Floating Fulcrum Concept
By Timothy Winey
Wednesday, September 10, 2003

Figure 1 shows a shaft (both rigid [theoretical] and flexible [actual]) pivoting about an axis (as a kind of double-pendulum with the club handle (grip) extending beyond the pivot point or fulcrum) with an adjustable weight fixed to said shaft at different points along the shaft (1-6); attached to the end of the rigid shaft is a striking mallet (club head).

Consistent with the laws governing potential energy and it’s transfer, the more proximally the adjustable weight is fixed to the striking mallet along the shaft, the further a ball should travel when struck with said mallet dropped from a fixed height; so, for example, a ball struck after the mallet was dropped from a position parallel to the horizon (9:00 o’clock) with the weight placed at position 1. should travel further than a ball struck by the same mallet dropped from the same position with the weight placed at position 2. Position 2. should result in more potential energy transfer than position 3, and 3 more than 4. etc. Thus, any given putt struck with weight closer to the mallet should travel further than putts struck with the weight placed further up the rigid shaft.

If we substitute a flexible shaft for a rigid one, the predictability of proportional increases in distance as the weight is moved incrementally closer to the club head, is confounded owing to the dampening effect of weight on shaft flexion. Thus, a weighted flexible shaft’s behavior is altered along with its resonant frequency both before, during, an after a ball strike. In fact, the effect of adding weight to a flexible shaft actually reversed the theoretical model of adding weight to a non-flexing shaft; that is to say, weight at position 1 represented the heaviest possible mass striking a ball from a dropped position (parallel to horizon) and resulted, paradoxically, in the shortest vertical displacement on the incline plane. Thus, weight added near the grip resulted in the longest putts while actually weighing the least in terms of potential energy. Positions 3, 2 and 1 resulted in progressively shorter putts despite the putter becoming progressively heavier toward the mallet (putter head). Even if putts struck at position 1 traveled as far as putts struck at position 6, it would still represent a substantial dampening effect since added weight at position 1 should send the ball beyond that of putts struck with weight added at position 6. This demonstrates that added weight in the middle third section of a putter shaft represents a dampening effect that is far from insignificant since putts struck with weight fixed at position 4, should send the ball beyond those struck with weight at positions 5 and 6.

In the experiment, the small increase of surface area the weight added to the putter and resulting wind resistance was negligible, owing to the relatively small cross-sectional area increase and slow club head speeds involved.

Robotic putting obviously varies markedly from that of humans, human putting being characterized by unpredictable variations in shaft loading, typically influenced by factors such as grip pressure, body movement (shifting centers of gravity), variations in muscular effort as well as variations in stroke paths often resulting in ball strikes where the striking surface of the putter is often not oriented (ideally) at 90 degrees to the target line at impact.

The numbers and arrows in figure 1. represent, respectively, the positions of an adjustible weight added to a flexible shaft and the terminal positions of putts struck at each position (numbered 1-6) up the same incline plane. As figure 1. shows, fixing the weight at position 4 (midpoint), along with positions 5 and 6, resulted in the greatest vertical displacement (longest putts). Positions 5 and 6, however, do not represent a competitive putting advantage because the effort required to accelerate said weight (change its speed or direction) at positions 5 and 6, does not sufficiently load the musculature to enable a subject to “feel/sense” with reliable precision, the increase in energy required to lengthen a putt from 10 feet to 12, especially under stressful conditions where fluctuations in grip pressure, and the concomitant negative effect such fluctuations have on putting consistency, have been substantiated experimentally (please see the Mayo Clinic study synopsis below). Also, the dampening effect of the weight added to the upper third section of the flexible putter shaft was not robust enough to lower the impact ratio (IR) to the degree desired for enlarging the sweet spot for off-center struck putts (see Hurrion study).

It is well known among golfers that the addition of weight to the upper portion of a shaft can actually have a paradoxically “lightening” effect, by contrast, (reducing what is commonly termed “swing weight”) on the perceived weight of a putter head, making it even more difficult to employ, with any degree of reliable precision, the precise amount of muscular effort necessary to consistently putt a ball a given distance (longer putts obviously being more prone to variability than shorter ones). Conversely, substantial weight placed in the bottom 3rd of a shaft as in figure 1. at positions 1, 2, and 3, actually resulted in more dampening (less vertical putt displacement) despite the dramatic increase in (theoretical) potential energy confounded by the substitution of a flexible shaft for a rigid one. This extra dampening (below that of position 4) is not advantageous however, because the addition of substantial mass so near the club head requires so much more “muscular effort” to effect an increase in putt length from 10 to 12 feet for example, that it results in reduction of feel for distance beyond that of conventional putters. Along with reduced “feel for distance” also comes as a direct consequence of additional weight at either extreme of the shaft, a reduction in relative positional awareness of the club head, weight and hands. With substantial weight added to the lower third section of the shaft, the club head and weight are simply too close together resulting in the feeling of one unmanageably heavy club head due to its proximity to the weight rather than the perception of club head and weight as distinct masses that provide information to the golfer about each other’s relative positions, directions and speeds, as well as their relationship to the hands, during a putting stroke.

Conversely, substantial weight added too far up the shaft has the equally undesirable but opposite effect of making the hands “feel” too heavy (and by contrast, the putter head too light), and as a result, reduces the reliability/usability of information about the relationship of putter head to hands (that is to say, their relative positions, directions and speeds with the weight acting as their common reference point).

Thus, weight at the extreme upper portion of the shaft does not provide sufficient dampening (reduced impact ratio/enlarged sweet spot) for off-center struck putts nor does it provide sufficient positional awareness of all three masses (hands, weight, putter head) that central weighting (position 4) does, where the weight provides the optimal amount of mass in the best position, owing to the increased muscular effort required to reliably affect small increases in putt length while simultaneously providing enhanced positional awareness as the weight interrelates with (acting as a floating fulcrum for) hands and putter head.

It is critically important to note that lowering the impact ratio (enlarging the sweet spot) is an important advantage in putting but not the most important. It is the dampening effect that added weight in the middle third section of a flexible putter shaft that provides the all important ingredient of forcing the golfer to actually make a (perceptibly) greater effort to increase a putt’s length from 10 to 12 feet for example; this is no small feat, especially on faster greens. And since so much of putting is speed (contrary to certain popular fallacies that treat “line” and “speed” as if they were two, separable, and equally important ingredients of good putting), any technique, equipment or combination thereof, that improves feel for distance, is highly desirable. Stated differently, almost no putt is perfectly straight, and as a result, will break; this necessitates precise control for speed in order to ensure that the putt actually takes the break and is not hit too soft (breaks too much) or to hard (breaks very little). Given this fact, putt “line” cannot be disentangle from putt length (speed required to get the ball to the hole without running over it).

Thus, increasing the mass in the middle third section of a putter shaft provides more reliable information about the relative positions directions and speeds of the hands and club head, above that of traditional putters lacking such a reference point (weight) or “floating fulcrum” as I have coined it (meaning a fulcrum [pivot point] about which the hands and club head pivot).

It is proposed that the addition of extra mass to the middle third section of a putter shaft (position 4, fig.1) represents a competitive advantage over non-weighted (traditional) putters by increasing feel for distance due to:

• An improved feedback mechanism/loop informing the golfer in a more timely and accurate way about relative velocities, positions and accelerations (changes in speed and or direction) of all three masses (grip/hands, weight and putter head) resulting in a higher probability of more repeatable/similar strokes and
• Dampening effect on “sweet spot” putts resulting in a narrowing of putt length difference between equivalent putts struck at the toe, heel and sweet spot (effectively enlarging the sweet spot [see Hurrion study]). It should be noted, however, that off-center struck putts should be made less likely in the first place, if there is indeed, a genuine improvement in positional awareness of the hands, weight and club head which should translate into a higher probability of more repeatable/similar strokes and by extension, more putts struck squarely (90 degrees to target line) on the sweet spot.

Sufficient dampening, particularly on sweet spot-struck putts, requiring a greater increase in muscular effort to affect a small increase in a putts length (10 to 12, feet for example) hitherto not consistently possible with conventionally weighted putters except by only the most elite golfers.

My hypothesis was that in order to increase the length of a given putt with my center weighted putter (e.g., from 10 to 12 feet 20%), I would have to hit it much harder (as a percentage increase beyond the baseline putt, [10 feet]) than a traditional, “efficient,” putter (either by virtue of the fact that I am lifting and dropping a weight that is heavier while maintaining the same instantaneous velocity at impact, or because I have to exceed the instantaneous velocity, at impact with a demonstrably heavier putter; either scenario with a weighted putter involves expending more energy (the latter scenario representing the largest increase) to move the ball 12 feet (an increase of 20%).

Put simply, the heavier the putter, the greater the dampening effect, and with a greater dampening effect, the heavier putter should have a higher percent increase in instantaneous velocity at impact than the conventional putter (in order to increase a 10 foot put 20% (12 foot). Stated differently, if the dampening effect of weighted putters increases with putt length non-linearly when compared to conventional putters, (or exhibits “more” non-linearity than conventional putters [if conventional putters exhibit some non-linearity of force requirement with increasing putt length]), the below experiment should confirm this.

I decided to set up an experiment to demonstrate a dampening effect, not just comparing the relative dampening effect of the same putter with the weight placed at different positions along the shaft, but also to demonstrate that the energy requirements of increasing a putt’s length with a weighted putter does not follow the same curves on a force/distance continuum when compared to conventional putters. Thus, this new experiment will explore to what degree center-weighted putters dampen short putts, and more importantly, if the dampening effect actually increases with club head speed in a non-linear fashion as compared to equivalent increases in club head speeds (same drop height on Perfectionizer [putting robot]) with a conventional (twin) putter.

Let us assume that to putt a ball 40 feet with a conventionally weighted putter, one has to roughly double the club head speed at impact (impact velocity) normally required to putt a ball 20 ft. (with the same putter); now let's assume that in order to putt a ball 40 ft. with a center weighted putter, one has to triple the club head speed normally required to putt the same ball (with the same putter) 20 feet. Substantial, non-linear, increases in club head speed on the weighted putter (as compared with percent increases of the traditional putter for putts of the same length), would undoubtedly translate into improved feel for distance and might partially explain improved accuracy in “lag putting” (long putts).

Obviously, conventional putters may be non-linear also, what counts, is whether or not a weighted putter exhibits more non-linearity. In this way, one could circumvent comparing proverbial “apples to oranges” by simply calibrating the perfectionizer or similar device, to putt baseline putts a given distance, and then measure the difference, (if there is any) in club head speeds (drop height) to effect the same increase in putt length. Conversely, one could putt with weighted and non-weighted putters from the same drop points (assuming constant acceleration) and compare the percent increases in putt length; thus a weighted putter that hit a ball (dropped from 8:00 position and traveled 10 ft. and later struck another putt from 9:00 displacing the ball 12 feet, would be a 20% increase in length. The same experiment repeated with a conventional (non-weighted) putter might hit the ball 8 ft. on the first putt (8:00) and 12 feet on the second attempt. That would represent a 50% increase in length for the same increase in instantaneous velocity, at impact, on the second putt.

In this way, one can disentangle the difference between a weighted and non-weighted putter, because even though I proved a dramatic, albeit, "relative" dampening effect between upper and lower shaft weighting, the weighted putter, still hit the ball further than the non-weighted putter when dropped from the same height owing to the overwhelming increase in its theoretical potential energy (notwithstanding substantial, relative, dampening [that is to say, increased dampening as the weight (on the weighted putter) moved closer to the putter head]).

Thus, I propose to simply hit a number of putts from various heights; for example, a position of 8:00, and then another series from 9:00 and 10:00 with each putter (assuming that both club heads will have comparable instantaneous velocity at impact from the same drop positions), and then compare their relative increases in vertical displacement on an incline plane. If my hypothesis is correct, then it will predict a smaller percentage increase between the 8:00 to 9:00 positions (vertical ball displacement) with the weighted putts when compared to the traditional. If the percentage difference in vertical displacement on the weighted putts is higher between 9:00 to 10:00 than (8:00-9:00) after comparing both putters, it would demonstrate comparative non-linearity of force required to effect increases in putt length increasing the accuracy/consistency of putting a ball a specified distance whose relative accuracy/consistency (when compared to conventional, non-weighted putters) actually increases with every additional foot of putt length when compared to putts of equal length struck with conventional putters. Thus, the longer the putt, the greater the theoretical advantage (due to extra feel (more muscular effort [recruitment]) with every additional foot of length) over traditional putters.

If I am correct in my hypothesis about the comparative non-linearity of force characterizing the main difference between conventional and weighted putters, then putting with a weighted putter should become more “costly” (effortful) with each foot of additional putt length when compared (ft. for ft.) with conventional putters [more effort for each foot translates into more feel for distance).

It would be analogous to racing two identical cars (both equally powered) with one pulling a small parachute and the other not. At the beginning of the race they would accelerate at very close to the same rate (since wind resistance would not be a significant factor) but for every 10 MPH of additional velocity, the drag on the parachuted “dragster,” would disproportionately pull against (dampen) the acceleration of the disadvantaged car. Wind resistance is not the key factor in the “drag” on the putter in my experiment, but it illustrates how a dampening effect may be dramatically non-linear and that what may be disastrous for drag racing may prove to be quite the opposite for putting, especially lag putting over long distances.

I recently conducted the above-proposed experiment, and below are my results. The standard putter from 7:00-7:30 was 1.62 times more efficient (94% increase compared with 58%) than the weighted putter. From 7:30-8:00, the standard putter increased a further 7% compared with the 2% increase of the weighted putter (a difference of 3.5% more efficient). Thus, for the weighted putter to replicate the % increases of the standard putter from 7:00-8:00, it has to first strike the ball 1.6 times harder to break even with the standard putter from 7:00-8:00 and then again 3.5 times harder to match the 7:30-8:00 increase of the standard putter. This multiplier effect, 1.62 X 3.15 shows how dramatically force must be augmented for longer putts (5.67 times [567%] more force than the standard putter to achieve the same % increase from 7:00-8:00.

Standard Putter

Weighted Putter

Timothy Winey