Acceleration of clubhead

[iseekabetterswing]

A THREE DIMENSIONAL KINEMATIC AND KINETIC STUDY OF THE GOLF SWING

Steven M. Nesbit


Department of Mechanical Engineering, Lafayette College, Easton, PA, USA


Received 20 May 2005
Accepted 02 September 2005
Published 01 December 2005

© Journal of Sports Science and Medicine (2005) 4, 499 - 519

http://www.jssm.org/vol4/n4/17/v4n4-17text.php

re more convincing....

I'm not here to sell you anything. I'm not going to try to "close the deal". I'm showing you the way it is... take it or leave it. Models are well.. a model (profound I know ) and that's why the modeler must scrutinize carefully what elements get included. Ever hear the term: GIGO?... garbage in garbage out. As far as "the CF model" goes... what model? We're still waiting on a mandrin to produce a "CF model". He showed a simple compound pendulum with a constant hub torque. I outlined some of the deficiencies in that approach to modeling a golfer's swing in an earlier post.

If I were asked to design and build a "pingman".... I would pull out a compound pendulum model, like mandrin's, and use it to size the hub drive mechanism appropriately. If I wanted to model a golfer's swing (and did'nt have access to the software Nesbit uses) I would take an approach similar to the one I outlined. It would be a (parametric) model so I could adjust the variables that matter and I would optimize (given practical constraints). That's a way to see (mathematically) just what might be possible (in the way of say club head speed).

As far as the slowing hands myth goes... Nesbit's test results disproved it:
http://www.jssm.org/vol4/n4/17/f4.gif

All golfers tested had nearly identical hand velocity profiles (which is quite intriguing by itself) and none exhibited significant slowing prior to impact. That's not to say a golfer can't have slowing hands. Clearly they can as shown by the photographic evidence Dante produced in defense of the now falsified COAM myth. But its NOT a requirement (for "the energy to "flow" out to the clubhead" )

I do recall reading Nesbit mention CF with respect to release. He's no fool so I asked myself... why would he do that? Just speculation but... Academics are in a never-ending search for money; research funds grease the wheels of higher education. Professors are not unlike politicians in that regard.

From what I gather, funding for Nesbit's (golf) research comes from two sources: USGA and NSF. We know how ensconced the CF myth is in the golfing establishment. Heck the author of nearly every golf book published in the past century blathers on about it. Of course repeating a myth (like the CF myth) over and over again and again does not make it less false but what it does do is cement the misconception in the minds of the impressionable. If I were Nesbit I might choose not to fight the CF battle (and risk pissing off my funders) either...

 

[JeffM]

OK, gentlemen (fellow forum members)!

I'm also going to make an attempt to explain the release phenomenon. I don't at all agree with Brian's reasoning. I am also certain that my golf club releases in essentially the same way when I swing it horizontally (parallel to the ground), so gravity is not a significant factor.

I think I can explain the release phenomenon (in rudimentary fashion) without using centrifugal forces, or without having to change the speed of hand movement, and also without having to introduce the variable of external forces working "across the shaft line of the club". My explanation comes from NMGolfer's description of angular velocity developing because the line of action force is NOT at the centre of gravity (COG) of the club.

Imagine the following situation. Imagine a golfer's left arm (or PingMan's central arm) moving at constant velocity throughout the ENTIRE downswing, which means that the hands must also move at a constant velocity. However, the direction of movement of the hands is not a straight line path, but a more circular path (from the end-backswing position to the impact position). The grip end of the club must move exactly as the hands move - because the grip is within the hands. However, the clubhead does not have to do so, because the COG of the club is somewhere close to the end of the shaft, near the clubhead, and it is possible for the clubhead end of the club to lag behind the hands (or move in front of the hands if the momentum of the COG of the club causes the clubhead to move faster than the hands, and causes the clubhead to overtake the hands). Now let's start at the end-backswing position. As the hands start moving at a certain (constant) speed along a directional path (which is essentially the near-circular downswing hand path) a line of action (force) is applied to the grip end of the club. That line of action force is also applied to the clubshaft/clubhead and most of the line of action force may be along the length of the club. However, it is not necessarily perfectly in line with the COG of the club, so some of the line of action force working on the clubshaft causes the clubshaft to develop a small degree of angular velocity, which causes the clubshaft to rotate forward relative to the hands (which causes the peripheral end of the clubshaft to rotate anti-clockwise relative to the grip end of the clubshaft - as seen from the front). At the start of the dowswing, the amount of line of action force that produces angular velocity is small, so the clubshaft remains at 90 degrees to the left arm. However, as the downswing evolves, the amount of angular velocity increases progressively and eventually it must result in club release and eventually it must allow the clubhead to nearly catch up to the hands by impact. I was hoping that the mathematicians (eg. Mandrin/NM Golfer) could produce a mathematical model that would demonstrate the change in angular velocity over time, which may depend on many variables such as i) speed of hand movement during the downswing, ii) degree of circularity of the hand path (which represents the fractional change in direction of a straight line path per unit meaasure of time); iii) distance of the COG from the grip end of the club; iv) weight of the clubhead and peripheral end of the club relative to weight of the grip end of the club (? may be equivalent to the magnitude of the mass of the club's COG).

I don't have the expertise to solve this problem mathematically, but I intuitively suspect that the fundamental cause of the release is the fact that the line of action of the force driving the club is NOT at the COG of the club, and therefore the club has to rotate - because some of the line of action force produces clubshaft angular velocity.

Jeff.

 

[jmessner]

re more convincing....

I'm not here to sell you anything. I'm not going to try to "close the deal". I'm showing you the way it is... take it or leave it. Models are well.. a model (profound I know ) and that's why the modeler must scrutinize carefully what elements get included. Ever hear the term: GIGO?... garbage in garbage out. As far as "the CF model" goes... what model? We're still waiting on a mandrin to produce a "CF model". He showed a simple compound pendulum with a constant hub torque. I outlined some of the deficiencies in that approach to modeling a golfer's swing in an earlier post.

If I were asked to design and build a "pingman".... I would pull out a compound pendulum model, like mandrin's, and use it to size the hub drive mechanism appropriately. If I wanted to model a golfer's swing (and did'nt have access to the software Nesbit uses) I would take an approach similar to the one I outlined. It would be a (parametric) model so I could adjust the variables that matter and I would optimize (given practical constraints). That's a way to see (mathematically) just what might be possible (in the way of say club head speed).

As far as the slowing hands myth goes... Nesbit's test results disproved it:
http://www.jssm.org/vol4/n4/17/f4.gif

All golfers tested had nearly identical hand velocity profiles (which is quite intriguing by itself) and none exhibited significant slowing prior to impact. That's not to say a golfer can't have slowing hands. Clearly they can as shown by the photographic evidence Dante produced in defense of the now falsified COAM myth. But its NOT a requirement (for "the energy to "flow" out to the clubhead" )

I do recall reading Nesbit mention CF with respect to release. He's no fool so I asked myself... why would he do that? Just speculation but... Academics are in a never-ending search for money; research funds grease the wheels of higher education. Professors are not unlike politicians in that regard.

From what I gather, funding for Nesbit's (golf) research comes from two sources: USGA and NSF. We know how ensconced the CF myth is in the golfing establishment. Heck the author of nearly every golf book published in the past century blathers on about it. Of course repeating a myth (like the CF myth) over and over again and again does not make it less false but what it does do is cement the misconception in the minds of the impressionable. If I were Nesbit I might choose not to fight the CF battle (and risk pissing off my funders) either...

NM

CF Model - Well I guess I was referring to Jorgensen's model (I already know how you feel about that one) along with Mandrin's. Like you say, it's been a commonly used approach. And I have some swing analysis/modeling software (Swing Perfect?) from about 10 years ago and I'll have to dig it out but I would assume it uses a similar approach. Anyway, I think trying to prove or disprove on a forum like this is difficult/impossible. but the concept is certainly worth discussing. Peer review (Science of Golf maybe - I wish they wouldn't charge so much for their pubs) would be better.

Interesting comments about Nesbit - I would personally wouldn't have thought the CF issue a deal breaker but then again, I have no idea what the sponsors are thinking.

The hand speed graph you included has got me curious - I've got to find how (and where) he measured these. It doesn't mesh with my videos but I may be comparing apples and oranges. I'm going to read the article tonight and check it out.

This question for anybody (hopefully somebody still may be interested) - If a golfer woke up one morning with an epiphany that CF played no role in the release but instead it was the translation of the hands that caused the release, what would he do differently to take advantage of that fact?

I'll start: Nothing

 

[Jim Kobylinski]

I won't do the heavy lifting (the distillation) for Jim, Jeff or Puttmad. That would be doing them a disservice. It would also be doing myself a disservice because in their process of discovery they may come across something from which I myself can benefit. That's how we learn and we grow.

nmgolfer, i'm not lazy and am not inhibited in learning a lot about physics or any other science for that matter. The difference is i don't care to. I don't have an interest in it, i rely on other experts to explain it to me so that i can learn it to the best of my abilities of what i could actually do with that information.

from my limited experience in this life and in business, the best "groups" are the ones who have people with defined roles of expertise that work towards a common goal. For instance i work in finance, however each of us has a unique skill set that all achieves the goal of a finance department, which in a very generic defination are, business advisors. As an example, i have superior excel skills than other people in my group, these skills allows us as a group to work more efficiently. Now could i help others in the group learn these skills? Sure and i do, but only to a point. Because i am taking time away from something that they do extremely well that is again, helping the group. Do i have the same skills as the others do? Of course but maybe they are better at it than i do; again it doesn't matter because we all are working together.

So "dumbing something down" is not lazy. I have learned that one doesn't need to know everything. You simply need to know enough about what is that makes you successful. If you can find a way to harness that, you are sure going to be one happy successful person in anything you do and for those things that you don't have the necessary skills in you hire someone to do it for you to help you work towards your goal.

The people that i know who tend to be the least successful are the types who feel that they are the ones who have to do everything themselves instead of trusting others to perform tasks they do not know how to do.

Just my opinion

 

[jmessner]

Just read Nesbit.....

Just finished my first pass of the Nesbit article. I see has another one on Work and Power in a golf swing in that same publication. The only real surprise for me was that he shows a positive torque applied by the wrists through the downswing until just before impact as opposed to the negative torque (holding back) suggested by Jorgensen.

Interestingly, he mentions centrifugal force somewhat frequently and uses this passage the describe the effective release of the scratch golfer:

This subject exhibited a swing hub curve with a large initial radius of curvature that decreased continuously during the downswing. He also had a highest degree of initial wrist cocking. Together, these served to reduce the initial centrifugal acceleration which in turn diminished the tendency of the club to move outward even though a positive alpha torque was applied from the initiation of the downswing. This large radius path was carried through most of the downswing as the hand speed was increased by the linear force. Approaching impact, the hub radius was quickly reduced by a redirection of the linear force, which in turned caused a rapid increase in the centrifugal acceleration. This action which was coordinated with a large increase in alpha torque, pulled the club outward and through impact. These coordinated actions give the impression of a consciously delayed wrist motion. It is believed that this sequence of events are necessary to yield the optimum segmental addition, thus the largest possible club head velocities.

Lastly, I would say he believes the real driver for an effective release is the reducing of the hand swing radius just before impact.

Honestly, his results don't turn into anything actionable for me. Trying to do anything conciously with the wrists has always caused nothing but trouble and I'm not really sure how I'd go about trying to shorten the hand radius near impact. However, Brian and Jim may know how to achieve that using some simpler visualizations.

 

[iseekabetterswing]

Honestly, his results don't turn into anything actionable for me. Trying to do anything conciously with the wrists has always caused nothing but trouble and I'm not really sure how I'd go about trying to shorten the hand radius near impact. However, Brian and Jim may know how to achieve that using some simpler visualizations.

Open left shoulder and hip should shorten your hand radius.

 

[shortgamer]

Just finished my first pass of the Nesbit article. I see has another one on Work and Power in a golf swing in that same publication. The only real surprise for me was that he shows a positive torque applied by the wrists through the downswing until just before impact as opposed to the negative torque (holding back) suggested by Jorgensen.

Interestingly, he mentions centrifugal force somewhat frequently and uses this passage the describe the effective release of the scratch golfer:

Lastly, I would say he believes the real driver for an effective release is the reducing of the hand swing radius just before impact.

Honestly, his results don't turn into anything actionable for me. Trying to do anything conciously with the wrists has always caused nothing but trouble and I'm not really sure how I'd go about trying to shorten the hand radius near impact. However, Brian and Jim may know how to achieve that using some simpler visualizations.

Left shoulder up and back- Brian had it right the whole time. Which proves you don't have to understand the forces at all, you just have to know how to make the club do what it do.

 

[Bigwill]

nmgolfer, i'm not lazy and am not inhibited in learning a lot about physics or any other science for that matter. The difference is i don't care to. I don't have an interest in it, i rely on other experts to explain it to me so that i can learn it to the best of my abilities of what i could actually do with that information.

from my limited experience in this life and in business, the best "groups" are the ones who have people with defined roles of expertise that work towards a common goal. For instance i work in finance, however each of us has a unique skill set that all achieves the goal of a finance department, which in a very generic defination are, business advisors. As an example, i have superior excel skills than other people in my group, these skills allows us as a group to work more efficiently. Now could i help others in the group learn these skills? Sure and i do, but only to a point. Because i am taking time away from something that they do extremely well that is again, helping the group. Do i have the same skills as the others do? Of course but maybe they are better at it than i do; again it doesn't matter because we all are working together.

So "dumbing something down" is not lazy. I have learned that one doesn't need to know everything. You simply need to know enough about what is that makes you successful. If you can find a way to harness that, you are sure going to be one happy successful person in anything you do and for those things that you don't have the necessary skills in you hire someone to do it for you to help you work towards your goal.

The people that i know who tend to be the least successful are the types who feel that they are the ones who have to do everything themselves instead of trusting others to perform tasks they do not know how to do.

Just my opinion

Good post, Jim. There's nothing wrong with discovery, and encouraging it. However, it's also important that your target audience understands what you're trying to convey; otherwise, you lose them.

 

[Bronco Billy]

A THREE DIMENSIONAL KINEMATIC AND KINETIC STUDY OF THE GOLF SWING

Steven M. Nesbit


Department of Mechanical Engineering, Lafayette College, Easton, PA, USA


Received 20 May 2005
Accepted 02 September 2005
Published 01 December 2005

© Journal of Sports Science and Medicine (2005) 4, 499 - 519

http://www.jssm.org/vol4/n4/17/v4n4-17text.php

Hi There

Nesbit Takes as whole Bunch of TRASH Golfers and Measures a lot of parameters etc. and builds a Mathematical/Computer Model that Represents and describes the Collective Swings of a Group of TRASH golfers......

Now if Your Swing Parameters Match the Results Predicted by the Nesbits Model then You are Truly/Scientifically a TRASH Golfer...... Which You Actually Knew before the Analysis.....

Cheers

 

[JeffM]

jmessner stated-: "Lastly, I would say he believes the real driver for an effective release is the reducing of the hand swing radius just before impact."

Interestingly, and most importantly, the PingMan machine doesn't have a changing hand swing radius, and yet it executes a perfectly natural release. I think that the Pingman machine cannot be ignored because it has a perfectly natural release, and yet it doesn't have ACTIVE wrists/hands or a varying hand swing radius, or external forces operant. It only has a single force operating at the cenral hinge point, which causes the central arm and peripheral hinge joint (hands) to move at a constant rate of speed.

Any explanation for the release phenomenon in human golfers should also apply to the PingMan machine. NMGolfer's explanation is simple and pertinent - the single linear action force operating on the club doesn't occur at the COG of the club and therefore the clubshaft is constantly developing angular velocity, and his explanation is the same for the PingMan machine and human golfers.

Jeff.

 

[tbone69]

Truth

nmgolfer, i'm not lazy and am not inhibited in learning a lot about physics or any other science for that matter. The difference is i don't care to. I don't have an interest in it, i rely on other experts to explain it to me so that i can learn it to the best of my abilities of what i could actually do with that information.

from my limited experience in this life and in business, the best "groups" are the ones who have people with defined roles of expertise that work towards a common goal. For instance i work in finance, however each of us has a unique skill set that all achieves the goal of a finance department, which in a very generic defination are, business advisors. As an example, i have superior excel skills than other people in my group, these skills allows us as a group to work more efficiently. Now could i help others in the group learn these skills? Sure and i do, but only to a point. Because i am taking time away from something that they do extremely well that is again, helping the group. Do i have the same skills as the others do? Of course but maybe they are better at it than i do; again it doesn't matter because we all are working together.

So "dumbing something down" is not lazy. I have learned that one doesn't need to know everything. You simply need to know enough about what is that makes you successful. If you can find a way to harness that, you are sure going to be one happy successful person in anything you do and for those things that you don't have the necessary skills in you hire someone to do it for you to help you work towards your goal.

The people that i know who tend to be the least successful are the types who feel that they are the ones who have to do everything themselves instead of trusting others to perform tasks they do not know how to do.

Just my opinion

Jim,
You make a valid point. That is why guys like NM Golfer will always be employed by guys like me. Very smug and think they know it all. Stick em in their cubicle and give em a job to do. They are great on projects, provide you with a ton of useless information and when you don't do anything with it, they will quietly tell their associates how they are much smarter than you and if they were in charge, yadayadayada.

 

[jmessner]

jmessner stated-: "Lastly, I would say he believes the real driver for an effective release is the reducing of the hand swing radius just before impact."

Interestingly, and most importantly, the PingMan machine doesn't have a changing hand swing radius, and yet it executes a perfectly natural release. I think that the Pingman machine cannot be ignored because it has a perfectly natural release, and yet it doesn't have ACTIVE wrists/hands or a varying hand swing radius, or external forces operant. It only has a single force operating at the cenral hinge point, which causes the central arm and peripheral hinge joint (hands) to move at a constant rate of speed.

Any explanation for the release phenomenon in human golfers should also apply to the PingMan machine. NMGolfer's explanation is simple and pertinent - the single linear action force operating on the club doesn't occur at the COG of the club and therefore the clubshaft is constantly developing angular velocity, and his explanation is the same for the PingMan machine and human golfers.

Jeff.

Jeff- You could say the same thing about the CF - it's not operating on the CoG of the club either. But, I'm starting to think the distinction between the two theories is not that important. If you move your hands in a curvilinear fashion the club will want to throw-out. The faster and tighter the radius of that movement, the more the "release". Pingman, was created to test clubs and not as a model for human golfers so I would expect that the profile of pingman "hand" and clubhead velocities would not necessarily be appropriate for us mortals. In fact, in clubmaking circles, there's been some discussion about trying to create a robot the more realistically mimics the human movements with rotation and the whole bit.

Left shoulder up and back- Brian had it right the whole time. Which proves you don't have to understand the forces at all, you just have to know how to make the club do what it do.

You're right - Sounds like a "throw a drunk off your shoulder" move to me.

Jay

 

[JeffM]

Jay

I think you are right to state that the faster and tighter the radius of the hand movement, the more the "release". It would presumably be due to the fact that the line of action force is at a greater angle to the clubshaft per unit time if the radius of curvature of the hand swing path narrows, and therefore more angular velocity is developed per unit time when the line of action force is not linearly in line with the COG of the club (as NM Golfer's drawings demonstrate). I suspect that mathematicians could calculate the difference in angular velocity for a constant hand radius swing (eg. PingMan's machine' swing) versus a narrowing radius swing (good golfer's swing).

I like NM Golfer's explanation because it doesn't involve use of the term "centrifugal" which many forum members think is a non-existent force. It only refers to a single force applied to the grip end of the club, and the idea of angular velocity developing is simply related to the fact that the force is not applied directly at the COG of the club.

Jeff.

 

[mandrin]

nmgolfer is indeed quite correct to advance that centrifugal forces are not required to explain the release action. It is stimulating to be challenged in one’s views as they quickly seem to crystallize, once developed.

The whole business of centripetal and centrifugal forces, and more in general inertial forces, and even more specifically inertial reaction forces is a big mess. Science/education is to be blamed for such mucky state of affairs.

One small specific point, adding to the confusion, is that centripetal and centrifugal forces are defined invariably in the simple context of a point mass moving in a perfect circle around a center. The mathematics is simple, limped and straight forward.

However, for multiple linked segments rotating around some fixed center the situation is much more complex. The mathematics is indeed rather complicated and the inertial forces are hidden in an opaque clutter of mathematical expressions.

The terms centrifugal and centripetal are not adequate anymore since the lines of action of the centripetal/centrifugal force pairs, acting on each and every particle of the ensemble, don’t pass anymore through a stable central pivot.

I have derived the inertial torque on the club shaft during the downswing. This torque is first negative, corresponding to bending the shaft. Once the angular velocity is somewhat increased the torque acting on the shaft reverses and starts acting to increase the angle, hence releasing.

The magnitude of torque passes through zero just a fraction before the two segments are aligned. The subsequent sign reversal indicates that the torque on the shaft is now acting to slow down the angular velocity of the shaft, even with central torque still fully active.

The time history of this inertial torque, acting on the shaft, depends on the various system parameters and on the time history of the external torques applied at both joints of the model. The mathematical formulation is given by relation (1) and, more conveniently, shown in Fig1.

 

[puttmad]

...

Jay

I think you are right to state that the faster and tighter the radius of the hand movement, the more the "release". It would presumably be due to the fact that the line of action force is at a greater angle to the clubshaft per unit time if the radius of curvature of the hand swing path narrows, and therefore more angular velocity is developed per unit time when the line of action force is not linearly in line with the COG of the club (as NM Golfer's drawings demonstrate). I suspect that mathematicians could calculate the difference in angular velocity for a constant hand radius swing (eg. PingMan's machine' swing) versus a narrowing radius swing (good golfer's swing).

I like NM Golfer's explanation because it doesn't involve use of the term "centrifugal" which many forum members think is a non-existent force. It only refers to a single force applied to the grip end of the club, and the idea of angular velocity developing is simply related to the fact that the force is not applied directly at the COG of the club.

Jeff.

OK
So what pingman "proves" is that an ideal release will happen (also) with a constant hand speed and that this will involve an optimum speed, i.e. too slow and you release to early, too fast and you release too late...

Is that the only useful conclusion we can come to from the previous 12 pages of bumff?..........

So how do we figure the vast differences in clubhead speed (30-40mph) between ordinary golfers and say, long drivers?....

Long drivers do have fast hand speed, but it is not 30-40 mph faster....
Plus the fact that the long drivers produce lots of lag, so what do they do to release it on time?
There's a bit more to this than just "letting it happen"...

 

[jmessner]

Mandrin-

Your statement on the point mass vs having to integrate the forces across all the particles in the system was the clearest statement of the problem so far - at least for me.

I'm wondering about the negative torque you showed on the shaft at the beginning of the downswing - what bending does that cause? Could that also translate into a further cocking of the wrists at the start of the downswing if the golfer allowed that to happen (did you include the 90 degree wrist stop in your analysis)?

 

[mandrin]

Mandrin-

Your statement on the point mass vs having to integrate the forces across all the particles in the system was the clearest statement of the problem so far - at least for me.

I'm wondering about the negative torque you showed on the shaft at the beginning of the downswing - what bending does that cause? Could that also translate into a further cocking of the wrists at the start of the downswing if the golfer allowed that to happen (did you include the 90 degree wrist stop in your analysis)?

jmessner,

There is indeed a passive 90 deg dead stop used in the modeling. As long as the torque is negative the shaft remains pressed against this stop. When the torque becomes positive it is free to leave and to start releasing the club.

The negative torque is directly related to the drag felt in the hand(s)/finger(s), especially felt when one has a dynamic loading of the shaft with a recoil action - starting down when the club is still going back.

If you do it rather dynamically one can indeed develop a very big negative torque which will definitely strive to increase the cocking of the wrists. I could readily model this dynamic recoil to show it quantitatively.

This negative torque is directly responsible for the initial bending of the shaft, referred to as loading of the shaft. I don’t think this to be very appropriate term even if it seems intuitively right, since there is no unloading.

 

[JeffM]

Puttmad

I was at the NationWide tour event here in Salt Lake City yesterday, watching our local 17 year golfer - Tony Finau - play. He averages 350 yards per drive. I saw him drive a 387 hole and land on the green about 30 feet short of the flag.

He has an amazingly fast swing, but I don't think that he does anything differently than us mere mortals. He simply does everything faster - faster downswing pivot action => therefore faster arm/hand speed => therefore faster clubhead speed. His release action is conventional as he is a swinger.

Jeff.

 

[Bronco Billy]

Jay

). I suspect that mathematicians could calculate the difference in angular velocity for a constant hand radius swing (eg. PingMan's machine' swing) versus a narrowing radius swing (good golfer's swing).

Jeff.

Hi There

What you said Maybe the Crux of the Matter.......Pingman's Constant Hand(FREE HINGE) Radius Produces a PERFECT RELEASE no Matter what PingMan's ARM VELOCITY is ....... Ring Any Bells????? ThereFore The Closer a Human Golfer can Produce a Constant Hand Radius the More Perfect a Hand Release at ANY Arm Velocity will be Achieved....... ThereFore Maximum Efficiency is Achieved..... This is the F=Ma of Golf...... I just became Immortal.... No Charge.......

Cheers

 

[jmessner]

Of course the other factor not included in the simplified 2-D models is the effect of the rolling of the forearms just before impact. In TGM terms, I guess that's Accumulator #3. I was just looking at a video of Tiger on youtube, and when his club is parallel to the ground, the angle between his left arm and the shaft is around 110 degrees and the back of his left hand looks like it's basically still on plane. So, he's got about 70 degrees of wrist cock and almost 90 degrees of forearm rotation that takes place from there to impact.