Generally Eclectic

Some Elementary Physics

Chapter Ten: Guide to the Golf Swing

It's elementary (my dear Watson)

CLUB HEAD SPEED AND SHOT DISTANCE

Speed and DistanceThis should not come as a surprise. Club speed is related directly to the distance of a golf shot. The faster the club moves, the farther the ball will go.

The graph relates distance to club head speed. The table shows a direct relationship between club speed and distance. For every 1 mile per hour increase in club speed, total distance increases by about 2.57 yards. Keep this in mind as a point of reference.

DISTANCE TRAVELED BY THE CLUB HEAD

There are two elements to club head speed: distance traveled and time. Speed is the distance traveled divided by the time taken to travel the distance.

We are all familiar with straight line distance. We measure straight line distance with familiar measuring devices such as our feet, our paces, rulers, yard sticks, tape measures, and range finders.

Distance around a circle can also be measured using measuring devices, but it is usually easier to calculate this distance. To do so, we need to know the circumference of the circle, and the portion of the circle traversed.

Almost all movements in the golf swing, taken individually, cause the club head to move around the circumference of a circle.

Determining the radius of the circle traversed by the club head through particular movements (taken in isolation) is more complicated, and involves two notions: circle radius, and distance from the circle centre to the ball. In some cases, the circle radius is the distance from the circle centre to the ball. In other cases, it is different.

To illustrate the difference, picture a stick hanging down from a shaft that can rotate vertically to the ground. If the shaft rotates very slowly, the stick appears to not move but continues to hang vertically to the ground. The distance from the circle centre to the tip of the stick hanging from the shaft is the length of the stick, but the radius of the circle traced out by the hanging end is zero.

If the shaft rotates sufficiently quickly, the stick will move in a circle perpendicular to the shaft and horizontal to the ground. The radius of the circle traced out by the loose end of the stick will be the length of the stick, which is also the distance from the circle centre to the circumference.

One can imagine the situation where the shaft rotates at a rate that causes the loose end of the stick to trace a circle with a radius greater than zero but not the full length of the stock. The distance from the circle centre to the circumference of the circle traced by the loose end of the stick is the length of the stick, but the radius of the circle being traced is less than the length of the stick.

The picture below depicts what is happening. As the angle between the axis of the shaft and the stick increases from 90 degrees to 180 degrees, the circle being traced out by the loose end gets smaller. Note the difference in size between the circle with the dotted line compared with the one with the solid line. In both cases, the distance from the circle centre to the circumference is the same.

Speed and Distance

Call outs in the picture emphasize key concepts to be applied to the movements in the golf swing: the rotation centre; the axis of rotation; the distance from the rotation centre to the circle circumference traced out by the golf club and including the golf ball; and the angle between the axis of rotation and the line from the rotation centre to the golf ball at the circumference of the circle.

The picture shows that the distance to the circumference from the centre of rotation is not always the radius of the club head path/circle. The critical issue is the angle between the axis of rotation and the line from the centre of the circle to the circumference.

Speed and DistanceThe sine of this angle is used to calculate the radius of the club head path/circle when the angle is from 90 to 180. The table provides the sine of various angles between 90 and 180 degrees. Note how the sine of the angle starts to drop quickly after 130 degrees.

When the angle is 90 degrees, the radius of the circle traced out by the club is the distance to the circumference from the centre of rotation. When the angle is 130 degrees, the radius of the circle traced by the club head is the distance from the circumference of the circle from the rotation centre times .766.

CALCULATING DISTANCE TRAVELED

A key aspect of physics is measurement, and here are some basics we will apply for the golf swing in total and individual movements:

MEASURING TIME

Measuring the time required for the golf swing and its components is essential for calculating club head speed. Accurate measurements require sophisticated equipment, but a simple technique can help.

High speed video cameras typically take pictures at rates defined in terms of frames per second. Counts of the number of pictures in the downswing will let you determine the seconds required for the downswing.

An analysis of all the frames during the downswing can generate a great deal of time related information, including duration of the downswing, the duration of particular movements within the downswing, the number of degrees of rotation of the club during the frame and the relationship between degrees of club rotation and time in the downswing.

The table below illustrates the results of a detailed analysis of the golf swing pictures from a typical high definition camera. The results have been incorporated into the golf swing model.

Golf Swing Video Frame Analysis
Frame Number Club Angle (Horizontal = 180 Degrees) at End of Frame Degrees of Rotation Observations
0 180 - Start of downswing - club is parallel to ground
1 178 2 Hips have started to rotate
2 175 3
3 169 6
4 162 7
5 154 8 Spine has started to untwist - the angle between the shoulders and the hips has begun to decrease
6 142 12 Upper arms have started to move in shoulder sockets - trailing elbow has moved closer to the body. Shoulder sockets have started to move - lead shoulder socket has moved away from chin
7 115 27
8 85 30 Forearms have begun to roll and wrists begin to uncock
9 50 35
10 -10 60
11 -90 80 Impact - Club has reached perpendicular to ground

Observations from the table include:

AVERAGE SPEED AND IMPACT SPEED

In all movements, we will be calculating the distance travelled through the movement divided by the time required for it. The result is the average speed during the movement.

More relevant than the average speed for the movement is the speed at the moment of impact.

We are not in a position to provide a definitive relationship between average speed and impact speed. However, here are some ideas:

Each movement will likely see acceleration during the downswing because of the need to overcome inertia, muscle weakness at the end of range of movement, lack of muscle conditioning at the end of the range of movement, and the sequencing of contraction instructions from the brain at the end of the range of movement. However, the acceleration may not be rapid because the club head is light relative to the strength in most muscle groups and the fact that for the most part brain messages are instantaneous.

This Guide refers to the "scalability factor", which is impact speed divided by average speed. In essence, this Guide calculates average speed in the downswing, and recognizes that these average speeds will need to be scaled up to determine impact speed. Because of the uncertainty around scalability factor, this Guide assumes a factor of 1 for all movements and recognizes that impact speeds will likely be greater than speeds estimated herein. With a scalability factor of 1, all speed estimates are minimums.

As an observation, average speeds calculated using the golf model in this Guide are about 15 percent less than overall impact speeds calculated through golf club speed measuring devices.

THE BASIC ROTATION EQUATION

Basic Rotation Equation

In applying the above to the movements in the golf swing, for each movement we need to know:

In the following chapter, we shall explain how to estimate the club head speed from the individual movements in the swing.

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