of the Swing will be the reference for club kinetics for decades. I’m sure you’ll learn a ton from it, as I have. It’s been great being part of this fabulous team and I relish my role in helping folks understand how knowing what really happens in the golf swing can be powerful and liberating.

Brian Manzella Golf Digest 50 Best Teacher Golf Magazine Top 100 Teacher New Orleans, La.

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Acknowledgments

ACKNOWLEDGMENTS Organizing a project of this magnitude was a professional milestone for me. I can’t thank Dr. Steven Nesbit enough for empowering me with the mathematical models to make this possible. The last nine years have been the most challenging and rewarding of my career, and I could not have accomplished it without the support of my friend Brian Manzella. He pushed me every day to find a practical explanation for each detail of this mathematical convention. I remember the day when I was walking around a hobby and crafts store on Long Island and spotted a model airplane. I purchased that airplane instantly, ripped it out of its packaging and ran next door to the sporting goods store and bought a golf club. I stood in the parking lot and created the airplane analogy you saw in this book. I connected with Brian on Face-time right there and showed him the explanation I came up with and I will never forget the look on his face. That night, he had his own airplane attached to a club. It’s that kind of passion—like two high school guys trying to solve the world’s problems—that has made this journey so special and worthwhile.

The countless hours of discussion Matt Rudy and I have had all along the way have been priceless. He’s instrumental in turning these complicated ideas into something digestible for my books, videos and presentations. Matt is a great writer and an even better friend.

Keri Ello Reiter did a fantastic job designing this book. She’s extremely talented, and I look forward to working with her on my future projects. A special thanks goes to the first two advisory members of Jacobs 3D—Rick Silva and Tom Rezendes. You guys have done an excellent job teaching this great information. I look forward to working with you both for a long time. You will lead the way for many advisory members to follow.

To our “European Ambassador,” Enrico Villo of Estonia—you are my brother from the other side of the world. Keep up the great work and show the rest of Europe what Jacobs 3D is all about.

My mom and dad, Viv and Mick, are the two best parents on the planet. You taught me to chase my dreams and I am doing just that. Alexander Slayton, you have been a massive part of this project as an engineer. Your ability to help me turn these complex models into an instantaneous golf analysis has been awesome. I look forward to working with you for a long time. I couldn’t do this without the staff at Rock Hill. The great job you do, lets me put the extra time and effort into all this research and development.

Dr. Nesbit, you are the greatest engineer and an even better teacher. Every time I leave a meeting with you, I am so invigorated and inspired to work harder. You designed the models and have had the patience to let me work my way through a

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very complex analysis. I hope that I have made you proud, and I hope seeing your models play out in all golfdom is very rewarding for you. We’re just warming up!

And to all my students who visit me on Long Island and the swing enthusiasts around the world studying this book: Thank you for going on this journey with me. It will take some time to absorb this information, but it’s a fun ride. When the going gets tough and the kinetics get confusing in the user frame, go back to the space frame and perform the kinetic—then transpose it to where you were in the swing. There’s a reason we started with the fundamental space frame. It’s Jacobs 3D’s “home plate.”

And if you really get stuck, reach out to me on my website, www.Jacobs3D.com and I’ll do my best to straighten you out.

Happy golfing to you all!

Michael Jacobs

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Acknowledgments

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Dr. Steven Nesbit  B.S., M.S., Ph.D., West Virginia University Teaching interests: mechanical design; mechanism analysis and design; robotics

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Acknowledgments

Michael Jacobs Golf Digest Top 50 Teacher in America Golf Magazine Top 100 Teacher in America PGA Professional

ENGINEER

ALEXANDER SLAYTON Alexander Slayton is a recent graduate of Lafayette college, where he studied mechanical engineering and the biomechanics of the golf swing with Dr. Steven Nesbit. He has always enjoyed the sport recreationally and is excited to be working with Michael Jacobs at the forefront of golf swing science.

JOURNALIST

MATTHEW RUDY A native of Saginaw, Michigan, Rudy graduated with a journalism degree from Michigan State University in 1994. Before joining Golf Digest in 1999, he was an editor at Basketball Times and a reporter at Sports Illustrated. Rudy also has an MBA with a specialization in management from Fairfield University, which he completed in 2006. He lives in Easton, Connecticut, with his wife and three children—and at least one mostly operational vintage muscle car. Matt has helped Michael write all of his books and media.

DIRECTOR OF INSTRUCTION

BRIAN MANZELLA Brian Manzella is one of Golf Digest’s 50 Best Teachers in America and a Golf Magazine Top 100 Teacher in America. As a 30year member of the PGA of America, Brian has taught players at every level and holds the rank as the Director of Instruction of Jacobs 3D.

ADVISORY MEMBERS

RICK SILVA

Tom Rezendes

Enrico Villo

RICK DANDY

Movement 3 Golf Chicago, Illinois

NorCal Golf Academy Walnut Creek, California

Ambassador to Europe Tallin, Estonia

Philanthropist Bethesda, Maryland

DESIGNER

ON-SITE STAFF

MASCOT

MATT SCALA General Manager

jc kemp Personal Assistant

Eric feltman Teaching Professional

JAMES HARRIS Human Resources

KERI ELLO REITER MLIS, BFA in Digital Art and Design East Northport, New York keriello@gmail.com

JOE IANNOLO Superintendent

Front cover art design by Tim Oliver and Mark Hooper

BOSSY Born 2013 Manorville, New York