Modelling The Golf Swing
In Chapter 10, we presented the basic rotation equation. We noted that the equation depends on:
- the rotation centre;
- the distance from the rotation centre to the ball;
- the angle between the line from the rotation centre to the ball and the axis of rotation;
- the amount of rotation in the downswing;
- the duration of the movement within the downswing; and
- a factor converting the average downswing speed of the club head from the movement, to speed at impact.
Chapter 10 also looked at the duration of movements in the downswing, and the factor converting the average downswing speed of the club from the movements to speed at impact.
In Chapter 11, we looked at each movement in the golf swing in terms of rotation centre, distance of the rotation centre to the ball, the angle between the line from the rotation centre to the ball and the axis of rotation.
In this chapter, we build on the foregoing to develop a “big picture” model of the golf swing. The model is necessary because the individual movements are to some extent interdependent. Changes in the way some of the movements are performed affect the performance of other movements.
Our model has three components:
- Parameters. These are the inputs to the model, and are based on the characteristics of the individual golfer, including physical dimensions, flexibility, equipment, swing posture, and duration of movements in the swing. For purposes of our discussion, default values based on the author are provided. Changes in some default values will be explored to determine their impact. The model is designed so that you can insert your own values into a spreadsheet to get a perspective of your swing.
- Calculated values. These are values determined from parameters and used as inputs into the Club Speed Calculator Table.
- Club Speed Calculator Table. The table consists of the application of the basic rotation equation, lateral movement and spinal tilt, for each movement in the golf swing.
The parameters used in the model are listed below, with the default values on which the conclusions of the model are based.
- How many frames per second in your video camera? Default=27
- How many frames to uncock the wrists in the downswing? Default=4
- How many frames to roll your forearms and rotate your upper arm in the shoulder socket? Default=4
- How many frames to move the upper arm in the shoulder socket? Default=6
- How many frames to move the shoulder sockets around the spine? Default=6
- How many frames to untwist the spine? Default=11
- How many frames to rotate the hips? Default=11
- Acceleration Scaling Up Factor. Default=1
- What is the length of your club (inches)? Default=45.5
- What is the length of your arms in inches? Default=24.0
- How many inches do you move your shoulder sockets around the spine in the downswing? Default=3.0
- What is the distance in inches between your two shoulder sockets? Default=13.0
- How many inches do your hips move laterally in the Push and Clear? Default=3.0
- What is the distance in inches between your hip joints? Default=7.0
- How many degrees do you tilt your spine/upper body forward at the hips relative to the vertical? Default=30
- How many inches from your shoulders to the base of the spine? Default=17.5
- How many inches from the base of your spine to the centre between the two hip joints? Default=7.5
- What is the angle in degrees between the club shaft and the arm? Default=130
- What is the distance from the ground to the hip joint (inches) when standing erect? Default=32.0
- How much distance should be subtracted to allow for knee bend, use of tee, etc.? Default=2.5
- Downswing Rotation of Wrists (degrees) Default=45
- Downswing Rotation of Forearms (degrees) Default=45
- Downswing Rotation of Upper Arms in Shoulder Socket (degrees) Default=45
- Downswing Rotation of Upper Arms Around Shoulder Socket – Basic (degrees) Default=45
- Downswing Rotation of Spine – Basic – Top to Start (degrees) Default=60
- Downswing Rotation of Hips – Pure Rotation – Basic – Top to Start (degrees) Default=45
- Downswing Rotation of Spine – Additional – Start to Impact (degrees) Default=5
- Downswing Rotation of Hips – Pure Rotation – Additional – Start to Impact (degrees) Default=10
Key observations about the parameters include:
- Parameters 1 to 7 enable calculations required for the movements in the downswing. They are based on video of the downswing, and the examination the individual frames to determine when particular movements start.
- Parameter 8 is the “Acceleration Scaling Up Factor”, which is the amount by which average club speed during the downswing needs to be increased to determine impact speed. The default value of 1 denotes no increase. As such, club speed estimates must be viewed as minimum speeds.
- Parameter 9 deals with club length. The default value approximates the 2015 average men’s driver. Note that club lengths have been increasing in recent years.
- Parameters 15 and 18 involve angles determined from measures using pictures of the golf swing.
- Parameters 19 and 20 are taken together. Parameter 19 allows for a physical measurement. Parameter 20 allows for adjustments to that measurement for knee bend, use of tees, etc.
- Parameters 11 and 21 to 28 are based on observations of the joints in the gymnasium. As such, they are maximums. These degrees of rotation may be greater than those that actually occur in the swing.
- Parameters 25 to 28 address the fact that in the downswing, the hips and spine rotate beyond the start position by a few degrees. This is evident from photos that show the hips and shoulders are slightly open to the target line at impact.
From these parameters, a number of additional values needed to calculate club speed can be calculated as follows:
- How many inches does the centre of the spine move away from the target as a result of the forward lean in Pure Rotation? Answer: 8.8 inches
- What is the angle in degrees between the line from the shoulder socket to the ball and the ground? Answer: 53.5 degrees
- How many inches does the lead hip move forward in the backswing in Pure Rotation? Answer: 2.7 inches
- How many inches does the centre of the spine move away from the target as a result of the forward lean in Push and Clear? Answer: 4.7 inches
- What is the distance (inches) from the ball to the shoulder centre? Answer: 63.64 inches
- Downswing Rotation of Shoulder Socket Around Spine – Basic. Answer: 26.7 degrees
- Downswing Rotation by Hips –Push and Clear – Basic (degrees). Answer: 22.1 degrees
The table on the following page summarizes the combined effect of rotation, lateral movement and spinal tilt for each movement in the golf swing.
Can the results for the individual movements be added to create a total? To address this, note the rotation circles resulting from the movements in the golf swing. While the circles show some variability, note that what really matters is the instant of impact. All of the rotation circles pass through the ball, and the point when they pass through the ball is the instant of impact. Proper execution of the various movements should ensure maximum consistency among the movements in terms of propelling the ball straight down the fairway (rather than left or right) at the instant of impact. As such, while adding up the club head speeds from the individual movements may overstate the actual club head speed, the overstatement is likely to be minimal. On this basis, we shall continue to use the practice of adding up the speeds of the individuals movements to get the overall club head speed.
The Bottom Line:
- Through the application of the principles of physics and some basic measurements, we have calculated the minimum club head speed arising from each movement in the golf swing.
- We have added the impact of the individual movements to estimate a minimum club speed from the golf swing, based on given parameters.