# TGM power accumulators - science or metaphor?

G.O.L.F. is a game for thinkers, hence I hope that my post is appreciated for what it is, some considerations of a thinker trying to comprehend Homer Kelley’s concepts. Since Homer Kelley based his G.O.L.F. system on scientific principles we will use equally an objective scientific approach.

In TGM one of the basic concepts is that of power accumulators. Hence it is particularly interesting to have a closer look at them and see what they are and how they are meant to be used. It is clear from Chapter 6 and the glossary that Homer Kelley is referring to some form of potential power to be accumulated.

First of all, in science, it is energy which is accumulated, not power. Power refers to the way (rate) we use the accumulated energy, once at least some of it has been accumulated. Strictly speaking therefore accumulation of power is not very precise but nevertheless understood intuitively.

The traditional examples for illustrating mechanical type potential energy are the gravitational potential energy and the potential energy of a spring, e.g., slingshot. In a golf swing the contribution due to gravity are quite small. There are also no springs active in a golfers body. With no springs, and gravity to be ignored, what really are we trying to store in the accumulators #1, #2,# 3 and #4 ?

If we raise an object and let it drop the situation is limpid. First, we increases the gravitational potential energy and then, dropping, have it convert its potential energy back into kinetic energy of motion. Now what can we say about a golfer? What is he doing to increase his potential energy which is to be accumulated into the power accumulators? There are no springs, no gravity to be reckoned with, so what is to be taken as the potential energy, accumulated in the back swing?

Homer Kelley in his glossary of TGM indicates the out-of-line configuration of the power accumulators as being the source for power accumulation. This definition is only valid if the out of line configuration is situated in an appropriate force field. At the top of the backswing and with the power angles set, what then can be identified as this force field required to be able to define some form of potential energy?

There is no such force field and hence the potential energy at the top of the back swing for all practical purposes is zero. If we conclude therefore that the power accumulators don’t accumulate potential energy then we are forced to look for another explanation(s) why setting the angles is seemingly so beneficial in a golf swing.

To get a better feel for the real reason for the usefulness of the 'power angles' we will use a 2D model of a golf swing, as shown in Fig1, very similar in nature to the action of a golf robot used for developing/testing golf equipment. The closest in real life would be a one-armed golfer. The motion of the two levers is governed by two differential equations:

Two cases have been analyzed, as illustrated in Figs 2a & 3a. In TGM terms the difference is the power angle β not being used in case 1 (Fig2a). In both cases we applied an identical constant torque to the center. There is no external torque exerted at the hinge. As can be seen from Figs 2b and 3b, the ‘impact clubhead velocity’ in case 2 (Figs 3b) is substantial higher.

Initially, for case 2 (Fig3a), the overall moment of inertia is made small, with the golf club mass closer to the center of rotation. This allows for a given torque to obtain maximum angular velocity of the overall system. The inertial release torque acting on the hinge becomes very large in the downswing and forces the golf club towards the in-line arrangement. This is the typical action of a flail.

Closer analysis shows that the 'downswing' of Fig 3a can be seen as having three distinct phases. This is shown in more detail in Figs 4, 5, 5a,b,c. They are indicated by the vertical dashed lines. The green line corresponds approximately to time t1 when lever 2 starts to open up. The brown line corresponds to the time t2 when the in-line condition of the two levers is reached.

During phase 1 the heavier inner segment operates effectively as an energy accumulator. Phase 2 starts when the hinge angle β starts to release, and subsequently virtually all of the inner segment's accumulated energy flowing into the lighter secondary segment. Phase 3 starts when the in-line condition is reached. From thereon there is a rapid reversed flow of kinetic energy, back from the outer segement (club) into the inner segment (arms).

The angular acceleration of the outer lighter segment causes, during phase 2, a substantial inertial torque back on the upper segment. This explains that in a golfer's downswing the hands/arms slow down considerably through impact. During phase 3 this process is reversed, it is now the outer segment accelerating the inner segment.

Figs 6 and 7 show the kinetic energy and the power for each segment as well as the total amount. The three phases are clearly to be seen in both Figs. The inner segment (red trace in Fig 6) is first increasing its kinetic energy. During phase 2 (from the green to the brown line) it is generously giving up its energy to the outer segment. In phase 3 the direction of energy flow reverses.

It is quite interesting to look also at the power situation as shown in Fig 7. The red trace between the two vertical dashed line (phase 2) is negative in magnitude indicating that the outer segment's energy is flowing out of it and hence toward the inner segment. Notice that the resultant peak power levels are much lower than the peak power levels of each segment. This is due to work done by the linear reaction forces at the hinge. (This fact was seemingly unknown to both Jorgensen and Cochran/Stobbs et all )

The angular moment of inertia, relative to the center, for the motion shown in Fig 3a, is shown individually and collectively in Fig 8. The angular moment of inertia of the inner segment (red trace) is constant. As can be seen from Fig3a the outer segment is first folding up a bit before opening up subsequently. This behaviour is reflected in the moment of angular inertia of the outer segment (blue trace), it first decreases a bit before sharply increasing and reaching a maximum for the in-line condition.

The angular momentum of the segments is shown in Fig9. The total is indicated by the black trace. It shows clearly an error made by Homer Kelley, and indeed by everyone, when invoking the law of 'Conservation of Angular Momentum' to explain the golf swing. This law is only applicable for systems for which the total moment due to external forces and couples is zero, leading to total angular momentum being conserved. This is clearly not the case as is evident from Fig9.

The kinetic energy and the angular momentum show a very similar behaviour. The inner segment is first accumulating and subsequently giving most of it up to the outer segment, and as soon as the inline condition is reached, there is a reverse flow back form the outer segment towards the inner segment.

Conclusions

One sees on occasion in golf literature the expression - ‘one can then from the top release the power generated in the back swing’. This seems to be intuitively correct - one kind of feels powerful, being tightly wound up in the back swing. However, I just think of this as the brain screaming to release the uncomfortable feeling created due to a tight windup.

Homer Kelley has translated this intuitive notion into a concept of power angles, accumulating some form of potential energy. I disagree with this approach as I have explained above. Instead, I do associate Kelley's power angles with minimizing the angular moment of inertia in the backswing to allow maximum accumulation of kinetic energy, in the proximal segments, in the first part of the downswing (phase1).

mandrin