It's elementary (my dear Watson)

Cocking and uncocking the wrists was discussed in Chapter 2. The picture below summarizes the key physical aspects of the movement.

- The rotation centre is the wrist in the lead hand, which grips the club at its end.
- The distance from the rotation centre to the ball is the length of the club.
- The angle between the line from the ball to the centre of rotation and the axis of rotation is 90 degrees, when the movement is properly executed.

The forearm roll is discussed in Chapter 3. The picture below summarizes the key aspects of the forearm roll:

- The rotation centre is the wrist in the lead hand, which grips the club at its end.
- The distance from the rotation centre to the ball is the length of the club.
- The axis of rotation is the line along the forearm.
- " The angle between line from the rotation centre to the ball and the axis of rotation can be measured with a protractor from pictures such as the one below. As we saw in Chapter 3, this angle depends on a variety of factors, including how the club is gripped (palms versus fingers) and the lead wrist is held (radial abduction versus ulnar adduction).
- Club speed will be at least the distance traveled divided by the time required for the movement.

The rotation of the upper arm in the shoulder socket was addressed in Chapter 5. The physics of upper arm rotation in the shoulder socket are the same as the forearm roll, with the same rotation centre, axis of rotation, and distance to the ball.

Chapter 4 discussed the proper movement of the upper arm in the shoulder socket. The picture below illustrates key physical components of the movement:

- The rotation centre is the lead shoulder socket.
- The rotation axis in a properly executed movement is perpendicular to the plane traced out by the line from the ball to the lead shoulder socket during the downswing. The upper arm can rotate along this axis because the shoulder socket is a ball and socket joint that can move in a variety of directions and there are no anatomical restrictions on the axis of rotation from the joint.
- The distance from the rotation centre to the ball can be calculated from the length of the golf club, the length of the arm from the shoulder socket to the wrist, and the angle between the shaft of the club and the straight lead arm using the law of cosines expressed through the equation x2 = y2 + z2 - 2yzcosX, where x is length of the side to be determined, y and z are the lengths of the two known sides, and X is the angle opposite the length to be calculated and between the two known sides.
- Club speed will be at least the distance traveled divided by the time required for the movement.

Shoulder socket rotation was addressed in Chapter 6, which noted that the forward movement of one shoulder socket and the backward movement of the other socket, in combination, lead to a rotation of the shoulder sockets around the spinal column.

The picture below illustrates the key aspects of this movement:

- One can calculate the number of degrees of rotation caused by moving the shoulder sockets, if one knows the amount of movement of the shoulder socket when it goes from a neutral start position to the forward position and backward positions. With this information, one can calculate the amount of rotation of the shoulder sockets through the equation Y = arccos((x2 + z2 - y2)/2xz) where x and z are the distances from the mid-point to the shoulder socket, y is the linear movement of the shoulder socket, and Y is the angle opposite the amount of linear movement.
- The rotation centre is the mid-point between the shoulder sockets.
- The axis of rotation is the spine, around which the shoulder sockets rotate. Typically, the golfer leans forward at the hips, so that the spine twists around an axis that is tilted forward.
- The angle between the axis of rotation (the spinal column) and the line from the rotation centre to the ball can be determined through a behind-view picture of the golf swing and a protractor.
- Typically, the shoulder sockets will rotate slightly beyond the start position at impact, so additional degrees of rotation should be added to the base rotation calculated in the previous point.
- The distance from the rotation centre to the ball is approximately the same distance as from the two shoulder sockets to the ball. The distance from the rotation centre to the ball can be calculated from the length of the golf club, the length of the arm from the shoulder socket to the wrist, and the angle between the shaft of the club and the straight lead arm using the law of cosines expressed through the equation x2 = y2 + z2 - 2yzcosX, where x is distance from the rotation centre to the ball, y and z are the lengths of the arm and club respectively, and X is the angle between the arm and the club.
- Club speed will be at least the distance traveled divided by the time required for the movement.

The spinal twist was discussed in Chapter 7. The physics of the spinal twist are almost identical to that of moving the shoulder sockets.

- The rotation centre is the mid-point between the shoulder sockets.
- The axis of rotation is the spine, around which the shoulder sockets rotate. Typically, the golfer leans forward at the hips, so that the spine twists around an axis that is forward leaning.
- The angle between the axis of rotation (the spinal column) and the line from the rotation centre to the ball can be determined through a behind-view picture of the golf swing and a protractor.
- Typically, the spine will rotate slightly beyond the start position at impact, so additional degrees of rotation should be added to the base rotation calculated through the foregoing points.
- The distance from the rotation centre to the ball is approximately the same distance as from the two shoulder sockets to the ball. The distance to the rotation centre to the ball can be calculated from the length of the golf club, the length of the arm from the shoulder socket to the wrist, and the angle between the shaft of the club and the straight lead arm using the law of cosines expressed through the equation x2 = y2 + z2 - 2yzcosX, where x is distance from the rotation centre to the ball, y and z are the lengths of the arm and club respectively, and X is the angle between the arm and the club.
- Club speed will be at least the distance traveled divided by the time required for the movement.

As noted above, there are four ways in which hip rotation can be executed:

- Pure Rotation without spinal tilt.
- Pure Rotation with spinal tilt.
- Push and Clear without spinal tilt.
- Push and Clear with spinal tilt.

The picture below illustrates key aspects of the physics of Pure Rotation, without tilting the spine.

- The axis of rotation is a vertical line from the ground through the mid-point between the two hip joints. The line is vertical because the hip joints rotate in a circle parallel to the ground. The leg movements do not change the elevation of the hip joints.
- As we saw in Chapter 9, the forward lean causes the shoulder sockets to rotate in a circle around the axis of rotation. The effect of this is to move the rotation centre to a point on the axis of rotation where the projection of the line from the ball through the shoulder sockets meets the axis of rotation.
- To calculate the radius of the rotation circle that the club would follow from this movement, we need to know the angle between the axis of rotation and the swing plane at the rotation centre and the distance from the ground to the rotation centre.
- The angle between the axis of rotation and the swing plane can be measured from a picture with a protractor.
- The distance from the ball to the rotation centre consists of two components: the distance from the ball to the shoulder socket, and the distance from the shoulder socket to the rotation centre.
- As we have seen, the distance from the ball to the shoulder socket can be calculated from the length of the arm, the length of the club, and the angle between the arm and the club.
- To determine the distance from the shoulder socket to the rotation centre, notionly draw a line from the mid-point between the hips and the shoulder sockets to create a triangle defined by the rotation centre, the shoulder socket, and the mid-point between the hips. In this triangle, all the angles can be estimated from a picture using a protractor. In addition, we can use a measuring tape to determine the distance from the mid-point between the hip joints and the mid-point between the shoulder sockets. The distance from the shoulder socket to the rotation centre can be calculated from this information using the sine rule (x/sin(X) = y/sin(Y) = z/sin(Y) where the small letters refer to lengths of sides and the capital letters refer to angles opposite the side with the small letter.
- Club speed will be at least the distance traveled divided by the time required for the movement.

There are three aspects of Push and Clear without spinal tilt.

- Compared with Pure Rotation, the amount of rotation is less, because only the lead hip is moving. The trailing hip remains in the same place. We need to determine how much less.
- The picture below illustrates how a Pure Rotation hip movement would translate into a Push and Clear hip movement. The blue dotted line represents the initial start position for both Push and Clear and Pure Rotation. The blue end dots represent the hip joints. The black line and end dots reflect the Pure Rotation hip movement, with the trailing and leading hips moving around a circle circumference (red dotted circle). The green line and end dots illustrate the Push and Clear hip movement. The trailing hip remains at the initial start position. In Pure Rotation, the lead hip moves toward the ball and away from the target. In the picture below, the solid yellow line depicts the amount of linear movement of the lead hip in Pure Rotation. We assume the lead hip in Push and Clear has the same linear movement. In other words, the solid yellow and purple dotted lines have the same length. The length of these lines in Pure Rotation can be calculated if one knows the distance between the hip joints and the amount of rotation. The calculation is the sine of half the angle of rotation times the half the distance between the hip joints times 2. Assuming the length of this line in Pure Rotation is equal to the length of purple line, the amount of rotation in Push and Clear can be determined. The lengths of the black, blue and green lines are equal, as these lines represent the distance between the hip joints. The amount of rotation is 2 times the angle whose sine is half the length of the yellow line divided by the distance between the hip joints.
- The physics principles underlying the basic rotation in Push and Clear will be exactly as described for Pure Rotation, except that the amount of rotation will be less.
- There is intrinsic lateral movement in Push and Clear in the absence of spinal tilt. It arises because the centre point between the two hip joints must move forward toward the target as a result of the Push and the Clear. This intrinsic lateral movement will move the shoulder centre, arms and ultimately the club head toward the ball, generating a distance effect that will be the amount of lateral movement divided by the time required for the movement. The amount of lateral movement can be measured from photographs.
- The total effect on club head speed from Push and Clear without spinal tilt will be the sum of the basic rotation effect and the intrinsic lateral movement.

The spinal tilt involves lateral side bending. The amount of lateral side bending is generally that amount required to keep the head/eyes/shoulder centre stable in the face of movement away from this stable centre that would come from hip rotation and the forward lean. The physics of Pure Rotation with spinal tilt involves (1) calculating the effect on club speed from hip rotation when the "forward lean" effect is neutralized by spinal tilting, (2) calculating the amount of lateral movement being neutralized by the spinal tilt, and (3) determining the effect on club speed from the spinal tilt, given the amount of lateral movement neutralized by the spinal tilt.

In the discussion of Pure Rotation without spinal tilt, the forward lean widens the circle that the club head would follow as a result of the hip rotation. The picture below illustrates the physics of Pure Rotation with spinal tilt.

To calculate the club head speed from hip rotation:

- The axis of rotation is a vertical line from the ground through the mid-point between the shoulders. The line is vertical because the hip joints rotate in a circle parallel to the ground. The leg movements do not change the elevation of the hip joints. The line goes through the mid-point between the shoulder sockets, as the rotation of the hips is transferred directly to the shoulder sockets. No allowance is made for the forward lean, because the spinal tilt neutralizes it.
- To calculate the radius of the rotation circle that the club would follow from this movement, we need to know the angle between the axis of rotation and the swing plane at the rotation centre and the distance from the ball to the rotation centre (shoulder socket).
- The angle between the axis of rotation and the swing plane can be measured from a picture with a protractor.
- As we have seen, the distance from the ball to the shoulder socket can be calculated from the length of the arm, the length of the club, and the angle between the arm and the club.
- The distance traveled by the club head will be sine of the angle between the axis of rotation and the swing plane times the distance from the rotation centre to the ball times the amount of rotation in the downswing to impact.
- Club speed will be at least the distance traveled divided by the time required for the movement.

As discussed above, the rotation combined with forward tilt in the absence of spinal tilt causes lateral movement of the shoulder sockets. The diagram looks at the golf swing from the top and illustrates this lateral movement. The red dotted circle is the path that the mid-point in the shoulder socket would trace as a result of hip rotation with forward lean. The diagram shows that there will be lateral movement away from the target in the back swing.

Calculating the amount of lateral movement comes through a two step process.

The first step involves calculating the radius of the rotation circle for the mid-point between the shoulder sockets. We can calculate the distance from the hip joints to the mid-point between the shoulder sockets through measurement. We can determine the angle between the vertical and the forward leaning spine through a picture and protractor. The radius of the rotation circle is the sine of the spine angle times the distance between the mid-point between the hip joints and the mid-point between the shoulder sockets.

The second step involves the calculation of the lateral movement. From the first step, we can calculate the radius of the rotation circle. We can know the amount of hip rotation by observing individual golf swings. The amount of lateral movement is the sine of the angle representing the hip rotation times the radius of the rotation circle.

The picture below illustrates the physics of the spinal tilt. In essence, the spinal tilt involves two rotation circles with a common centre. One circle is the tilting shoulders circle, while the other is the club head circle.

The amount of rotation in the tilting shoulders circle is also the amount of rotation in the club head circle.

Regarding the tilting shoulders circle:

- The centre of the tilting shoulders circle is approximately the base of the spine. The radius of this circle is the distance from the base of the spine to the mid-point between the shoulder sockets. The word "approximately" reflects the fact that spinal column bends toward the top and is not a straight line.
- The mid-point between the shoulder sockets moves a particular distance away from start position in the back swing to counter the lateral movement arising from the forward lean and lateral movement intrinsic to Push and Clear. We have developed the calculation for this lateral movement above.
- The amount of rotation in the back swing is the angle whose sine is the lateral distance of shoulder movement from the start position divided by the radius of the tilting shoulders circle.

Regarding the club head circle:

- The amount of rotation in the back swing of the club head circle is the same as the rotation in the tilting shoulders circle.
- As we have seen above, the distance from the ball to the mid-point between the shoulders can be estimated from the length of the arm, the length of the club, and the angle between the club and arm. The radius of the club head circle is the distance from the club head to the shoulder mid-point less the radius of the "tilting shoulder" circle (e.g. mid-point between shoulder sockets and the base of the spine).
- The downswing movement of the club head from the spinal tilt can be estimated from the radius of the club head circle and the amount of rotation.
- Club speed will be at least the distance traveled divided by the time required for the movement.

The physics of the Push and Clear with spinal tilt has four elements:

- The club head speed resulting from the effect of the hip rotation taken by itself.
- The lateral movement in the basic rotation as a result of the forward lean.
- The lateral movement intrinsic to Push and Clear.
- The club head speed resulting from spinal tilt effect, which is ultimately based on the lateral movement in the basic rotation as a result of the forward lean plus the lateral movement intrinsic to Push and Clear.
- Summing the club head speed from the basic hip rotation and from the spinal tilt.

The basic rotation effect is based on the same physics as described under Pure Rotation with spinal tilt, except that the amount of rotation will be less because Pure Rotation has two hips moving while the Push and Clear keeps the trailing hip in a fixed place and includes movement only in the lead hip.

The physics of calculating the amount of rotation resulting from hip rotation in conjunction the forward lean are outlined in the section on Pure Rotation with spinal tilt, except the amount of rotation will be less because there is less rotation in Push and Clear.

There is a certain amount of lateral movement intrinsic to the Push and Clear, and this amount is independent of the forward lean.

Assuming the spinal tilt functions to a large extent to keep the head still in the back swing and downswing while lateral movement is occurring, the amount of spinal tilt in the Push and Clear with spinal tilt will be the sum of the lateral movement from the basic rotation and the lateral movement intrinsic to the Push and Clear movement.

The physics of calculating the impact of the spinal tilt on club head speed resulting from a given amount of lateral movement will be the same as that described in the section on Pure Rotation with spinal tilt.

The Bottom Line

- For each movement in the golf swing, we can calculate a minimum club head speed.