Dear Jerry,
My view is that the putter should be soled flat to the surface, not the world. The reason is that the ball rolls in reference to the surface like a tire or wheel with an internal "rotation disc" that acts as the stabilizer. The "tire" or disc of the ball rolls in a manner that is perpendicular to the surface, not to gravity. This matters in two main ways: 1) AIM PERCEPTION BIAS: the toe-up (or heel-up) putter complicates the perception of where the stroke is aimed and biases the aim to the inside (outside for heel-up) in two ways, one of which is very uncertain in extent and very dependent upon the specific putt distance and contour; and 2) BALL ROLL CORRUPTION: the toe-up (or heel-up) putter combined with the specific upward trajectory of the putter head thru the ball results in a specific orientation of the rotational plane of the ball (similar to an internal "tire" embedded in the "sphere" of the ball) and any orientation of this plane of rotation other than perpendicular to the surface reduces the ball's inherent tendency to "take the correct break offered by the surface" so that a gravity-plumb orientation of this rotational plane tends to keep the direction of roll too high and on the startline too long promoting lip outs and misses on the high side and this tendency varies with the surface contour and the length of the putts whereas in the surface-perpendicular orientation there are no surprises between what the surface and putt length offers for break and what the ball does in the roll to "take the break." It's probably advisable to discuss these two issues in reverse order.
BALL ROLL CORRUPTION
If you hit a ball with a putter face that starts the ball off rolling with the disc oriented vertical to gravity (gravity-plumb) instead of vertical to the slope (surface-perpendicular), the ball will "settle" to the plane of the slope sort of like a bowl set down on a tilted table top, and then there is a "wobble" due to this settling of the disc out of its starting plane into the new tilted plane. The (tilted / sloped) surface meeting the bottom of the ball also promotes this reorientation of the ball's rotating disc. This effect varies from green to green depending upon the "tightness" or the grass surface, with a plush surface tending to resist the resettling and a tight surface allowing more of the resettling. During the very starting of the roll, however, the ball does not experience the same downhill-directed torque as it "should" and therefore the ball's roll will be artificially biased to remain too high too long instead of falling off the start -line in the appropriate way.
On the other hand, if you first orient the putter face to the surface and then stroke the ball with a putter face that remains square or flush to the surface plane, the rotating disc of the ball will start out vertical to the plane of the surface and will also not experience this resettling. At this point, gravity will "tug" the top of the disc downhill a little perpendicular to the direction of roll and planar orientation of the rotating disc. This "torque" does not make the rotational plane of the ball "lean further downhill" as is intuitively and naively and commonly supposed, but instead redirects or "turns" the rotating disc downhill in the same way that a slight turn in the steering wheel of a car redirects the car out of its straight-ahead direction to the right or left. So gravity acts like a turn in a steering wheel, but the rotating disc stays perpendicular to the slope's surface plane.
This is a bit counter-intuitive in physics. Here is
an explanation of "the conservation of angular momentum of a rotating wheel" by applied torque, in which the axis of rotation remains level but the direction of the wheel changes. The rotating disc acts like a gyroscope that resists the tilting of the torque force of gravity and converts it's effect to a redirection of the rolling. This in turn means that the plane of rotation of this internal gyroscopic "disk" of the rolling ball remains perpendicular to the surface plane and merely "turns" downhill as if a tractor driver simply put a little turn angle in his steering wheel. The plane of rotation of the ball's internal disk does not lean over in the downhill direction (i.e., downhill to the right, lean top of ball over to the right) as one might expect from the center of the sphere of the ball being displaced "downhill" from the bottom spot of the ball's contact with the surface when the rotation plane is perpendicular to the surface.
This drawing illustrates balls correctly oriented to the surface and then compares the internal rotational plane of the rolling ball in the two orientations (surface-perpendicular at top, and gravity-plumb at bottom):
The next drawing illustrates how the ball's center of gravity (also the rotational plane's center of gravity COG) being either in plumb with gravity (directed to the center of the earth) or flush to the slanted surface affects differently the rotational plane of the rolling ball and the ball itself as a sphere. The rotational plane is what is being "turned" by the torque, and a gravity-plumb orientation requires "more turning" to get the ball to take the break downhill that the surface / putt offers, and this "more" is not a fixed variable but one that increases or decreases depending upon the surface contour (mismatch between the two orientations of the rotational plane) and the length of the putt, whereas in the surface-perpendicular orientation there is no similar variable and instead you get what there is, with the ball taking the surface break correctly with the "degree of turn" offered by the slope without the necessity of any extra and variable degree of turning from the steepness or slant of the slope or the length of the putt.
This third drawing illustrates how a gravity-plumb orientation biases the rolling path of the ball to remain too high, thus promoting high-side lip outs and misses. Even if the golfer "more or less" adapts to this oddity in his putting when it comes to reading the break and in aiming along the read's start-line, he is constantly "at sea" somewhat on the exact extent of the variability for every putt he faces. A better plan is to "accept" the full measure of break offered by the green for a given putt, as this is really the only way to get the variability of read, aim, stroke, and touch out of the system.
With the above in mind, let's examine how different orientations of the putter face and different trajectories of this putter face orientation thru the ball during impact result in starting orientations of the rolling plane of the ball.
Orientation of Putter Face:
While the above-described dynamic of the internal rolling "disk" of the ball is the same whether the ball starts with the disk perpendicular to the surface or with the disk perpendicular in gravity and thus with the plane of rotation oriented somewhat "uphill" with the ball's center displaced (uphill or left when downhill is to the right of the ball's forward direction), the only way to start the ball rolling with the plane of rotation vertical in gravity on a sloped surface (e.g., ball below feet at address) is to strike the ball with a toe-up putter orientation to conform the lofted face of the putter "normal" to a gravity-vertical plane for the ball rotation (the face is perpendicular to the plane of rotation given the ball). Direction-wise, this "toe-up" lofted putter face will not start the ball in the same direction as the alignment marker on the top of the putter head, but will direct the roll slightly to the inside (left for a right-hander). (This redirection does not arise when the face of the putter at impact presents zero dynamic loft, although there is still some mild "sliding" action as the neutral face imparts the blow thru the ball in a plane out of perpendicular with the surface plane.) (SEE BELOW FOR THIS AIMING ISSUE.) In the above drawing, the bottom depiction of the gravity-plumb orientation requires a toe-up orientation of the putter that is then moved vertically up in gravity as opposed to vertically up from the surface. The depiction of the surface-perpendicular plane of rotation corresponds to a putter that is soled flatly to the surface (to whatever surface slope there is) and then the putter is moved up thru impact with the ball vertically off the surface regardless of gravity.
In the case of a ball-above-the-feet putt (right-to-left for a righthander), addressing the ball with a heel-up orientation of the putter head has the effect of biasing aim to the outside, but the rolling bias given the rotational plane at the start is the same as with the ball-below-the-feet putt: to the high-side.
My mental image to help see all this is of a football field (American football) with the field tilted in space out of level with slant downhill to the kicker's right facing the golaposts where a kicker is attempting a 30-yard fieldgoal thru two uprights planted at the back of the endzone. These upright poles are perpendicular to the tilted field, not perpendicular to gravity. If the kicker wears a kicking shoe with a lofted toe, he needs to deliver the kick in a plane of leg action that is perpendicular to the field surface. If he stood erect in gravity and used a leg action in the kick that is perpendicular to gravity instead, he cannot send the ball thru the goalposts without first aiming his kick slightly downhill and letting the lofted toe do its thing to redirect the flight of the ball slightly uphill to his left.
Orientation of Stroke:
There is another dynamic. That is, a putter soled flat on a slope with downhill to the right of the aim of the putter (heel is physically higher above sea level than the toe), and the golfer moves the sweetspot of the putter during impact vertically upward in gravity. This is as opposed to starting with the toe up so that the heel and toe are at the same elevation above sea level. The "stripe" that tracks the ball contact point down the putter face during impact does not traverse the same sort of loft plane in these two cases. The three scenarios then are:
1. the putter flatly soled to the downhill-sloping surface moved vertically upward in gravity,
2. the putter flatly soled to the downhill-sloping surface moved upwards from the surface plane vertically, and
3. the toe-up putter with heel-toe level in gravity moved upwards vertically in gravity.
(It would be "weird" to include a fourth case, with the the toe-up putter with heel-toe level in gravity moved upwards from the plane of the surface vertically, as this requires an odd downhill overleaning of the body or odd "lifting" of the putter in the stroke in some fashion.)
If the impact point on the face of the lofted putter starts at the center of the face in the heel-toe dimension and also in the up-down dimension, the end of the "stripe" of ball-face contact after impact is over is as follows in the above three cases:
1. toe-ish, so the "stripe" is vertical in gravity but slanted down the putter face with the bottom of the stripe further downhill towards the toe than the center of the bottom of the putter face in the heel-toe dimension;
2. centered, so the "stripe" is vertical in reference to the surface plane with the bottom of the stripe centered in the heel-toe dimension directly "below" the starting point of the stripe which is also centered heel-toe; and
3. centered, so the "stripe" is vertical in reference to gravity with the bottom of the stripe centered in the heel-toe dimension directly "below" the starting point of the stripe which is also centered heel-toe.
These "stripes" correspond to the initial rolling plane imparted to the ball and they are not the same for the direction of the roll of the ball in relation to the "aim" of the putter face at address and at impact, and only case 2 starts the rolling plane of the ball headed off in the same "line" that the putter face aims at address.
Putts Stay on the Ground
Another major source of confusion here is the mistaken comparison of a putting stroke to a full-swing with an iron. If the iron's lofted clubface is moved in a plane on a surface sloping downhill-to-right-of-aimline / ball-below-feet, so that the blow thru the ball is in a plane that is perpendicular to the slope instead of vertical in gravity, the "launching" of the ball into the air frees the ball up from the support of the ground and thus subjects the ball to the influence of gravity while airborne. The ACTUAL ball flight will not stay in the starting plane, but the ball will drift to the right while airborne out of this starting direction. But if the blow imparts a starting plane of flight that is vertical in gravity, there is no tendency of the ball's ACTUAL flight to change out of the starting plane. So for the full swing on a sidehill lie, the golfer is advised to conform his clubface lie to the slope and to conform his setup orientation to the slope and to make a swing that imparts a flight plane that is vertical to the slope, BUT to aim a little more uphill rather than straight at the target.
This is not the same in putting, because, as Ben Hogan observed, there are TWO SEPARATE GAMES in golf -- one played in the air and one played on the ground. When it comes to putting, the golfer should setup with the putter aimed straight at the target, with the sole conforming to the slope, with the setup of the body conforming to the slope, and by using a stroke that moves thru impact in a plane that rises vertically upwards from the slope, AND this does not require aiming a little more uphill since the ball does not go airborne (except to the undesired extent that a golfer "launches" his putts with too much loft at impact or some other dynamic -- which makes keeping the rolling ball in contact with the ground right at the start or as early as possible with the least launching into the air a desirable characteristic of good putting).
This renders my fieldgoal-kicking analogy inappropriate, so let me amend the imagery so that the kicker is not kicking a football thru the air thru the goalposts but is instead kicking the back of a tire so the tire rolls along the ground straight thru the goalposts.
What this comes down to is that a ball rolling across a sloped surface with the plane of rotation perpendicular to the surface "turns" its plane of rotation downhill as the roll progresses laterally across the green but does not "lean over" to get the ball's plane of rotation back in conformance with gravity and the appropriate or required degree of turning can either be simple and uncomplicated ("it is what it is") or can present unneccesary complications for every putt. . The principal effect of golfer's not having an appreciation for this reality in physics is that they commonly underestimate how much the ball will turn downhill, and therefore they "under-read" the break. Trying to "fix" this under-reading bias by stroking the ball with an initial rolling plane that is vertical in gravity re-aims the starting roll of the ball alright, but almost never by enough required to make the startline have enough "break" built in for what will happen with the ball. The CORRECT approach is to aim straight at a target for a startline that appreciates this physics reality which is to say "play enough break" to begin with, and use a stroke dynamic that rolls the ball the same direction the lofted putter face aims at address by stroking the ball with the plane of rotation perpendicular to the slope surface.
Consider a 20-foot left-to-right sidehill putt from the 9 o'clock position for a right-hander with the slope being 3 percent (100' straight downhill from the ball is 3' lower in elevation) and the green stimp being 10'. This putt will probably have a target spot about 6" above the cup on the fall-line (and in this case, "hole-high" is also on the fall-line, which is a correspondence only true for the two sidehill putts from 9 o'clock and 3 o'clock), so the putt's "read" in conventional jargon is about "four balls out". Fewer than 5 in 100 golfers will actually see this much break and trust an aiming startline that aims the putter ALL four balls out. But to stick with the dynamics of the stroke, let's assume the golfer "wants" to aim at the target spot all four balls out, but he uses a "toe-up" orientation of his putter in the setup. He aims the aiming mark / line on the top of the putter head straight at the target spot. This aiming mark on the putter is a two-dimensional "stick", but the actual "aim" of the lofted putter face is slightly uphill of the target. If the golfer uses a blow dynamic that rolls the ball vertically in relation to the surface, which requires a blow of the putter thru impact that rises vertically upwards from the surface to impart the right rotational plane in the ball's rolling, the startline will be too high for the putt. The golfer won't really know "how much" too high except by long, vaguely registering experience, and then will only sort of know by implicit learning without conscious awareness of the specific details. Once the golfer sort of locks in on this aiming bias (most golfers never will), he will then also have to learn by trial and error how to adjust his touch. So there is no longer a connection between the starting line as defined by the target spot and the touch reference as defined also by the target spot on the fall-line. Confusion and uncertainty attends every putt. And this aim line bias varies in magnitude with the length of the putt, having more uphill bias with longer putts, and also varying with greater or lesser slope percentages, with steeper slopes having a greater mismatch between the alignment "stick" of the putter's aiming mark and the actual aim of the lofted putter face and in the mismatch between the orientation of the rolling plane of the ball in relation to the surface plane (and more loft in the putter face makes this worse as well). None of this mess is the case when the golfer conforms the sole to the slope and uses a stroke that rises straight up from the sloped surface and the putter loft matters not at all for the straightness of the starting roll matching up to the aim of the putter face at address.
AIMING PERCEPTION BIAS
To see this more clearly, plant a short laser pointer into the lofted face of a putter so the laser "aims" out of the face with the same loft as the putter face and aim the putter on a flat and level surface (like a basketball court) straight along the floor at a target at the base of a wall. The center of the putter face is, for example, 1/2" above the floor. The laser's spot on the wall does not hit the wall at a spot 1/2" above the floor, but some HIGHER distance up the wall vertically above the "aim spot" straight away from the putter face that IS 1/2" above the floor. (For a 3-degree loft on the putter over 240 inches or 20 feet, trigonometry shows that the laser hits the wall 12.7 inches above the 0.5 height of the putter's sweetspot, or 13.2 inches above the floor.) Because the golfer is aiming by using a 2-dimensional sense of "the putter" rather than a 3-dimensional sense of the aim of the lofted putter face, the golfer is in effect aiming ONLY the plane of the sole of the putter, or (which is effectively the same) the bottom leading edge of the putter face or the top leading edge of the putter face, but not the lofted plane of the putter face. The sense of "aim" the golfer uses is of a 2-D line staying on the surface that runs perpendicularly / square away from the leading edge of the putter face, and not of a "vector in 3-D space" aiming thru the air where the lofted face points. To use a laser pointer in the same way the golfer aims the putter, the laser cannot aim where the lofted face aims (e.g., angled up from the floor by 3 degrees), but must aim horizontally to the floor out of the face, and this is the same orientation as the plane of the sole of the putter when the putter is soled flat to the surface. Then, the laser will aim right smack on the aim spot on the base of the wall 1/2" high above the floor.
So we have two laser pointers to consider: one aiming where the lofted face aims (Putter A), and one aiming squarely away from the leading edge (top or bottom edge, take your pick) (putter B). Now consider how these two putters A and B with laser pointers embedded in them as described actually work on a sloped surface.
On the same sidehill putt (9 oclock from 20' / 7 meters) with a true break that requires a startline aimed at a target spot 4 balls out to the left of the left edge of the cup, with vertical strip of white metal that is 20 inches / 50 cm high and 4 inches / 10 cm wide stuck in the ground at the target spot extending straight up from the ground vertically in gravity so the vertical middle of the metal strip conforms to a plumb line:
Putter B soled flat to the surface: sends a laser line straight along the surface and hits the target spot and lights up the metal strip 1/2" above the ground but the spot in the air is along a "stripe" that leans downhill 3 percent so the exact laser spot is to the right of the mid-line of the metal strip a certain distance.
Putter A soled with the plane of the sole horizontal in gravity and thus "toe-up" with reference to the surface: sends a laser line straight thru the air on an angle up from the sole of 3 degrees and hits the target spot and lights up the metal strip well above the 1/2"-high spot that corresponds to the putter face center and the laser spot in the air is along a "stripe" that leans uphill 3 percent so the exact laser spot is right on the mid-line of the metal strip a certain distance up from the ground (13.2 inches for a 3-degree loft).
Lasers can project either a beam or a line, and if a line, the line can be oriented to another reference: for example, a line-projecting laser can aim a line out of a lofted putter face so that the line runs vertically up-down with the center of the putter face or so that the line extends horizontally in the heel-toe dimension. Aiming a laser putter with the line vertically out of the face across a basketball court at a wall runs the lower half of the laser line line running straight along the floor all the way to the base of the wall and also the higher half of this projected laser line running vertically up the wall, with the center of the projected laser line being some distance up the wall from the floor. Let's imagine that the exact center of this projected line shows up as a "blue dot" while the lower half of the line is "red" and the upper half of the line is "yellow". Using this laser in Putters A and B:
The "stripe" up the far wall is how the ball's rotation plane will be oriented after impact if the stroke "rises" in a plane that meets the surface in the same angle as the toe is up (if any). If the stroke "rises" thru impact in a different plane than its toe-up orientation (such as vertically in gravity or up away vertically from the surface plane), then the resulting roll of the ball will also have some slipping on the face that influences the rotational plane at the start. So not only does a toe-up putter aim to the inside; it also gives the ball an initial rotational disc that is tilted out of plumb to the surface and in an attitude that seldom if ever corresponds with plumb in gravity except by happenstance.
The visual appearance of the alignment line from the perspective of looking down from beside the ball at address at the top of the flatly soled putter face and its alignment mark (as a left-right line at the center of the putter that is square to the leading edge of the putter face from heel to toe) compared to the visual appearance from the same perspective of the top of a toe-up putter shows two basic facts:
1. The two alignment marks are still parallel to one another;
2. The toe-up alignment mark is offset slightly to the inside and is slightly higher and closer in to the golfer.
In sum, a toe up putter aims to the inside in two different ways (the alignment mark is closer in albeit parallel and the lofted face aims farther and farther to the inside the greater the loft, the greater the mismatch between the sole and the surface planes, and the greater the length of the putt) AND the toe-up putter imparts a biased rotational plane in the ball's initial roll out of plumb to the surface and also out of plumb to gravity except in unusual cases of happenstance.
All this being true, it is also necessary to consider the exact geometry of the bottom of the ball in contact with the green surface. Compare rolling a very thin metal disc across slanted marble with rolling a very fat tire across a slanted field of high grass. When the ball's rotational plane is NOT plumb to the surface, the width of the effective contact of the disc as defined by the bottom of the ball in the given thickness of grass on the surface is also slanted off the surface -- a situation that very quickly is corrected by gravity. In comparison, there is no such correction when the rotational plane is plumb to the surface.
In summary, making a habit of trying to roll the ball in a rotational plane that is vertical / plumb in gravity has naive appeal, but is in fact not the "Yellow Brick Road" to happiness that it seems. The end of this line is poor reading, poor aiming, poor stroking, and poor touch. Altogether, it is much simpler and better and uncomplicated to "just get along" with reality a little more. A gravity-plumb roll from a heel-up or toe-up putter is really just a bandaid attempt to correct for habitual under-reading the break (which is chicken-and-egg with habitually stroking the ball gravity-plumb so it artificially stays a bit higher than the real break) and it comes at the price of variability in every putt, whereas simply accepting the extent of break that comes with a surface-perpendicular roll gets the junk out of reading, aiming, stroking, and touch.
As a sidenote, one can experiment with a rolling plane that starts the ball off leaning "uphill" MORE than gravity-plumb. When I tried this, the ball had an uphill torque that "turned" the direction of the ball's roll uphill! I think this dynamic has never been observed or commented upon before in golf, so I plant my flag on it!
Finally, all of the above is subject to rigorous and well-designed and controlled experimental verification or falsification. I think the separation of the effects of the COG being in plumb or out of plumb with gravity between the COG of the rotational plane and the COG of the ball itself may be an important contribution, or at least a very subtle and under-appreciated insight.
Cheers!
Geoff Mangum
Putting Coach and Theorist
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