Dear Dave,
The heaviness of the putter has several distinct meanings to the golfer on the green. Let me sort them out a little:
1. Mass versus weight:
Mass is the quantity of matter in an object and only has "weight" in reference to another mass, such as the earth. In deep space, a mass is weightless. The same mass weighs differently depending on the other mass, between which the attractive FORCE (we call gravity) operates to assign that mass a corresonding weight.
2. Mass of putter and the physics of the pendulum free-fall:
The Mass and the Weight of a putter does not matter at all in the physics of a pendulum motion, because in the physics the term Mass cancels out of the equation. For an IDEAL pendulum, the only factor that determines the timing of the pendulum is the distance of the point mass (imaginary mass or bob) along the rod from the pivot. For a REAL pendulum, mass and shape has some effects, but they are not all that significant for putters.
3. Mass and Momentum:
The "send" of a putter depends on the Mass of the putter head and it's velocity at impact thru the golf ball (assuming all balls are the same Mass). This is the Momentum of the stroke (mass times velocity). The "heavier" (more massive) a putter, the greater the "send" for identical stroke velocities at impact. For this purpose, the putter is essentially viewed in physics as a rock on a rope, where the putter head is the rock, and the shaft and grip mass don't much matter.
4. Mass and Backstroke Length:
Because of 3 above, and since in 2 above a gravity-based tempo is the same for a light putter as for a heavy putter (since the mass does not affect the gravity free fall), the two putters will have the same VELOCITY at the bottom of the stroke for the same backstroke, but the lighter putter will have less Momentum than the heavier putter, and will "send" the ball, say, only 7 feet, whereas the identical stroke size and impact speed with the heavier putter will send the same ball, say, 9 feet.
5. Mass and Green Speed:
For a green speed in which backstroke X with a light putter sends the ball a total roll of, say, 11 feet, a shorter backstroke is needed with a heavier putter to also send the ball 11 feet on this green speed. This makes it possible to groove a 10-foot stroke on a Stimp 9 green with a heavy putter and then move to a Stimp 12 green and keep the exact same backstroke and timing for a 10-foot putt, so long as the "send" of the lighter putter on the faster green is adjusted appropriately. Sean Murphy sometimes uses this system in moving from one course to another with different Stimp greens to keep his basic 10-foot stroke the same size -- heavier putter for slower greens versus lighter putter for faster greens keeps the same backstroke for all distances. IF you can get the weight adjustment correct ...
6. Mass and Stroke Motion:
The heavier the putter, the greater the inertia of the putter. The inertia must be overcome at the start of the stroke, but then the inertia tends to keep the putter head from changing directions or motion pattern. This effect smooths out the stroke and tends to keep the putter head moving evenly in only one direction.
7. Mass and Feel:
"Feel" in the hands (once set on the grip) comes from CHANGES in pressure from the mass of the handle pressing more firmly or less firmly against the skin. The human "feel" system, viewed as mostly tactile feedback via mechanoreceptors in the hands plus proprioceptive feedback from joint and muscle receptors "feeling" muscle activity and joint changes, reacts differently to a light putter as opposed to a heavy putter. For this purpose, everything in the hands (putter grip, shaft, putter head) and not just the mass of the putter head matters. Part of this is right at the moment of initiation of the stroke, when the inertia has to be overcome. Part of this is the sense of the putter weight pulling the arms down, or weighting them down, during the stroke. Part of this is the "feel" that is associated with impact. Each person has his own relative body mass and set of receptor sensitivities (in the range of human physiology) to a given putter weight.
8. Mass and Swingweight:
This is just an elaboration of 7 above. The swingweight is the relationship of the head weight versus the grip-end weight about a balance point. Longer putters usually need greater head weight to keep the same swingweight. Swingweight is sort of the "feel" of the putter head as a "heft" at the end of a stick. broomstick putters and belly putters have heavier heads than conventional putters. Some golfers buy a belly putter and reshaft it to a conventional putter to get a heavier putter head than comes off the rack.
9. Mass, "Feel", and the Gravity Free-fall Stroke:
In the gravity free-fall stroke, where mass is irrelevant to timing and from 7 above where "feel" in the hands comes from CHANGES, the IDEAL "feel" inside the hands from the mechanorecptors during the well-timed stroke movement is NOTHING CHANGING. There has to be some basic muscle tension or tone to set the shape of the triangle of shoulders, arms, and hands, in a stable form given the stroke forces and there has to be some slight change in feel inside the hands right at the start of the stroke if the putter starts from a position of the sole resting on the ground with inertia (much less if the putter sole slightly hovers on the grass tips, but still a non-zero amount of inertia to overcome). But even so, once the stroke is going, and than coasting to a stop and transition at the top of the backstroke, and then accelerating smoothly down thru the impact zone, NOTHING CHANGES in the feel inside the hands. It is just like poising a basketball on your upturned palm in an elevator and then someone cutting the elevator cables and everything free-falling down the shaft with the basketball suspended weightless on your palm. The only feel that occurs in the hands would come from changing the putter motion out of the pattern used by gravity. All the other sources of "feel" are after-the-fact (e.g., impact recoil) or have very little to do with putter weight.
Discussion
The above means that the putter weight ought to match your body, your stroke dynamics, the typical range of putts you face, and the greens that you play. The putters of a decade ago off the rack generally came with putter heads in the 325 gram range. That is, the designers took a look at golfer anthropometry for the fattest demographic in the market and at typical greens and putts (i.e., bad adult males putting on so-so greens), and settled on about 325 grams for head mass. Today, the tendency is to heavier heads, between 350 grams and 400 grams typically.
But your optimal putter head weight really depends on your body, your stroke dynamics, your typical putts, and your typical greens. Your body has segmental masses (e.g., hands, forearms, etc.) with their own inertial properties and also with your developed "feel" and body-sense sensitivities. There is doubtless an outer boundary here, where the putter becomes too heavy for a good starting back, and in all setups the putter head will be held out a little from the body suspended in air a bit due to the putter's lie angle, and a too-heavy putter can make the putter head drop in towards the body overcoming the set muscle tone of the triangle. But within these parameters, a slightlty heavier head is usually better because it makes for a more compact backstroke and a more stabilized inertial system.
On the other hand, there is a minimun stroke size needed to engage the proprioceptive signals of the body so as to promote accuracy and consistency in touch. The minimum stroke size for this is "something more than a dangle" or the range of free-swinging of the arms in a mild dangling of the triangle. It is usually best that even short putts have a stroke size that gets ourtside this free-dange zone into a real body action, and that is usually a backstroke of 7-10 inches for most people.
Paradoxically, an ultralight putter is a really nice training aid to help get rid of handsiness in the stroke. If the stroke proceeds from the upper torso as a whole (shoulder frame moved by upper torso) with no hands in moving the putter, an ultralight putter tests your ability to keep the hands out of the stroke.
The human arms and hands are "steady" only by virtue of brain signlas for muscle tone that damps out underlying, ever-present tremors at about 12 shakes per second. In Parkinson's Disease, this control system wears out and unmasks the underlying tremors in the body. The lighter the putter and the lighter the grip (pressure or muscle tone in hands and forearms), the less engaged this tremor-damping system and the more likely the golfer's stroke will shake during the stroke. Also, when the human brain anticipates impact, the brain signals a "flinch" change into the arms and hands to prepare for impact. This seems to be a major source of yipping in putting. So using an ultralight putter challenges your brain and body to set a good grip pressure (not too light, as the ultralight putter in a Siren-song fashion deceptively suggests), NOT use the hands and arms to move the putter but to use the shoulders, and NOT to make a hit stroke with anticipation of ball impact and flinching.
Thereafter, if you use a heavier putter, it's an insurance policy from the greater inertia, but the heavier putter should not be an invitation to let handsiness or a hit stroke creep back in.
It's really a question of getting a real expert to fit you, and not just in a studio, but on a green somewhere.
Cheers!
Geoff Mangum
Putting Theorist and Instructor
Geoff Mangum's PuttingZone
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