H.A. Templeton's Vector Putting: The Art and Science of Reading Greens and Computing Break (Fort Worth, TX, 1984), is the only book I've ever seen so far that seriously analyzes "break" on a putting green. Templeton certainly knows his physics, and has done the work. The result is a very detailed discussion of how gravity affects a rolling ball and how the "break" varies dependent upon slope, green speed, and distance. Along the way, Templeton also discusses in detail the Stimpmeter, the physics of ball roll and speed, ball balance, grain, and the psychophysics of human detection of surface tilt. The end result is a much better understanding of the factors involved in reading putts.
Templeton applied his studies to the greens at the golf course at Carswell Air Force Base in Texas. From this work, he gained lots of empirical data about the combinations of green speed, slope, and length of putts as these affect break. He actually surveyed and charted the greens in a grid pattern of slope percentages and charted data for rolls (rolling speeds and break for given green speeds). Templeton uses the "zero break line" (ZBL) approach to locating an aim point above the hole on the "fall line" straight uphill-downhill through the cup, and this means he is constrained to assume that the surface over which the putt rolls is all flat but tilted. So this whole method has its limits. he also has adjustments in locating the aim spot for uphill putts (quicker initial putt speed) and downhill putts (slower initial putt speed), as these putts have variable total time from start to finish, and hence experience the influence of gravity in different ways. Templeton then summarizes all this in charts, with a separate chart for different green speeds (slow, medium slow, medium, medium fast, fast) that correlate slope percentage and distance of putt with location of aim spot above the hole on the ZBL. Thus, for a ten-foot putt on a medium fast green with 4 percent slope, the aim spot is located about 14 inches above the cup's edge on the ZBL for a putt directly along the axis of tilt, with adjustments for uphill up to 3 fewer inches to 11, and for downhill up to 4 more inches to 18. So each "cell" of aim spot locations usually has a range of inches above the cup on the ZBL.
My approach simplifies all this by intuitively integrating slope, green speed, and distance by having the golfer go to the axis of tilt and imagine putting straight at the hole from the same length as his putt with drop speed, and visualizing just how far down the ZBL such a putt would cross the fall line. This distance gives the location of the aim spot on the high side of the ZBL. I haven't done all the empirical data gathering that Templeton has done, but my experience so far has been that using this approach establishes a ball-park aim spot and that thereafter the golfer has to fine-tune his targeting of the actual path into the cup. I suggest that after getting a ball-park sense of the aim spot, the golfer then visualize a movie of the putt in real time but running in reverse, to watch the ball back out of the hole and retrace the final three feet or so of the actual curving path headed towards the address position. This visualization shows the "hump" of the break over the critical make-or-break part of the putt, and shows exactly where the ball enters the cup rolling at the cup's center, and (by extending the movie back farther towards the address position of the ball) also shows how the curve of the putt eventually straightens out and thus establishes the starting line for the putt and the orientation of the putterface.
Doing this visualization ends up with the face pointing approximately at the previously identified aim spot on the ZBL. The golfer's task is then to start the putt off straight in the direction the face is aimed so that the ball breaks off or drops off this startline as it nears the hole, stays on the high side of the hump shape of the critical part of the putt, and then enters the cup on a trajectory aimed straight at the center of the cup. The total energy or touch needed for this is just about the same as that to send the ball all the way to the ZBL at the aim spot and not much (if any) farther. This sense of touch also works for long lags, where the golfer sets as a goal for touch purposes rolling the ball just to the fall line at the aim spot as if the putt were a straight putt, albeit with uphill-downhill adjustments to get the ball all the way (only) to the aim spot.
I personally appreciate the hard work involved in the Templeton book, but I find it unrealistic and impractical to expect the golfer to commit the empirical data points of the aim spot to memory. So the usefulness of the charts of aim spots is limited on the course. More importantly, the basic assumption that the whole path of the putt is "flat-but-tilted" is rarely the case, and intervening undulations in contour are the rule, especially as putts exceed about 15 feet in length. And since he does not precisely resolve the variation in the aim spot for uphill-downhill effects, some aim spots have as much as 15 inches range to sort out. Even with Templeton's work, the golfer still needs to fine-tune the aim intuitively for all putts significantly off the axis or the fall line itself, and this is the great bulk of all putts.
So, yes, I think Templeton's book is "great" and "correct," but it is also very involved and daunting. It is somewhat like an operating manual for a nuclear power station when the golfer only needs to know how to flip the switch and get the lights on. (Reading this analogy just now, I am struck by its absurd exaggeration of the basic valid point.) But the book is delightful overkill -- delightful to read and savor for the many insights into putting for the obsessed among us, but potentially misleading by its overkill. Charts are always impressive, but they can conceal actuality as much as they reveal it. In the final analysis, putting is not numbers or math or physics, but something humans do with a putter and a ball on a specific green.
Cheers!
Geoff Mangum
Putting Theorist and Instructor
PuttingZone.com
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