Tutorial: Golf Swing Biomechanics

Dave Tutelman  --  started February 26, 2020

UNDER CONSTRUCTION!
This is not finished yet.
Comments are welcome.


What can you get out of this tutorial?

You have undoubtedly heard of "biomechanics" -- whatever that is -- becoming important in golf performance. This should help give you a little insight into what  golf biomechanics is and what it says. My intent is for this insight to be sufficient that:
  • It will help golf instructors understand the new things they are hearing that could apply to what they teach. It may also disabuse them of things they have heard over and over in the past that are, frankly, wrong.
  • It will show golfers diligent enough to slog through it, and moreover to practice as much as it takes, some new things about how to swing that are different from the traditional golf swing.
  • It will allow you to read some of the published papers and articles in journals on biomechanics, sports medicine, and kinesiology. You might, or might not, be able to read and follow the details, but you should be able to understand what the results are. You will also gain an appreciation of how science figures out what is going on in a golf swing.

A few points in the use of this tutorial:

  • If you choose to read or skim it from beginning to end, there are "next page" and "previous page" arrows at the top and bottom of each page.
  • Below is a table of contents of the course, with links to the pages. You can dive in where you wish, but be forewarned that the material assumes you know and understand what came in earlier pages.
  • I do expect you to know a little math. It is all stuff you should have learned before or in high school, including:
    • Eighth grade algebra. Solving simple equations, and manipulating equations with multiple letters as unknowns.
    • Eighth grade trigonometry. We may use a bit of ninth and tenth grade stuff, but we'll develop what we need; I don't expect you to know it when we start.
    • Basic geometry, at least the terminology.
    • How to read and understand graphs. Seriously, folks! This is a survival skill in today's world anyway.
    Every now and then, I hear someone say (or see them write on social media), "Well, how many equations have you had to solve this year? Learning that was a waste of time." And I shake my head. If you are like that, I hope I can convince you otherwise. A sense for algebra is absolutely essential to thinking quantitatively.
  • You should pay attention to the examples. The deeper we get into the physics, the more opportunity to include golf situations as examples, and I try to do so whenever I can. Even if you don't sweat the numbers in the examples, it is essential to understand what the problem was and roughly how we got to the answer. Often, the answer itself is enlightening; I will try to discuss the message in the answer whenever possible.
  • Occasionally there will be an optional point where you may get some deeper insight if you can handle the math. Such optional notes will be inserts with a green background, and might even be listed in green in the table of contents. You can skip it if your math skills can't deal with it. You will not have as deep a grasp of the material if you skip it, but you will still have a decent working knowledge.
  • Some, certainly not all, of those green notes will require more math than the bullets in the list above. Occasionally, I may explain something in terms of calculus or some other branch of math or science. Again, it may be an opportunity to grasp a little better the concept I am explaining, but you will still have a decent working knowledge of my point even without the green note.


Introductory concepts

Kinematics vs kinetics

Units of measurement

Vectors

Vectors in golf

Adding vectors

Resolving vectors


Forces

Kinetics

Newton's laws

1st law: Body at rest

2nd law: F = ma

3rd law: Equal and opposite reaction

Kinematics

Position to velocity to acceleration - slope

Acceleration to velocity to position - area

Notes - calculus

Curved motion


Torques

Force-torque relationship

What is torque?

Force required to produce torque

Levers

Couples

Moment of a force

Kinetics and kinematics

Newton's three laws

1st law: Body at rest

2nd law: Τ = Iα

3rd law: Equal and opposite reaction

Angular measurements

Moment of inertia

Why r squared?

Example: bicycle wheel

Demonstration

Examples and more analysis tools

Moment of inertia of golf club

Center of mass (center of gravity)

Parallel axis theorem

Example: hollow tube

Example: Io of the golf club

Equivalent force couple system

Textbook example

Golf club example

The leverage myth

What golf instructors too often mean

The fallacy of the "whoosh drill"

Force multiplier

Length vs moment of inertia

Conclusion

Math note: Proof that longer does not equal faster


Energy and Momentum

Energy

Work

Potential energy

Other forms of energy

Angular energy

Momentum

Consequence of F=ma

Lossless

Angular momentum


Biology

Muscles & joints

Range of motion

Force-speed and torque-speed curves


Apply to the Golf Swing

Coordinate systems

World coordinates - x,y,z

Swing plane coordinates - alpha,beta,gamma

Club coordinates

Functional swing plane

Stability

Allows 2D analysis

Torques in the downswing

Ground reaction force

Weight and pressure shift

Kinetic and kinematic sequence

Classic kinematic sequence

Some consequences

Rory McIlroy's hip reversal. (Lots of reaction torque)

Scottie Scheffler's slipping right foot. (Pressure shift too early for reaction torque)

Andreas Zanardelli's Facebook post. (Too little reaction torque)

Instrumenting the swing

Direct kinetic measurement

Force plates

Transducer in grip

Launch monitor

Motion capture

Inverse dynamics analysis

Recent published results

What produces clubhead speed?

What does shaft flex do?




I've been planning to write this tutorial for a half-dozen years. Once, I even got started. But the enthusiasm lasted for only a few days. There was never a clear organization to the material in my mind.

Then, in early February of 2020, Kathy Ricci, an instructor at our Monmouth County Parks golf courses, called and asked for a tutorial on the physics that is increasingly important to understand the new biomechanics research on the golf swing. That motivated me to put together a few pages of notes as a "lesson plan" for my meeting with Kathy. We met at the Shark River Park clubhouse on February 8 and spent about two hours going over the material I had planned, plus detours for her questions. At the end, she felt she understood the things we talked about. This sounded pretty much like what I originally intended the tutorial to do, and for the sort of person I hoped to help: a professional golf instructor without a lot of physics or biomechanics background. So I used the lesson plan as the outline for the tutorial. As I made progress, the outline has evolved.

At this point, I'm making the draft public for comment. It is still a work in progress, but I think it is ready for reader input. Any comments you have to make are welcome. Anything from errors of fact to topics you'd like to see covered to the smallest typo. Thanks in advance for any help you can give.

DaveT