# Putter Weighting and Topspin

Joined: March 7th, 2004, 10:07 pm
Geoff:

Has any research been done on the optimal placement of the center of gravity (COG) to enable the golfer to most easily impart topspin to the ball? Ping and other putter manufacturers have low COG putters and clain that because of the gear effect, this most effectively enables topspin. Recently I have read other manufacturers, (Yes/Big Oak), claims that putting the COG close to the top edge of the putter enables topspin. Any thoughts or ideas on this?

Geoff Mangum
Geoff Mangum
Boy, did you ever put your finger on the heart of the matter! There are two big issues in putter design right now -- location of the COG in 3 dimensions and how to hosel. The COG issue is being handled in diametrically opposite ways by three camps among putter manufacturers (low, high, level), each backed up by "true roll" studies, and neither really communicating or debating the issue directly. I'm not sure how this will all finally sort itself out, but clearly there must be some basic uncertainties in the definitions or understandings about the underlying physics. perhaps it is only a matter of the "relevant" physics, and the real choices are occuring in how the golfer actually uses one type versus another.

The three dimension of COG location in the putter head can be related to the X, Y, and Z axes of a standard Cartesian coordinate system with its origin (intersection of axes) located in the ball's COG. The X axis is the same as the direction of the putt or left-right from the golfer's point of view, the Z axis is up-down, and the Y axis if front-back or near-far. The choices are 1) centered heel-toe in the Y axis, 2) high or low in the Z axis in relation to the ball's COG at impact, and 3) close to the putter face or farther back in the putter head in the X axis. The one dimension addressed by your question is the Z axis (2).

The Golfer stands where the upright blue arrow is located. The ball is located in the center of the axes.

The Center of Gravity (COG) of the ball is located in the center of the sphere, unless the ball is out of balance or out of round.

Let's leave aside for the moment the fundamental question of whether topspin is desireable, and if so, why and how desireable is it -- or the correlated question of whether backspin is undesireable, and if so, why and how undesireable is it -- questions that seems to be somewhat unexamined in detail, and certainly deserving of greater scrutiny and scientific investigation.

Camp 1 - LOW COG FOR "GEAR EFFECT"

Those who make a low COG putter include C-Groove / Yes!, Scotty Cameron, Ping Craz-E, Q-Roll, the Resso, and many others. And there are different approaches to accomplishing the same thing.

Typically, the putter design simply has a concentration of mass low on the back flange, as does the C-Groove Amy model:

Ontic, for example, in effect has a "heel-toe" scheme in the vertical dimension, with low sole plates on the heel and toe, and a raised sole in the center. This effectively lowers the putter COG.

The person who seems to have the best studies supporting a low COG putter design is Norman Lindsay at his website Lindsay Putters. He combines a number of design features into his "All Topspin (All-TS)" putters, including a low COG. His site illustrates the high-speed camera studies he's done, and explains the "gear effect" producing topspin by a low COG combined with certain lofting features and certain impact dynamics resulting from the way the golfer presents the putter face to the back of the ball.

Lindsay writes:

The facts are:

* All conventional putters impart backspin.
* Some can also generate a little topspin.
* The amount and direction of spin depends on where the ball impacts the striking face.
* With any golf club (from putter through to driver), the higher the point of impact on the clubface, the less the backspin.
* With a putter  if the design is right  the spin becomes topspin for impacts near the top of the face.
* A badly designed putter can give so much backspin that the ball loses 35% or more of its initial energy through skidding before it gets rolling. (High topspin putters can reduce this to 20% or less.)

Lindsay putters impart high topspin over the entire striking face, providing modern-age performance that would enthral bygone masters such as Bobby Locke. This unique achievement is the result of expertly combining the only two mechanisms that genuinely put spin on a golf ball, namely;

* Gear-effect, which relies on the putter-head weight distribution, but is also critically dependent on the way the shaft attaches to the head.
* Oblique impact - the workhorse of golf shots. This shapes flight trajectory and puts backspin on the ball. Backspin is essential for distance in long shots and control in approach shots. In putters, it can be used in reverse to give topspin.

So Lindsay says reducing backspin / increasing topspin comes ONLY from the gear effect and certain dynamic loft thru impact, which he terms "oblique impact."

Lindsay elaborates about these two sources:

WHAT GIVES TOPSPIN?

* Vertical gear effect
Its well known that hitting the ball off the heel or toe of a driver puts sidespin on the ball, even if the clubface is square at impact. The same happens with a putter. Whats less well known is that vertical spin changes with impacts above or below the sweet spot. Hits above the sweet spot (on a putter) give topspin. Hits below the sweet spot give backspin.

* Low centre of gravity
The sweet spot must be low to ensure vertical gear effect works to give topspin. In most putters the CG is not low enough to place the sweet spot below the centre of the striking face. Lindsay putter-heads have exceptionally low CG with the sweet spot well below centre. For hits at or near the centre, topspin compensates for linear ball velocity changes, giving superb putt length consistency. [This is the Z-axis.]

* Deep centre of gravity
Gear effect is proportional to the depth of the CG behind the putter face. For good topspin you need the putter-head CG positioned from half to two inches behind the face. [This is the X-axis.]

* Low minimum inertia
Low minimum inertia (front-back weighting) assists vertical gear effect, giving higher topspin. At the same time its important to have high heel-toe weighting (i.e. high maximum inertia).

* Variable face loft
Gradual loft reduction (face roll) can be used on the bottom of the putter-face to introduce a small amount of negative loft. This generates topspin by oblique impact, even though the ball is hit on the upswing on this part of the putter-face. This arrangement is especially beneficial for length control on long putts.

* Centred shaft axis
Lindsays recent pioneering research into putter impact has revealed a major problem - the position of the shaft axis is critical for vertical gear effect. Aligning the shaft axis with the putter-head CG ensures the best performance for topspin and feel. [This refers to centering on the Y-axis heel-toe.]

Apparently, the "gear effect" adds topspin when the point of impact on the putter face is centered in the Y-axis, the putter COG is lower than the point of impact on the back of the ball in the Z-axis. Lindsay considers locating the COG back along the X-axis, plus hoseling the shaft in the center of the Y-axis, plus minimum front-back weighting, plus the radiusing of the face in the lower half of the face to help out when the point of impact on the ball is too low, plus minimal lofting or even negative lofting in the radiusing low on the face, all as promoting topspin in some supplemental or complementary way. But I gather that the real fundamental is the "gear effect." So the "gear effect" is pretty much a low COG in the putter face, impact high on the face, impact on the equator of the ball, and the putter COG lower than the ball COG at impact.

Camp 2 - HIGH COG AND THE CUE-BALL LEVEL BLOW THRU THE TOP QUADRANT

The second approach is to locate the putter COG high on the face (Z-axis) and replicate what happens when a cue stick imparts top spin to a cue ball in billiards. Daish in his book The Physics of Ball Games describes how a level blow of the cue stick thru the top quadrant of the cue ball at a height 5/7th the way up from the bottom of the ball perfectly matches the forward translational force with the rotational top-over rolling of the ball to eliminate skid entirely. In effect, the pointed stick delivers the stick's COG level thru the top quadrant of the ball higher than the ball's COG. Putters that take this design approach include the Tear Drop, the Breeds Confidence, the Big Oak, the Aserta, and others.

But since the putter face COG is above the ball COG with the face moving level or rising thru impact, doesn't this present a "gear effect" scenario in reverse -- one in which the putter face tilts bottom-back-up so that the face ought to wheel down counterclockwise on the back of the ball, imparting back spin (which would be slice spin for the driver)? In this case, it is probable that the vertical hosel has less tendency to oppose the counterclockwise action of the putter face than it does in the case of a clockwise gear effect. So a high-COG putter ought to impart back spin the same as or perhaps more than a low-COG putter ought to impart top spin by virtue of the "gear effect."

The Aserta company has comparisons of skid distances of the Aserta putter versus other putters, based on robotic putting tests performed with the Swing Dynamics Putting Track Monitor. The description of the testing procedure does not make clear the trajectory of the putter COG in relation to the ball's COG. Even so, the data shows a forward spin on the Aserta putts in excess of 100 revolutions per minute (about 1.7 revolutions per second) versus back spins of the order of 35 to 60 revolutions per minute (about 0.5 to 1.0 revolutions per second) back spin. See Aserta Inverted Mass Technology. This data just deepens the mystery.

Camp 3 -- COG-to-COG Level

The T-Roll Putter from perry Golf has a design in which the putter COG is the same height as the ball COG. The ball COG is one-half the diameter of the ball up, or in the center, 0.84 inches above the bottom of the ball. The idea is to promote "solid" impact and solid "feel."

The relative positions of the COGs is described for the T-Roll versus the conventional design:

The T-Roll company has a fairly clear explanation of the theory;

Most golf putter heads are heel and toe weighted to create a larger 'horizontal' sweet spot. They have very little mass at the center and top of the putter head. Most of the weight is at the bottom or sole of the putter head. The 'Sweet Spot' is positioned below the center of mass of the golf ball. Since the 'sweet spot' is located below the center of mass of the golf ball, the putter upon contact with the golf ball does not have a very solid feel. Also, most putters are designed with the shaft connected at the heel, inside the center of mass. Upon contact with the golf ball, the putter head tends to twist and rotate on a horizontal plane.

The T-Roll® golf putter is designed with most of the weight located away from the center of mass, creating a very high moment of inertia. (The T-Roll® Defiant with Brass plug inserts is 4699 gm*cm^2.  The T-Roll® Defiant with Tungsten plug inserts is 6431 gm*cm^2.)  Also, the 'T' shaped mass on the The T-Roll® golf putter shifts the center of mass towards the top of the putter head, aligning itself horizontally with the center of mass of the golf ball. By aligning the 'Sweet Spot' on the putter head perfectly with the center of mass of the golf ball, this creates the most solid feeling putter possible. The shaft is connected to the 'T' shaped mass near the sightline. The putter head does not twist or rotate upon contact with the golf ball. Due to its high moment of inertia, even off-center hits cause minimal twisting or rotation of the putter head.

This analysis leaves out, however, the PATH of the putter COG relative to the ball COG thru the ball / impact zone. I suspect that in practical use the T-Roll's "level with the ball" COG merely functions to ensure that the path of the T-Roll COG stays above the ball''s COG. Afterall, a truly level COG-to-COG blow thru the ball would result in all skid. I would not think the 3-degree lofting of this putter would help reduce skid, as this makes the ball rise on the putter face so the ball COG is higher than the putter COG. However, if this effect is overcome by the putter rising into the back of the ball on a high trajectory, then the face loft effect is neutralized and overcome.

SORTING THIS OUT AS BEST WE CAN

Let's get a drink of water, and then go back to the basic idea of "gear effect."

GEAR EFFECT & PUTTING

In a driver, the "gear effect" imparts some hook spin on a ball hit near the toe, or slice spin on a ball hit near the heel, with the driver COG centered on the Y-axis heel-toe. Placing the COG back in the driver from the face on the X-axis increases the gear effect. According to Cochran and Stobbs, Search for the Perfect swing, pages 117-119 (and especially Fig. 19-10), the toe gear effect has the club COG moving along a line not thru the ball COG but inside it, so the toe hits the back of the ball and not the center of the club and COG hitting the back of the ball. This sort of impact knocks the face of the club open. The ball and club face act as if in contact like two enmeshed gears. The backward opening of the face (clockwise for a right-hander looking down at the top of the club) spins the ball the opposite way, counterclockwise, which is a hook spin. The opposite tendencies at work are an open face imparting some slice spin and starting angle off to the right, versus the gear effect imparting hook spin. The trick is for the gear effect to be designed in just right to overcome the slice spin so the ball starts right but then curves hookish back to the center of the fairway.

The "bulge" of a driver face is a curvature of the face along the Y-axis horizontally. This toe curve increases the slice spin and the start angle to the right. Most golfers probably think the bulge increases the gear effect, but this is not correct. A FLAT driver face basically has too much gear effect designed in, and the bulging removes some of the gear effect to get the balance adjusted between slice and hook spin. Too much bulge and the balls just slice.

Applying all this to a VERTICAL gear effect and considering the difference between driver and putter impacts with a ball and the difference in the heel hoseling of drivers that is essentially like a stick entering the driver head horizontally at the heel versus a putter hosel that is a stick entering the head vertically and the difference between balls spinning in the air and balls rolling on the ground, it is fairly evident that the driver "gear effect" horizontally and the putter "gear effect" vertically may not have all that much in common in their physics.

SKID, ROLL, and SPIN

Let's get another drink of water and go back even further, this time to the physics of imparting roll or spin to a ball.

When a putter impacts the equator of a ball moving level thru the back of the ball, and with the putter COG level with the ball COG, the blow imparts all skid and no roll. The roll that eventually shows up is all due to the friction of the grass on the bottom of the sliding ball, making it roll top-forward-down / bottom-back-up. This is not the sort of phenomenon we are looking for, as the "gear effect" imparts spin to the ball solely from the impact dynamics of the relative face and ball COGs in motion and the reaction of the face and ball. For a blow to impart spin of some sort (not resulting from skid), the blow needs to be such that the COG of the instrument moves not thru the center of the ball but above or below the center.

A blow of sweetspot-thru-sweetspot level with no loft produces all skid and no roll. Any roll that eventually shows up comes solely from friction of the grass on the bottom of the ball causing the ball to roll more and more until the rolling speed matches the translational speed, and then there is no more skid. For the blow itself to impart some "early" roll not dervived from the grass "sliding friction," the blow has to "torque" the sphere of the ball. This means a blow directed above or below the ball's COG.

The relevant physics is explained in detail in the great little site named The Physics of Pool.

Once the ball is struck, there is an initial period in the roll of pure acceleration up to a velocity of the ball away from the face. Then, the ball is ordinarily sliding across the ground as the "sliding friction" makes the ball start rolling top-forward. Once the rotational speed of the ball increasaes sufficiently to match the translational speed of the ball's COG horizontally across the green, there is no more "sliding friction" and no more "skid" - the ball is only rolling subject to "rolling friction." Rolling friction is somewhere around 1/10th as much as "sliding friction," but it is enough eventually to bring the ball to a gradual stop (on level ground, where gravity is not adding or subtracting forces).

This chart from the Oxford Croquet website shows the three phases of acceleration (very short), skidding-to-rolling, and only rolling.

In fact, there is a final phase called the "decay" phase where the ball's rolling slows to a point that allows the ball to sink back into the grass a little. This increases the rolling friction, and brings the ball to a halt a little quicker. Slow greens have more "decay rolling friction" than fast green. Indeed, slow greens have more "sliding friction" and more "rolling friction" in general, so putts on slow greens have a quicker skid phase, not as long a rolling phase, and a more abrupt decay phase.

This chart shows the "knee" where the decay phase onset occurs for various green speeds:

The "knee" is around 9-10 feet out in this 11-foot putt.

The function of back spin and top spin in all of this is to shorten or even prolong the skid phase. In general, back spin makes the skid phase last longer, while top spin makes the skid phase end sooner. Altering the ball-green friction at the outset of the roll can also affect the length of the skid phase.

When the putter COG is low, does the higher ball COG knock the putter face top-back? It seems that the shafting and hoseling would likely resist this pretty good, as if the driver had the shaft inserted horizontally into the toe-end of the driver face. That is, the fact that the hosel is attached to the putter face in the VERTICAL plane would seem to cancel or greatly reduce any tendency of the putter face to get knocked top-back. This would seem to be the case even if the putter head COG is recessed back from the face (on the X-axis). If the putter face is not "opening" vertically top-back, there would seem to be no "gear effect" at all. Perhaps I am wrong about the flexibility of the shaft-hosel-putter head assembly. If so, then putter shaft flex should be a great big issue.

If the putter face is moving "level" thru the ball, it is worth noting that a "loftless" face presentation to the ball would necessarily impact the ball on the equator. In the vertical look at the profile of the back of the ball, the equator is closest to the putter face of all parts of the ball. In order for a putter face to be lofted but moving level so that the point of impact on the ball was actually above or below the equator, the lofting (positive or negative) would have to be pretty severe, slanting the leading edge of the tilted face sufficiently that the putter face first comes in contact with a point on the back of the ball not as near the face as the equator. In order to hit the back of the ball on a point below the equator, it is necessary as a practical matter to move the putter not level but upwards into the lower back quadrant of the ball. Similarly, in order to hit the back of the ball higher than the equator, it is necessary as a practical matter to move the putter not level but downwards onto the upper back quadrant of the ball.

Let's try something else. Suppose the putter face is NOT moving level thru the ball, but instead is moving on a rising trajectory with the face COG curling up and passing thru the ball's COG. Assume further that the rising trajectory does not add dynamic loft to the face at impact, but the face is vertical and parallel to the line in the ball from top of ball to bottom of ball on a level green. In this case, there would still not be any "gear effect" as in a driver. In a driver, the face of the club runs toe-back and center-out in a clockwise face turning that slides outward across the back of the ball to give hook spin. And the path of the driver COG does not pass thru the ball COG, but inside it. The putter-ball impact here envisioned would seem simply to launch the ball along the rising trajectory of the face COG, but not otherwise impart overspin -- just a dead-ball punch upward off the ground a bit.

So how do we configure a putter face-ball impact in order to give the ball overspin? The first question is why does a normal putter give the ball backspin?

A "normal" putter has about 3 degrees of loft. Assuming the lofted face is moving level thry the ball with face COG level with ball COG, what happens? It seems the point of contact would be on the equator of the ball, but then the ball would start to slide or roll up the face of the putter because of the 3-degree tilt top-back. And from a vertical perspective, back spin is slice spin. So it's fairly easy to see how positive loft creates back spin.

But, as soon as the ball slides up the face, then we have the scenario of the driver "gear effect." So why doesn't loft create "gear effect" hook spin, or does it? The face COG is moving inside, the ball COG is outside, and the face is "open" top-back in a slice (upward) presentation to the ball - just like in a driver "gear effect." So far, we have slice spin (back spin vertically). The "gear effect" giving hook spin comes about only when the face COG moves upward toward the ball COG away from the ground (on the Z-axis). Does it? This is where I think the vertical hosel comes into play to reduce or eliminate this action. By preventing the face from "opening" more top-back, the only way the face COG can move up across the back of the ball is for the whole putter to rebound vertically. This is opposed by the golfer's whole body extending the putter downward to the ball.

Does negative loft reduce backspin or impart top spin? Assuming a level blow with a negative-loft face (top edge of face tilted ballward), the ball could not slide down the face because it is already on the ground and there is no more "down" to go (except punching the ball into the turf). Apparently what happens is that the face initially hits the ball's equator, forces the ball a little into the turf thus lowering the ball COG below the face COG, and redirects the impact dynamics so that the face COG is moving level thru the upper quadrant of the ball. This is something of a glancing blow with a little less energy than a flush face-sweetspot thru ball-sweetspot impact trajectory. But it would seem to reduce back spin and increase top spin.

What role does having the COG recessed back from the face play? This is one of the key features for driver gear effect. But in the putting stroke, I believe that the recessed COG really just means that face impact occurs while the putter COG is in a retarded phase of the putting arc, not yet rising as much as the face. So having the putter COG recessed is just a way to get a lower start up thru the ball than otherwise. If the path of that recessed sweetspot cuts upward thru the ball higher than the ball's COG, perhaps that's all that really matters.

All that said, it seems to me that the only real way to get topspin is to have something of a glancing blow in which the face COG is not moving on a trajectory thru the ball's COG, but is instead moving either up from the lower back quadrant on a path higher than the ball COG or moving from the equator on a path that takes the putter COG higher than the ball's COG or moving thru the top quadrant of the ball on a path higher than the ball's COG. It's all about the path of the face COG staying above the ball's COG.

This explains to me why Harold Swash teaches a hands-ahead rising blow thru the ball that presents the face "tangentially." On any point on the surface of a sphere like a golf ball, there is a direction aimed at the center of the ball (it's COG), and a "plane" that rests on the outter surface of the ball at this point is a "tangent" plane when the plane is perpendicular to the radial line aimed at the center of the sphere. I gather that Harold Swash is referring to the putter face matching this tangential plane on the ball at impact. That explains the hands-ahead delofting the putter so the face can match the tangential plane on the ball. The delofting also implies that the impact point is either on the equator or the top quadrant of the ball, but not the lower quadrant. The rising blow implies that the path of the face COG is moving thru the ball higher than the ball's COG.

Personally, I believe that reducing the back spin and increasing the top spin can be done without the hands-ahead delofting of the putter and a top-quadrant blow. By simply moving the putter's COG up thru the ball on a path higher than the ball's COG, the objective is accomplished. This can be done without the hands-ahead delofting by using a normal pendulum stroke with dead hands and ball position well forward of the bottom of the stroke that presents the face of the putter to the back of the ball when it is rising AND on a path that takes the putter COG up thru the back quadrant of the ball and out thru the ball higher than the ball's COG. Keeping the loft to a minimum would reduce launching the ball in the air, and negative loft used in this sort of impact probably helps the top spin.

In conclusion, I'm not convinced that the true physics of back spin and top spin have been propely described. I believe it is the PATH of the putter sweetspot thru the ball, and not so much the "gear effect" or even the "cue stick" type blow.

This brings us back to the underlying issue that has not received sufficient attention -- whether back spin or absence of top spin matters? If we have to craft a stroke so carefully that the trajectory of the sweetspot of the putter has to fall within a very narrow range or possible trajectories, is it worth all the trouble?

Skid robs a ball of energy, and so the stroke doesn't send the ball as far as it would otherwise. Who cares, so long as the ball gets to the hole? One can become very proficient and have great touch even though the ball skids a lot, so long as the technique is consistent and the skidding is consistent. The real question is whether the skid does something worse to the putt, like send the ball off line or make it hop. I've never seen a study about this.

It stands to reason that a skidding ball is "more violent" in a sense than a rolling ball, and a more "violent" ball is more likely to do something unwanted. Maybe so, but how likely? Is the reward of not worrying about true roll worth the risk of the ball running seriously off line? I don't really know, and so far as I can tell, neither does anyone else.

The C-Groove testing does conclude that a shorter skid phase and a more accurate holding of the line go hand in hand. According to robotic tests, the C-Groove has a 3-inch skid versus the typical 18-inch skid for most putter designs (factor of 6), while the C-Groove has a mere 1-inch dispersion over a 50-foot putt versus a conventional design dispersion of 3 inches (factor of 3).

Unfortunately, the exact trajectory of the putter COG thru the ball is not indicated.

Assuming that a "truer" roll is worth the price of extra trouble and fragility in the technique, I would suggest the simplest technique to improve the roll and reduce the skid is the best technique. For this reason, I prefer ball position and dead hands rather than forward pressing loft out and then impacting the ball with hands-ahead and perhaps a descending blow as well (too complex).

With this approach, then, whether a high-COG or low-COG is better is anyone's guess. I suspect that a high-COG with little positive loft used with dead hands and a rising blow is safer to make sure the putter COG stays above the ball COG on its way thru the ball. But I have to say that only carefully designed high-speed camera work that carefully accounts for the trajectory of the putter COG thru the ball is likely to get this sorted out properly.

We'll get it figured out one day. In the meantime, I'm not convinced that "true roll" is worth all the bother. Just play the ball well forward of the bottom of the stroke, use a simple stroke technique, and use a slow tempo without "percussion" against the ball. Keep the violence out, and that's probably good enough until we know more.

Cheers!

Geoff Mangum
Putting Theorist and Instructor
Geoff Mangum's PuttingZone
http://puttingzone.com
Golf's most advanced and comprehensive putting instruction.

Over 600,000 visits and growing strong ...

518 Woodlawn Ave
Greensboro NC 27401
336.230.0612 home
336.402.1602 cell

Last edited by aceputt on March 11th, 2004, 10:17 am, edited 1 time in total.

John McHugh
John McHugh
Enjoyed your COG analysis. Though it was somewhat over my head, I think I got most of it.

I just got a futura and have had great luck with it on the rug (I live in Boston). I caught the "cup" 8 out of 10 @ 14 feet. I'm playing the ball a bit forward and trying to use 'a quiet eye'. Do you feel the ball placement is helping or should I go back center the ball at address?

I'd appreciate any advice you might have.

Thanks

John

Geoff Mangum
Geoff Mangum
Dear John,

I haven't swung the Futura putter all that often, but I seem to recall a sense that the hosel attaches to the putter head well in front of the COG, which makes it a little different from a conventional design, and more like a gooseneck putter.

This design probably shifts the bootom of the stroke arc a bit forward, so that when the COG is bottoming out, the hands and putter face and hosel are all forward of that bottom in the middle of your stance a bit. This all suggests to me that a ball position forward of the middle of your stance and inside your lead-side heel (assuming a stance about as wide as your shoulders) is probably fine. Too far forward of that would probably make the putter have too much loft at impact, and a little back of that (just a little) is probably still ok. So the range of choices is somewhere between about 1 inch ahead of the middle of the stance to about 3-4 inches ahead of this point -- probably favoring the 1-2 inch part of that range. Just a guess. You'll have to experiment, but I am suggesting the hosel-COG relation will influence the final pick.

Cheers!

Geoff Mangum
Putting Theorist and Instructor
Geoff Mangum's PuttingZone
http://puttingzone.com
Golf's most advanced and comprehensive putting instruction.

Over 615,000 visits and growing strong ...

518 Woodlawn Ave
Greensboro NC 27401
336.230.0612 home
336.402.1602 cell

Simon
Simon
Boy, did you ever put your finger on the heart of the matter! There are two big issues in putter design right now -- location of the COG in 3 dimensions and how to hosel. The COG issue is being handled in diametrically opposite ways by three camps among putter manufacturers (low, high, level), each backed up by "true roll" studies, and neither really communicating or debating the issue directly. I'm not sure how this will all finally sort itself out, but clearly there must be some basic uncertainties in the definitions or understandings about the underlying physics. perhaps it is only a matter of the "relevant" physics, and the real choices are occuring in how the golfer actually uses one type versus another.

The three dimension of COG location in the putter head can be related to the X, Y, and Z axes of a standard Cartesian coordinate system with its origin (intersection of axes) located in the ball's COG. The X axis is the same as the direction of the putt or left-right from the golfer's point of view, the Z axis is up-down, and the Y axis if front-back or near-far. The choices are 1) centered heel-toe in the Y axis, 2) high or low in the Z axis in relation to the ball's COG at impact, and 3) close to the putter face or farther back in the putter head in the X axis. The one dimension addressed by your question is the Z axis (2).

The Golfer stands where the upright blue arrow is located. The ball is located in the center of the axes.

The Center of Gravity (COG) of the ball is located in the center of the sphere, unless the ball is out of balance or out of round.

Let's leave aside for the moment the fundamental question of whether topspin is desireable, and if so, why and how desireable is it -- or the correlated question of whether backspin is undesireable, and if so, why and how undesireable is it -- questions that seems to be somewhat unexamined in detail, and certainly deserving of greater scrutiny and scientific investigation.

Camp 1 - LOW COG FOR "GEAR EFFECT"

Those who make a low COG putter include C-Groove / Yes!, Scotty Cameron, Ping Craz-E, Q-Roll, the Resso, and many others. And there are different approaches to accomplishing the same thing.

Typically, the putter design simply has a concentration of mass low on the back flange, as does the C-Groove Amy model:

Ontic, for example, in effect has a "heel-toe" scheme in the vertical dimension, with low sole plates on the heel and toe, and a raised sole in the center. This effectively lowers the putter COG.

The person who seems to have the best studies supporting a low COG putter design is Norman Lindsay at his website Lindsay Putters. He combines a number of design features into his "All Topspin (All-TS)" putters, including a low COG. His site illustrates the high-speed camera studies he's done, and explains the "gear effect" producing topspin by a low COG combined with certain lofting features and certain impact dynamics resulting from the way the golfer presents the putter face to the back of the ball.

Lindsay writes:

The facts are:

* All conventional putters impart backspin.
* Some can also generate a little topspin.
* The amount and direction of spin depends on where the ball impacts the striking face.
* With any golf club (from putter through to driver), the higher the point of impact on the clubface, the less the backspin.
* With a putter  if the design is right  the spin becomes topspin for impacts near the top of the face.
* A badly designed putter can give so much backspin that the ball loses 35% or more of its initial energy through skidding before it gets rolling. (High topspin putters can reduce this to 20% or less.)

Lindsay putters impart high topspin over the entire striking face, providing modern-age performance that would enthral bygone masters such as Bobby Locke. This unique achievement is the result of expertly combining the only two mechanisms that genuinely put spin on a golf ball, namely;

* Gear-effect, which relies on the putter-head weight distribution, but is also critically dependent on the way the shaft attaches to the head.
* Oblique impact - the workhorse of golf shots. This shapes flight trajectory and puts backspin on the ball. Backspin is essential for distance in long shots and control in approach shots. In putters, it can be used in reverse to give topspin.

So Lindsay says reducing backspin / increasing topspin comes ONLY from the gear effect and certain dynamic loft thru impact, which he terms "oblique impact."

Lindsay elaborates about these two sources:

WHAT GIVES TOPSPIN?

* Vertical gear effect
Its well known that hitting the ball off the heel or toe of a driver puts sidespin on the ball, even if the clubface is square at impact. The same happens with a putter. Whats less well known is that vertical spin changes with impacts above or below the sweet spot. Hits above the sweet spot (on a putter) give topspin. Hits below the sweet spot give backspin.

* Low centre of gravity
The sweet spot must be low to ensure vertical gear effect works to give topspin. In most putters the CG is not low enough to place the sweet spot below the centre of the striking face. Lindsay putter-heads have exceptionally low CG with the sweet spot well below centre. For hits at or near the centre, topspin compensates for linear ball velocity changes, giving superb putt length consistency. [This is the Z-axis.]

* Deep centre of gravity
Gear effect is proportional to the depth of the CG behind the putter face. For good topspin you need the putter-head CG positioned from half to two inches behind the face. [This is the X-axis.]

* Low minimum inertia
Low minimum inertia (front-back weighting) assists vertical gear effect, giving higher topspin. At the same time its important to have high heel-toe weighting (i.e. high maximum inertia).

* Variable face loft
Gradual loft reduction (face roll) can be used on the bottom of the putter-face to introduce a small amount of negative loft. This generates topspin by oblique impact, even though the ball is hit on the upswing on this part of the putter-face. This arrangement is especially beneficial for length control on long putts.

* Centred shaft axis
Lindsays recent pioneering research into putter impact has revealed a major problem - the position of the shaft axis is critical for vertical gear effect. Aligning the shaft axis with the putter-head CG ensures the best performance for topspin and feel. [This refers to centering on the Y-axis heel-toe.]

Apparently, the "gear effect" adds topspin when the point of impact on the putter face is centered in the Y-axis, the putter COG is lower than the point of impact on the back of the ball in the Z-axis. Lindsay considers locating the COG back along the X-axis, plus hoseling the shaft in the center of the Y-axis, plus minimum front-back weighting, plus the radiusing of the face in the lower half of the face to help out when the point of impact on the ball is too low, plus minimal lofting or even negative lofting in the radiusing low on the face, all as promoting topspin in some supplemental or complementary way. But I gather that the real fundamental is the "gear effect." So the "gear effect" is pretty much a low COG in the putter face, impact high on the face, impact on the equator of the ball, and the putter COG lower than the ball COG at impact.

Camp 2 - HIGH COG AND THE CUE-BALL LEVEL BLOW THRU THE TOP QUADRANT

The second approach is to locate the putter COG high on the face (Z-axis) and replicate what happens when a cue stick imparts top spin to a cue ball in billiards. Daish in his book The Physics of Ball Games describes how a level blow of the cue stick thru the top quadrant of the cue ball at a height 5/7th the way up from the bottom of the ball perfectly matches the forward translational force with the rotational top-over rolling of the ball to eliminate skid entirely. In effect, the pointed stick delivers the stick's COG level thru the top quadrant of the ball higher than the ball's COG. Putters that take this design approach include the Tear Drop, the Breeds Confidence, the Big Oak, the Aserta, and others.

But since the putter face COG is above the ball COG with the face moving level or rising thru impact, doesn't this present a "gear effect" scenario in reverse -- one in which the putter face tilts bottom-back-up so that the face ought to wheel down counterclockwise on the back of the ball, imparting back spin (which would be slice spin for the driver)? In this case, it is probable that the vertical hosel has less tendency to oppose the counterclockwise action of the putter face than it does in the case of a clockwise gear effect. So a high-COG putter ought to impart back spin the same as or perhaps more than a low-COG putter ought to impart top spin by virtue of the "gear effect."

The Aserta company has comparisons of skid distances of the Aserta putter versus other putters, based on robotic putting tests performed with the Swing Dynamics Putting Track Monitor. The description of the testing procedure does not make clear the trajectory of the putter COG in relation to the ball's COG. Even so, the data shows a forward spin on the Aserta putts in excess of 100 revolutions per minute (about 1.7 revolutions per second) versus back spins of the order of 35 to 60 revolutions per minute (about 0.5 to 1.0 revolutions per second) back spin. See Aserta Inverted Mass Technology. This data just deepens the mystery.

Camp 3 -- COG-to-COG Level

The T-Roll Putter from perry Golf has a design in which the putter COG is the same height as the ball COG. The ball COG is one-half the diameter of the ball up, or in the center, 0.84 inches above the bottom of the ball. The idea is to promote "solid" impact and solid "feel."

The relative positions of the COGs is described for the T-Roll versus the conventional design:

The T-Roll company has a fairly clear explanation of the theory;

Most golf putter heads are heel and toe weighted to create a larger 'horizontal' sweet spot. They have very little mass at the center and top of the putter head. Most of the weight is at the bottom or sole of the putter head. The 'Sweet Spot' is positioned below the center of mass of the golf ball. Since the 'sweet spot' is located below the center of mass of the golf ball, the putter upon contact with the golf ball does not have a very solid feel. Also, most putters are designed with the shaft connected at the heel, inside the center of mass. Upon contact with the golf ball, the putter head tends to twist and rotate on a horizontal plane.

The T-Roll® golf putter is designed with most of the weight located away from the center of mass, creating a very high moment of inertia. (The T-Roll® Defiant with Brass plug inserts is 4699 gm*cm^2.  The T-Roll® Defiant with Tungsten plug inserts is 6431 gm*cm^2.)  Also, the 'T' shaped mass on the The T-Roll® golf putter shifts the center of mass towards the top of the putter head, aligning itself horizontally with the center of mass of the golf ball. By aligning the 'Sweet Spot' on the putter head perfectly with the center of mass of the golf ball, this creates the most solid feeling putter possible. The shaft is connected to the 'T' shaped mass near the sightline. The putter head does not twist or rotate upon contact with the golf ball. Due to its high moment of inertia, even off-center hits cause minimal twisting or rotation of the putter head.

This analysis leaves out, however, the PATH of the putter COG relative to the ball COG thru the ball / impact zone. I suspect that in practical use the T-Roll's "level with the ball" COG merely functions to ensure that the path of the T-Roll COG stays above the ball''s COG. Afterall, a truly level COG-to-COG blow thru the ball would result in all skid. I would not think the 3-degree lofting of this putter would help reduce skid, as this makes the ball rise on the putter face so the ball COG is higher than the putter COG. However, if this effect is overcome by the putter rising into the back of the ball on a high trajectory, then the face loft effect is neutralized and overcome.

SORTING THIS OUT AS BEST WE CAN

Let's get a drink of water, and then go back to the basic idea of "gear effect."

GEAR EFFECT & PUTTING

In a driver, the "gear effect" imparts some hook spin on a ball hit near the toe, or slice spin on a ball hit near the heel, with the driver COG centered on the Y-axis heel-toe. Placing the COG back in the driver from the face on the X-axis increases the gear effect. According to Cochran and Stobbs, Search for the Perfect swing, pages 117-119 (and especially Fig. 19-10), the toe gear effect has the club COG moving along a line not thru the ball COG but inside it, so the toe hits the back of the ball and not the center of the club and COG hitting the back of the ball. This sort of impact knocks the face of the club open. The ball and club face act as if in contact like two enmeshed gears. The backward opening of the face (clockwise for a right-hander looking down at the top of the club) spins the ball the opposite way, counterclockwise, which is a hook spin. The opposite tendencies at work are an open face imparting some slice spin and starting angle off to the right, versus the gear effect imparting hook spin. The trick is for the gear effect to be designed in just right to overcome the slice spin so the ball starts right but then curves hookish back to the center of the fairway.

The "bulge" of a driver face is a curvature of the face along the Y-axis horizontally. This toe curve increases the slice spin and the start angle to the right. Most golfers probably think the bulge increases the gear effect, but this is not correct. A FLAT driver face basically has too much gear effect designed in, and the bulging removes some of the gear effect to get the balance adjusted between slice and hook spin. Too much bulge and the balls just slice.

Applying all this to a VERTICAL gear effect and considering the difference between driver and putter impacts with a ball and the difference in the heel hoseling of drivers that is essentially like a stick entering the driver head horizontally at the heel versus a putter hosel that is a stick entering the head vertically and the difference between balls spinning in the air and balls rolling on the ground, it is fairly evident that the driver "gear effect" horizontally and the putter "gear effect" vertically may not have all that much in common in their physics.

SKID, ROLL, and SPIN

Let's get another drink of water and go back even further, this time to the physics of imparting roll or spin to a ball.

When a putter impacts the equator of a ball moving level thru the back of the ball, and with the putter COG level with the ball COG, the blow imparts all skid and no roll. The roll that eventually shows up is all due to the friction of the grass on the bottom of the sliding ball, making it roll top-forward-down / bottom-back-up. This is not the sort of phenomenon we are looking for, as the "gear effect" imparts spin to the ball solely from the impact dynamics of the relative face and ball COGs in motion and the reaction of the face and ball. For a blow to impart spin of some sort (not resulting from skid), the blow needs to be such that the COG of the instrument moves not thru the center of the ball but above or below the center.

A blow of sweetspot-thru-sweetspot level with no loft produces all skid and no roll. Any roll that eventually shows up comes solely from friction of the grass on the bottom of the ball causing the ball to roll more and more until the rolling speed matches the translational speed, and then there is no more skid. For the blow itself to impart some "early" roll not dervived from the grass "sliding friction," the blow has to "torque" the sphere of the ball. This means a blow directed above or below the ball's COG.

The relevant physics is explained in detail in the great little site named The Physics of Pool.

Once the ball is struck, there is an initial period in the roll of pure acceleration up to a velocity of the ball away from the face. Then, the ball is ordinarily sliding across the ground as the "sliding friction" makes the ball start rolling top-forward. Once the rotational speed of the ball increasaes sufficiently to match the translational speed of the ball's COG horizontally across the green, there is no more "sliding friction" and no more "skid" - the ball is only rolling subject to "rolling friction." Rolling friction is somewhere around 1/10th as much as "sliding friction," but it is enough eventually to bring the ball to a gradual stop (on level ground, where gravity is not adding or subtracting forces).

This chart from the Oxford Croquet website shows the three phases of acceleration (very short), skidding-to-rolling, and only rolling.

In fact, there is a final phase called the "decay" phase where the ball's rolling slows to a point that allows the ball to sink back into the grass a little. This increases the rolling friction, and brings the ball to a halt a little quicker. Slow greens have more "decay rolling friction" than fast green. Indeed, slow greens have more "sliding friction" and more "rolling friction" in general, so putts on slow greens have a quicker skid phase, not as long a rolling phase, and a more abrupt decay phase.

This chart shows the "knee" where the decay phase onset occurs for various green speeds:

The "knee" is around 9-10 feet out in this 11-foot putt.

The function of back spin and top spin in all of this is to shorten or even prolong the skid phase. In general, back spin makes the skid phase last longer, while top spin makes the skid phase end sooner. Altering the ball-green friction at the outset of the roll can also affect the length of the skid phase.

When the putter COG is low, does the higher ball COG knock the putter face top-back? It seems that the shafting and hoseling would likely resist this pretty good, as if the driver had the shaft inserted horizontally into the toe-end of the driver face. That is, the fact that the hosel is attached to the putter face in the VERTICAL plane would seem to cancel or greatly reduce any tendency of the putter face to get knocked top-back. This would seem to be the case even if the putter head COG is recessed back from the face (on the X-axis). If the putter face is not "opening" vertically top-back, there would seem to be no "gear effect" at all. Perhaps I am wrong about the flexibility of the shaft-hosel-putter head assembly. If so, then putter shaft flex should be a great big issue.

If the putter face is moving "level" thru the ball, it is worth noting that a "loftless" face presentation to the ball would necessarily impact the ball on the equator. In the vertical look at the profile of the back of the ball, the equator is closest to the putter face of all parts of the ball. In order for a putter face to be lofted but moving level so that the point of impact on the ball was actually above or below the equator, the lofting (positive or negative) would have to be pretty severe, slanting the leading edge of the tilted face sufficiently that the putter face first comes in contact with a point on the back of the ball not as near the face as the equator. In order to hit the back of the ball on a point below the equator, it is necessary as a practical matter to move the putter not level but upwards into the lower back quadrant of the ball. Similarly, in order to hit the back of the ball higher than the equator, it is necessary as a practical matter to move the putter not level but downwards onto the upper back quadrant of the ball.

Let's try something else. Suppose the putter face is NOT moving level thru the ball, but instead is moving on a rising trajectory with the face COG curling up and passing thru the ball's COG. Assume further that the rising trajectory does not add dynamic loft to the face at impact, but the face is vertical and parallel to the line in the ball from top of ball to bottom of ball on a level green. In this case, there would still not be any "gear effect" as in a driver. In a driver, the face of the club runs toe-back and center-out in a clockwise face turning that slides outward across the back of the ball to give hook spin. And the path of the driver COG does not pass thru the ball COG, but inside it. The putter-ball impact here envisioned would seem simply to launch the ball along the rising trajectory of the face COG, but not otherwise impart overspin -- just a dead-ball punch upward off the ground a bit.

So how do we configure a putter face-ball impact in order to give the ball overspin? The first question is why does a normal putter give the ball backspin?

A "normal" putter has about 3 degrees of loft. Assuming the lofted face is moving level thry the ball with face COG level with ball COG, what happens? It seems the point of contact would be on the equator of the ball, but then the ball would start to slide or roll up the face of the putter because of the 3-degree tilt top-back. And from a vertical perspective, back spin is slice spin. So it's fairly easy to see how positive loft creates back spin.

But, as soon as the ball slides up the face, then we have the scenario of the driver "gear effect." So why doesn't loft create "gear effect" hook spin, or does it? The face COG is moving inside, the ball COG is outside, and the face is "open" top-back in a slice (upward) presentation to the ball - just like in a driver "gear effect." So far, we have slice spin (back spin vertically). The "gear effect" giving hook spin comes about only when the face COG moves upward toward the ball COG away from the ground (on the Z-axis). Does it? This is where I think the vertical hosel comes into play to reduce or eliminate this action. By preventing the face from "opening" more top-back, the only way the face COG can move up across the back of the ball is for the whole putter to rebound vertically. This is opposed by the golfer's whole body extending the putter downward to the ball.

Does negative loft reduce backspin or impart top spin? Assuming a level blow with a negative-loft face (top edge of face tilted ballward), the ball could not slide down the face because it is already on the ground and there is no more "down" to go (except punching the ball into the turf). Apparently what happens is that the face initially hits the ball's equator, forces the ball a little into the turf thus lowering the ball COG below the face COG, and redirects the impact dynamics so that the face COG is moving level thru the upper quadrant of the ball. This is something of a glancing blow with a little less energy than a flush face-sweetspot thru ball-sweetspot impact trajectory. But it would seem to reduce back spin and increase top spin.

What role does having the COG recessed back from the face play? This is one of the key features for driver gear effect. But in the putting stroke, I believe that the recessed COG really just means that face impact occurs while the putter COG is in a retarded phase of the putting arc, not yet rising as much as the face. So having the putter COG recessed is just a way to get a lower start up thru the ball than otherwise. If the path of that recessed sweetspot cuts upward thru the ball higher than the ball's COG, perhaps that's all that really matters.

All that said, it seems to me that the only real way to get topspin is to have something of a glancing blow in which the face COG is not moving on a trajectory thru the ball's COG, but is instead moving either up from the lower back quadrant on a path higher than the ball COG or moving from the equator on a path that takes the putter COG higher than the ball's COG or moving thru the top quadrant of the ball on a path higher than the ball's COG. It's all about the path of the face COG staying above the ball's COG.

This explains to me why Harold Swash teaches a hands-ahead rising blow thru the ball that presents the face "tangentially." On any point on the surface of a sphere like a golf ball, there is a direction aimed at the center of the ball (it's COG), and a "plane" that rests on the outter surface of the ball at this point is a "tangent" plane when the plane is perpendicular to the radial line aimed at the center of the sphere. I gather that Harold Swash is referring to the putter face matching this tangential plane on the ball at impact. That explains the hands-ahead delofting the putter so the face can match the tangential plane on the ball. The delofting also implies that the impact point is either on the equator or the top quadrant of the ball, but not the lower quadrant. The rising blow implies that the path of the face COG is moving thru the ball higher than the ball's COG.

Personally, I believe that reducing the back spin and increasing the top spin can be done without the hands-ahead delofting of the putter and a top-quadrant blow. By simply moving the putter's COG up thru the ball on a path higher than the ball's COG, the objective is accomplished. This can be done without the hands-ahead delofting by using a normal pendulum stroke with dead hands and ball position well forward of the bottom of the stroke that presents the face of the putter to the back of the ball when it is rising AND on a path that takes the putter COG up thru the back quadrant of the ball and out thru the ball higher than the ball's COG. Keeping the loft to a minimum would reduce launching the ball in the air, and negative loft used in this sort of impact probably helps the top spin.

In conclusion, I'm not convinced that the true physics of back spin and top spin have been propely described. I believe it is the PATH of the putter sweetspot thru the ball, and not so much the "gear effect" or even the "cue stick" type blow.

This brings us back to the underlying issue that has not received sufficient attention -- whether back spin or absence of top spin matters? If we have to craft a stroke so carefully that the trajectory of the sweetspot of the putter has to fall within a very narrow range or possible trajectories, is it worth all the trouble?

Skid robs a ball of energy, and so the stroke doesn't send the ball as far as it would otherwise. Who cares, so long as the ball gets to the hole? One can become very proficient and have great touch even though the ball skids a lot, so long as the technique is consistent and the skidding is consistent. The real question is whether the skid does something worse to the putt, like send the ball off line or make it hop. I've never seen a study about this.

It stands to reason that a skidding ball is "more violent" in a sense than a rolling ball, and a more "violent" ball is more likely to do something unwanted. Maybe so, but how likely? Is the reward of not worrying about true roll worth the risk of the ball running seriously off line? I don't really know, and so far as I can tell, neither does anyone else.

The C-Groove testing does conclude that a shorter skid phase and a more accurate holding of the line go hand in hand. According to robotic tests, the C-Groove has a 3-inch skid versus the typical 18-inch skid for most putter designs (factor of 6), while the C-Groove has a mere 1-inch dispersion over a 50-foot putt versus a conventional design dispersion of 3 inches (factor of 3).

Unfortunately, the exact trajectory of the putter COG thru the ball is not indicated.

Assuming that a "truer" roll is worth the price of extra trouble and fragility in the technique, I would suggest the simplest technique to improve the roll and reduce the skid is the best technique. For this reason, I prefer ball position and dead hands rather than forward pressing loft out and then impacting the ball with hands-ahead and perhaps a descending blow as well (too complex).

With this approach, then, whether a high-COG or low-COG is better is anyone's guess. I suspect that a high-COG with little positive loft used with dead hands and a rising blow is safer to make sure the putter COG stays above the ball COG on its way thru the ball. But I have to say that only carefully designed high-speed camera work that carefully accounts for the trajectory of the putter COG thru the ball is likely to get this sorted out properly.

We'll get it figured out one day. In the meantime, I'm not convinced that "true roll" is worth all the bother. Just play the ball well forward of the bottom of the stroke, use a simple stroke technique, and use a slow tempo without "percussion" against the ball. Keep the violence out, and that's probably good enough until we know more.

Cheers!

Geoff Mangum
Putting Theorist and Instructor
Geoff Mangum's PuttingZone
http://puttingzone.com
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High Jeff

Damn you have tapped into my mind from USA to New Zealand

ie your words " Skid robs a ball of energy, and so the stroke doesn't send the ball as far as it would otherwise. Who cares, so long as the ball gets to the hole? One can become very proficient and have great touch even though the ball skids a lot, so long as the technique is consistent and the skidding is consistent. The real question is whether the skid does something worse to the putt, like send the ball off line or make it hop. I've never seen a study about this.
"

IMHO There is more marketing nonsense spoken about this area than any other area in putter design!

Cheers

Simon

Dr Norman Lindsay
Dr Norman Lindsay
Boy, did you ever put your finger on the heart of the matter! There are two big issues in putter design right now -- location of the COG in 3 dimensions and how to hosel. The COG issue is being handled in diametrically opposite ways by three camps among putter manufacturers (low, high, level), each backed up by "true roll" studies, and neither really communicating or debating the issue directly. I'm not sure how this will all finally sort itself out, but clearly there must be some basic uncertainties in the definitions or understandings about the underlying physics. perhaps it is only a matter of the "relevant" physics, and the real choices are occuring in how the golfer actually uses one type versus another.

The three dimension of COG location in the putter head can be related to the X, Y, and Z axes of a standard Cartesian coordinate system with its origin (intersection of axes) located in the ball's COG. The X axis is the same as the direction of the putt or left-right from the golfer's point of view, the Z axis is up-down, and the Y axis if front-back or near-far. The choices are 1) centered heel-toe in the Y axis, 2) high or low in the Z axis in relation to the ball's COG at impact, and 3) close to the putter face or farther back in the putter head in the X axis. The one dimension addressed by your question is the Z axis (2).

The Golfer stands where the upright blue arrow is located. The ball is located in the center of the axes.

The Center of Gravity (COG) of the ball is located in the center of the sphere, unless the ball is out of balance or out of round.

Let's leave aside for the moment the fundamental question of whether topspin is desireable, and if so, why and how desireable is it -- or the correlated question of whether backspin is undesireable, and if so, why and how undesireable is it -- questions that seems to be somewhat unexamined in detail, and certainly deserving of greater scrutiny and scientific investigation.

Camp 1 - LOW COG FOR "GEAR EFFECT"

Those who make a low COG putter include C-Groove / Yes!, Scotty Cameron, Ping Craz-E, Q-Roll, the Resso, and many others. And there are different approaches to accomplishing the same thing.

Typically, the putter design simply has a concentration of mass low on the back flange, as does the C-Groove Amy model:

Ontic, for example, in effect has a "heel-toe" scheme in the vertical dimension, with low sole plates on the heel and toe, and a raised sole in the center. This effectively lowers the putter COG.

The person who seems to have the best studies supporting a low COG putter design is Norman Lindsay at his website Lindsay Putters. He combines a number of design features into his "All Topspin (All-TS)" putters, including a low COG. His site illustrates the high-speed camera studies he's done, and explains the "gear effect" producing topspin by a low COG combined with certain lofting features and certain impact dynamics resulting from the way the golfer presents the putter face to the back of the ball.

Lindsay writes:

The facts are:

* All conventional putters impart backspin.
* Some can also generate a little topspin.
* The amount and direction of spin depends on where the ball impacts the striking face.
* With any golf club (from putter through to driver), the higher the point of impact on the clubface, the less the backspin.
* With a putter  if the design is right  the spin becomes topspin for impacts near the top of the face.
* A badly designed putter can give so much backspin that the ball loses 35% or more of its initial energy through skidding before it gets rolling. (High topspin putters can reduce this to 20% or less.)

Lindsay putters impart high topspin over the entire striking face, providing modern-age performance that would enthral bygone masters such as Bobby Locke. This unique achievement is the result of expertly combining the only two mechanisms that genuinely put spin on a golf ball, namely;

* Gear-effect, which relies on the putter-head weight distribution, but is also critically dependent on the way the shaft attaches to the head.
* Oblique impact - the workhorse of golf shots. This shapes flight trajectory and puts backspin on the ball. Backspin is essential for distance in long shots and control in approach shots. In putters, it can be used in reverse to give topspin.

So Lindsay says reducing backspin / increasing topspin comes ONLY from the gear effect and certain dynamic loft thru impact, which he terms "oblique impact."

Lindsay elaborates about these two sources:

WHAT GIVES TOPSPIN?

* Vertical gear effect
Its well known that hitting the ball off the heel or toe of a driver puts sidespin on the ball, even if the clubface is square at impact. The same happens with a putter. Whats less well known is that vertical spin changes with impacts above or below the sweet spot. Hits above the sweet spot (on a putter) give topspin. Hits below the sweet spot give backspin.

* Low centre of gravity
The sweet spot must be low to ensure vertical gear effect works to give topspin. In most putters the CG is not low enough to place the sweet spot below the centre of the striking face. Lindsay putter-heads have exceptionally low CG with the sweet spot well below centre. For hits at or near the centre, topspin compensates for linear ball velocity changes, giving superb putt length consistency. [This is the Z-axis.]

* Deep centre of gravity
Gear effect is proportional to the depth of the CG behind the putter face. For good topspin you need the putter-head CG positioned from half to two inches behind the face. [This is the X-axis.]

* Low minimum inertia
Low minimum inertia (front-back weighting) assists vertical gear effect, giving higher topspin. At the same time its important to have high heel-toe weighting (i.e. high maximum inertia).

* Variable face loft
Gradual loft reduction (face roll) can be used on the bottom of the putter-face to introduce a small amount of negative loft. This generates topspin by oblique impact, even though the ball is hit on the upswing on this part of the putter-face. This arrangement is especially beneficial for length control on long putts.

* Centred shaft axis
Lindsays recent pioneering research into putter impact has revealed a major problem - the position of the shaft axis is critical for vertical gear effect. Aligning the shaft axis with the putter-head CG ensures the best performance for topspin and feel. [This refers to centering on the Y-axis heel-toe.]

Apparently, the "gear effect" adds topspin when the point of impact on the putter face is centered in the Y-axis, the putter COG is lower than the point of impact on the back of the ball in the Z-axis. Lindsay considers locating the COG back along the X-axis, plus hoseling the shaft in the center of the Y-axis, plus minimum front-back weighting, plus the radiusing of the face in the lower half of the face to help out when the point of impact on the ball is too low, plus minimal lofting or even negative lofting in the radiusing low on the face, all as promoting topspin in some supplemental or complementary way. But I gather that the real fundamental is the "gear effect." So the "gear effect" is pretty much a low COG in the putter face, impact high on the face, impact on the equator of the ball, and the putter COG lower than the ball COG at impact.

Camp 2 - HIGH COG AND THE CUE-BALL LEVEL BLOW THRU THE TOP QUADRANT

The second approach is to locate the putter COG high on the face (Z-axis) and replicate what happens when a cue stick imparts top spin to a cue ball in billiards. Daish in his book The Physics of Ball Games describes how a level blow of the cue stick thru the top quadrant of the cue ball at a height 5/7th the way up from the bottom of the ball perfectly matches the forward translational force with the rotational top-over rolling of the ball to eliminate skid entirely. In effect, the pointed stick delivers the stick's COG level thru the top quadrant of the ball higher than the ball's COG. Putters that take this design approach include the Tear Drop, the Breeds Confidence, the Big Oak, the Aserta, and others.

But since the putter face COG is above the ball COG with the face moving level or rising thru impact, doesn't this present a "gear effect" scenario in reverse -- one in which the putter face tilts bottom-back-up so that the face ought to wheel down counterclockwise on the back of the ball, imparting back spin (which would be slice spin for the driver)? In this case, it is probable that the vertical hosel has less tendency to oppose the counterclockwise action of the putter face than it does in the case of a clockwise gear effect. So a high-COG putter ought to impart back spin the same as or perhaps more than a low-COG putter ought to impart top spin by virtue of the "gear effect."

The Aserta company has comparisons of skid distances of the Aserta putter versus other putters, based on robotic putting tests performed with the Swing Dynamics Putting Track Monitor. The description of the testing procedure does not make clear the trajectory of the putter COG in relation to the ball's COG. Even so, the data shows a forward spin on the Aserta putts in excess of 100 revolutions per minute (about 1.7 revolutions per second) versus back spins of the order of 35 to 60 revolutions per minute (about 0.5 to 1.0 revolutions per second) back spin. See Aserta Inverted Mass Technology. This data just deepens the mystery.

Camp 3 -- COG-to-COG Level

The T-Roll Putter from perry Golf has a design in which the putter COG is the same height as the ball COG. The ball COG is one-half the diameter of the ball up, or in the center, 0.84 inches above the bottom of the ball. The idea is to promote "solid" impact and solid "feel."

The relative positions of the COGs is described for the T-Roll versus the conventional design:

The T-Roll company has a fairly clear explanation of the theory;

Most golf putter heads are heel and toe weighted to create a larger 'horizontal' sweet spot. They have very little mass at the center and top of the putter head. Most of the weight is at the bottom or sole of the putter head. The 'Sweet Spot' is positioned below the center of mass of the golf ball. Since the 'sweet spot' is located below the center of mass of the golf ball, the putter upon contact with the golf ball does not have a very solid feel. Also, most putters are designed with the shaft connected at the heel, inside the center of mass. Upon contact with the golf ball, the putter head tends to twist and rotate on a horizontal plane.

The T-Roll® golf putter is designed with most of the weight located away from the center of mass, creating a very high moment of inertia. (The T-Roll® Defiant with Brass plug inserts is 4699 gm*cm^2.  The T-Roll® Defiant with Tungsten plug inserts is 6431 gm*cm^2.)  Also, the 'T' shaped mass on the The T-Roll® golf putter shifts the center of mass towards the top of the putter head, aligning itself horizontally with the center of mass of the golf ball. By aligning the 'Sweet Spot' on the putter head perfectly with the center of mass of the golf ball, this creates the most solid feeling putter possible. The shaft is connected to the 'T' shaped mass near the sightline. The putter head does not twist or rotate upon contact with the golf ball. Due to its high moment of inertia, even off-center hits cause minimal twisting or rotation of the putter head.

This analysis leaves out, however, the PATH of the putter COG relative to the ball COG thru the ball / impact zone. I suspect that in practical use the T-Roll's "level with the ball" COG merely functions to ensure that the path of the T-Roll COG stays above the ball''s COG. Afterall, a truly level COG-to-COG blow thru the ball would result in all skid. I would not think the 3-degree lofting of this putter would help reduce skid, as this makes the ball rise on the putter face so the ball COG is higher than the putter COG. However, if this effect is overcome by the putter rising into the back of the ball on a high trajectory, then the face loft effect is neutralized and overcome.

SORTING THIS OUT AS BEST WE CAN

Let's get a drink of water, and then go back to the basic idea of "gear effect."

GEAR EFFECT & PUTTING

In a driver, the "gear effect" imparts some hook spin on a ball hit near the toe, or slice spin on a ball hit near the heel, with the driver COG centered on the Y-axis heel-toe. Placing the COG back in the driver from the face on the X-axis increases the gear effect. According to Cochran and Stobbs, Search for the Perfect swing, pages 117-119 (and especially Fig. 19-10), the toe gear effect has the club COG moving along a line not thru the ball COG but inside it, so the toe hits the back of the ball and not the center of the club and COG hitting the back of the ball. This sort of impact knocks the face of the club open. The ball and club face act as if in contact like two enmeshed gears. The backward opening of the face (clockwise for a right-hander looking down at the top of the club) spins the ball the opposite way, counterclockwise, which is a hook spin. The opposite tendencies at work are an open face imparting some slice spin and starting angle off to the right, versus the gear effect imparting hook spin. The trick is for the gear effect to be designed in just right to overcome the slice spin so the ball starts right but then curves hookish back to the center of the fairway.

The "bulge" of a driver face is a curvature of the face along the Y-axis horizontally. This toe curve increases the slice spin and the start angle to the right. Most golfers probably think the bulge increases the gear effect, but this is not correct. A FLAT driver face basically has too much gear effect designed in, and the bulging removes some of the gear effect to get the balance adjusted between slice and hook spin. Too much bulge and the balls just slice.

Applying all this to a VERTICAL gear effect and considering the difference between driver and putter impacts with a ball and the difference in the heel hoseling of drivers that is essentially like a stick entering the driver head horizontally at the heel versus a putter hosel that is a stick entering the head vertically and the difference between balls spinning in the air and balls rolling on the ground, it is fairly evident that the driver "gear effect" horizontally and the putter "gear effect" vertically may not have all that much in common in their physics.

SKID, ROLL, and SPIN

Let's get another drink of water and go back even further, this time to the physics of imparting roll or spin to a ball.

When a putter impacts the equator of a ball moving level thru the back of the ball, and with the putter COG level with the ball COG, the blow imparts all skid and no roll. The roll that eventually shows up is all due to the friction of the grass on the bottom of the sliding ball, making it roll top-forward-down / bottom-back-up. This is not the sort of phenomenon we are looking for, as the "gear effect" imparts spin to the ball solely from the impact dynamics of the relative face and ball COGs in motion and the reaction of the face and ball. For a blow to impart spin of some sort (not resulting from skid), the blow needs to be such that the COG of the instrument moves not thru the center of the ball but above or below the center.

A blow of sweetspot-thru-sweetspot level with no loft produces all skid and no roll. Any roll that eventually shows up comes solely from friction of the grass on the bottom of the ball causing the ball to roll more and more until the rolling speed matches the translational speed, and then there is no more skid. For the blow itself to impart some "early" roll not dervived from the grass "sliding friction," the blow has to "torque" the sphere of the ball. This means a blow directed above or below the ball's COG.

The relevant physics is explained in detail in the great little site named The Physics of Pool.

Once the ball is struck, there is an initial period in the roll of pure acceleration up to a velocity of the ball away from the face. Then, the ball is ordinarily sliding across the ground as the "sliding friction" makes the ball start rolling top-forward. Once the rotational speed of the ball increasaes sufficiently to match the translational speed of the ball's COG horizontally across the green, there is no more "sliding friction" and no more "skid" - the ball is only rolling subject to "rolling friction." Rolling friction is somewhere around 1/10th as much as "sliding friction," but it is enough eventually to bring the ball to a gradual stop (on level ground, where gravity is not adding or subtracting forces).

This chart from the Oxford Croquet website shows the three phases of acceleration (very short), skidding-to-rolling, and only rolling.

In fact, there is a final phase called the "decay" phase where the ball's rolling slows to a point that allows the ball to sink back into the grass a little. This increases the rolling friction, and brings the ball to a halt a little quicker. Slow greens have more "decay rolling friction" than fast green. Indeed, slow greens have more "sliding friction" and more "rolling friction" in general, so putts on slow greens have a quicker skid phase, not as long a rolling phase, and a more abrupt decay phase.

This chart shows the "knee" where the decay phase onset occurs for various green speeds:

The "knee" is around 9-10 feet out in this 11-foot putt.

The function of back spin and top spin in all of this is to shorten or even prolong the skid phase. In general, back spin makes the skid phase last longer, while top spin makes the skid phase end sooner. Altering the ball-green friction at the outset of the roll can also affect the length of the skid phase.

When the putter COG is low, does the higher ball COG knock the putter face top-back? It seems that the shafting and hoseling would likely resist this pretty good, as if the driver had the shaft inserted horizontally into the toe-end of the driver face. That is, the fact that the hosel is attached to the putter face in the VERTICAL plane would seem to cancel or greatly reduce any tendency of the putter face to get knocked top-back. This would seem to be the case even if the putter head COG is recessed back from the face (on the X-axis). If the putter face is not "opening" vertically top-back, there would seem to be no "gear effect" at all. Perhaps I am wrong about the flexibility of the shaft-hosel-putter head assembly. If so, then putter shaft flex should be a great big issue.

If the putter face is moving "level" thru the ball, it is worth noting that a "loftless" face presentation to the ball would necessarily impact the ball on the equator. In the vertical look at the profile of the back of the ball, the equator is closest to the putter face of all parts of the ball. In order for a putter face to be lofted but moving level so that the point of impact on the ball was actually above or below the equator, the lofting (positive or negative) would have to be pretty severe, slanting the leading edge of the tilted face sufficiently that the putter face first comes in contact with a point on the back of the ball not as near the face as the equator. In order to hit the back of the ball on a point below the equator, it is necessary as a practical matter to move the putter not level but upwards into the lower back quadrant of the ball. Similarly, in order to hit the back of the ball higher than the equator, it is necessary as a practical matter to move the putter not level but downwards onto the upper back quadrant of the ball.

Let's try something else. Suppose the putter face is NOT moving level thru the ball, but instead is moving on a rising trajectory with the face COG curling up and passing thru the ball's COG. Assume further that the rising trajectory does not add dynamic loft to the face at impact, but the face is vertical and parallel to the line in the ball from top of ball to bottom of ball on a level green. In this case, there would still not be any "gear effect" as in a driver. In a driver, the face of the club runs toe-back and center-out in a clockwise face turning that slides outward across the back of the ball to give hook spin. And the path of the driver COG does not pass thru the ball COG, but inside it. The putter-ball impact here envisioned would seem simply to launch the ball along the rising trajectory of the face COG, but not otherwise impart overspin -- just a dead-ball punch upward off the ground a bit.

So how do we configure a putter face-ball impact in order to give the ball overspin? The first question is why does a normal putter give the ball backspin?

A "normal" putter has about 3 degrees of loft. Assuming the lofted face is moving level thry the ball with face COG level with ball COG, what happens? It seems the point of contact would be on the equator of the ball, but then the ball would start to slide or roll up the face of the putter because of the 3-degree tilt top-back. And from a vertical perspective, back spin is slice spin. So it's fairly easy to see how positive loft creates back spin.

But, as soon as the ball slides up the face, then we have the scenario of the driver "gear effect." So why doesn't loft create "gear effect" hook spin, or does it? The face COG is moving inside, the ball COG is outside, and the face is "open" top-back in a slice (upward) presentation to the ball - just like in a driver "gear effect." So far, we have slice spin (back spin vertically). The "gear effect" giving hook spin comes about only when the face COG moves upward toward the ball COG away from the ground (on the Z-axis). Does it? This is where I think the vertical hosel comes into play to reduce or eliminate this action. By preventing the face from "opening" more top-back, the only way the face COG can move up across the back of the ball is for the whole putter to rebound vertically. This is opposed by the golfer's whole body extending the putter downward to the ball.

Does negative loft reduce backspin or impart top spin? Assuming a level blow with a negative-loft face (top edge of face tilted ballward), the ball could not slide down the face because it is already on the ground and there is no more "down" to go (except punching the ball into the turf). Apparently what happens is that the face initially hits the ball's equator, forces the ball a little into the turf thus lowering the ball COG below the face COG, and redirects the impact dynamics so that the face COG is moving level thru the upper quadrant of the ball. This is something of a glancing blow with a little less energy than a flush face-sweetspot thru ball-sweetspot impact trajectory. But it would seem to reduce back spin and increase top spin.

What role does having the COG recessed back from the face play? This is one of the key features for driver gear effect. But in the putting stroke, I believe that the recessed COG really just means that face impact occurs while the putter COG is in a retarded phase of the putting arc, not yet rising as much as the face. So having the putter COG recessed is just a way to get a lower start up thru the ball than otherwise. If the path of that recessed sweetspot cuts upward thru the ball higher than the ball's COG, perhaps that's all that really matters.

All that said, it seems to me that the only real way to get topspin is to have something of a glancing blow in which the face COG is not moving on a trajectory thru the ball's COG, but is instead moving either up from the lower back quadrant on a path higher than the ball COG or moving from the equator on a path that takes the putter COG higher than the ball's COG or moving thru the top quadrant of the ball on a path higher than the ball's COG. It's all about the path of the face COG staying above the ball's COG.

This explains to me why Harold Swash teaches a hands-ahead rising blow thru the ball that presents the face "tangentially." On any point on the surface of a sphere like a golf ball, there is a direction aimed at the center of the ball (it's COG), and a "plane" that rests on the outter surface of the ball at this point is a "tangent" plane when the plane is perpendicular to the radial line aimed at the center of the sphere. I gather that Harold Swash is referring to the putter face matching this tangential plane on the ball at impact. That explains the hands-ahead delofting the putter so the face can match the tangential plane on the ball. The delofting also implies that the impact point is either on the equator or the top quadrant of the ball, but not the lower quadrant. The rising blow implies that the path of the face COG is moving thru the ball higher than the ball's COG.

Personally, I believe that reducing the back spin and increasing the top spin can be done without the hands-ahead delofting of the putter and a top-quadrant blow. By simply moving the putter's COG up thru the ball on a path higher than the ball's COG, the objective is accomplished. This can be done without the hands-ahead delofting by using a normal pendulum stroke with dead hands and ball position well forward of the bottom of the stroke that presents the face of the putter to the back of the ball when it is rising AND on a path that takes the putter COG up thru the back quadrant of the ball and out thru the ball higher than the ball's COG. Keeping the loft to a minimum would reduce launching the ball in the air, and negative loft used in this sort of impact probably helps the top spin.

In conclusion, I'm not convinced that the true physics of back spin and top spin have been propely described. I believe it is the PATH of the putter sweetspot thru the ball, and not so much the "gear effect" or even the "cue stick" type blow.

This brings us back to the underlying issue that has not received sufficient attention -- whether back spin or absence of top spin matters? If we have to craft a stroke so carefully that the trajectory of the sweetspot of the putter has to fall within a very narrow range or possible trajectories, is it worth all the trouble?

Skid robs a ball of energy, and so the stroke doesn't send the ball as far as it would otherwise. Who cares, so long as the ball gets to the hole? One can become very proficient and have great touch even though the ball skids a lot, so long as the technique is consistent and the skidding is consistent. The real question is whether the skid does something worse to the putt, like send the ball off line or make it hop. I've never seen a study about this.

It stands to reason that a skidding ball is "more violent" in a sense than a rolling ball, and a more "violent" ball is more likely to do something unwanted. Maybe so, but how likely? Is the reward of not worrying about true roll worth the risk of the ball running seriously off line? I don't really know, and so far as I can tell, neither does anyone else.

The C-Groove testing does conclude that a shorter skid phase and a more accurate holding of the line go hand in hand. According to robotic tests, the C-Groove has a 3-inch skid versus the typical 18-inch skid for most putter designs (factor of 6), while the C-Groove has a mere 1-inch dispersion over a 50-foot putt versus a conventional design dispersion of 3 inches (factor of 3).

Unfortunately, the exact trajectory of the putter COG thru the ball is not indicated.

Assuming that a "truer" roll is worth the price of extra trouble and fragility in the technique, I would suggest the simplest technique to improve the roll and reduce the skid is the best technique. For this reason, I prefer ball position and dead hands rather than forward pressing loft out and then impacting the ball with hands-ahead and perhaps a descending blow as well (too complex).

With this approach, then, whether a high-COG or low-COG is better is anyone's guess. I suspect that a high-COG with little positive loft used with dead hands and a rising blow is safer to make sure the putter COG stays above the ball COG on its way thru the ball. But I have to say that only carefully designed high-speed camera work that carefully accounts for the trajectory of the putter COG thru the ball is likely to get this sorted out properly.

We'll get it figured out one day. In the meantime, I'm not convinced that "true roll" is worth all the bother. Just play the ball well forward of the bottom of the stroke, use a simple stroke technique, and use a slow tempo without "percussion" against the ball. Keep the violence out, and that's probably good enough until we know more.

Cheers!

Geoff Mangum
Putting Theorist and Instructor
Geoff Mangum's PuttingZone
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Skids, Squirts & Scandals

Dear Geoff,

I recently found your essay entitled Path of COG - not Height - is Probably Key. You state that there must be some basic uncertainties in the definitions or understandings about the underlying physics of this subject.

On the contrary, I know that the physics is well understood, certainly well enough to decide whether low or high COG generates more or less topspin. There is a wealth of good experimental data that proves the accepted theory.

A year ago I sent you a draft copy of my paper Topspin in putters a study of vertical gear-effect and its dependence on shaft coupling (Lindsay 2003). This paper gives chapter and verse on the subject of putter weighting and topspin and also presents significant original research on how the shaft affects clubhead rotation at impact. It describes new techniques for measuring spin performance and some results of these measurements are published, including data from the C-Groove putter and the Odyssey 2-ball.

Your reply to J P Vegas is a tour de force, and I admire your obvious enthusiasm for the subject, but the guy just needed the right answer and not a choice of three!

Lets start with your Camp 2, i.e. locate the putter COG high on the face and replicate what happens when a cue stick imparts top spin to a cue ball in billiards

For the record - a small correction. Striking a ball with a cue at height 7/10ths diameter eliminates skid (Daish 1972).

However, simply elevating a putters COG above the ball equator to 7/10ths diameter does not achieve the same effect as the cue stick in billiards or pool. Its impossible to contact a golf ball at a height of 7/10ths diameter with the face of a legal putter unless you are hitting down or otherwise de-lofting the face very severely. At 7/10ths diameter, the tangent (i.e. the slope of the balls surface) is -23.6 degrees to the vertical but the R&A and USGA have put a limit of 15 degrees on the permitted amount of negative loft in conforming putters.

Even if you did hit the ball with a -23.6 degrees negative loft putter face, you would not get the ball to roll without skidding. Initially, the ball would dig into the putting surface at an angle of about 20 degrees and, yes it would have some topspin, but probably less than a quarter of true rolling spin. It would then undergo a severe and abrupt skid, probably jump into the air, and its anyones guess what spin it would have after that.

YOU CANNOT INVOKE MATHEMATICS FROM POOL OR BILLIARDS TO EXPLAIN GOLF IMPACTS. The only instance where this is valid is for direct central impact.
There are huge differences between a billiard cue and a putter or any other golf club. The soft leather tip on the cue plays an important part but there are other obvious differences between the two implements. This is something I will attempt to explain in more detail at some future date on my website <a>Lindsay Putters</a>.

Meanwhile, to whet your appetite, have a look at these clips from a really good website for pool physics:

</a><a href="http://www.engr.colostate.edu/~dga/pool ... NV4-13.htm> (Squirt due to high speed English)

</a><a href="http://www.engr.colostate.edu/~dga/pool ... HSV4-4.htm> (High speed English close up)

The first clip is an elevated view of a cue ball demonstrating high speed left English where the ball is struck left of centre to give it clockwise spin (in plan view). The remarkable aspect of this sequence is that the deflection to the right, or squirt, is really quite small. If, instead of a cue, the ball was struck by a putter swung along the line of the cue stroke and with open face to hit the left side of the ball, the ball would get pushed to the right cushion and not go almost straight along the swing path as it does in the clip.

The second clip shows a close-up of the stick-on-ball impact in slow motion a brilliant demo. View this with zoom at 200% (right click to get zoom). Here, the cue stick hits the ball off centre at about 7/10ths diameter from the right edge and sure enough the ball rotates roughly 220 degrees over a distance of about two diameters, which approximately equates to the no skid at 7/10ths impact scenario. Also, note the momentary jump of the cue tip to the left very revealing.

Now to Camp 3. COG-to-COG Level

You cite the T-Roll Putter as a design in which the putter COG is the same height as the ball COG. I had a quick browse through the T-Roll website and, despite other nonsensical claims (e.g. 'Pushed' or 'Pulled' putts create sidespin on the golf ball and cause the golf ball to 'spin out' of the hole unless the golf ball hits the cup dead center), I could not find any claim that the T-Roll imparts topspin, so it is not really in contention.

However, delving into the origins of the Aserta Putter, I discover that the original science behind this novel putter is as follows

The club has a raised center of gravity intended to be in alignment with the center of a golf ball.This allows the club to strike the ball in a manner similar to a pool cue. In other words, forces transmitted to the ball along a horizontal line, parallel to the ground, which would go through the center of the ball. This imparts to the ball a forward rolling motion, without topspin. (Bonneau 2002)

I interpret the above extract from US Patent No. 6,383,089 as meaning that a horizontal strike on a ball with a pool cue right on its horizontal equator imparts immediate pure roll without over-spinning.

This is dangerous territory. There are a number of highly respected physics websites, not to mention a wealth of literature from Sir Isaac Newton onwards, that describe how under these impact conditions the ball skids until its linear velocity reduces to 5/7ths of its initial velocity before rolling. The over-spinning or topspin in US 6,383,089 is what you would expect from hitting a cue ball above 7/10ths diameter with a cue stick.

US 6,383,089 is a typical example of how patents are granted despite the invention being based on principles that are contrary to the known laws of physics. (In the above case, the law of conservation of angular momentum.)

Now, I have no doubt that some golfer swear by the Aserta (and dont even need to be paid to do so). They may be really convinced - and in some instances may actually experience - that it provides game improvement. But would the majority of Aserta buyers still be convinced of its amazing benefits if they knew it creates more backspin than a traditional, low COG putter? How many golfers have been duped by the Aserta website animation showing Immediate True Roll , thinking that this is the real McKoy and not realising that it was created by a graphic artist and bears absolutely no semblance to reality? This is all part of the scandal that pervades putter manufacture and putter marketing.

Now for Camp 1 LOW COG FOR "GEAR EFFECT"

Karsten Solheim, the founder of modern putter design, advocated maximising the weight low in the putter head to improve overspin at impact (Solheim 1995). His pioneering ideas, dating back to 1959, have since been copied and adapted in countless putter designs. So its not unusual to find lots of putters that more or less provide low COG, but your selection of examples of low COG putters is strange. Why the C-Groove Amy model is an example of concentration of mass low on the back flange is a mystery.

Your next example, the Ontic is even more surprising. Here you see a conventional putter body raised off the ground on two sliders or rails. How in the name of all that is wonderful does this lower the COG? It does the complete opposite. The bottom surface of the rails determine how low the body of the putter-head can be positioned relative to the golf ball. Therefore, the bottom of the rails form the datum from which the height of the COG is measured.

You are correct to question that Camp 1 and Camp 2 are completely contradictory but your conclusion that the Aserta data just deepens the mystery skirts round the really big issue in all this, namely, the habit that putter manufacturers have of lying shamelessly about the technology of their designs. In the case of Aserta, the invention is undoubtedly based on wishful thinking rather than deliberate deception. (After all, its been patented WOW!) However, the data they publish, while appearing to be better than competitors, goes nowhere near supporting the immediate true roll theory.

Incidentally, when is someone going to tell them that 2.216 inches is NOT the circumference of a standard regulation golf ball?

So how do some manufacturers demonstrate their putters giving more roll than the competition? The answer is, they show their putters giving earlier roll by simply arranging a flatter launch trajectory. This is shown in the following frames of video footage of the C-Groove putter, which claims to impart immediate pure roll (where have we heard that before?) by virtue of its unusually shaped grooves

FRAME 1 Note the C-GROOVE putter-head (lower picture) is about 3 inches behind the zero mark on the scale.

FRAME 2 The ball struck by the OTHER brand putter is off the ground you can see this from the shadow it casts. This ball is slowly spinning in mid-air with a combination of slight backspin and sidespin imparted by the putter impact.

Meanwhile, the C-GROOVE ball has already landed on the ground because its launch trajectory angle is one or two degrees lower. It is therefore skidding and at the same time picking up forward roll, which obliterates its initial launch spin. Note that the C-GROOVE putter-head has swung through 7 inches from FRAME 1 (-3 inches) to FRAME 2 (+4 inches).

FRAME 3 The ball struck by the OTHER brand putter is still just off the ground and has continued to rotate slowly in mid-air with its initial launch spin. As soon as it touches the ground it will start to pick up forward roll, just like the C-GROOVE ball.

The C-GROOVE ball continues to skid and so starts to rotate faster.

Note that the C-GROOVE putter-head has only swung 3 inches between FRAME 2 (+4 inches) to FRAME 3 (+7 inches). A putter-head decelerates slightly during impact but typically by only 20% or so and not by nearly 60%. Explanation?
THERE IS A MISSING FRAME JUST AFTER IMPACT !!

The video clip tells us nothing about the initial spin imparted on the C-GROOVE ball. The frame that might have given this information has been mysteriously deleted. It does show the C-GROOVE ball starting to roll earlier but this is entirely due to the fact that it also started to skid earlier, so the comparison is contrived and meaningless.

Working in golf technology, you soon realise that putter design is very much the poor relation in golf equipment research and development. Most research expenditure is in metal woods and golf balls, so a telling way of settling the controversy is to have a look at metal wood technology. </a><a href="http://www.bs-sports.co.jp/english/basi ... lub_5.html> (Basics of golf club design) is a page from Bridgestones excellent guide to golf equipment design. This gives simple, clear definitions and explanations to non-technical readers. Rest assured, behind every statement is a wealth of knowledge and research. Opening this page and scrolling down to Gear Effect, you will find a diagram illustrating both horizontal and vertical gear effect in a metal wood club, and there we see

Bottom of the face = more backspin
Top of the face = less backspin

In a lofted metal wood club the predominant ball spin is backspin but for impacts on the top of the face, gear effect generates a component of topspin (shown in the diagram), which reduces overall backspin, while the vertical gear effect generates additional backspin for impacts on the bottom of the face.

One thing that you wont find in the Bridgestone site is discussion of how the shaft affects gear effect. Until I published my research on shaft compliance modes (Lindsay 2003), the universally held theory was that the effect of the shaft could be neglected during the sub-millisecond duration of impact. This is often referred to as the free body model of club-on-ball impact. You only need to look at some recently published patents describing finely tuned mass and inertia designs of metal woods from some of the top golf research establishments to confirm that the free body model was until recently the accepted wisdom.

I note with interest that you have picked up on my research findings (Lindsay 2003) and use them in your essay as if they are common knowledge. Since this is recent research, it is standard practice and courteous to properly acknowledge the source of your information.

Path of COG - not Height - is this the answer?
Your theorising that topspin is best created by a rising blow so that the path of the face COG is moving thru the ball higher than the ball's COG has some validity but in practice wont work. What you are advocating is similar to getting topspin on a tennis ball. With tennis, the racquet is swung on a steep upward trajectory (e.g. 45 degrees or so) yet the ball is still stuck near the centre of the racquet. Putting topspin on a tennis ball struck from the middle of the racquet is a perfect example of vertical oblique impact a basic concept found in all good dynamics textbooks. It is impossible to achieve any useful degree of vertical oblique impact with a putter. A rising blow with just a few degree of upward attack angle will lift the putter-head to make contact on the lower half of the putter face. This in turn will negate any slight topspin created by the oblique impact.

Have a look at </a><a href="http://www.lindsayputters.com/spinmeasu ... ements.htm> (Spin measurements) on my website. This shows that the higher the putter head at impact, the lower the impact point on the putter face and the greater the backspin. The effect is particularly strong with mallets, which usually have greater gear effect characteristics than blade designs.

I strongly advise that you temper your theorising with experiments and measurements of what actually happens. Science is about making the theory fit the facts and not the other way round. It doesnt take much to replicate the measurements shown on my website and you dont need to have huge budget or a PhD in engineering or physics. Take a look at </a><a href="http://tuhsphysics.ttsd.k12.or.us/Resea ... hysics.htm> (Kyle Peytons experiments).
I dont agree with many of her findings but here is a school kid who shows fantastic determination, diligence and ingenuity in a practical quest to find out what make putters work.

References

Bonneau, M.D. (2002) Inverted Mass Relieved Putter. U.S. Patent Number 6,383,089

Daish, C.B. (1972) The Physics of Ball Games. The English Universities Press Ltd., London, UK.

Lindsay, N.M. (2003) Topspin in Putters a study of vertical gear-effect and its dependence on shaft coupling, Sports Engineering,6(2), 81-93

Solheim, K. (1995) Putter Head Design. In: Golf the Scientific Way, (ed. A.J. Cochran), p. 69. Aston Publishing Group, Hemel Hempstead, UK.

Last edited by aceputt on December 27th, 2013, 2:49 pm, edited 1 time in total.

Neville
Neville
Hi Geoff
As an person interested in the cut and thrust of debate, this is all good stuff. However, in the real world of improved putting at amateur level, it does not matter a darn. The average golfer who comes to me for a putting assessment couldn't hit a cow's backside with a banjo even if he or she had a magic wand and the cow was only 6 foot away. The problems I see are basic such as putter too long, head position out of wack, shoulder alignment skewed, gating stroke path and so on. And this is even before we get to putt reading.
Nevertheless love the debate, even though it can get a touch personal
Nev
Oz

Geoff Mangum
Geoff Mangum
Skids, Squirts & Scandals

Dear Geoff,

I recently found your essay entitled Path of COG - not Height - is Probably Key. You state that there must be some basic uncertainties in the definitions or understandings about the underlying physics of this subject.

On the contrary, I know that the physics is well understood, certainly well enough to decide whether low or high COG generates more or less topspin. There is a wealth of good experimental data that proves the accepted theory.

A year ago I sent you a draft copy of my paper Topspin in putters a study of vertical gear-effect and its dependence on shaft coupling (Lindsay 2003). This paper gives chapter and verse on the subject of putter weighting and topspin and also presents significant original research on how the shaft affects clubhead rotation at impact. It describes new techniques for measuring spin performance and some results of these measurements are published, including data from the C-Groove putter and the Odyssey 2-ball.

Your reply to J P Vegas is a tour de force, and I admire your obvious enthusiasm for the subject, but the guy just needed the right answer and not a choice of three!

Lets start with your Camp 2, i.e. locate the putter COG high on the face and replicate what happens when a cue stick imparts top spin to a cue ball in billiards

For the record - a small correction. Striking a ball with a cue at height 7/10ths diameter eliminates skid (Daish 1972).

However, simply elevating a putters COG above the ball equator to 7/10ths diameter does not achieve the same effect as the cue stick in billiards or pool. Its impossible to contact a golf ball at a height of 7/10ths diameter with the face of a legal putter unless you are hitting down or otherwise de-lofting the face very severely. At 7/10ths diameter, the tangent (i.e. the slope of the balls surface) is -23.6 degrees to the vertical but the R&A and USGA have put a limit of 15 degrees on the permitted amount of negative loft in conforming putters.

Even if you did hit the ball with a -23.6 degrees negative loft putter face, you would not get the ball to roll without skidding. Initially, the ball would dig into the putting surface at an angle of about 20 degrees and, yes it would have some topspin, but probably less than a quarter of true rolling spin. It would then undergo a severe and abrupt skid, probably jump into the air, and its anyones guess what spin it would have after that.

YOU CANNOT INVOKE MATHEMATICS FROM POOL OR BILLIARDS TO EXPLAIN GOLF IMPACTS. The only instance where this is valid is for direct central impact.
There are huge differences between a billiard cue and a putter or any other golf club. The soft leather tip on the cue plays an important part but there are other obvious differences between the two implements. This is something I will attempt to explain in more detail at some future date on my website <a>Lindsay Putters</a>.

Meanwhile, to whet your appetite, have a look at these clips from a really good website for pool physics:

</a><a href="http://www.engr.colostate.edu/~dga/pool ... NV4-13.htm> (Squirt due to high speed English)

</a><a href="http://www.engr.colostate.edu/~dga/pool ... HSV4-4.htm> (High speed English close up)

The first clip is an elevated view of a cue ball demonstrating high speed left English where the ball is struck left of centre to give it clockwise spin (in plan view). The remarkable aspect of this sequence is that the deflection to the right, or squirt, is really quite small. If, instead of a cue, the ball was struck by a putter swung along the line of the cue stroke and with open face to hit the left side of the ball, the ball would get pushed to the right cushion and not go almost straight along the swing path as it does in the clip.

The second clip shows a close-up of the stick-on-ball impact in slow motion a brilliant demo. View this with zoom at 200% (right click to get zoom). Here, the cue stick hits the ball off centre at about 7/10ths diameter from the right edge and sure enough the ball rotates roughly 220 degrees over a distance of about two diameters, which approximately equates to the no skid at 7/10ths impact scenario. Also, note the momentary jump of the cue tip to the left very revealing.

Now to Camp 3. COG-to-COG Level

You cite the T-Roll Putter as a design in which the putter COG is the same height as the ball COG. I had a quick browse through the T-Roll website and, despite other nonsensical claims (e.g. 'Pushed' or 'Pulled' putts create sidespin on the golf ball and cause the golf ball to 'spin out' of the hole unless the golf ball hits the cup dead center), I could not find any claim that the T-Roll imparts topspin, so it is not really in contention.

However, delving into the origins of the Aserta Putter, I discover that the original science behind this novel putter is as follows

The club has a raised center of gravity intended to be in alignment with the center of a golf ball.This allows the club to strike the ball in a manner similar to a pool cue. In other words, forces transmitted to the ball along a horizontal line, parallel to the ground, which would go through the center of the ball. This imparts to the ball a forward rolling motion, without topspin. (Bonneau 2002)

I interpret the above extract from US Patent No. 6,383,089 as meaning that a horizontal strike on a ball with a pool cue right on its horizontal equator imparts immediate pure roll without over-spinning.

This is dangerous territory. There are a number of highly respected physics websites, not to mention a wealth of literature from Sir Isaac Newton onwards, that describe how under these impact conditions the ball skids until its linear velocity reduces to 5/7ths of its initial velocity before rolling. The over-spinning or topspin in US 6,383,089 is what you would expect from hitting a cue ball above 7/10ths diameter with a cue stick.

US 6,383,089 is a typical example of how patents are granted despite the invention being based on principles that are contrary to the known laws of physics. (In the above case, the law of conservation of angular momentum.)

Now, I have no doubt that some golfer swear by the Aserta (and dont even need to be paid to do so). They may be really convinced - and in some instances may actually experience - that it provides game improvement. But would the majority of Aserta buyers still be convinced of its amazing benefits if they knew it creates more backspin than a traditional, low COG putter? How many golfers have been duped by the Aserta website animation showing Immediate True Roll , thinking that this is the real McKoy and not realising that it was created by a graphic artist and bears absolutely no semblance to reality? This is all part of the scandal that pervades putter manufacture and putter marketing.

Now for Camp 1 LOW COG FOR "GEAR EFFECT"

Karsten Solheim, the founder of modern putter design, advocated maximising the weight low in the putter head to improve overspin at impact (Solheim 1995). His pioneering ideas, dating back to 1959, have since been copied and adapted in countless putter designs. So its not unusual to find lots of putters that more or less provide low COG, but your selection of examples of low COG putters is strange. Why the C-Groove Amy model is an example of concentration of mass low on the back flange is a mystery.

Your next example, the Ontic is even more surprising. Here you see a conventional putter body raised off the ground on two sliders or rails. How in the name of all that is wonderful does this lower the COG? It does the complete opposite. The bottom surface of the rails determine how low the body of the putter-head can be positioned relative to the golf ball. Therefore, the bottom of the rails form the datum from which the height of the COG is measured.

You are correct to question that Camp 1 and Camp 2 are completely contradictory but your conclusion that the Aserta data just deepens the mystery skirts round the really big issue in all this, namely, the habit that putter manufacturers have of lying shamelessly about the technology of their designs. In the case of Aserta, the invention is undoubtedly based on wishful thinking rather than deliberate deception. (After all, its been patented WOW!) However, the data they publish, while appearing to be better than competitors, goes nowhere near supporting the immediate true roll theory.

Incidentally, when is someone going to tell them that 2.216 inches is NOT the circumference of a standard regulation golf ball?

So how do some manufacturers demonstrate their putters giving more roll than the competition? The answer is, they show their putters giving earlier roll by simply arranging a flatter launch trajectory. This is shown in the following frames of video footage of the C-Groove putter, which claims to impart immediate pure roll (where have we heard that before?) by virtue of its unusually shaped grooves

FRAME 1 Note the C-GROOVE putter-head (lower picture) is about 3 inches behind the zero mark on the scale.

FRAME 2 The ball struck by the OTHER brand putter is off the ground you can see this from the shadow it casts. This ball is slowly spinning in mid-air with a combination of slight backspin and sidespin imparted by the putter impact.

Meanwhile, the C-GROOVE ball has already landed on the ground because its launch trajectory angle is one or two degrees lower. It is therefore skidding and at the same time picking up forward roll, which obliterates its initial launch spin. Note that the C-GROOVE putter-head has swung through 7 inches from FRAME 1 (-3 inches) to FRAME 2 (+4 inches).

FRAME 3 The ball struck by the OTHER brand putter is still just off the ground and has continued to rotate slowly in mid-air with its initial launch spin. As soon as it touches the ground it will start to pick up forward roll, just like the C-GROOVE ball.

The C-GROOVE ball continues to skid and so starts to rotate faster.

Note that the C-GROOVE putter-head has only swung 3 inches between FRAME 2 (+4 inches) to FRAME 3 (+7 inches). A putter-head decelerates slightly during impact but typically by only 20% or so and not by nearly 60%. Explanation?
THERE IS A MISSING FRAME JUST AFTER IMPACT !!

The video clip tells us nothing about the initial spin imparted on the C-GROOVE ball. The frame that might have given this information has been mysteriously deleted. It does show the C-GROOVE ball starting to roll earlier but this is entirely due to the fact that it also started to skid earlier, so the comparison is contrived and meaningless.

Working in golf technology, you soon realise that putter design is very much the poor relation in golf equipment research and development. Most research expenditure is in metal woods and golf balls, so a telling way of settling the controversy is to have a look at metal wood technology. </a><a href="http://www.bs-sports.co.jp/english/basi ... lub_5.html> (Basics of golf club design) is a page from Bridgestones excellent guide to golf equipment design. This gives simple, clear definitions and explanations to non-technical readers. Rest assured, behind every statement is a wealth of knowledge and research. Opening this page and scrolling down to Gear Effect, you will find a diagram illustrating both horizontal and vertical gear effect in a metal wood club, and there we see

Bottom of the face = more backspin
Top of the face = less backspin

In a lofted metal wood club the predominant ball spin is backspin but for impacts on the top of the face, gear effect generates a component of topspin (shown in the diagram), which reduces overall backspin, while the vertical gear effect generates additional backspin for impacts on the bottom of the face.

One thing that you wont find in the Bridgestone site is discussion of how the shaft affects gear effect. Until I published my research on shaft compliance modes (Lindsay 2003), the universally held theory was that the effect of the shaft could be neglected during the sub-millisecond duration of impact. This is often referred to as the free body model of club-on-ball impact. You only need to look at some recently published patents describing finely tuned mass and inertia designs of metal woods from some of the top golf research establishments to confirm that the free body model was until recently the accepted wisdom.

I note with interest that you have picked up on my research findings (Lindsay 2003) and use them in your essay as if they are common knowledge. Since this is recent research, it is standard practice and courteous to properly acknowledge the source of your information.

Path of COG - not Height - is this the answer?
Your theorising that topspin is best created by a rising blow so that the path of the face COG is moving thru the ball higher than the ball's COG has some validity but in practice wont work. What you are advocating is similar to getting topspin on a tennis ball. With tennis, the racquet is swung on a steep upward trajectory (e.g. 45 degrees or so) yet the ball is still stuck near the centre of the racquet. Putting topspin on a tennis ball struck from the middle of the racquet is a perfect example of vertical oblique impact a basic concept found in all good dynamics textbooks. It is impossible to achieve any useful degree of vertical oblique impact with a putter. A rising blow with just a few degree of upward attack angle will lift the putter-head to make contact on the lower half of the putter face. This in turn will negate any slight topspin created by the oblique impact.

Have a look at </a><a href="http://www.lindsayputters.com/spinmeasu ... ements.htm> (Spin measurements) on my website. This shows that the higher the putter head at impact, the lower the impact point on the putter face and the greater the backspin. The effect is particularly strong with mallets, which usually have greater gear effect characteristics than blade designs.

I strongly advise that you temper your theorising with experiments and measurements of what actually happens. Science is about making the theory fit the facts and not the other way round. It doesnt take much to replicate the measurements shown on my website and you dont need to have huge budget or a PhD in engineering or physics. Take a look at </a><a href="http://tuhsphysics.ttsd.k12.or.us/Resea ... hysics.htm> (Kyle Peytons experiments).
I dont agree with many of her findings but here is a school kid who shows fantastic determination, diligence and ingenuity in a practical quest to find out what make putters work.

References

Bonneau, M.D. (2002) Inverted Mass Relieved Putter. U.S. Patent Number 6,383,089

Daish, C.B. (1972) The Physics of Ball Games. The English Universities Press Ltd., London, UK.

Lindsay, N.M. (2003) Topspin in Putters a study of vertical gear-effect and its dependence on shaft coupling, Sports Engineering,6(2), 81-93

Solheim, K. (1995) Putter Head Design. In: Golf the Scientific Way, (ed. A.J. Cochran), p. 69. Aston Publishing Group, Hemel Hempstead, UK.

Dear Dr Lindsay,

I greatly appreciate the time and trouble you have expended in posting some wonderful information! You and I are definitely taking the same basic approach. As your website states:

"Lindsay Golf champions scientific objectivity and tries to clarify important aspects of putter design. Real facts are explained and simple measurement techniques are shown to help illustrate these facts. Future research will look at the whole putting scenario to increase understanding and help golfers to improve and enjoy their game."

So let's get back to that.

For some quick housekeeping, I would like to respond directly to three statements you make:

1. "For the record - a small correction. Striking a ball with a cue at height 7/10ths diameter eliminates skid (Daish 1972)." I stand corrected. My use of 5/7th is due to the fact that skid always stops once the surface friction has reduced the initial translational velocity of the ball to 5/7th its initial velocity, and I simply confused this for the 7/10th figure.

2. "Your next example, the Ontic is even more surprising. Here you see a conventional putter body raised off the ground on two sliders or rails. How in the name of all that is wonderful does this lower the COG? It does the complete opposite. The bottom surface of the rails determine how low the body of the putter-head can be positioned relative to the golf ball. Therefore, the bottom of the rails form the datum from which the height of the COG is measured." I think I am correct about this. If a level see-saw has weight added to the right side, the COG of the see-saw shifts in the direction of the added weight (to the right). If you add weight to the bottom of a putter as the Ontic putter does with the mass that constitutes the bottom two "runners," this will LOWER the COG of the putter face below what it was before the addition of the runners below all the existing mass.

3. "I note with interest that you have picked up on my research findings (Lindsay 2003) and use them in your essay as if they are common knowledge. Since this is recent research, it is standard practice and courteous to properly acknowledge the source of your information." You also say you sent me your unpublished paper. This may well be true but I don't recall ever having recieved it. I have tried on several occasions to communicate with you since our earliest contact, without reply. (Could you please resend the paper?) In any case, all the information I reference comes from your website, which perhaps duplicates the information in your paper. All my references to your work CLEARLY is noted as coming from you. The suggestion that I do not credit my sources is not very polite, as I work with utmost diligence to distinguish myself as the ONLY putting instructor who is extremely careful to give proper credit where credit is truthfully due, and not to pass off as my own work the labors and ingenuity of others.

Back to the topspin issue:

The whole thrust of my post is that I find the discussion and data by others less than clear, and certainly contradictory. There are two main points I hope we can clarify.

Specifically, I question whether the "gear effect" of the driver really applies to the putter in a wholesale manner or in some modified way. You response only indirectly addresses this point, and does not shed much light on how the "gear effect" really operates with a putter. Does the (vertical) hoseling for putters reduce or perhaps eliminate the vertical "gear effect"? If so, in what way?

Similarly, I don't think your reply to my suggestion about the path of the putter COG moving above the ball COG is very clear. At the moment of impact (and for the duration of impact for the "impulse"), the putter momentum (mass times velocity) is a vector and the direction of this vector thru the ball may be directed above the ball's COG notwithstanding the immediate geometrical relationship between putter face as lofted and back of spherical surface of ball. I don't think a rising putter head necessarily needs to impart "oblique impact" on the tennis raquet model you depict. You write:

"What you are advocating is similar to getting topspin on a tennis ball. With tennis, the racquet is swung on a steep upward trajectory (e.g. 45 degrees or so) yet the ball is still stuck near the centre of the racquet. Putting topspin on a tennis ball struck from the middle of the racquet is a perfect example of vertical oblique impact  a basic concept found in all good dynamics textbooks. It is impossible to achieve any useful degree of vertical oblique impact with a putter. A rising blow with just a few degree of upward attack angle will lift the putter-head to make contact on the lower half of the putter face. This in turn will negate any slight topspin created by the oblique impact."

I gather from this that you are depicting a raquet held so that its hitting "face" is vertical and not tilted or lofted as presented to the ball, and that the trajectory of the center of the raquet is moving up across the level flight of the oncoming ball at a 45-degree angle. The reason you cite for stating that this cannot usefully be accomplished with a putter is that a rising trajectory necessarily means that the point of impact will be on the lower half of the face, and this produces backspin that overcomes the topspin produced by the "oblique impact." This strikes me as unclear and confusing. You seem to grant that the sort of blow DOES impart topspin, but then state that the low-face impact gives backspin that negates the topspin, and so a net backspin results. A normal putting stroke is radiused such that extending the vertical arc of the stroke into a complete circle generates a cirle approximately 9 feet in diameter, and about 55 feet (660 inches) in circumference. The segment of the putting stroke arc that we are concerned with immediately before and during impact is at most 1-2 inches of this circumference, and the rising of the putter face in relation to the back of the ball is on the order of under 1/8th of an inch at the most. This rising of the putter face COG may or may not result in an impact point on the face that is BELOW the putter COG. It depends on where the putter face COG started at the bottom of the arc before it rose a little into impact, doesn't it? And in any event, even if the face of the putter is dynamically lofted a little, combined with the momentum vector of the putter at impact aimed above the ball's COG, then we are discussing whether the ball gets launched off the surface so that the earliest skid is delayed, which in turn delays the early onset of roll, aren't we? Purely in terms of backspin and topspin, what are the relative contributions of putter COG directed above ball COG versus low impact point on putter face (i.e., below the putter COG)?

I much appreciate your time on this, so let me thank you richly in advance for any reply.

Cheers!

Geoff Mangum
Putting Theorist and Instructor
<a href="http://puttingzone.com" target=_new>
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Joined: March 7th, 2004, 10:07 pm
Geoff:

Has any research been done on the optimal placement of the center of gravity (COG) to enable the golfer to most easily impart topspin to the ball? Ping and other putter manufacturers have low COG putters and clain that because of the gear effect, this most effectively enables topspin. Recently I have read other manufacturers, (Yes/Big Oak), claims that putting the COG close to the top edge of the putter enables topspin. Any thoughts or ideas on this?
Dr Lindsay and Geoff:

Thank-you both for the wealth of information that you have provided on putter weighting and top spin. It is going to take a while to digest the information, but I think the information is worth looking at closely.

Dr. Lindsay: Where can you purchase one of your putters. I keep checking your website and I can find information on the putter, but not where to purchase.

Thanks again.

Joined: July 20th, 2003, 9:40 pm
Geoff:

Has any research been done on the optimal placement of the center of gravity (COG) to enable the golfer to most easily impart topspin to the ball? Ping and other putter manufacturers have low COG putters and clain that because of the gear effect, this most effectively enables topspin. Recently I have read other manufacturers, (Yes/Big Oak), claims that putting the COG close to the top edge of the putter enables topspin. Any thoughts or ideas on this?
Hi Geoff

At the end of the day does it matter if a putter has a High COR, Low COR HI or Low MOI if it is back-weighted, counter balanced, Face balanced, Toe balanced, Upright, Flat, Long or Short??

It seems to me that you have to first see the line, Second determine the speed and third practice until you can do both well.

In spite of all the "NEW PUTTER DESIGNS" the 40 plus year old Cameron design is still the number one putter on tour. My own design is starting to catch on and players on all the tours are giving it a try.

Seems to me that if you can find a putter that you like and then put in the time on the putting green you will get better. No matter what type of putter you use. Golfer are always looking for a magic bullet that will cure their failure to put in the time needed to get better.

Your brief thoughts are as always welcome

Chuck
American Putter