[Jeff]

12 piece bucket

You wrote-: "Jeff . . . keep in mind that Homer was simply using the Endless Belt to illustrate a CONCEPT. I don't think Homer ever thought that hands move on anything but an Arc. It is the player's intent to move the hands in a straight line . .. but as you say in reality that don't happen. I'm sure that Homer was certainly aware of that fact.
The Endless Belt is a nice way to think about things particularly with different "pulley diameters" controlled by hand path and #3 angle."

I agree with you that the endless belt is a nice way to think about it, but there are alternative ways of thinking about the release phenomenon that may be more compatible with reality.

If you look at the hand arc of many professional golfers swinging a driver, you will see that the hand arc is C-shaped with a broad curve of near-constant radius (near-circular or elliptical). There is no J-shaped hand arc that would fit in with the endless belt analogy. So, the question becomes - how best to explain the release phenomenon in those golfers who have C-shaped hand arcs (like Bobby Jones, Tiger Woods and the Pingman machine).



I think that the best mathematic explanation was provided by nmgolfer in that link. Even David Tutelman has recently accepted his mathematical explanation as a better alternative than thinking about centrifugal forces (which is a controversial concept). The fundamental mathematical principle underlying the release phenomenon is that a golf club will develop angular acceleration when the pull force on the grip is at an angle to the COG of the club, and that the club progressively builds up angular momentum because of the cumulative effect of these angular acceleration forces at every moment of the downswing.

Although Bagger doesn't think that the waterskier analogy is useful in trying to understand the release phenomenon, I think that he is not thinking of the waterskier analogy in the correct manner. He was talking of water resistance, when one should ignore water resistance and consider the situation from the following perspective.



Image 1 - there is a constant pull force from the connecting rope because the motorboat is traveling at a constant speed. Therefore, the two waterskiers will travel at the same speed as the boat because the rope pull force is linearly in line with the angle of the skiers skis. Image 2 - now, if waterskier number 2 angles his skis to the side so that they would intentionally carve a curved path of constant radius, thereby creating a C-shaped path, he starts to accelerate relative to waterskier number 1 and the boat. Why? It is secondary to the fact that the pull force from the rope is now at an angle to the direction of his skis. He subsequently experiences angular acceleration. The amount is very small at first, but imagine that there are 1,000 time-points between the start of his curved path and point A. At every one of those 1,000 time-points, he develops an additional amount of angular acceleration because the constant pull force is at angle to his direction of travel. The effect is compounded and his velocity increases. Now imagine another 1,000 time-points between point A and point B. At every one of these 1,000 time-points, he continues to accrue even more angular acceleration because the pull force from the rope is at an increasing angle to his direction of travel. Therefore, it is not difficult to understand how waterskier will be travelling much faster at point B than point A - even though the boat and waterskier number 1 are travelling at a constant speed. This process of accumulating additional angular acceleration in very small incremental amounts continues to point C when the waterskier is traveling at maximum speed and catches up the boat. In other words, his speed increases constantly due to the cumulative effect of additional amounts of angular acceleration at every moment of his C-shaped curved path (of constant radius).

I believe that the same phenomenon occurs in the Pingman machine and professional golfers like Tiger Woods.

Consider the situation of Tiger Woods.



Note that at point A, Tiger still has a 90 degree angle between the left arm and clubshaft and the club has not released, while it is released by impact (point C). Both the hand arc and clubhead arc is C-shaped between point A and point C. So, how does the release phenomenon occur? It occurs because at every moment between point A and point C, the pull force on the grip end of the club is at an angle to the COG of the club, and the club therefore develops angular acceleration. Between point A and point B, the cumulative effect of the angular acceleration increments is very small so the degree of release is very small by point B, but between point B and point C the release happens faster-and-faster because of the cumulative effect of incremental amounts of additional angular acceleration at every moment in that C-shaped curved hand/clubhead path.

There are many logical/intellectual benefits to nmgolfer's mathematical explanation.

1) It doesn't invoke the idea of centrifugal forces, which some people believe is an abstract concept.

2) It explains why the clubshaft reaches maximum speed at impact, while the endless belt concept incorrectly predicts maximum clubhead speed at the time of "going through the acute J-shaped curve bend". HK has to provide an additional explanation for the fact that clubhead speed increases all the way to impact, and he writes about factors that must maintain hand speed all the way to impact.

3) It is not depend on any COAM-belief. HK invoked COAM in his TGM book and apparently implied that the hands have to slow down as the clubhead speeds up, unless the golfer did "something" in addition to ensure that the hands maintain a constant speed. In nmgolfer's mathematical explanation, there is no COAM-effect, and the hand speed can easily remain constant while the club constantly develops angular acceleration at every fractional moment of the release phase of the swing.

Now, if any forum member can demonstrate a flaw in nmgomfer's mathematical explanation, I would like to learn of that flaw, so that I can more correctly understand the physics of the release phenomenon.

Jeff.