Dear Neville,
Responding to your questions:
1. Am I correct in understanding that in order to encompass both direction, and a feel for distance, the putterface should be square from the bottom of the stroke, that is 2 inches behind the ball, through the impact area of 1/13th of an inch, and then beyond for 3 to 4 inches? A distance of 6 inches all up.
Yes. This span is about the same scale as the human hand, and is more or less the minimum stroke size in which the golfer will have substantial distance control in the putt. Anything shorter than this is one of those "just start the ball" strokes on a slick downhill putt at Augusta National.
The reason I advise keeping the putter square thru this impact zone has to do with optimizing the putting. While it is true that some golfers can use a gating stroke path thru this area and hit lots of putts right where they aim the putter (or where they intend the ball to go, regardless of the putter's aim), at the critical moment of truth the putter needs to be square and moving online or else the golfer has to inculcate a repeating combination of across-the-line path plus face open or closed, always in the same manner. No matter what anyone says about how good they can be with this gating path and the face opening and closing, this approach makes ball position, timing, and stroke consistency critical. It puts an unnecessary stress on fine-motor skills and hand-eye coordination for each and every putt. In contrast, moving the putter squarely down the line is biomechanically simple to perform (even if some find it tricky to teach or to learn), essentially eliminates ball position as a concern, expands the realm for acceprtable and effective timing, and reduces stress for repeating the stroke enormously.
The real difference between a gating stroke and a down-the-line stroke is between a hit stroke and a hitless stroke. The gating stroke is all about impacting the back of the ball to send the ball rolling off at a target. The down-the-line stroke is a gesture of the putter squarely along the line in which the straight rolling of the ball is a mere side consequence of good form.
In a hit stroke, the human brain is chiefly concerned with anticipating and timing impact dynamics when the putter face meets the back of the ball. The actual impact is over so quickly and the movement of the putter at this time is so swift in relation to the eyes' ability to track and monitor the dynamics that most people think they are a lot better at this on a consistent basis than they really are. Everything of importance is out there at the end of the stick of the putter, and managing what happens out there is a try-whatever-works sort of deal. In contrast, when the task is to make the same straight down-the-line gesture each time, the focus moves into the body and the body movement, with the arms and hands simply holding the putter steadily, without participation in any action at the end of the stick. The whole motion is a simple body motion, only, and not a moving of the putter head except incidentally. This way, there is no need to anticipate or manage the brief moment of impact. It is a very liberating and freeing way to putt straight.
Also, a hit stroke is usually accompanied by a swift closing of the putter face thru impact, or at least an out-to-in path in the stroke. This is because the anticipation of the precise moment of impact causes a very subtle "lunging" action in the golfer's total body into the back of the ball to "make sure" impact is done as intended. This subtle "lunging" action is not accompanied by concerns for the form of the stroke, and so defaults to the "around the feet" pulling of the putter and the rotating closed of the forearms and hands as if reaching thru the ball. Golfers who manage this last-moment inside pulling / closing action well often do so by learning poor aiming habits in which the target is believed to be to the outside of its true location, so the pulling / closing action ends up being no-harm, no-foul. If the golfer has an out-to-in stroke path, he learns over time to open the face in a "cut stroke." If the golfer uses a gating stroke that gets pretty square right before impact, he tends to rotate the putter closed a little more quickly thru impact when he is making a "hit" stroke, and if he doesn't do it consistently, he leaves the ball out to the outside. This pulling / closing action also trains this sort of golfer to aim to the outside. In both cases, consistency suffers and general technique degrades. If the golfer's sense of timing or hand-eye coordination or vague "feel" changes from day to day or over the course of years, as it inevitably will, the golfer gets left stranded with a goofed-up technique and no understanding of how to get back on a consistent, accurate track.
Keeping the span of the impact zone about as large as a hand in size is a way to train the golfer out of the hit stroke and into the gestural stroke, for purposes of optimizing accuracy and consistency over the long haul.
2. An off center hit affects the distance that a putt will travel because the mass of energy is less than optimum. It also affects somewhat the direction of the putt because of a slight twisting of the putter blade. Am I correct in assuming that this twisting can only occur during the millisecond moment when the ball and putterface are in contact?
Yes.
3. How much spin does the putter path cutting across the ball affect its direction? Does the change of direction occur immediately or only when the ball starts to slow down at the end of its journey? I don't understand how they estimate that the putter path is responsible for directional errors of about 17%. Your example of a putter path moving diagonally across the ball with the putter face held open (a la Billy Mayfair) implies that the combination of these two errors cancels out any side spin. Am I correct in this assumption?
The side spin washes out pretty quickly due to interaction of the ground with the bottom of the ball. The side spin doesn't really get real traction in this washout time so as to change the ball's direction. You would have to spin the bejeebers out of the ball with side spin to see much effect on the forward line of roll. People with a pronounced cut spin stroke sometimes see a little effect on the ball's direction of roll a little way into the putt, but not often.
The physics of oblique sideways putter path across the intended line of putt has been discussed by CB Daish in his book The Physics of Ball Games, section 14.7. The formula is
tan(angle of roll off intended line) = 2(M +m)/7M(1 + e) x tan(path angle across intended line)
Using a putter head with mass M 7 times that of the ball's mass m (which is fairly typical), and using a coefficient of restitution e of the ball during impact of about 0.8, for a path error of 10 degrees out to in, the resulting ball roll error is:
arctan[2(8 +1)/7*8(1 + 0.8) x tan(10)] = 1.8 degree line error in ball roll.
That's about 18% of the path error. As Daish says, "So the angle [ball rolling offline] is clearly much smaller than the angle [of path error]."
With respect to a face-angle error at impact, the situation is similar to delivering a blow with a lofted club -- the direction or path of the club is straight online but the striking face is angled off line. If the face is twisted to the outside (open) by 10 degrees, the blow imparts two components of motion to the ball -- one perpendicular to the face of the putter by the term Vcos(face angle error) (with V being the velocity along the intended line), and the other a motion of sliding sideways on the face of the putter by the term Vsin(face angle error). The cosine of 10 degrees is 0.98, while the sine of 10 degrees is 0.17. Hence, the component of ball motion is more off line. The net effect of both the offline (cosine) component and the sliding sideways (sine) component is that the ball heads offline with a 10-degree face twist about 8.3 degrees to the outside of the intended line, accompanied by a little side spin that soon washes out (see Daish section 14.11).
I have visited the website of Dr Norman Lindsay, but my grasp of the scientific data presented is limited by a lack of education in physics. Have you tried the putter he has designed?
No, but I have tried putters with similar design features. The requirement to impact the ball high on the face of the putter is a little contrary to the way I teach putting the middle of the stroke / stance and thereafter allowing the putter to rise into the back of the ball. In order to keep the impact point high on the face of a putter like Dr Lindsay's, it is necessary to play the ball fairly tight in close to the bottom of the stroke near the center of the stance and/or deliver the putter thru impact without its natural up-rising arc, either with a hands-ahead style or with a deliberate manipulation of the putter to keep it artificially low thru impact. This puts the spotlight right on whether this technique artifice (and the risks of inconsistency) are worth the gain in reduced skid. So far, my answer is "not usually." This particular trade-off needs some serious testing to sort out.
Cheers!
Geoff Mangum
Putting Theorist and Instructor
Geoff Mangum's PuttingZone
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