Geoff,
In your experiences teaching and playing what have you found to be the most effective way to "ride" the putter down from the end of the backstroke? It seems like any added power from any limb/hand while using this gravity stroke would be detrimental. Thank you.

Dear Kibler,

My thoughts recently are "never think of the downstroke until AFTER the backstroke is over."

I also have a thought that if I bring the putter down, it will drift out across the line, whereas if I "let" the putter (and hands, arms, shoulders with it) drop "where it wants to", the downstroke seems to work great and the hands stay close in above the line across the toes. Letting the putter down is real simple: just "drop the whole shebang beneath the pivot of the base of the neck" and "let the hands and arms drop where gravity wants them to drop" so long as the whole moving system swings beneath a still neck.

I guess part of the move down is to feel the hands swing straight above the toe line in an arc down to the bottom of the stroke right before the ball and then upward into the back of the ball. This vertical arcing of the stroke is mild and the hands and arms need to stay relaxed and "out there" without any sense of using the forearm muscles or "lifting" the putter as it moves forward. (Some people refer to this as keeping the putter low, but I think it is really not lifting the putter going backward or coming forward.)

I also have two other thoughts: there is one muscle NOT to use and it is the muscle on the top side of the left forearm, as this is the muscle that lifts the putter and changes the fingers on the grip; and never hurry, as the backstroke alone must determine the distance, so there is NO SENSE in trying anything during the downstroke -- just trust that the distance is correct and you have nothing to do with that now, and your sole focus is rolling the ball straight on the chosen line.

Of course, this is a concentrated dose all at once. I really just have these thoughts in the background, having learned their value the hard way.

Thanks for this very interesting question. I could go on and on about this one thing, but that's not a good idea.


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.

If you only depend on the force of gravity to pull the arm-hand-putter assembly down in a pendulum stroking manner, how much potential energy is there at the end of the backstroke ready to be converted to kinetic energy at the bottom of the downswing?

With a straight back and through putting action, I would think that the putter is not lifted very much for gravity to act on it. Perhaps additional body torque and hand forces are necessary to actuate the "putting pendulum".

Perhaps the putting stroke is more linear translation than pendular rotation since the angular displacement is very small due to the large radius and small nearly tangential arc path.

Dear Sammy,

You obviously know some physics!

The trouble with sensing how much energy there is in the backstroke is that humans sense it all the time and get so used to it that they can't notice it very well. In other words, "feel" is not very good, the way most people think about "feel".

Try this: While seated, place your left hand on top of your left thigh. Lift your hand above your thigh 8-10 inches high or so. Relax your left arm so it dead-falls. "Feel" the impact. Repeat this three times to focus your sense of "feel" of how hard your hand lands on your thigh. Now, raise your hand substantially higher. Relax and drop the hand onto your thigh. Notice how much greater the impact "feels". Could you accurately predict this "feel" ahead of time? Not likely. So there are two points here: 1. There is plenty of energy in even a short drop. and 2. Humans aren't very good at discriminating and prediciting in advance the "feel" of impacts.

You can also try this: While standing with arms hanging relaxedly down along your sides, lift your right arm sideways to separate your hand from your thigh about 8-10 inches. Relax your arm so that it dead-falls and the hand hits the side of your thigh. This impact is much like what happens when a putter swings down from the top of the backstroke. Increase the distance out that you lift the hand sideways, and simply observe the down-swinging of the arm and hand when you let it drop. With every increase in the size of these strokes, there is a perfectly corresponding increase in impact velocity against the thigh. Notice that even differently sized side-arm "strokes" like this all take exactly the same time from top of backstroke to impact on thigh -- always about 1/2 second. Bigger strokes go faster, but ALL strokes big or small take the same time to impact.

Finally, try this: Stand with your left foot stepped forward to position your left ankle on the line of your putt where the ball ordinarily would be. With your putter held normally at address behind your left ankle bone, shift your ankle slightly further down the line of the putt so that the thru-swinging and up-swinging putterhead will strike the ankle bone squarely in a normal stroke. Now move the putter back to the top of a backstroke that is perhaps one foot back from the starting position. Relax the whole "triangle" by releasing tension in the gut and lower back muscles so that the triangle as a whole is allowed to dead-fall downward and swing past the bottom of the arc and then upward smack into your ankle. This exercise will show you how much "momentum" is generated by this free-fall in the mass of the putterhead. If you think of your ankle as a calcium golf ball, it would not take much of a backstroke to fracture the ball, especially as the ball-ankle is immobile, planted by the weight of your body to receive the blow of the putterhead in an unforgiving manner. Increase the backstroke if you dare, to sense the added energy of a larger backstroke, but be warned that this is in fact dangerous and will likely injure your ankle if the backstroke gets much real size.

Now if you examine what is moving where, the shoulderframe is moving the whole "triangle". The left shoulder movement that corresponds with a backstroke of about one foot (for a normal adult male, right-hander) is a "dip" down and back under of not more than a couple of inches from the beginning position of the shoulder. The length of the triangle from pivot at base of neck to end of putter amplifies this modest shoulder motion, so the putterhead goes back from the ball about one foot. But the whole system of the triangle contributes to the potential energy at the top of the backstroke. The side-arm exercise above illustrates only about 1/2 to two-thirds of this contribution (arms and hands sans putter and sans shoulderframe dip). So a putting downstroke is more powerful in its energy than the side-arm exercise indicates.

Still another way to get a sense of this is to lean an upside-down putter against a wall so the shaft makes an angle to the wall -- place the butt of the putter on the floor about one foot from the wall and lean the putterhead against the wall. (Some putters are better suited for this than others, and you will have to brace the butt from sliding back away from the wall with your foot.) Now lift the putterhead away from the wall a short distance and let it drop back against the wall. You will quickly see that this is something you wouldn't want to try by leaning the putterhead against a window!

The mildness of arcing that you describe is not something that lessens the force of the blow, really. The length of the "triangle", just like the length of a pendulum, establishes both the radiusing of the swing and the tempo of the swing in gravity. A short pendulum has a tightly radiused swing and is fast. A long pendulum has a mildly radiused swing and is slow. That's all very interesting, but the reality is that your setup and putter results in only one specific pendulum system. In my case, the distance from pivot to end of putter is about 4.5 feet in length. The complete circle that this triangle would make if I could swing it all the way round over the top of my head would be a circle nine feet in diameter. A backstroke that is about one foot in length will raise the bottom of the putter off the ground about 3 inches or so. But the potential energy is not simply "putterhead above ground 3 inches" -- it's the lifting back of everything in the whole system: putterhead, putter shaft, putter handle, hands, arms, even shoulderframe. Considered independently, each point of mass in this system is like the "bob" at the end of its own pendulum. The hands, for example, are at the end of the arms about three feet out from the pivot (just plant a yardstick at the base of your neck and grip the far end like a putter -- you'll be near the end of the yardstick with your hands.) So there's more energy here than simply the height of the putterhead off the surface.

But you are correct that there is translational motion. A pendulum free-fall from the top of the backstroke is a combination of down (vertical) and across (lateral, or translational) motion. The "rod" of the pendulum is the connection between the pivot and the "bob" -- and this rod constrains the downward fall and converts this energy into tranlsational motion across and beneath the pivot. Even so, your notion that this translational movement of the putterhead requires effort by the human is not accurate. The pendulum does not require effort by the rod absent which there will not be any translational motion. The translational motion is simply the consequence of the contraint the rod imposes on the force of gravity.

Moreover, the force of gravity acts on the bob and also on all points along the rod, and the actual motion is the summation of all these contributions. The biggest contributor in this is the arms, not the putter. One of my arms weighs about 5 pounds, and both weigh about 10 pounds -- quite a few times more than the putter (between 1-2 pounds). And because the total motion is radial, things closer (more proximal) to the pivot move shorter arcs than points in the system at the far (distal) end, but all points of the system cover their separate distances in the same time. So the putterhead is moving on its greater arc faster than the hands on their lesser arc. That means that the "energy" of the putterhead at impact (which is its mass times its velocity, or its "momentum") will be a lot more than the "momentum" of the same mass covering a shorter arc in the same time.

For example, if the right hand weighs the same as a putterhead (not too far off), and you compared the energy of the putterhead at impact after a one-foot backstroke with the energy of the hand hitting the thigh from, say, only four inches off the thigh (as this is all the motion required for the hands to correspond to a putterhead backstroke of one foot), you will see that not only does the putterhead "drop" farther and swing in an arc longer, but it also gets going a lot faster at impact than the hand. This means that a 4-inch side-arm stroke in the exercises above (a 3-foot rod / pendulum) is being compared to a one-foot backstroke free-fall of the putterhead at the end of a 4.5-foot rod / pendulum. There is plenty of energy in the "natural" gravity-sponsored free-falling pendular stroke, and a lot more than humans seem to appreciate.

This is the toughest nut to crack in teaching experienced golfers about the characteristic properties of an easy, natural, gravity-tempo stroke: they just don't get how much energy is in there, and how non-existent the need is to "torque" and "accelerate" the putter with voluntary muscle whacking! If you just let the putter and whole triangle swing freely, there is more than enough power for any putt on any green.

I often have to get students to put the putter at the top of a backstroke that aims the shaft at a spot on the ground about 4 feet back from the ball (about 20 degrees back off the address vertical). From here, if I can successfully get the student to release the whole triangle and let the putter and arms swing down and across beneath the pivot in the neck, the putterhead will gather a nice head of steam coming down unrestrained by the human's trying to control things with tension. The putterhead will reach a peak speed at the bottom as it "swipes" thru the impact zone, all by itself. This particular backstroke on a normal green of Stimp 9-10 will very likely roll the ball 40-50 feet without the slightest contribution by the human.

Because gravity imparts to the stroke a perfection in timing, acceleration and impact velocity every single stroke that depends solely on the backstroke size, the same backstroke ALWAYS results in exactly a perfectly predictable and knowable-in-advance motion pattern. A human choosing his tempo is nowhere near this consistent, and so the predictability and knowing-in-advance what is coming from a golfer trying to make a certain tempo and motion pattern happens is just plain suboptimal. Period. The big thing to disabuse from the golfer's mindset is the notion that he has to "do something" in the downstroke to "get" the ball to the hole. He doesn't. If he can get the backstroke right, all the rest is just something to witness and enjoy.

[Sidenote: The ceaselessly doled out advice to "accelerate thru the ball" is without reason, actually. The usual reasons given run the gamut from "to prevent decelerating before impact", "to prevent left-wrist breakdown", "to make a positive stroke that holds the line", and the like. Drivel, tosh, and balderdash. A gravity stroke never decelerates, so there is never any need to avoid deceleration. Just let the swing gather its own steam naturally. A stroke that is "handled" by the shoulderframe moving a stable "triangle" setup renders left-wrist breakdown irrelevant. A "positive" stroke is code for a "hit" stroke, and that has its own problems for putterface, path, and distance control. So this well-worn advice is simply ill-advised.]

Getting the backstroke right is instinctive and is mostly knowing how to count your own gravity swing's timing, so you DON'T voluntarily add or subtract from the pattern and mess it up. But that is about as simple as it can be -- the backstroke always lasts twice as long as your downstroke to impact -- never less, and never more. In the case of a gravity downstroke (which is about 1/2 second for a normal adult male with a conventional length putter), the backstroke is one full second (very thereabouts). If you count this backstroke ("one potato" said to last twice as long as your downstroke actually takes) and intend for this backstroke to last that time before it coasts to a stop at the end of this interval (putterhead comes to rest at top on the speaking of the count "-tay/TOE" and not before on "tay"), the brain instinctively will produce this correct backstroke size for the putt when you just pull the trigger. The way the brain does this is that your sense of green speed and your information about the distance of the roll to the target conspire in the non-conscious processes of the brain to power-up your takeaway just right so that the backstroke coasts to a stop at a size just right for the gravity-sponsored swing to impact the ball with just the right velocity and momentum to roll the ball all the way to and not past your target. All normal adult humans have this in-built system in them and can putt with great touch repeatedly as soon as they stop fighting it with voluntary efforts that screw up the timing.

Power just isn't the issue in putting. It's the backstroke timing that matters.

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.

Wow Geoff, there is a lot to digest in your message, but could you clarify these points:

1. Is the slow backstroke conscious or non-conscious? My backstroke seems to be a conscious cranking of the putter back and a conscious reversal of the putter head once is has reached the end of the swing. In fact I think my entire putting stroke is conscious and shared applied forces from my shoulders and hands.

2. Since we are dealing with angular motion in the putting stroke, we must consider the angular momentum of all the moving segments for MOI or moment of inertia (mr^2) and angular velocity. Since the arms and hands have a low MOI contribution they can be considered negligible to the pendulum feel. Just interlock your hands together in a putting pose and swing the back and forth as you would in a putt and I doubt you will feel the effects of gravity on them.

The greatest MOI is from the putter head and the lower part of the shaft, which provides the resistance to movement and subsequent reactive feel. The force of gravity must be rather negligible in the putting stroke when compared to the kinetics of the putterhead.

3. A pendular gravity drop may be significant for a golf club but I question whether it applies to the very short putting stroke. If you only pull the putter back say 3" in your 54" stroke radius, the putting stroke is torqued because deceleration to the reversal stop point is so close to the vertical. Perhaps gravity may have some influence with a 12" stroke arc, but from 3' - 6" is must be negligible.

4. In your example of a 12' backstroke rising 3" on your 54" radius seems a bit much. My trigonometry gives me about 1.3" elevation rise, which does not provide much potential energy for the putter head to be converted to kinetic energy based on pendulum physics.

5. Has anybody wired up the muscles for EMG data when putting, typically for their master's thesis? Perhaps that would settle the issues!

Dear Sammy,

Let me respond seriatim:

1. Is the slow backstroke conscious or non-conscious? My backstroke seems to be a conscious cranking of the putter back and a conscious reversal of the putter head once is has reached the end of the swing. In fact I think my entire putting stroke is conscious and shared applied forces from my shoulders and hands.

Non-conscious, in the sense that the exact place where the backstroke will stop is "unknown and unknowable and not wanted to be known" when the stroke is initiated by a ballistic muscle movement back that sends the putterback with a beginning torquing action that soon lapses to allow the putter to "coast" to the top of a backstroke somewhere yet to be witnessed by the golfer. Your stroke is doubtless not this sort of stroke.

2. Since we are dealing with angular motion in the putting stroke, we must consider the angular momentum of all the moving segments for MOI or moment of inertia (mr^2) and angular velocity. Since the arms and hands have a low MOI contribution they can be considered negligible to the pendulum feel. Just interlock your hands together in a putting pose and swing the back and forth as you would in a putt and I doubt you will feel the effects of gravity on them.

Human moments of inertia for arm segments are not easy to determine. Some efforts have been made, though. Taking this "standard" human from the work of V. Zatsiorsky, The Mass and Inertia Characteristics of the Main Segments of the Human Body, Biomechanics V-IIIB(1983)1152-1159, as reported in this website:

UPPER ARM:

Segment COG from proximal end is from Segment COG (%)=Constant (from table)+ Segment Mass factor*Body Mass (kg)+Segment Length factor*Total Body Height (cm), with upper arm having table values Constant=0.167, SMF = 0.0300, SLF = 0.05400;

Segment Mass is from Segment Mass (kg)=Constant (from table)+ Segment Mass factor*Body Mass (kg)+Segment Length factor*Total Body Height (cm), with upper arm having table values Constant=0.25, SMF = 0.03012, SLF = -0.00270;

Segment Moment of Inertia (about frontal or x_axis) is from Segment MOI (kg-cm2)=Constant (from table)+ Segment Mass factor*Body Mass (kg)+Segment Length factor*Total Body Height (cm), with upper arm having table values Constant=-250.7, SMF = 1.56, SLF = 1.512;

FOREARM:

Segment COG from proximal end is from Segment COG (%)=Constant (from table)+ Segment Mass factor*Body Mass (kg)+Segment Length factor*Total Body Height (cm), with upper arm having table values Constant=0.192, SMF = -0.0280, SLF = 0.09300;

Segment Mass is from Segment Mass (kg)=Constant (from table)+ Segment Mass factor*Body Mass (kg)+Segment Length factor*Total Body Height (cm), with upper arm having table values Constant=0.31850, SMF = 0.01445, SLF = -0.00114;

Segment Moment of Inertia (about frontal or x_axis) is from Segment MOI (kg-cm2)=Constant (from table)+ Segment Mass factor*Body Mass (kg)+Segment Length factor*Total Body Height (cm), with upper arm having table values Constant=-64, SMF = 0.95, SLF = 0.34;

HAND:

Segment COG from proximal end is from Segment COG (%)=Constant (from table)+ Segment Mass factor*Body Mass (kg)+Segment Length factor*Total Body Height (cm), with upper arm having table values Constant=4.11, SMF = -0.0260, SLF = 0.03300;

Segment Mass is from Segment Mass (kg)=Constant (from table)+ Segment Mass factor*Body Mass (kg)+Segment Length factor*Total Body Height (cm), with upper arm having table values Constant=-0.1165, SMF = 0.00360, SLF = -0.00175;

Segment Moment of Inertia (about frontal or x_axis) is from Segment MOI (kg-cm2)=Constant (from table)+ Segment Mass factor*Body Mass (kg)+Segment Length factor*Total Body Height (cm), with upper arm having table values Constant=-19.5, SMF = 0.17, SLF = 0.116;

In my case, I am 6'1" tall (185 cm) and weigh 160 pounds (72 kg).

Hence, Upper arm COG is 12% down, Mass about 2 kg, MOI 141.3 kg-cm2; Forearm COG is 15% down, 1.15 kg, MOI 67.3 kg-cm2; Hand COG is 2.4% down, 0.18 kg, 14.2 kg-cm2.

Treating the arms as "rods" for which the MOI is 1/12 * (ML^2), the upper arm being about 12" or 30.5 cm, the forearm about the same, and the hand about 15 cm long, the Ls are respectively 3.7 cm, 4.6 cm, 0.36 cm, the "rod" MOIs are then Upper arm: 2.28 kg-cm2; Forearm: 2.03 kg-cm2; Hand: 0.002 kg-cm2.

Treating the whole upper-forearm-hand assembly as a single "rod," with a balance point perhaps 20% down from the shoulder and the total L=30" or 76.2 cm, L=15.2 cm and M=3.33 kg, the "rod" MOI is 64.5 kg-cm2.

For a typical putter, treating the system as a point mass equal to the total putter mass at a balance point X cm from the hand on the grip, the numbers are something like:

COG 10"/35" (25.4 cm/ 88.9 cm) that is, 53.3 cm from the axis at the hand on the grip 4" below the top of the club or 28%, Mass 0.5 kg, MOI 1420 kg-cm2. Treating the putter system as a "rod" with a balnce point 53.3 cm down, the "rod" MOI is 118.4 kg-cm2.

Treating the TWO arms and one putter as a unified "triangle" of total length 54" (137.2 cm) with a balance point perhaps 30% (41 cm) down from the pivot at the base of the neck, with a total mass of 7.16 kg, the single-lever "triangle as a whole" has an MOI of 12,036 kg-cm2, and a "rod" MOI of 1003 kg-cm2. If you deliver this single-lever system into the back of the ball at 70 in./sec. or about 28 cm/sec., with a firm left wrist or no left-wrist breakdown, that is quite a lot of force available!

Since the minimal initial grip pressure in the hand is what makes the arms and putter join as one, the torquing is "felt" only when the arms-hands come down "faster" than the putter itself falls. But in the Einsteinian universe, as proved by Galileo on the Leaning Tower of Pisa, objects of different masses all fall at the same rate in the same gravitational field. That means "no feel" in the hands when the arms-hands free-fall with the putter, even if they have different masses.

The separate segmental MOIs come into play when there is torquing, as then the added speed of the arms imparts a force to the club depending upon their relative MOIs. But when there is no added speed in the hands-arms, there is no role for MOI in "feel."

The greatest MOI is from the putter head and the lower part of the shaft, which provides the resistance to movement and subsequent reactive feel. The force of gravity must be rather negligible in the putting stroke when compared to the kinetics of the putterhead.

In the stroke I teach, the kinetics of the putter head come ONLY from gravity from the top of the stroke to the bottom of the stroke, although there is a little torque applied from the bottom into and thru the ball.

3. A pendular gravity drop may be significant for a golf club but I question whether it applies to the very short putting stroke. If you only pull the putter back say 3" in your 54" stroke radius, the putting stroke is torqued because deceleration to the reversal stop point is so close to the vertical. Perhaps gravity may have some influence with a 12" stroke arc, but from 3" - 6" is must be negligible.

In a pure ideal pendulum (point mass bob at end of imaginary dimensionless rod), without friction or air resistance, there is no torquing. The force of gravity alone provides just the correct deceleration to bring the upswing to a conclusion precisely at the same height the swing began from. Even if a 3" backstroke has "negligible" acceleration from gravity, the smallness of the effect does not mean the pattern of acceleration and its mathematical regularity is any less -- it's not. The putter will rise up about 0.1" and yield a peak velocity of the putter head at the bottom of SQR(2*gH) where g=384 in./sec.-sec., or 6.2 inches/sec. With my putter head mass, this sends the ball off at 9.7 inches per second. One roll of the ball is 5.28 inches, so 1 revolution per second is 5.28 in./sec. So the 3" backstroke imparts 1.8 revolutions per second rolling to the ball -- that's a gracious plenty for short putts. My typical "terminal speed" of ball roll at the lip after a 20-foot trip is about 2 revolutions per second, and a miss on normal-speed greens will send this ball 8-10 inches past the hole's rear wall for a total roll on most greens of about 8-12". A 3" backstroke is good for an 8-12" roll, from gravity alone.

It is a separate issue altogether whether this short of a backstroke is BIG enough for the body motion to be controlled effectively. I believe that the shoulder frame muscles, nerves, and tissues require a minimum amplitude of motion to fully engage the controls that are needed for effective use of this stroke. Strokes of 6" and larger, however, in my experience, do not require torquing down for accurate management, and a gravity-sponsored shoulder stroke is just fine for these strokes.

4. In your example of a 12" backstroke rising 3" on your 54" radius seems a bit much. My trigonometry gives me about 1.3" elevation rise, which does not provide much potential energy for the putter head to be converted to kinetic energy based on pendulum physics.

I was estimating. This Trigonometry Applet gives the calculation if you use a 54" hypotenuse and enter the backstroke length as the "opposite leg" and then press enter to calculate the values. The height of the putter off the ground at the top of the backstroke is 54" less the "adjacent side" value. In this case, the adjacent side computes as 52.65", so the height is 1.35".

5. Has anybody wired up the muscles for EMG data when putting, typically for their master's thesis? Perhaps that would settle the issues!

No, but it would help. It depends on the golfer's training and ability to execute this sort of stroke.

For more in this same vein, see this Flatstick Forum post.

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.