Tutorial: Golf Swing Biomechanics

Dave Tutelman  --  started February 26, 2020

This is not finished yet.
Comments are welcome.

Straight to
table of

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.
  • You may be able to better understand other things about golf besides swing biomechanics, because now you know the physics. Some of my examples relate to golf, but not specifically the biomechanics of the swing; I talk about golf clubs, golf balls, and their interaction. I hear golf instructors and golfers discuss these topics at length, so I am not hesitating to bring them up in this discussion. They illustrate a golf-relevant point of physics, and they may be easier to understand in terms of a club or a ball.

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.
  • It is organized in two "books": Principles and Applications.
    • The "Principles" section is a tutorial on the physics and biology you will need for a quantitative understanding of golf biomechanics.
    • The "Applications" section applies those principles to golf. It covers my current (2023) understanding of the swing, and draws upon published papers and articles -- and gives you links to them for more detail.
  • 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! Understanding graphs 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 -- about golf and about almost anything.
  • You should pay attention to the examples. The deeper we get into the principles, 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. But they are optional! 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.

Book 1 - Principles

Introductory concepts

Kinematics vs kinetics

Units of measurement


Vectors in golf

Adding vectors

Resolving vectors



Newton's laws

1st law: Body at rest

2nd law: F = ma

3rd law: Equal and opposite reaction


Position to velocity to acceleration - slope

Acceleration to velocity to position - area

Notes - calculus

Curved motion


Force-torque relationship

What is torque?

Force required to produce torque



Moment of a force

Handy rule of thumb

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


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


Math note: Proof that longer does not equal faster

Energy and Momentum



Potential energy



Kinetic energy

Golf examples


Shaft bend

Angular energy

Example: Waggle

Other forms of energy







Just another way of saying F=ma

Collisions and conservation of momentum

Example: the essential divot

Comparing energy and momentum

Angular momentum



Skeletal muscles

Muscle energy

Naive model

More detailed model

Fascia, tendons, and the Stretch-Shorten Cycle



Types of joints

Tendons, ligaments, and cartilage



Maximum force

Range of motion

Exceeding range of motion

Force-velocity curve

Antagonistic muscle pairs

What can we do about the limitations?

Energy again

The problem

1. Find the kinetic energy

2. Find and subtract potential energy

3. Compute muscle mass for the rest of the energy

4. Apply limitations

Antagonist muscles

Range of motion

Sanity check

Stretch-shorten cycle


Book 2 - Application to the golf swing


The goal of the swing

Function: the impact model

Clubhead speed

The D-plane

Position of impact on the clubface

Bottom of the swing


Coordinate systems

World coordinates - x,y,z

Swing plane coordinates - alpha,beta,gamma

Club coordinates

Functional swing plane


Allows 2D analysis

The swing

The kinematic sequence

Torques in the downswing

Ground reaction force

Weight and pressure shift

Net GRF and its moment

Kinetic and kinematic sequence

Classic kinematic sequence

Some consequences

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

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

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

Recent published results

What produces clubhead speed?

What does shaft flex do?

How do we know this stuff?

Empirical studies

Instrumenting the swing

Direct kinetic measurement

Force plates

Transducer in grip

Launch monitor

Motion capture

Modeling the swing

Forward dynamics

Numerical integration

Inverse dynamics

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.


Last modified  --  Apr 25, 2023