Silly season? Quiet days at LBG it seems. Maybe this is a good time to discuss Accumulator #4 and the pivot. Some of you may have seen some of the same from me before. But I haven't presented it properly earlier and it has never kicked off a proper discussion. It is a strictly theoretical argument.
I don't know whether it has any practical implications for stroke patterns etcetra. But in the spirit of HK, precise information has value regardless.
It has relevance to the understanding of swinging vs hitting, and certainly relevance to the infamous introduction of "Accumulator 5" by "Lag" Erickson in a very long thread down under. Erickson has illuminated a glitch in TGM, but he dosen't seem to be capable of describing what it really is.
I am probably close to the opposite of mr Erickson as far as credentials go. He was educated to test his stroke against some of the best in the world but his mechanical understanding is limited. I have just a vague idea about what it takes to play for a living but I did learn my mechanics from the experts. While he honed his golf stroke and toured the world, I was doing exams in various mechanical subjects at the Norwegian Institute of Technology.
TGM is by far the most precise and holistic framework for understanding the golf stroke that I have in my golf library (which is about the length a testing putt). But I still think Accumulator #4 isn't developed properly in the book. And I think it only honours Homers legacy to address all unanswered questions under the TGM paradigm instead of doing it on the outside. Informed critique is good for TGM. As opposed to ignorance.
I'm using 6. edition by the way.
First out:
Illustration 1-L: Basic Golfing Machine.
* The hinge pin: Is it centered or is it left shoulder located?
* The pivot post: Does it turn the hinge around its own center or is it a static post?
Of course, this is a very simplified figure, and since it only has one lever it isn't reasonable to look for such minute details like how the pivot works. It is OK. It doesn't include a pivot and it doesn't include a secondary lever either. So the level of detail is consistent. Nothing wrong there. But no important info of how the pivot works either.
Move to the glossary:
Centrifugal Force Example - whirling weight on a string.
Mechanical - The resistance of the Inertia in an orbiting object to change in direction
Golf - The effort of the Swinging Clubhead to pull the Primary Lever Assembly (Right arm and Club) into a straight line.
This definition isn't wrong, but it may be misleading. Because it doesn't separate reaction to linear pull force from reaction to centripetal pull force. I suspect that this definition - together with several other vague descriptions of the rope pulling creates a misleading impression of what really happens. And the confusion around that was very vivid in the Lag's Golfing Machine thread down under. I would preferred to see a definition of centripetal force instead. Centripetal force acts on the lever. Centrifugal force is just a reaction back to the swing center.
In accordance with Homer's theoretical framework, he treats Accumulator #4 as a lever type of accumulator. The mass is the primary lever mass, the fulcrum is the left shoulder and the force is PP#4 pressure.
According to wictionary,
http://en.wiktionary.org/wiki/pivot, a pivot is
"a thing on which something turns. /..../ Such as the end of an axle or a spindle."
So in general a pivot does not explicit produce any work. What about Homer's pivot? We know it delivers work, but how does it deliver it?
Move to 6-B-4-0:
The fourth Power Accumulator
"As Accumulator #4 it is Pivot (Body) Power supplying the initial acceleration of the Downstroke to throw the Lever Assemblies towards Impact by the Thrust of the Shoulder Turn. See 7-13. Another major contribution to Impact Power is geometric - it is the first link in the Swing Radius power train between the Club and the Feet."
6-B-4-A. "Maximum Power is obtained by using maximum On Plane Shoulder Turn Thrust against Pressure Point #4 per 7-19."
Something important is missing here. Maybe taken for granted by the certified people, but then again maybe not. Certainly creating a lot of confusion amongst a lot of TGM followers and TGM criticians.
First a very short crash course in mechanical engineering: We all know that a force is a push or a pull with a certain direction. Engineers use vectors to describe and analyze forces. The vectors are arrows. They have a certain direction and a certain length. One cm can for instance mean 20 lbs, and if so, two cm would mean 40 lbs (we would actually use Newton, but that is not essential here).
For instance, if we want to know the resultant force of two forces that works on the same object, but not in the entirely same direction we can do vector addition. It is a very simple graphical exercise where you place the start of the next vector where the last one ended. The resultant vector –or the resultant force – is the straight line between the start and end point of the forces involved. Such as this:
The next thing that is very usual to do is to decompose forces. You can have a force that is inclined, and you want to find the vertical component and the horizontal component. Then you can do it this way:
"But these aren't real forces!" I can almost hear some of you thinking that. And it is true. The decomposites aren't there for real. They are analytical devices, produced by engineers such as myself to find out what is really going on in dynamic and static systems. Or to help us design machinery that does what we want them to do.
You can basically decompose a force any way you wish. But to get anywhere you need to have a purpose.
The purpose I have is to separate the rope pulling from the left shoulder into a centripetal component that keeps the lever in orbit and a linear component that powers the stroke. The linear part of the rope pulling force works the club. The centripetal part just keeps it going in circle.
Here we go:
The picture is a very schematic presentation of the working of accumulator #4 after the right arm has separated from pp#4. The red circular arrow is the torque we produce by rotating the shoulder around the swing center. The pivot rotation. It drives the left shoulder in a circle. And therefore the left shoulder pulls the primary lever assembly (the dark red bar) like a rope around the swing center.
If the shoulder were pulling the lever assembly directly towards the swing center it would be pure centripetal force. And if the shoulder stopped rotating just before impact, the shoulder would become the swing center and there would only be centripetal force. But as long as the shoulder pulls the lever around the swing center it keeps powerering the stroke.
The pull of the rope is measurable with the right gear. I think I just read that Jorgensen measured something like 200 lbs for a driver. That would be the “total force pulled by rope handle technique” in the figure. I have decomposed that total in one component towards the swing center and one linear (or in Newtonian: Radial / tangential) components. The tangential component is probably roughly around 10-15% of the total – like 20-30 lbs. (the distance between swing center and shoulder; 10 inches? divided by the primary lever length; 80 inches?. This math is oversimplified and far from precise, but we are talking serious power delivered by the club head. If my numbers are in the ball park you probably need much more than 50 lbs at PP#3 to beat the pull.
Max linear force from Accumulator 4# will be produced when the shoulders are parallel to the inclined plane line*. The further the lever is pointing away from the swing center the larger the linear force - everything else being equal. But regardless of the degree of shoulder rotation through impact power will be delivered. Accumulator #4 isn’t inline before a long way into the finish.
Accumulator #4 is a very strong accumulator, with and without the push from PP#4. And with proper pivot action it never runs out of “arm” so to speak.
Another thing worth noting: Swinging or hitting – as long as you can feel weight of the “rope pulling” in the left hand and shoulder through impact the left shoulder will keep on powering the club. The only requirement is shoulder rotation. And the more weight you feel, the more linear force the pull produces.
Lag Ericsson wants to have a prestressed shaft through the ball. That may be a good Idea as seen from the right pushing side – pp#1/3. But if you see it from the left pulling side this is a slack in the rope and a source to power leak. The primary lever better be as tight and as stretched as a rope made of steel and bones can be. The left shoulder wants it to be straight. (within the geometric requirements of the stroke ). Minimum slack and a totally flat left wrist gives a very inflexible power transmit between the left shoulder and the club head - and tremendous resistance against slowdown through the impact area. This resistance is most evident and can easily cause serious damage if you're unlucky enough to trap the ball in a root or something on the ground. Axing a club into a rock is a much more gentle to the ligaments.
As for my own game I discovered quite some time ago that the safest and most powerful way out of thick grass for me is to be easy with PP#1/3 and instead pull hard through impact. Ripp my left arm out of the shoulder. If I try to drive it through with pp1/3, the lag pressure doesn't cut it and I get very unreliable result. But then again, I am far from as strong in the upper body as the best golfers.
There is no doubt in my mind that the pure rope handling produces a very significant linear force through the ball – hitting or swinging. And that the stroke patterns make a difference to how much power it delivers and when it maxes.
The pivot torque also does significant work on the pushing side as long as there's some pushing going on, hitting or swinging. The right arm only does work insofar as it is extended. If it's driven hard but not extended, the power is produced by the pivot. Analytically the right side pivot power delivery can be dealt with in the same way as the pull force. Part of the push will just stretch the primary lever and not power the stroke, part of it will produce linear (or radial) force. But it is our understanding of the "swinging" side of the body that suffers most from this glitch in TGM.
To finalize the whole matter:
The shoulder torque - and the linear force produced by pure rope handling - is not present in 6-A-2 where it naturally belongs. The illustration is so early in the down stroke that there wouldnt be much of it yet, and a second illustration - closer to impact with more Accumulator # 4 release would be required to display it properly.
I am quite sure that Homer would have found place for some torque diagrams and some vector decompositions as I've done here if he had the education to do it. It belongs in chapter 2 and chapter 6, and possibly other places as well.
*There are potentially two maxes for accumulator #4: PP#4 may produce an even bigger force than the pure rope handling. Thus, it would be very interesting to explore how the two phases of Accumulator #4 could be optimized.
I hope this was interesting and that none of the fellow TGM enthusiasts take this as an attack on the yellow book. All is written with the best wishes of continued progress within TGM.
Besides I can't afford to provoke anyone here now that I - thanks to good help from several forum members - have started to take some of the good stuff into my own stroke.
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