NOTE: THIS THREAD IS AN OUTGROWRTH OF THIS PREVIOUS THREAD.

THE BALL AS VIEWED AT ADDRESS IS SEEN AT THE CENTER OF THREE INTERSECTING COORDINATE PLANES: THE X-Y PLANE THAT IS THE GROUND, THE X-Z PLANE THAT ARISES VERTICALLY FROM THE LINE OF THE PUTT ALONG THE GROUND, AND THE Y-Z PLANE PERPENDICULAR TO THE X-Z PLANE AND VERTICAL TO THE GROUND.

Geoff:

Your reference to Cartesian coordinates centered in the ball raises several points, namely:

1. Your coordinates are based on looking down on the ball in plan view rather than the normal side elevation, just for our clarification.

2. All three coordiate locii are significant to the putting stroke -- the x-axis for the horizontal stroke path, the y-axis for the putter face lateral positioning and the z-axis for the elevation of the putter from the ground or ball equator.

3. For the straight back and forth stroke, what physical controls must be applied to maintain alignment in the x-z plane and defeating the x-y plane, and, since gravity is a non-factor in a 3" - 6" backstroke?

4. For the arc path stroke, what physical controls must be applied to consistently maintain alignments in all 3 axes?

5. Since you indicated you agreed with my choice of putter construction for straight and arc path putting, can you relate these putters to their actions in the three axes?

Thanks for your responses.

Dear Sammy,

Neat questions! Thanks. In response to 3 and 4 above:

3. For the straight back and forth stroke, what physical controls must be applied to maintain alignment in the x-z plane and defeating the x-y plane, and, since gravity is a non-factor in a 3" - 6" backstroke?

4. For the arc path stroke, what physical controls must be applied to consistently maintain alignments in all 3 axes?

The main idea is captured by the exercise of putting facing a wall with the toe of the putter next to or against the baseboard of a wall. Because the stroke action of the putter head either parallels the action of the upper torso (in the case of a vertical-plane shoulder stroke) or is centrifugally constrained to the central pivot of the body or the axis of rotation thru the body (in the case of tilted-plane strokes or arcing strokes), in all cases there is a Y-dimension (near feet / far from feet) boudary to observe and not cross -- the baseboard.

In terms of our coordinate planes, the baseboard parallels the X-Z plane arising vertically out of the line of the putt. So in general, the putt line itself marks the location of the X-Z vertical plane of the putt. The "putt line" is equivalent to the "aim of the well-positioned putterface" -- i.e., the line that is perpendicular to the putter face extending targetward from the sweetspot of the putter face, as the sweetspot is centered on the back of the ball. The line thru the ball that matches this aim is thru the back of the sphere out the front of the sphere thru the center of the sphere, and this line thru the ball establishes a vertical plane thru the ball that is coincident with the X-Z plane of the putt. The line of the putt and vertical plane of the putt matches the line thru the center of the ball and the vertical plane thru the center of the ball, both of which match the aim line of the putter face at the sweetspot and the vertical plane that corresponds with this. Now the whole business comes down to the fourth "line" and "plane" -- the line of the stroke of the putter face at impact thru the center of the ball down the line on the ground. At least during putter-ball contact, a straight putt is BEST (not solely) achieved consistently and accurately by a stroke that sends the center of the putter thru the center of the ball down the line without too much upward or downward trajectory.

Your question asks about "physical controls" operative during the stroke that accompany this simply-defined task -- putting straight (also with good touch). There is a faint suggestion in this terminology of the sort of mechanical physics associated with machinery that is inappropriate when discussing the physical controls in human action. Human action is body action in relationship to perceived spatial relationships under the guidance of intention / goal, perceptions, and motor control processes. The intention / goal channels the perceptions, the perceptions form the motor controls, and the motor controls effectuate the intention by moving the body in relationship to objects and locations and conditions in the environment. It's a good thing "all putts are straight" -- it simplifies matters immensely! So to identify the controls of this human action, we look to intentions, perceptions, and motor controls in the physical environment of puttin straight (with good touch) with a conventional putter and ball on a green.

INTENTIONS / GOALS: The intention / goal of a motor action is partially formed by habit and partially formed by knowledge and expectations. Intentions for physical conduct require the ability ACCURATELY to predict cause and effect in reality. The world trains our brains about this constantly from the very beginnings of sentient existence. Even so, the more you KNOW from study and past experience what to expect, the sharper and more focused and efficacious your intentions. The "skill" in putting resides in the piece-meal learning of subroutines and the fluid integration of these subroutines into a unitary action, so there are sub-intentions as well as the overarching main intention (putt straight with good touch).

BACKSTROKE PATH: In putting, you have to know what to look for in terms of visual and "feel" cues and also to know accurately what to expect from certain movement choices available when forming the movement. For example, if you know in advance that using your hands and arms to start the putter back from the ball is much more likely to direct the putter across the line to the far side of the X-Z plane (creating a loop path) in comparison to using your lead shoulder to direct the bottom of the putter back from the ball in a dipping that parallels the shoulder frame alignment at address (which sends the putter back either straight or slightly to the inside), you are more likely to putt straight if you KNOW this and prompt yourself to intend to use the shoulder to start the stroke. A "casual" or "indifferent" putt is one in which the golfer neglects to do this, inadvertantly uses the hands, and causes a problem in the backstroke requiring recovery. So this "learning" from study and experience instills an intention at address to use the shoulder to start the stroke instead of the hands so that the putter travels back either straight or slightly inside and a problem is averted in advance. Again, putting along a baseboard is the same, as "crossing the line" in the backstroke would direct the toe of the putter against the wall. Visually, seeing the vertical plane of the putt at address as rising thru the center of the ball and also as coincident thru the sweetspot of the putter creates the intention in the golfer not to allow the sweetspot of the putter to get on the far side of the X-Z plane -- either going back OR coming forward. That would be a big boo-boo.

BACKSTROKE TIMING: A backstroke timing intention is to allow the backstroke to be "full" - that is, take twice as long as the downstroke will take. In the case of a gravity downstroke, this backstroke is full at one full second. Anything shorter or longer is going to mess up distance control or invoke some downstroke movement that is not well-honed. The intention is NOT to decide in advance WHERE the top of the backstroke ought to be, but simply to make the backstroke LAST one full second, always coasting to the top of every backstroke at the end of the count -- short backstrokes or long. This way, the instincts handle the size of the backstroke and the size is free and accurate so long as the timing is observed.

DOWNSTROKE FACE ORIENTATION -- TETHER-BALL STYLE: Another intention is to resquare the putter face coming into the impact zone. The easiest way to get this done is to respect the tether-ball way in which the stroke can resquare itself naturally without human effort during the gravity-sponsored downstroke. There is a certain "memory" of the body postures in the backstroke that guides the downstroke back along the same path. This memory is built in to the body postures involved -- the structural and soft-tissue properties. The requirements or "controls" for using this memory are: 1. be gentle with the timing and inertial forces in the backstroke so the backstroke does not overly challenge the capacity of the return-path memory of the body postures; 2. fix the location in space of the pivot of the stroke (front base of neck) no later than the transition at the top of the backstroke or otherwise maintain the unfixed motion of the pvot in an appropriately symmetrical pattern; and 3. "let" the putter, hands, arms, and shoulder frame simply swing beneath the pivot as they will in gravity.

The moment of truth is at the top of the backstroke when the golfer stills the base of the neck and switches from voluntary movement of the putter sent and then coasting back to the top of the backstroke into the "letting go" of the triangle as a unit so the whole swings gracefully down and under beneath the neck all by itself. What I have learned about this is that "bringing" the putter down with arms and hands is much more likely to direct / shove the putter along a path athwart the putt line coming into imapct. That's mostly because of human biomechanics -- using the arms and hands activate the elbow joints, and the ONLY way the elbow joints can bend in a putting posture are AWAY from the feet and "across the line". If you feel any slight, very subtle increase in tension in the upper arms or forearms or even in the small muscles of the hand and fingers coming down with the putter, this is not a good sign. You are abandoning the body memory approach to resquaring the putter and shifting to Plan B without a good Plan B in mind. My way of "controlling" this "letting" the putter drop is to intend to maintain the same level of tension all the way thru the stroke and to abandon voluntary guidance of the stroke the same way a parent "abandons" a two-year-old child upon releasing hold of the swing at the top of the backswing, knowing that the swing will carry the child securely straight down and under the top bar of the swingset without violence or misdirection.

DOWNSTROKE FACE ORIENTATION -- RECOVERY / MANIPULATION STYLE: If you can't get skilled at this sort of automatic resquaring (and even if you are skilled, you need a backup for bad days), then you need to know what to expect from the cues in the hands on the putter -- especially as these indicate putter face orientation at points in the stroke. In a no-arms / shoulders-only stroke, the putter face should not change at all in relation to the hands, so the expected feeling in the hands during the stroke is "no change." If there is a change going back, the putter is 99% going to "open" and the feeling in the hands is a subtle twist of the handle against the thumb tips and the walls of the palms. Noticing this opening would be the first key to resquaring the putter face thru impact, but knowing the feel of square hands at the bottom of the stroke is key to getting the intended feel accomplished. Another key is timing the resquaring. Don't be late! Being early is not nearly as troublesome. And part of the timing is: once you get back to square by closing the open face, stop closing the face. On this point, the tip to move the back of the lead hand down the line (parallel) is a good one, and the advice to avoid wrist breakdown thru impact is okay, too. The main thing is not to use the hands at all unless you have to requare the putter face, and then ONLY resquare the putter face and otherwise don't use the hands. Sometimes, when the putter head travels across the line in the backstroke, the face comes out of square. And the hands are slightly farther from the body than they should be. My experience is that just relaxing the elbows to allow them to sink back to suspension immediately below the shoulders will both bring the stroke coming down back on line and resquare the putter face (see more in the next paragraph).

FOLLOW-THRU UPSTROKE MOVEMENT: A closely related intention involves what to do right during impact. Because the human frame as postured at the top of the backstroke is being held by gut and lower back muscles against gravity and so upon relaxation will nicely drop down back to the starting posture at address, but thereafter the human frame impedes the free-swinging upwards past the bottom of the stroke against gravity, there is a need to "finish" the stroke by returning to voluntary effort somewhare at the bottom of the stroke. This is both a timing issue and a movement strategy issue.

TIMING DOWN: Timing the bottom is ridiculously simple if you have a good tempo, since all strokes always reach the bottom in exactly the same amount of time, regardless of the length of the backstroke. For a gravity tempo, this is about 1/2 a second from the top of backstroke to the bottom of the stroke. So the timing intention is "be patient, it's not up to you to make the timing happen -- gravity will deliver the putter in exactly 1/2 second as always so long as you stay out of it, so just count and watch and wait for the putter to bottom out."

MOVEMENT UP: The movement strategy coming down to the bottom is also ridculously simple: do nothing except stay the same. That is, do NOT use arms or hands to deliver the putter to the bottom of the arc on your personal schedule. But going up, the strategy is "move the whole triangle by moving the lead shoulder vertically up away from the ground so that the shoulder motion stays in a plane parallel to the plane of the putt." This action "casts" the putter face square down the line on a slightly rising trajectory, flush to the plane of the putt. This is what I call the "magic move" in putting for putting straight. Personally, I have found this thought pattern to be helpful in "controlling" this: "There is one muscle in particular NOT to use coming down or going up and that is the muscle on the top side of the left forearm; keep this muscle inactive; instead, note the feeling of the lead shoulder as a body part as a cue to use this body part to lead the vertical lifting of the upstroke right at the bottom to lift and cast the putter face square on a rising trajectory thru the back and center of the ball down the line." The accuracy of this up-move of the lead shoulder (and the shoulder frame as a whole) depends critically upon the pivot staying centered at the bottom or midline of the stroke. It is fatal to allow the pivot to "wander with" the follow-thru, as this sends the shoulder frame twisting to the inside of the line in a pull action and reintroduces timing problems and Y-direction problems that don't exist otherwise.

TIMING UP: The timing issue of the voluntary move up is to mesh the movement pattern into a natural tempo. The COMPLETELY natural pattern of a gravity-only downstroke is for the putter at the top of the bacsktroke to gradually and steadily accelerate down, reach a peak speed right at the bottom of the stroke, lose a little momentum during impact, and stall out with the putter head drifting back in around the feet as the human frame resists going up and down the line. To mesh voluntary movement into this pattern to continue the downstroke pattern in reverse into the follow-thru requires sensing the timing coming down and then continuing this in reverse going up. Basically, the putter coasts to the top of the backstroke, gradually accelerates down, and then past the bottom needs to coasts to a finish poisition roughly as high as the backstroke. So the up-stroke of the lead shoulder is patient and graceful and symmetrical -- no "hit", no jab, no abrupt stopping. This casts the putter face square down the line on a slightly rising trajectory in a symmetrical continuation of the stroke in the opposite timing pattern of the downstroke. That's the upstroke intention: "once the bottoming occurs, move the lead shoulder gracefully vertically up from the ground in a timing that reverses the downstroke." You really only have to sweat this for 5-6 inches past the bottom of the stroke, since after that, the putt is over. Even so, it is helpful to pre-see the putter head traveling gracefully and squarely thru the ball and down the line on a slight rising before the stroke is started. This orients the body to the X-Z plane for purposes of the movement dynamics to come.

That's pretty much it -- straight putt accomplished, with good touch. The perceptions and motor control processes get structured by the intentions, formed in response to learning and experience for the purpose of acting with accurate and effective causes and effects.

PERCEPTIONS AND MOTOR CONTROL PROCESSES: Knowing how to use the senses to general accurate perceptions is one key, and knowing what perceptions to generate or pay attention to is another. If you feed the brain accurate and relevant perceptiual cues with focused intention, the motor prcesses use the perceptions under the guidance of intention to formulate the ensuing motion. The "plan" has to be designed first by intention and perception. A well-designed, accurate plan promotes accurate movement in execution. There is an encyclopedia of information to share about what are relevant perceptions, how to generate accurate relevant cues, and how these are used to generate effective movements.

SAMPLE PERCEPTION CUES: Just as an example, Tiger Woods uses a string line mostly to work on getting his setup posture square to the line (and plane) of the putt -- not simply for seeing the line or good stroking mechanics. This is establishing and learning visual physical cues about what is a square setup and how a straight stroke out of a sqaure setup looks and feels, and these relevant cues are taken from the practice and deployed / employed during play on course. Personally, I spend a lot of time being sure that I integrate the aim of the putter with my visual sense of the line thru the ball (and out its front and down the line a little ways) with my physical / mental preview of delivering the stroke on line in the plane of the putt thru and past the ball. This happens at address. One way I do this is the "two Ts" -- the T of the putter face and its alignment line meeting flush to the T on the ground beneath the ball aiming its stem at the target. I take the putter back on the stem of its T and then putt the ball down the stem of the ball's T. Another is to see the one point down the aim line of the putter face opposite in a perpendicular way from the big toe of my left (lead side) foot. The ball must always exit my setup visually by rolling straight sideways over this one and only one spot.

Another perceptual cue is to check that in the setup the sweetspot of the putter a) gets out to the back center of the ball, and b) does not get beyond the line of the putt. Just noticing this in the setup helps avoid the backstroke going across the line. Bobby Locke used to set his putter up with the toe behind the ball, not the sweetspot, as he planned to deliver his putter on an inside-to-out path into the back of the ball and NEVER from out to in. So any error in positioning or in delivering the putter face into the back of the ball should be to the inside. I like to square the putter sweetspot behind the ball to help make sure I see the line thru the ball correctly and to remind myself not to cross the line going back, but coming into the back of the ball it is better to arrive with the sweetspot one dimple inside the exact back of the ball with a square face than to get overly concerned by the thought that unless you hit the ball with the sweetspot there will be disaster -- there won't be. It's far more important to hit the ball with a square face even if a little off the sweetspot than it is to risk face squareness for the sake of getting the sweetpsot onto the back of the ball. It's always good to think: "Make a solid putt" as solid is centered and flush, but a tiny miss to the inside is definitely okay!

PHYSICAL CUES: The main ones are balance and comfort in the setup, but there are others. There is balance at the top and a sense that the movement of the putter back at the start does not require snatching the putter back out of the ground (Nicklaus' "unweighting" the putter from the turf, not quite the same as lifting it off the ground to "hover" it). There is a preview of the stroke mentally, visually, and physically. There is a breathing rate compatible withn the intended tempo. There is the expectation that the hands feel square at address and will not experience anything unexpected during the stroke. There is even balance left-right on the balls of the feet. There is a sense of rootedness with the earth. There is an awareness of the feeling of the lead shoulder as the initiator of the backstroke and as the progenitor of the upstroke past the bottom. There is an awareness of the alignment of the shoulder frame and the relationship of the lead shoulder vertically to the balls of the foot on the lead side. There is a sense of the straightness of the sweep of the stroke beneath the neck and face. There is an intended sense of patience in the body about the backstroke and then the downstroke. There is a level of grip pressure that is light and meant to be kept constant thru the stroke. There is a physical awareness of the orientation of the line across the skull and eyes that is in the same or a parallel plane to the plane of the putt. There is a sense of linear connection from lead shoulder socket down thru the arm and hand and putter shaft to the sole of the putter at its sweetspot behind the ball, as this will be dipped back off the ground and up in the takeaway.

COMFORT: These cues include relaxed arms and hands suspended naturally from the forward-canted torso balanced over the balls of the feet, and slightly counter-balanced by the rear projecting back from the balls of the feet. Comfort also implies no thoughts or worries about what to do or how to do it, as the plan is "the same as always --just do what you know works best as you know how to do it best." You can get "comfortable" with a bad setup and stroke pattern, so comfort is not really all its cracked up to be in and of itself.

BALANCE: A physical control that avoids crossing the line with the putter in addition to the muscle issues and timing issues above is balance. The putting postures and the putter are out of vertical with normal standing posture, so the body leans forward into a new posture and then moves with forces tempting the body out of balance. For a shoulder stroke, the main tendency of these forces THRU THE IMPACT ZIONE is to send the stroke to the outside, across the line. The centrifugal action of these postures with the "triangle" mostly in front of the body and not in line with the center of gravity, when making a stroke from left to right, for example, is to toss the whole further from the feet. This is avoided mostly by placing the weight on the balls of the feet, or at least by catching and holding the weight transfer on the balls of the feet, to prevent this moving across the line. My personal thought comes from Akido and the martial arts: "My feet are rooted into the earth, and the stability of my center of gravity and balance is secure like an old oak."

The unbalancing tendency that accompanies an armsy stroke persist at all points in the stroke and especially thru the impact zone. Moreover, their management depends on the timing of resquaring. Going back to the top of the backstroke, the tendency is for the weight to shift to thew right side and towards the feet and away from the plane of the putt. Coming forward, the centrifugal arcing forces of the stroke send the weight mostly at the balls of the left foot and direct the putter across the line thru the plane of the putt. Once resquared, the voluntary muscle action swinging the arms is basically thereafter a "pull" that redirects the putter back in towards the feet or around the feet to the inside. In accordance with what David Lee in his "Gravity Golf" has learned about this sort of action, it is probably best for the arcing golfer to stay back on his left heel coming forward, as this selects one and only one point on the ground to stabilize the arc of the stroke. That probably explains why many of these arcing-stroke putters like a little forward press at the start, to establish weight preference into the lead foot. Bobby Locke's putting stroke came from far inside and then sharply thru the ball and down the line, and this action basically pivoted around his left foot.

There are other supporting visual and physical cues to help navigate the X-Z plane thru the impact zone, but the above seem to me to be the main ones: Gentleness of tempo, respect for the properties of biomechanics and balance, and focused intentions forged from accurate cause and effect learning and experience.

In response to your last question:

5. Since you indicated you agreed with my choice of putter construction for straight and arc path putting, can you relate these putters to their actions in the three axes?

The center-shafted face-balanced putter is better suited for a shoulder stroke in a vertical plane than is a heel-shafted blade. The idea that the heel-shafted blade is better suited for the arcing stroke than a center-shafted putter is suspect to me. The heel-shafted putter is an historical, largely undesigned putter that adds forces to the stroke above and beyond those imparted by the movement of the golfer's body. The standard rationale seems to be that "toe flow" helps the golfer get done what he can't quite get done with his body in an arcing stroke -- that is, time the resquaring accurately. That's suspect, purely as a matter of physics, as "toe flow" is extra inertia in the toe, and this opens the toe going back and makes it SLOWER to close coming forward. This might be helpful if golfers typically resquare the putter in an arcing stroke TOO EARLY, but that doesn't appear to be the case.

Scotty Cameron seems to think that "toe flow" helps the golfer get the arc coming to the inside, in a "release" of the putter. This is what Ernie Els reports:

"The month before I played in my first tournament after knee surgery, I took a trip to California to see Scotty Cameron at his putting workshop. We made some interesting changes to my putter and my setup that have really helped me.

I had always played with a 35-inch putter, but Scotty used his cameras to show me that I was too hunched over, and I wasn't releasing the putter the way I should. I was cutting across the ball and pushing my putts. I switched to a 36-inch model and set up with the same bend at the hips, but with my spine not slumped, like before. I immediately had more room to release the putter through impact with the face rotating to the left. My putting stance got closer to the stance I use for a regular shot, and my putting stroke started feeling like a small version of a full swing."

Golf Digest, Apr. 2006. This is all in accord with Scotty Cameron's statements about "toe flow" on his website:

"Toe Flow - The amount the putter head closes at impact due to the position of the hosel and balance. e.g., A blade style putter such as the Napa has a lot of toe flow because it is heel shafted. Conversely, a Newport style putter has less toe flow due to its plumbing neck."

Scotty Cameron Studio, Library. The so-called "toe flow" is just a variant of Karsten Solheim's heel-toe weighting for Ping putters that made them 45-degree hangers. Scotty Cameron varies the degree of toe hang by his hoseling and weighting so that the more toe hang, the more the designer gets into the stroke to influence the opening and closing of the toe during the stroke in addition to what the golfer is doing with his body. The putter hangs more toe down when the mass distribution favors the toe. My question is: How can extra mass in the toe promote the timing of the resquaring of the stroke?

I understand how it can make the toe open MORE than it would otherwise going back, as that is from the added toe inertia out from the hosel not wanting to stop at the top of the backstroke. I can understand how extra toe mass KEEPS the toe open coming forward, as that is from the inertia of the added mass resisting coming forward more than the rest of the putter. I can understand how the extra toe mass can make the putter close MORE than it would otherwise in an arcing follow-thru, as that is from the added toe inertia not wanting to stop at the end of the thru-stroke. But the $64,000 question is what does "toe flow" have to do with timing the resquaring of the putter?

With the heel-hoseling, the center of gravity of the putter in relation to the hoseling is in the heel, so there is actually more mass in the heel. Theoretically, I suppose, closing the heel side of the putter "whips" the farther-out-there and lighter-than-the-heel toe closed quicker than otherwise, sort of like swinging a bat. The Tour Edge Equator putter was a center-shafted mallet with a weight plug in the heel, and the supposed effect was to help close the putter thru impact.

Bottom:


Top:


But in actual practice, the tool is getting adjusted to by the human, and the timing is really the human's problem.

The only thing I can see about it is that "toe flow" alters the way the human senses the putter as a tool and therefore alters the way the human moves his body using that tool. The physics alone won't help, but instead would keep the toe more open than otherwise. How would "toe flow" alter a stroke? By making the arcing thru the impact zone a little harder to accomplish and therefore causing a more deliberate effort by the golfer to get the job done, and also perhaps by altering the tactile signalling in the hands at the top of the backstroke and the end of the follow-thru. Perhaps the felt effects of "toe flow" prompt the golfer to alter the stroke movement of his body more in the direction of a "snap hook" hit stroke. I suppose for some golfers at some skill levels, this is helpful, or at least helps sell putters.

But if you look back at Ernie's words, boy is there confusion there! he says that before: "I was cutting across the ball and pushing my putts." What the heck is that? Does he mean that sometimes he was "cutting" his putts and at other times he was "pushing" his putts, or does he mean that in one and the same stroke he was both "cutting across" and "pushing"? Let's assume he means only the former. What's the cause of cutting across the ball? Lack of "toe flow"? No, it's stroke path from across the line to inside the line, or at the very least a path coming inside off the line. What's the cause of pushing putts? Too much "toe flow" opening the face and not enough closing of the toe, mainly. But Ernie reports the cure for both: a taller stance plus added "toe flow" "to release the putter through impact with the face rotating to the left." Well, "toe flow" won't do that by physics, but only by altering the stroke dynamics of the golfer more towards a "snap hook" style of putting.

I think we can look for Ernie's putting to fall a little off some of his earlier greatness. Els was 9th in putts per GIR before his injury and is now 72nd headed south. We'll see.

Cheers!

Geoff Mangum
Putting Coach and Theorist
PuttingZone
http://puttingzone.com
Golf's most advanced putting instruction -- you're either in the PuttingZone, or not.

Dear Geoff:

I have carefully read your response to my queries, and I must say I am impressed by the thoroughness of your research and explanations, however I must take issue with you on several points, namely:

1. Your exercise of putting facing a wall with the toe of the putter next to or against the baseboard of a wall sounds good, but how much practice is necessary before this drill is engrammed into the brain for use on the putting greens? It would seem that dependence on a wall may not be a good idea and disorient the golfer when this prop is removed and you must fly on your own. I am very skeptical about guided putting gizmos that promise a straight putting stroke, and have no relationship to the way the brain is trained. In fact, once the gizmo is removed and visual cues vanish, the brain is lost resulting in a "best guess" attempt.

2. As for generating a straight stroke action, this depends on minute realignment of the shoulders and arms to overcome the rotative action of the upper torso, or central pivot of the body or the axis of rotation thru the body. Somehow the curvilinear actions of the body must be translated into the rectilinear movement in a x-z plane straight putting stroke. I believe this can be verified with a simple geometric construct. To further illustrate this point just move the putter head more than 12" along the wall, and bring it up to say hand level to feel the changes in the shoulders, arms and even the spinal axis. When reduced to a putting stroke these articulations become minute but necessary to achieve a straight stroke; and, again due to the small movements involved, it again becomes a "best guess" action not solidly programmable into the brain because we are using gross motor movements of the torso, shoulders and arms.

3. As for the "gravity-sponsored downstroke", I again take issue with this concept for the very short length of most putting strokes. Attributing "pendulum" physics to the body-arms-putter assembly that is only displaced 3" to 12" max from the vertical just does not seem realistic. If you could provide calculations to back up the "feel" of pendular actions, that would settle the issue. My intuitive knowledge of the physics tells me that the putting stroke is not a free pendulum action but a fully torqued movement in both directions, and as such is fully conscious, thus removing the automatic non-conscious concept (which only applies to the full-blooded high speed golfswing downswing). To abandon the putting stroke to non-conscious state will only destabilize the gross motor movements as the brain attempts to make sense of assumed non-sense.

4. Some of your detailed explanation of the sensation of putting seems to be based on a non-inertial frame of reference, which is not meant to be a criticism, but rather a suggestion that the physics and feelings of the putting stroke (and the full golfswing too) should not be mixed when analyzing it. The beauty of science is that it simplifies, while feelings complicate, as evidenced by the plethora of golfswing books and personal theories attached to the game. Your theories about the putting game certainly attempt to reveal it's universal science, but still not to ignore the psychological inputs.

5. "Toe-flow" putters present an interesting sensory feedback to the golfer, while the face-balanced putter removes that sensory feel in the hands. Toe-flow putters require a fully conscious awareness of the unbalanced putter head, while face-balanced putters can be ignored if the golfer depends on a non-conscious gross motor movement body and dead hands putting stroke. Personal preference may be the factor that dictates which type of putter the golfer chooses.

Again, can you help me by explaining simply whether you believe the putting stroke should be fully non-conscious or partially conscious and non-conscious, during the backstroke or the downstroke, and if conscious which body parts are being consciously controlled? Thanks again.

Dear Sammy,

Let me respond seriatim:

1. Your exercise of putting facing a wall with the toe of the putter next to or against the baseboard of a wall sounds good, but how much practice is necessary before this drill is engrammed into the brain for use on the putting greens? It would seem that dependence on a wall may not be a good idea and disorient the golfer when this prop is removed and you must fly on your own. I am very skeptical about guided putting gizmos that promise a straight putting stroke, and have no relationship to the way the brain is trained. In fact, once the gizmo is removed and visual cues vanish, the brain is lost resulting in a "best guess" attempt.

It's not an exercise, but a conceptual explanation via imagery. I generally agree with you about training devices.

2. As for generating a straight stroke action, this depends on minute realignment of the shoulders and arms to overcome the rotative action of the upper torso, or central pivot of the body or the axis of rotation thru the body. Somehow the curvilinear actions of the body must be translated into the rectilinear movement in a x-z plane straight putting stroke. I believe this can be verified with a simple geometric construct. To further illustrate this point just move the putter head more than 12" along the wall, and bring it up to say hand level to feel the changes in the shoulders, arms and even the spinal axis. When reduced to a putting stroke these articulations become minute but necessary to achieve a straight stroke; and, again due to the small movements involved, it again becomes a "best guess" action not solidly programmable into the brain because we are using gross motor movements of the torso, shoulders and arms.

I have been doing these sorts of experiments for years now, and I'm thoroughly familiar with the feelings of a stroke that goes straight back and straight thru. It is easily demonstrable under a 10" high string line -- just move the lead shoulder downward towards the balls of the foot and back -- the putter head will rise up to the string dead square without any manipulation. There are no minute articulations or small movements. I have no idea what you mean by "solidly programmable into the brain." After many years reading neuroscience to understand how intentions, perceptions and motor actions are integrated by brain processing, I can safely say that it is nothing similar to "programming" a computer. You might want to survey a few of the more interesting Neuroscience Resources I've posted in the "Science" section of the PuttingZone.

3. As for the "gravity-sponsored downstroke", I again take issue with this concept for the very short length of most putting strokes. Attributing "pendulum" physics to the body-arms-putter assembly that is only displaced 3" to 12" max from the vertical just does not seem realistic. If you could provide calculations to back up the "feel" of pendular actions, that would settle the issue. My intuitive knowledge of the physics tells me that the putting stroke is not a free pendulum action but a fully torqued movement in both directions, and as such is fully conscious, thus removing the automatic non-conscious concept (which only applies to the full-blooded high speed golfswing downswing). To abandon the putting stroke to non-conscious state will only destabilize the gross motor movements as the brain attempts to make sense of assumed non-sense.

I attribute "pendulum-like" physics. Your intuitive knowledge is incorrect. The final sentence above doesn't make any sense to me: that's just not what happens. It appears to imply some assumptions about how the brain and body movements work that I have not found to be the case in years of studying neuroscience. As far as "calculations" are concerned, I'm not sure that would settle anything. If you have read Theodore Jorgensen's admirable book, The Physics of Golf (American Institute of Physics 1994), the application of Newtonian mechanics to a golf swing is far too tedious to attempt for a three-rod model of the swing and even for a two-rod model (simply arms plus club), the differential equations are too complicated to be written directly, and the Lagrangian function of energies is used instead (p 134). (See in general Marion Thornton, Classical Dynamics of Particles and Systems (Harcourt Brace & Co. 1995).

Nonetheless, very simple calculations are available from pendulum physics. The peak velocity (V) of an undamped simple pendulum's bob at the bottom of the stroke is V = SQR(2*gH) where g is the acceleration due to gravity (32 feet/sec*sec or 384 inches/sec*sec) and H is the height above the ground of the bob at release. A 12" backstroke (horizontal distance from midline to putter head at top of backstroke is 12", angle 12.8 degrees) rises off the ground 1.35". (See Trigonometry Applet using 54" as the hypotenuse from pivot to ground at address and 12" as the "opposite leg" of backstroke horizontally back from the address position -- the "height" of putter head at the top of the backstroke is the hypotenuse less the "adjacent side"). The peak speed due solely to a gravity-sponsored dropping of the downstroke is about 32 inches/sec. (nearly 3 feet/sec.). The formula for the velocity of the ball (Vb) after impact with a putter head is Vb = Vp * (1+e) * (Mp)/(Mp + mb), where e is the coefficient of restitution of the ball, Vp is the putter velocity at impact, Mp is the mass of the putter head, and mb is the mass of the ball. The masses of the putter head and ball typically stand in about an 8:1 ratio these days for my putters (360 grams to 45 grams). A ball's "e" is roughly .75. So, for a Vp of 32 in./sec., the ball velocity after impact is 32 * 1.75 * 8/9 (a multiplier of 1.56), or 50 inches/sec. Very roughly, this is about an 8 foot putt on a Stimp 10 green, as the ball coming off a Stimpmeter is rolling on the order of 65-70 in./sec. Certainly, the size of a gravity-sponsored backstroke is larger than a usual stroke by most golfers, and the tempo is much more graceful, but it is STILL powerful.

Doubling the size of the gravity-sponsored stroke to 24 inches off midline raises the putter head 5.6 inches off the ground, and generates a peak putter head speed of 65.6 in./sec., generating a ball speed 1.56 times faster, or 102.3 in./sec. In order for this gravity-sponsored stroke to send a ball the SAME distance as a Stimpmeter (with an off-roll speed of, say, 70 in./sec.), the putter head speed would need to be 70 / 1.56, or 44.8 in./sec. The Height for this would be 44.8 * 44.8 / (2g), which is 2.62 inches off the ground. This is a 17.8 degree backstroke that moves the putter head 16.5 inches back off the midline. In contrast, the Stimpmeter "inclined plane roll down a V-shaped channel" starts from a release height of about 10.5 inches, a LOT higher. Perhaps your intuitive physics has failed to take into account the multiplier effect of the mass of the putter head, or perhaps you don't fully appreciate the gathering speed in a pendulum free-fall as applied to the putting stroke in the magnitude of the length of the system.

Additional information is gleaned from Ray Penner, The Physics of a Golf Putt (in PuttingZone Science, Physics.) He shows in Fig. 9 a range of initial ball speeds for successful putts over a range of distances on an "average" speed green. The range runs from 2 meters/sec. (78.7 in./sec. or 6.6 feet/sec.) for a 5-foot putt to 4 meters/sec. (157.5 in./sec. or 13 feet/sec.) for a 30-foot putt. Consistent initial ball speed information is also shown in this chart for different green speeds for an 11-foot putt:



If I'm not mistaken, this chart comes from Cochran and Stobbs, Search for the Perfect Swing (1968), so the info has been around a while, and "tournament fast" may be a bit quicker by today's standards. The range is 9 feet/sec. (108 in.sec. or 2.74 meters/sec.) on a "Tournament fast" green to 13 feet/sec. (156 in./sec. or 3.9 meters/sec.) on a "slow green. For my 8:1 putter, the putter speed range would be 69.2 in./sec. at impact (fast green) to 100 in./sec. (slow green). On a "fast" green, this putter head speed is just a touch above my core putt's backstroke.

In the stroke I teach, with the "hands riding the putter down" experiencing "no change" on the handle followed at the bottom by a voluntary uplift into the back of the ball, which is not impact for about 1-2 inches past the bottom, there is doubtless some torquing thru impact. The timing of the upstroke, however, builds on the ever-regular peak speeds at the bottom of the stroke (set by the size of the backstroke in gravity) and the timing of the backstroke to mesh with the downstroke serves to regularize the torquing forces thru the ball so that the impact is very closely correlated with the gravity-sponsored peak speed at the bottom. My personal "core putt" that calibrates my stroke, ball, putter, and tempo to a specific green speed is about 12" off the midline, so the putter head starts down from just past my rear foot, given the width of my stance. My core putt yesterday was rolling balls about 10 feet on a green probably Stimping 10-11. So apparently I do impart some mild torque in the upstroke into impact, as this implies an impact speed close to 70 in./sec. as compared to the pure-gravity-only ball speed for this stroke of about 50 in./sec. I can get some precise measurements, for a clearer look at this.

For comparison, Jack Nicklaus has been measured putting a 20-foot putt with a peak putter head speed of 2.4 meters/sec (94.4 in./sec.). The pattern of his hand torquing (in Newton-meters) is under 0.5 for the first 25% of the downstroke, then steadily rising to 2.0 N-m 75% of the way down, and then dropping precipitously to 0.0 at impact (100% of the downstroke). The putter starts itself down and then Jack torqued the stroke mildly and then let it coast thru impact. two golfers trained in this same torquing pattern then were measured on 12-foot putts (presumably about the same green speed), and one reached a peak torque of 0.27 N-m at 70% of the downstroke for a putter head peak speed of 1.4 meters/sec (55.1 in./sec., for a ball speed with a putter-ball ratio of 7:1 of about 84.4 in./sec) and the other reached a peak torque of 0.4 N-m at 70% of the downstroke for an identical putter head speed at impact. Both golfers slightly missed reducing torque to zero at the impact point (100%) and instead reached zero torque after only 90% of the downstroke, and thereafter experienced slight negative torque from the hands the rest of the way into impact.

4. Some of your detailed explanation of the sensation of putting seems to be based on a non-inertial frame of reference, which is not meant to be a criticism, but rather a suggestion that the physics and feelings of the putting stroke (and the full golfswing too) should not be mixed when analyzing it. The beauty of science is that it simplifies, while feelings complicate, as evidenced by the plethora of golfswing books and personal theories attached to the game. Your theories about the putting game certainly attempt to reveal it's universal science, but still not to ignore the psychological inputs.

Galileo's insight were also with a non-inertial frame of reference, as were Einstein's. The whole insight of the General Theory of Gravity in Einstein proceeds from the insight that inertial mass and gravitational acceleration are equivalent. "The local equivalence of 'gravitation' and 'inertia', or the local 'cancellation' of the gravitational field by local inertial frames, inspired Einstein to the the theory of general relativity." I. Ciufolini & J. Wheeler, Gravitation and Inertia (Princton Univ. Press 1995), ix. I mix the feelings attended to in nearly 4 million mindful putts with the physics because in explaining this to golfers, the feelings are the most helpful in communicating the pattern. Golfers generally have "naive physics", which are commonly-held notions of physics that are simply incorrect, as all High School and College physics teachers know from overcoming "naive physics" on a daily basis. (See, e.g., Michael McCloskey, Naive theories of motion, in Dedre Gentner and Albert L. Stevens, editors, Mental Models. Lawrence Erlbaum Associates, 1983.) You may find this definition from Wikpedia especially traces this arc in the steady dis[atching of naive physics by real physics:

"Na•ve physics or folk physics is the untrained human perception of basic physical phenomena. In the field of artificial intelligence the study of na•ve physics is a part of the effort to formalize the common knowledge of human beings.
Many ideas of folk physics are simplifications, misunderstandings, or misperceptions of well understood phenomena, incapable of giving useful predictions of detailed experiments, or simply are contradicted by more thorough observations. They may sometimes be true, be true in certain limited cases, be true within a large degree of approximation, or predict the same effect but misunderstand the underlying mechanism.

Examples

Some examples are:
What goes up must come down.
A dropped object falls straight down.
A dropped lead cup hits the ground before a glass cup dropped at the same time and at the same height.
An object is either at rest or moving, in an absolute sense.
Two events are simultaneous or they are not.
The ideas that the world is flat, and that the sun and moon orbit the Earth (the geocentric model), were also, until about 2000 to 500 years ago, part of mankind's commonsense understanding of the world.
These and similar ideas, in some cases too obvious for anyone to think of questioning them, were the basis for the first work in formulating and systematizing physics, e.g., by Aristotle and the medieval scholastics. In the modern science of physics, they were gradually contradicted by the work of Galileo, Newton and others. The final one survived until 1905, when it was contradicted by the special theory of relativity."

Wikpedia, "Naive Physics". I personally am not especially susceptible to inappropriate mixing of physics and feeling, but that is because I work pretty hard at understanding the difference so I can accurately explain things to people not as deeply interested in physics or feeling as I perhaps am.

5. "Toe-flow" putters present an interesting sensory feedback to the golfer, while the face-balanced putter removes that sensory feel in the hands. Toe-flow putters require a fully conscious awareness of the unbalanced putter head, while face-balanced putters can be ignored if the golfer depends on a non-conscious gross motor movement body and dead hands putting stroke. Personal preference may be the factor that dictates which type of putter the golfer chooses.

So-called "toe flow" putters do not, as you suppose, "require a fully conscious awareness of the unbalanced putter head." Some putters are more "toe flow"ed than others, and not even a fully "toe flow"ed putter results in "fully conscious awareness" as you suggest. I don't think you completely appreciate what is meant by "conscious," either in terms of processes and time-course or more simply in terms of experiential content. (See, e.g., David J. Chalmers, The Conscious Mind: In Search of a Fundamental Theory (Oxford Univ. Press 1996). The "toe flow"ing of a putter doesn't add much contribution to conscious awareness at all, especially as there is no comparison involved with a non-"toe flow" experience, the feelings are subtle and require pretty intense focus and attentional resources to experience in awareness, and none of this sort of attention is utilized in putting anyway, as the attentional resources are limited and almost always otherwise occupied. Your notion of "a non-conscious gross motor movement body" doesn't mean anything to me. Movement is accompanied by a mixture of conscious, subconcious, and NON-conscious processes, but understanding the processes in the generation of movement in the animal brain (including the human animal) at an instinctive level takes us to meaningful discriminations about fine moto versus so-called "gross" motor movements and everything in between. I certainly don't "ignore" the feelings generated by a non-conscious gross motor movement produced by torques of the handle against the tactile mechanoreceptors of my hands and fingers -- to the contrary, I teach that the hand feeling serves to monitor the tempo of the stroke in gravity, as sharp inertial forces in abrupt, poorly-timed movements of the putter signal the hands that the stroke is out of pattern. Your sentence -- "Personal preference may be the factor that dictates which type of putter the golfer chooses." -- is precisely what I fight most against: the idea that whatever the golfer chooses is best for him, or even more strongly, the notion that whatever he can find to work best for him is best. The fact of the matter is that "personal preference" can't hold a candle to "intelligent choices." Helping golfers discriminate among choices is what teaching is all about, never personal preferences. personal preferences are what you need to get better than.

I really appreciate getting challenged on some of these ideas, so please don't feel I am being overly aggressive in responding. I'm just real sure about most of what I say before I bother to say it.

Cheers!

Geoff Mangum
Putting Coach and Theorist
PuttingZone
http://puttingzone.com>
Golf's most advanced putting instruction -- you're either in the PuttingZone, or not.

Thanks Geoff .... now let's just cut to the quick on the issue of pendulum drop and kinetic energy. Take your putter and prop it up against a vertical plane like a smooth door ... draw a line on the door at the top of the grip and then draw another line 1.35" (~1 3/8") higher .... raise the putter to the upper line and then drop it vertically. That's an approximate example of a generous amount of kinetic energy at impact when the putter is swung pendulum-like. This is based on the correct calculated rise of 1.35" on your 54" putting radius and 12" backstroke .... and applying the rules of Newtonian physics.

As for the vertical rise and drop of your distal hands and assuming a 34" putter with 20" from your left wrist joint to the pivot center (for a total 54" radius) ... let us assume that the center of the overlapping hands occur at the left thumb or about 24" from the pivot center. Overlaying this on your 12" backstroke and 1.35" putter rise and proportioning it for the hands, we get: 0.6" hand rise and ~5" hand backswing.

So using your example of raising your left arm above your leg when seated and letting it drop to "feel" the kinetic energy ... raise your left arm 0.6" (~5/8") and let it drop to feel the kinetic contribution to the gravity drop of the arms .... not much .. eh ?

Now let's get back to the full putting stroke. On the backstroke you say you lower your lead shoulder which pushes the lead hand, and you then must raise the rear shoulder and that pulls up the rear hand ... and since both hands are holding the putter grip there is an applied torque from the shoulders to raise the putter head 1.35". This applied torque is generated from the torso core muscles. In effect the putter is part of a cantilever assembly being raised a rather small distance.

Just before the putter is reversed, it must decelerate and stop instantaneously to reverse, and the resistive force for deceleration is generated from the shoulders and core muscles again. From the reversal stop point, the arm-hand-putter assembly must accelerate to impact, and that is generated by a combination of gravity and applied torque as the lead arm is pulled and the rear arm is pushed by the applied rotation of the shoulders. The putter is pushed and pulled with the hands over a very short distance to reach the desired putter head velocity.

Since the hand grasp pressure on the putter handle is rather light, there is virtually a sensation of disconnect between the hands and the putter after the initial acceleration forces from the reversal point. The ~5" of hand movement and the 0.6" of hand rise are for all significant purposes a linear motion. The visual impression that a pendulum stroke has occurred is based on the rotation of the shoulders and the movement of the putter head. The short sensation at the hands deceives one into believing a significant pendular motion has occurred all due to a "gravity drop" of 0.6" at the hands and 1.35" at the putter head. The inclined putting stroke has a horizontal component that must also be considered, which adds to the torque contribution. Proper free-body vectoring of the putting stroke must be done and not only viewed as a pendulum-like motion from a face-on position.

Perhaps a better definition of the putting stroke is that it is a partial torque and partial ballistic rather than a pure pendular motion ... because the putter is pushed and pulled at the reversal from back to downstroke ... gliding through impact and then caught at the end of the followthru. Because the distances moved are short, the putter is virtually thrown at the ball because the applied torques are very much greater than any pendular kinetic energy.

The deceptive nature of the putting stroke is aggravated by the perception of "pendulum" kinematics without considering the "torque" kinetics .... a common mistake made by those who use "intuitive" physics and no qualifications to analyze nor apply Newtonian physics.

Yes it's a torque "stroke" as well as a gravity "swing" .... and the belief that it is a "pendulum" is only a neuroscientific delusion. That is my contention and contribution to this topic.

Dear Sammy,

I appreciate your contributions! It would be helpful to me and others if you could disentangle the steps a little with your own physics analysis. Would you provide us all with a free-body force diagram and some calculations using a typical golfer's arms and a sample putter?

If you don't believe in a gravity-sponsored stroke as having enough juice to power a putt, perhaps you could cut to the chase and take a look at a putting "robot" sometime. That is a mechanical pendulum that the operator makes stroke a putt simply by setting the height of the backstroke. Dave Pelz has one he named "Perfy".



The makers of the PuttingArc have another one. or you can make one with a putter simply by holding it at the top of the handle very lightly -- setup at a ball on your carpet and pull the putter back to raise it off the ground whatever height you are interested in and then let it free-fall into the back of the ball and just look at how far the ball rolls.

One of the drills I do regularly I call "Cupid's Bow": I make a backstroke with two hands and then at the top of the backstroke I release the rear hand from the handle like Cupid when he "plucks" his bow; the putter and lead arm are then allowed to swing freely under the pivot of the sinovial joint of the lead shoulder. There is no torquing coming down. The shoulder is still, the shoulder frame stays level, and the arm is not extending or lifting. These "Cupid Bow" strokes are strokes I make on putts right after making regular strokes, so I am familiar in advance with the size of the backstroke. I make the same size backstroke then when I switch to the "Cupid's Bow" drill and the balls roll the same distance. It's possible I have some very slight torquing that I'm not aware of, but I've done this thousands of times and now I'll do it more paying specific attention to the presence or absence of torquing, at your nice suggestion.



There is a great story told by physics genius Richard Feynmann, relating how his father taught him to be a scientist. His father asked the boy once what would happen to the baseball in the bed of the wagon if he pulled the wagon along. Richard said it would come with the wagon. His father said he should try it and just watch without preconceptions and then honestly tell him what he saw.

The moral of this is multivalent, but surely it means that "thinking and analysis" alone is not good science. You have to find out by doing and observing what actually happens and then honestly report accurate and relevant observations. Then the thinking and analysis starts afresh with the most recent information. This is something I have been doing for between 2 and 5 hours daily on a putting green seven days a week for 16 years. That's very nearly 4 million little "experiments" of one sort or another, and the count continues to grow. If anyone wants to help me with the building of an apparatus or research design and study, or funding, that would be absolutely peachy! In the meantime, I'll work on your suggestions to make sure I am seeing what is really happening and then I'll honestly report. That's hard work, but hey! someone's got to do it!

Cheers!

Geoff Mangum
Putting Coach and Theorist
PuttingZone
http://puttingzone.com
Golf's most advanced putting instruction -- you're either in the PuttingZone, or not.

Geoff:

I have tried to do a free-body diagram (FBD), but it seems to falter due to the human components, particularily at the hands. I can make assumptions to simplify the analysis, but again it fails due to the human components. So I just look at the boundaries and work back, and all I can do is isolate the putter from the human body.

For example, in the straight putter stroking, there must be a minute amount of flattening out the inclined circular motion, and this minutely reduces the elevating of the putterhead in the backstroke. Since many putting strokes are less than the 12" we have considered, we must also evaluate a 6" backstroke and it only has ~0.25" of circular rise .... hardly a significant potential energy level to be converted to kinetic energy in pendulum motion. Also this is the measurement at the sole of the putter and not properly higher up at the center of mass which is even less swing elevation than the putter sole. Do you get the significance of these numbers in the context of Newtonian physics?

As for the human body components, I again refer you back to my previous example of clasping both hands together and bringing the hands back about 6" which is the approx displacement for a 12" backstroke ..... then attempt to drop the hands and arms to vertical in a pendulum-like manner. Then place a 2 lb. dumbell between the clasped hands to concentrate the putter mass at that point and then do the same attempting to sense the force of gravity on the 6" backstroke. I challenge you to say that you "feel" the freewheeling flow of a gravity-sponsored pendulum swing ... by isolating the arms from the putter. What is your biomechanical analysis of this example experiment?


Obviously the mechanical putting robots are not equivalent to the human body + putter assembly. The arms divide the pendulum and the human joints do not function like the mechanical joints. Human joints have internal friction. Also these robots do not appear to articulate for a straight line putting action on an inclined plane, unless my assessment of the mechanism is not correct from the pictures shown.

The human body cannot be abandoned to gravity forces for very small movements if the internal joint resistances are significant. In my assessment, the neuro-muscular activity needed to execute a putting stroke is greater than the energy required or acquired for pendulum action of the putter head over the short distances in normal putting. I think that the neurosciences will back me up on that conclusion.


I tried your Cupid's Bow drill in several orientations, and I couldn't get the same no-torquing results over distances found in a putting stroke. I felt that torque within the shoulder joint was required to initiate a positive downstroke movement for these short distances. For large swings I felt the effects of gravity but this cannot be projected to the normal putting stroke. That would be incorrect.


"Science is built of facts as a house is built of bricks; but an accumulation of facts is no more science than a pile of bricks is a house." Henri Poincare.

I have read much of your website and I was impressed at the accumulation of knowledge that you presented, however I am having difficulty as to how you arrived at the gravity-sponsored putting stroke and how you were able to unify all that knowledge into your putting theory. Perhaps that is my shortcoming, but I believe that science should simplify .. not complicate. Perhaps you are projecting your many anecdotal experiences into a universal theory without a complete basic analysis. Continue your research because most theories are built on the shoulders of other's ... !!


I do enjoy our discussion, and I appreciate your efforts to explain your putting theories.

Dear Sammy,

You need a hands-on lesson. Your difficulty experiencing the gravity-sponsored putting stroke is by far the common experience of almost everyone who tries it without a qualified instructor's guidance. This is illustrated to me daily when I ask golfers (of any skill level or experience) to relax while standing still and allow me to lift their arm to horizontal and then drop it. If I were a butcher lifting meat above a table and then dropping it back onto the table, I would swear that meat can float in the air!! No one's arm ever drops -- the golfer is too much "in control". I usually have difficulty getting the arm lifted without intervention by the golfer, as well. It usually takes a few minutes of illustration to show them what a "drop" looks like. They are all surpirsed to see an arm drop!!

What is going on here neurologically is the opposite of voluntary movement. The basil ganglia and most of the brain's motor control processes are not positive, but negative. That is, "inhibition" of signalling is more important than signalling. That's how the brain can focus its processes appropriately, by cutting out the irrelevant. Almots all effective brain function depends upon cutting out the irrelevant so that assets are marshalled to good effect. There is a HUGE difference in the "feel" of a voluntary movement against gravity, the holding of a putter at the top of the backstroke against gravity, and the "release" of the muscle activiation by what is commonly called "relaxing".

With this in mind, again, let me respond seriatim:

"For example, in the straight putter stroking, there must be a minute amount of flattening out the inclined circular motion, and this minutely reduces the elevating of the putterhead in the backstroke."

This is incorrect, as maintaining the elevation and stability of the pivot is key to a good stroke. Also, the relaxed hanging of the arms precludes "sticking" or "extending" the arms to a greater length than at address during the stroke. The whole idea is to allow the putter to rise as required by the restraint of the "tirangle" to the pivot.

"Since many putting strokes are less than the 12" we have considered, we must also evaluate a 6" backstroke and it only has ~0.25" of circular rise .... hardly a significant potential energy level to be converted to kinetic energy in pendulum motion. Also this is the measurement at the sole of the putter and not properly higher up at the center of mass which is even less swing elevation than the putter sole. Do you get the significance of these numbers in the context of Newtonian physics?"

Apparently you haven't simply tried this with a putter on a carpet. It works fine. The point is not does the putted ball with a 6" stroke roll FAR, but whether you know how far it will roll. Then the brain adjusts the size of the stroke for the distance, instinctively. Most golfers, by far, are bad putters, and pros aren't as good as they think, either. The size strokes you describe ("since many putting strokes are less than 12") are strokes made by bad golfers, and a better golfer on the green is likely to make a larger stroke for the same distance over which other golfer perform so poorly. A slower stroke is a bigger stroke.

"As for the human body components, I again refer you back to my previous example of clasping both hands together and bringing the hands back about 6" which is the approx displacement for a 12" backstroke ..... then attempt to drop the hands and arms to vertical in a pendulum-like manner. Then place a 2 lb. dumbell between the clasped hands to concentrate the putter mass at that point and then do the same attempting to sense the force of gravity on the 6" backstroke. I challenge you to say that you "feel" the freewheeling flow of a gravity-sponsored pendulum swing ... by isolating the arms from the putter. What is your biomechanical analysis of this example experiment?"

"Feel" in a free-fall of the hand on earth comes solely from air resistance against the skin receptors. You are describing collisions of two masses, or are describing the sensation of the hand resisting the free fall of mass. "Feel" in the hands on the putter only happens when something changes -- grip pressure or toquing forces of the putter against the inside of the hands activating tactile receptors. In an un-torqued, free-fall of the hands and putter handle in synchrony, there is "no feel" of the mass of the putter or the forces of torquing. Ask Albert Einstein if you don't believe me.

"Obviously the mechanical putting robots are not equivalent to the human body + putter assembly. The arms divide the pendulum and the human joints do not function like the mechanical joints. Human joints have internal friction. Also these robots do not appear to articulate for a straight line putting action on an inclined plane, unless my assessment of the mechanism is not correct from the pictures shown."

Your assessment is not correct. The key to any putting robot is the manner the arm assembly is hinged to an axis of rotation. In the case of a vertical shoulder plane of motion, the axis of rotation at the hinge is level with the ground. If the axis of rotation is a small rotating pipe at the level of the "neck" and this pipe extends frontally and perpendicularly from the torso of the robot, and the arms assembly suspends from and rotates on this "pipe" as a pivot, then the putter head will move in a pendulum swing in a vertical plane of motion even though it is out farther from the feet than the pipe. The question is whether a human body can do the same, and the answer is certainly: I teach it and do it all the time, as do other putting instructors. I could teach you also. It's not hard to learn.

"The human body cannot be abandoned to gravity forces for very small movements if the internal joint resistances are significant."

Yes it can, and does so probably 40-50% of all human movements everday on earth among 6 billion plus humans, and has been doing so since before the apes climbed down out of the trees, and will continue to do so for as long as Ol' Sol doesn't baloon up and incinerate us all. That's partially what happens in an arm swing during walking, for example. Some of it is torquing by the shoulder frame swinging as we walk, and some is just relaxation in gravity. And your term "abandonment" is sort of a straw-man exaggeration to help win a point, as this falsifies what is happening. The golfer does not "abandon" the arms to gravity, but "allows" the upraised shoulder-frame-torso of the "triangle" as a whole to fall back to level equilibrium under the influence of gravity. The "triangle" itself has to be maintained in form with a certain mimimal and steady tonic muscle activation or tone. The word "let" the putter fall more accurately captures what is happening than the notion of "abandoning" muscles and body parts to gravity's mercy.

Moreover, your notion of "internal joint resistances" is not accurate anatomy. The human shoulder frame has a normal range of motion in a lateral sense of about 5" -- that is, you can "hunch" your shoulders 5" above their resting level. The human upper torso and spine has a normal range of motion laterally within which the left shoulder can be dipped towards the left hip nearly 10". Just try it yourself. And the synovial fluid of the human shoulder joint is the most highly prized lubricant known in Nature -- much better than whale oil, for example. So given the ranges of normal motion, a shoulder dip that traverses at most a 3" long path curling down and under the starting position does not offer much impedence to the gravity-sponsored "righting of the ship". Perhaps there is a little element of springiness in the structural response of the human torso in this situation, but it ain't much and it also ain't voluntary.

"In my assessment, the neuro-muscular activity needed to execute a putting stroke is greater than the energy required or acquired for pendulum action of the putter head over the short distances in normal putting. I think that the neurosciences will back me up on that conclusion."

I think neuroscience generally backs up facts. The way you have phrased this proposition is not an accurate statement of the facts as I have described them. The energy of a pendulm free-fall of the "triangle as a whole" generates quite a bit of force thru the ball, completely without voluntary torquing of the putter down by the human. You underestimate reality quite a bit here, probably from not doing much putting. It is not about the simple dropping of a putter head mass from 1" off the ground straight down, but the gathering velocity of the total system of the shoulders, arms, hands, putter and putter head falling under and across on the pendulum path with a 4.5-foot length. That alone in a semi-rigid system can move the ball with plenty of energy. But there is also as I have said the uplifting of the shoulderframe thru the bottom delivering this hefty system into the back of the ball. Please look again at the measurements from Nicklaus, as he does not use very much torquing at all on the way down -- it is sparse and carefully restricted to the mid-region only of the downstroke. Doubtless this (as does my shoulder upstroke) adds something significant to the velocity and thus momentum of the blow thru the ball, so it is part of what I describe. Given these facts, I'm pretty sure my ceaseless study of neuroscience over 16 years gives me a better position for betting who's right about the neuroscience entailed in these particular facts. Wanna bet?

I tried your Cupid's Bow drill in several orientations, and I couldn't get the same no-torquing results over distances found in a putting stroke. I felt that torque within the shoulder joint was required to initiate a positive downstroke movement for these short distances. For large swings I felt the effects of gravity but this cannot be projected to the normal putting stroke. That would be incorrect."

That's because you are like almost all golfers and don't really know what it is to relax and drop the arms. (See above.) You may think you do, but I have plenty of experience to the contrary with golfers who also think they can do this. They don't really get the difference between a voluntary muscle movement and a relaxation, nor do they comprehend just how much normal muscle tension they carry around with them controlling and presenting their body parts according to subconscious preferences.

"Science is built of facts as a house is built of bricks; but an accumulation of facts is no more science than a pile of bricks is a house." Henri Poincare."

Absolutely agreed! Frank Thomas, the former USGA science guru, is fond of proclaiming: "To measure is to know." Well, it's not. To measure something, you first have to decide what and how to measure. Once you obtain the measurements, you have to know how to interpret and understand the data. It's only then that "knowing" of the process or phenomenon under investigation seriously begins.

"I have read much of your website and I was impressed at the accumulation of knowledge that you presented, however I am having difficulty as to how you arrived at the gravity-sponsored putting stroke and how you were able to unify all that knowledge into your putting theory. Perhaps that is my shortcoming, but I believe that science should simplify .. not complicate. Perhaps you are projecting your many anecdotal experiences into a universal theory without a complete basic analysis. Continue your research because most theories are built on the shoulders of other's ... !!"

"Science should be as simple as possible, but not simpler." - Albert Einstein. That's why you need a teacher. Perhaps you are not able to follow my efforts simply by reading, and need some guidance. Glad to provide it! As should be obvious.

Cheers!

Geoff Mangum
Putting Coach and Theorist
PuttingZone
http://puttingzone.com
Golf's most advanced putting instruction -- you're either in the PuttingZone, or not.

Geoff:

Will you provide your formal qualifications to interpret and apply scientific knowledge? What are your formal educational qualifications since you seem to present yourself to the public as an authority in many fields?

Just reading and studying text books does not count unless you have been examined and certified as competent by professionals in the fields. You cannot present yourself as an authority on various sciences because you have read books, research papers, internet information. Unqualified knowledge cannot be given much weight in any scientific sense.

This should have been established before we started our lengthy discourse.

...............................................

I have parsed your above message sentence by sentence but it is too confusing to respond to in any conclusive way. I obviously cannot comment effectively on your personal anecdotal experiences, nor can I properly explain Newtonian physics in this forum format and that is my problem.

My impression of your knowledge of Newtonian physics is that you have never had to analyze or design anything using that science. If so I highly recommend that you obtain an assessment of your beliefs from somebody like a Professor of Mechanical Engineering - Statics & Dynamics ... and perhaps one who has worked in Biomechanics too. That would help you understand the application of the Laws of Motion to the putting stroke as you interpret it. Also seeking direct advice from somebody recognized in the field of Motor Control will be of help too.

However there is one passage in you posting that I must take exception, namely your response to me here:


"The energy of a pendulum free-fall of the "triangle as a whole" generates quite a bit of force thru the ball, completely without voluntary torquing of the putter down by the human.

You underestimate reality quite a bit here, probably from not doing much putting.

It is not about the simple dropping of a putter head mass from 1" off the ground straight down, but the gathering velocity of the total system of the shoulders, arms, hands, putter and putter head falling under and across on the pendulum path with a 4.5-foot length. That alone in a semi-rigid system can move the ball with plenty of energy."


To me this suggests your misunderstanding of Newtonian physics as applied to the pendulum and your attempt to transpose it to the human body without qualification. You claim there is "quite a bit of force" without quantitative proof of your assertion. I think the onus is on you to provide unequivocal proof since you are presenting yourself as a scientific-based authority.

I have paid the price in putting practice and personal research to understand what is happening, and I believe I can critique your theory based on my knowledge of Newtonian dynamics.

As for your rejecting the "simple dropping of the putter head mass 1" off the ground straight down" and then claiming that "the gathering velocity of the total system" in your gravity-sponsored pendulum-like putting stroke are not validly related only confirms your misunderstanding of Newtonian physics as applied to pendulums. What "gathering velocity" ?

Then your unsupported assertion of: "That alone in a semi-rigid system can move the ball with plenty of energy." .... without properly quantifying "plenty of energy" ... and again raises questions like: "How much "energy"? Judging the "energy" by the distance the ball rolls is not proper proof of "plenty" in any scientific sense. Newtonian physics must be backed up with correct numbers to back up your theories.

You have obviously staked your reputation on your interpretation of the putting stroke based on your personal research and conclusions. Thank you for your response to my postings and good luck in your future endeavors.

Dear Sammy,

Your tone is growing offensive and abusive (see the Rules of the Forum). Is there something specific you would like me to address?

A mildly-torque stroke is a very high-level skill. My contribution is to connect the timing of the torquing to the timing of a gravity-sponsored free-fall. This takes repeatability, preditability, and accuracy of putting up a very good notch for anyone who learns it. My researches are researches that I have carried out, but I have also studied golfers in history and of today in great extent, and I don't in the least shy away from learning something new. What do you have to teach me?

I generally have little regard for people who toss about scientific lingo without backing it up with real contributions. If you have some knowledge, share it. Otherwise, please don't misuse the good will of the people who come to this forum.

Do you have something specific to tell people from a scientific or experiential perspective? if so, then share it without getting abusive. You're more than welcome here as a contributer, even as a disprover. If that's what you feel you know, then just share the details and leave the emotional colorings out, please. Whoever makes more sense is the one who is correct.

Cheers!

Geoff Mangum
Putting Coach and Theorist
PuttingZone
http://puttingzone.com
Golf's most advanced putting instruction -- you're either in the PuttingZone, or not.

Looking back over the last from Sammy, there are some interesting questions there that should be addressed, so let me try to shed some further light here:

Sammy writes:

"You claim there is "quite a bit of force" without quantitative proof of your assertion. I think the onus is on you to provide unequivocal proof since you are presenting yourself as a scientific-based authority." .... As for your rejecting the "simple dropping of the putter head mass 1" off the ground straight down" and then claiming that "the gathering velocity of the total system" in your gravity-sponsored pendulum-like putting stroke are not validly related only confirms your misunderstanding of Newtonian physics as applied to pendulums. What "gathering velocity" ? ... Then your unsupported assertion of: "That alone in a semi-rigid system can move the ball with plenty of energy." .... without properly quantifying "plenty of energy" ... and again raises questions like: "How much "energy"? Judging the "energy" by the distance the ball rolls is not proper proof of "plenty" in any scientific sense. Newtonian physics must be backed up with correct numbers to back up your theories."

Okay, challenge accepted.

In a two-particle collision, the "momentum" of one mass transfers to another mass. Momentum is velocity times mass. (A basketball of say 0.5 kg traveling 5 mph has a lot less momentum or "punch" than a bowling ball (mass 6 kg) traveling the same velocity -- 30 times less.) If the second mass is stationary to begin with, its momentum is zero to begin with. The main idea is that no energy is lost -- the energy of the whole two particles before impact and after impact doesn't change, it just moves from one particle to the other during the collision. The expression for this basic truth is [just before impact] (Mp*Vpi + mb*Vbi) = (Mp*Vpf + mb*vbf) [just after impact], where Mp is the putter head mass (360 grams), Vpi is the initial velocity of the putter head at the moment of impact, Vbi is the initial velocity of the ball (zero), mb is the mass of the ball, and Vpf is the velocity of the putter right after impact and Vbf is the velocity imparted to the ball right after impact. The expression for the Vbf after impact is Vbf = Vpi * (1+e) * (Mp)/(Mp + mb). So the momentum of the ball after impact is Vbf*mb. The "force" depends upon how quickly the ball goes from zero to Vbf.

The "gathering velocity" is the gravity-sponsored acceleration of the putting "triangle" as it drops from the top of the backstroke down to a peak speed at the bottom of the stroke. In the case of a 12" backstroke (as previously defined), the putter head rises off the ground 1.35" at the top of the backstroke. At this position, the "velocity" of the putter head is zero. At the bottom of the swing the putter head velocity is 32 inches per second. This velocity "gathers" smoothly coming down under the influence of the force of gravity (from Newton, F=ma, where a is "g", the acceleration from gravity on mass). The "force" imparted to the ball may be viewed by the model of "a rock on a rope," as traditionally physicists model a pendular collision of the bob mass against another mass by ignoring the mass distribution of the "rod" and treating the "bob" as an idealized point mass. The momentum of the putter head transfers during the collision into the ball, and gives the ball a change in velocity from zero to an initial translational speed by the equation Vb = Vp * (1+e) * (Mp)/(Mp + mb), where Vb is the ball's initial velocity across the green right after impact, e is the coefficient of restitution of the ball (0.75), Vp is the putter head velocity at impact (32 inches per second), Mp is the mass of the putter head (360 grams), and mb is the mass of the ball (45 grams or 0.045 kg). The predicted velocity of the ball would then be 50 inches per second. Putter-ball impact last no more than 0.01 second. For a ball to change from zero velocity to 50 inches per second during the impact in 0.01 second, the "acceleration" imparted by the putter head is 50 / 0.01 is 5,000 inches / second / second or 19.7 meters/sec.^2. With the ball mass being 0.045 kg, the "force" applied by the putter head is 0.885 Newtons ("N" in SI units). For conversion to the English system where mass is "slugs" not "grams" and force is "pounds" (lb), 1 lb = 4.45 N. So 0.885 N / 4.45 N/lb = 0.2 pounds of force. In the cgs system of units (gram and cm's), the force is called "dyne" and 1 dyne = 10^-5 N. So 0.885 N / 10^-5 N/dyne = 88,500 dyne (or g*cm/sec^2).

In comparison, take the "force" and "gathering velocity" in the example of a putter head dropping vertically 1.35 inches onto a golf ball. What "force" is applied to the ball? How fast would the ball be traveling after impact if this force were applied horizontally for 0.01 seconds?

Any mass in gravity drops at the same rate (Galileo). A putter head of 360 grams will drop 1.35" according to Newtonian physics F = Mg, where g is the acceleration of gravity (32 feet per second per second, or 384 inches / sec.^2 or 9.8 meters / sec.^2). The acceleration "a" is the change in velocity over a time period, which is expressed mathematically as (Vf - Vi) / t, where Vf is the final velocity and Vi is the starting velocity (in our case, zero). We have only the distance 1.35" to start with, plus gravity, so we need the formula that relates distance traveled to velocity. Because the velocity changes in acceleration, we have to use "average velocity," which is all the different velocities divided by the number of velocities. If we had a million data points, we would know something. We don't; we have just two velocities: zero and the maximum (Vf) after 1.35" of free-fall. The distance D of travel under a steady acceleration is D = (a*t^2) / 2 and in the case of gravitational acceleration = (g*t^2) / 2. Isoltaing t, the equation is t = SQR(2*D/g). We have g (384 in./sec.^2) and we have D (1.35"), so t = 0.083 seconds. That's how long it takes a putter head in gravity to drop 1.35". How fast is the putter head moving when it hits the ball? The formula is Vf = Vi + g*t, and answers the question how long has the accelerating force been applied, as that tells how fast the mass gets going in the end. Vi = 0, so ignore that. Vf = g*t, with t being 0.083 sec. So Vf = 0.083 * 384 = 32 inches / second at impact. That is exactly the same velocity of the pendular swing of the putter head, so the forces of impact are identical and the acceleration imparted to the ball and the ball's velocity after impact would be the same as well.

Now to a tougher issue: taking the "triangle" as a rigid whole that swings beneath a fixed pivot under gravity, does this imply something MORE than "a rock on a rope" model of forces? If so, what, exactly?

Another way of asking this is: Considering a robot, is the putter head mass and velocity ALL that matters to the transfer of momentum to the ball? Or does the mass distributed thru the total triangle participate in some way?

If the focus is on the brief interval of contact between the putter head and ball (less than 0.01 sec.), the key word beomes "rigid." If there is ANY appreciable felxibility in the "triangle" (whether from the face of the putter, the hoseling, the flexibility of the shaft, the hand-handle connection, or even the structure of the golfer's limbs and body and his stability in his stance, this tiny time frame for contact means that the transfer of energy from putter head to ball is essentially uninfluenced by anything other than the putter face and the putter head. So, the answer is "no," not usually. It would require something especially "rigid" AND quick to change the forces during impact to any significant degree from what they are at the start of contact.

Now to a subtle issue: If the golfer torques the stroke somewhere near the bottom of the stroke to increase the velocity of the putter head from 32 inches per second to 50 inches per second, what sort of forces are involved?

The angular increase in velocity is due to an angular acceleration applied for a specific time. How much time is available? In other words, if the acceleration begins at the bottom with the ball played 2" further along the arc of the stroke, and the beginning velocity is 32 in./sec. and the ending velocity is 50 in./sec. (so that the average velocity thru this 2" span is 41 in./sec.), how long does it take to span 2" at 41 in./sec.? D = V*t so t= D/V, with D being 2" and V being 41 in./sec. Thus t = 0.048 seconds, the time the putter face takes to travel from the bottom of the stroke into the back of the ball in this particular movement.

Acceleration (a) is the change in velocity over the time span, so a = (50 - 32) / 0.048, or 369 inches / sec.^2. The "force" is the mass times this acceleration, but the trick question is "what mass? -- the putter head only or the distributed mass of the whole triangle"?

The answer is pretty complex, but put simply: The angular acceleration has to act on the whole rotating mass in a specific way described by newton's First Law: an object at rest or in a state of constant velocity tends to remain at rest or in the same velocity unless acted upon by a force that accelerates the object to a different velocity. This is the expression of Inertia's resistance to change without the application of force (thank goodness, too, or else things would move by themselves and not change with regularity and the universe would really suck!). in the case of rotational inertia, as opposed to linear inertia, the resistance is called "moment of inertia" (MOI). The MOI depends upon the distribution of mass in relation to the axis of rotation. In the case of a golfer swinging a putter, the mass that rotates is not simply the putter head, but the whole ensemble of shoulder frame, arms, hands, and putter about the pivot. the MOI is the totalling of every separable piece of mass and considering separately how tough it would be to get that specific pice rotating. The farther out from the center of rotation a particular lump of mass is located, the tougher it is to accelerate.

"Torque" (denoted by "tau") is MOI (denoted by "I") times acceleration. Tau = I*a. "This is the rotational equivalent of Newton's Second Law [F = m*a]." The MOI in the case of rotational motion plays the same role that simple mass does for linear or translational motion. So what exactly is MOI?

MOI is the sum of all specific mass points in a system multiplied individually by the radius squared from the center of rotation to that specific point mass. If a specific point is 2 cm from the center of rotation and weighs 3 grams, the MOI is 3 * (2*2) = 12 g-cm^2. If a second point mass is 8 cm away and weighs 2 g, the MOI there is 2*(8*8) = 128 g-cm^2, over ten times more inertia than the more massive but closer in point mass. The TOTAL MOI of this two-point system is just 12 + 128 = 140 g-cm^2.

So the force required to move different shapes of masses is not like the force required to move identical but differently shaped masses linearly. The shape (the way the mass is distributed and concentrated) matters for rotational force. That's the hard part: figuring out the shape of a specific golfer's mass in his shoulders and arms and hands as well as the mass as distibuted throughout his putter.

VERY ROUGHLY, we can just throw in some approximate guesses and see what the forces are. Guessing that two human arms weigh about 10 pounds (4.48 kg), and the putter weighs another pound (0.448 kg), the total system has a mass of about 5 kg. How is that mass distributed from pivot to sole of putter? Well, the great bulk of it is between the shoulders and hands, not from there down to the sole of the putter. Where might we find the center point of balance if we set the whole "triangle" (cut from the golfer's body) onto a balancing fulcrum so it rested there horizontally? Just guessing, perhaps one-third the way down from pivot to sole. If the distance of the whole is 4.5 feet from pivot to sole (54 inches), then the center point is 18 inches out from the pivot towards the sole. If we simply assumed the system is not arms etc. but a wad of mass (5 kg) on the end of a massless stick 18 inches long, we can get a sense of the force (torque) required to move that mass. Specifically, we want to know how much torque is needed to accelerate the 5 kg mass from 32 inches per second angular velocity to 50 inches per second angular velocity in 0.048 seconds. Or, how much torque is required to affect the rotational velocity with 369 inches / sec.^2 of angular acceleration?

The simple formula is tau = I*a, where here I = the MOI of the blob 18 inches out, and a = 369 inches / sec.^2. The MOI is mass * radius^2, with mass = 5 kg and radius = 18 inches or 0.4572 meters. The torque is 1.05 kg-m^2.

But let's look at another "movement" -- one where the lead shoulder "pulls" the left arm and putter weighted down by the right hand and arm all as a unit along the line from lead shoulder socket to putter sole, right when the sole is at the bottom of the stroke, and continues pulling until the putter face hits thru the ball. This is NOT the same as a torque applied by the right hand to the triangle to speed it up, or even the torque provided by the human body in general to the pivoting triangle. In this case, the relevant rotation is the lever from pivot out to lead shoulder socket (typically about 7.5" to 8" in length). In this "shape", the weight (mass) of the right side of the system doesn't contribute much to what the lead shoulder needs to do to lift the mass directly beneath it on that line of lifting. So the mass at the end of the lead shoulder is not much more than 2.5 kg. How "fast" is this shoulder moving when the stroke reaches the bottom and the putter head is moving 32 inches per second? At that time, the shoulder is level with pivot at the base of the neck, which is effectively the spindle on a record player when the putter head is the far edge of the album. If the "album" has a radius of 54", the putter head in one second traverses 32 inches of the circumference, which is 2*pi*r. The circumference of the stroke is 339 inches, so 32 inches is 32/339 or 9.4% of the total 360 degrees, or 34 degrees of rotation every second. If we look at a point that is merely 2" out from the pivot / spindle, this point moves 34 degrees as well in one second on its much smaller circumference. The circumference at a radius of 2" is 2*pi*2", or 2 * 3.14 * 2 = 12.5 inches compared to the 339 inches of the putter head's circumference. The distance the 2"-out spot travels in a 34 degree turn is 12.5 in. * 0.094 = 1.18 inches. That's not real, since for a 12" backstroke, the lead shoulder dips along the bottom half of a "C" shape only a total of about 4 inches, while here we are examining only the shoulder movement that corresponds to moving the putter head from the bottom of the stroke another 2" along into the back of the ball. Obviously, the effective distance of the shoulder "out from" the pivot is very tiny. So let's guess that level means level, but the spindle is at least 0.2" in radius and 0.4" thick. If the shoulder at the bottom of the stroke is considered to be moving on this radius, the circumference of this even tinier circle is only 1.25" around and the total movement over 34 degrees is only 0.12". While the putter head is moving at 34 degrees per second, so is this tiny shoulder action, and that is an angular velocity at the bottom of the stroke of 0.12 in./sec.

So how fast is the shoulder moving once the putter head has accelerated to 50 in./sec. over 0.048 seconds and 2" on the 339" circumference? Using ratios, 0.12 is to 32 as X is to 50, so X = 50 * 0.025 / 32 = 0.19"/sec.

Now how much FORCE does it take to accelerate the shoulder 8" (0.2032 meters) out from the pivot from 0.12 in./sec. to 0.19 in./sec. when it is dragging up a mass of 2.5 kg? The formula for this torque is just tau = lever arm * Force, or lever arm * mass*acceleration. The angular acceleration is from 0.12 to 0.19, which is 0.07 in./sec. or 0.0018 meters/sec. over a period of time of 0.048 seconds. So the angular acceleration (a) is 0.038 m/s^2. Thus the Force is 0.2032 m * 2.5kg * 0.038 m/s^2, which is 0.019 N-m, a torque.

Hey, that's a VERY SLIGHT torque for the shoulder to produce. It's not the hand but the shoulder that produces this. That's the basic truth of the full swing applied to the putting stroke: the shoulder turn is far more powerful than swinging the arms. The lever multiples effort. You have to be careful with the timing of the upstroke not to overdo it, because of the power available in the levering up of the little old putter!

But in more general terms, the free body diagram of the shoulder stroke is not about the hands! So the critical torques are much, much closer in over very short distances and tiny movements.

There are some assumptions here about angles and the like, but in the grand scheme of things, I believe this portrayal of the critical torques in a shoulder stroke are pretty accurate and remove a lot of misconceptions about the physics at issue. If I am significantly incorrect in this, will someone with details please show us the error of our ways?


Cheers!

Geoff Mangum
Putting Coach and Theorist
PuttingZone
http://puttingzone.com>
Golf's most advanced putting instruction -- you're either in the PuttingZone, or not.

Dear Geoff:

I sincerely apologize to you and the Forum if my last posting has been construed as improper. In hindsight I may have come off as somewhat rude, for which I apologize again. In defense of myself I can only say that I am a bit frustrated in not being able to relate all of what you post to the issue of putting methods. Your presentation of your knowledge base is to say the least - overwhelming. I did attempt to isolate my points so they could be addressed in a clear manner. Again I apologize to you and the forum.


Now, you have stated something very interesting, that I don't believe you have stated before, namely:


A mildly-torque stroke is a very high-level skill. My contribution is to connect the timing of the torquing to the timing of a gravity-sponsored free-fall.


To me this signifies that you too experience an applied torque within the putting stroke, as I admit that gravity also exists and affects the stroke in a pendulum-like manner. The difference that exists between us, as I see it, is how much torque and free-fall exists in the stroke. It's as simple as that.

I attempted to illustrate, based on sound Newtonian physics, that the contribution of the force of gravity is minimal, particularily on short backswing strokes. I also provided a quantitative geometric contruct that closely approximated your 54" putting stroke radius.

The principle is very simple and scientifically valid. A pendulum weight on a pivoted string radius elevated say 6" above resting at vertical, will swing to vertical in the same time as will take a free weight dropped vertically from 6". When applied to a putting stroke where the putter sole may elevate from 0.25" to 1.35", the free-fall equivalent is I believe minimal compared to the torque required to accelerate and decelerate the putter-arm assembly.

Since you have acknowledged the shared torque/free-fall model of the putting stroke, I look forward to your continued research into the connection of the timing of the torquing to the timing of a gravity-sponsored free-fall. If you have any quantitative data to share with us on the relative contribution of each modality, please share it with us. If your intent is to replace torque with free-fall in the putting stroke, that would be unique if not revolutionary in the sport of golf.

Thank you for your patience with me, and I again apologize for my untoward behavior on your fine forum.