Geoff Mangum's PuttingZone Research

Sample Section: 4.01.01.

4.01.01., .-- , -- BALL-GREEN -- INTERACTIONS, , ,

4.01.01., Crabtree, Bill, Pro pointer: Putting: putts, Golf Mag., 29(12), Dec 1987, 74, weight back on heels relaxes shoulder and back muscles for smoother stroke 4.01.01., Cunningham, Carl, To apply swing time, Golf World, 6(21), Oct 31, 1952, 14, mechanics applied to iron swing, noting constant time for varied-distance pendulum swings

4.01.01., Golf Magazine, How the putter works: Knowing how the flatstick works leads to better putts, Golf Mag., 31(7), Jul 1989, 98, 1. keep hands even with ball; hands ahead delofts putter, pinches ball into turf and makes it skip and bounce as it starts, likely losing line and distance; 2. toe-hit imparts hook spin and sends ball to the right [backwards]; 3. hell-hit imparts slice spin and sends ball left [backwards].

4.01.01., Pelz, Dave, Putting: Greens have hazards, too: You can hit a perfect putt that won't go in: Here's why, Golf Mag., 25(9), Sep 1983, 50, lumpy donut

4.01.01., Pelz, Dave, Putting: Hit your putts hard: My research proves that the best putts are those struck with enough force to carry them about 17 inches past the hole, Golf Mag., 25(8), Aug 1983, 32, note my criticism: research doesn't address any golfer's ability to hit the line at various putt speeds; may well be the case that a given golfer has a superior ability to hit the line at a given speed less than 17-past speed, or does not have a good ability to hit line at this speed; these factors may be concealed by the research. Even so, 17-plus is 5-plus past the dying wobble of the decay phase, so that's probably a good aiming point, even if in the event most putts get struck with 13-plus speed.

4.01.01., Pelz, Dave, What's a good putt: The secret to successful putting is speed, Golf Mag., 29(8), Aug 1987, 34,

4.01.01., Weathers, E., A matter of some gravity, Golf Dig., 46(10), Oct 1995, 70-80,

4.01.01.01., .-- , -- -- GREEN -- CONDITIONS / -- PLAYING CONDITIONS, , ,

4.01.01.01., Alliss, Peter & Trevillion, Paul, Easier Golf, (London: Stanley Paul, 1969), , 67: On soft wet greens the ball seems to travel more through the grass and slopes make less impression, but if the green is hard the ball will travel on top of the grass and any slope will have a marked effect.

4.01.01.01., Goetze, Vicki, A putting primer: Tips and drills from an acknowledged Tour expert, Golf Dig., 42(9), Sep 1991, 90-92, 94, 94: fast greens: I putt better on fast greens because I putt by feel. [meaning?] Good feel is a must if you're going to die the ball into the cup. Pick higher targets to allow for the extra break that occurs when the ball loses speed around the cup. Slow greens: longer stroke and concentrate on solid hit on sweet spot.

4.01.01.01., Golf Magazine , Golf Magazine's Handbook of Putting, (New York: Harper & Row, 1973; London: Pelham, 1975), , 85: If you are putting with the grain on Bermuda greens or any type of green that is fast, putt more toward the center of your stance. Putting off the left toe tends to put overspin on the ball and makes it move considerably faster. Playing it more toward the center of your stance gives you more control over the speed. Against the grain, you're better off putting off hte left toe, since you want overspin to help the ball toward the cup.

4.01.01.01., Golf Magazine , Golf Magazine's Handbook of Putting, (New York: Harper & Row, 1973; London: Pelham, 1975), , 124: Pay particular attention to the area around the cup. There may be spike scuffs, footprints, or ragged edges that could seriously hamper the line of your putt. Since the ball is traveling slowly near the cup, it is subject to the slightest imperfections on the green. When such imperfections exist, it is usually a good idea to putt more firmly, hoping that the ball will be able to resist the rough spots. That is, hit the ball harder and don't allow for as much break. Irregular greens are next to impossible to read, so it's hard to determine the exact break (or bounce) you're going to get. Even if you do have the ball breaking toward the hole, if it's moving too slowly the ball will be easily knocked off line by one bump or another. On this kind of green, it's best to take your chances of banging the ball at the hole, never giving up the cup unless the break is so severe as to dictate it.

4.01.01.01., Golf Magazine , Golf Magazine's Handbook of Putting, (New York: Harper & Row, 1973; London: Pelham, 1975), , 125: on fast greens, avoid downhill putts; look for uphill ans straight in putts, and even sidehill putts, rather than downhill putts. 126: Downhill putts on fast greens can slide away from the hole too easily and put you in a precarious position for three=putting. The point is, then, to stop your shots on the putting surface soemwhere below or beside the hole, rather than above it.

4.01.01.01., Golf Magazine , Golf Magazine's Handbook of Putting, (New York: Harper & Row, 1973; London: Pelham, 1975), , 126: on slow greens, play the ball forward a bit, place the hands a little ahead, and hit up on the ball or use more loft to get the ball rolling over the heavier grass, but going downhill on a slower green needs no adjustment and the slower surface should be taken advantage of. Guard against pulling the putt on slow green by stroking a little harder than normal, as you are apt to do on a slow green.

4.01.01.01., Golf Magazine , Golf Magazine's Handbook of Putting, (New York: Harper & Row, 1973; London: Pelham, 1975), , 1332: on winter greens, the green is likely to be hairy, coarse and stiff. Your sense of touch will lose something in the cold, so try to keep your hands warm. Concentrate on a solid -contact stroke that gets the ball up and rolling, and play the ball a bit forward. In early spring, some greens lack grass on certain places and may be uncut, so even grassed areas are unusually slow.

4.01.01.01., Kite, Tom & Dennis, Larry, How to Play Consistent Golf, (New York: Golf Digest/Tennis, 1990), , 173: Adapting to conditions is pretty easy. The faster the greens, the shorter and slower the stroke must be. The slower the greens, the longer and faster the stroke must be. [isn't this tampering with the tempo?] Penick to Sandra Palmer: Well, if the greens are that fast, you probably need to hit it easier.

4.01.01.01., McLean, Jim & Pirozzolo, Fran, The Putter's Pocket Companion, (New York: Harper-Collins Publishers, 1994), , 4: slow surfaces, play ball back towards middle of stance to preset hands ahead of ball, deloft putter, and encourage downward impact for better roll on slow greens.

4.01.01.01., McLean, Jim & Pirozzolo, Fran, The Putter's Pocket Companion, (New York: Harper-Collins Publishers, 1994), , 5: heavier putter is better for fast greens; much easier to move slowly; use a smooth, even-paced stroke.

4.01.01.01., Nicklaus, Jack, Jack Nicklaus' lesson tee: No. 25: Putting pointers, Golf Dig., 24(12), Dec 1973, 41-44, 42: 2 types of wet greens: moisture soaked into ground, and putts run slower and break less; only filmed with moisture, and putts only slightly slower.

4.01.01.01., Nicklaus, Jack, Jack's lesson tee: No. 8: Putting: Mental approach and strategy, Golf Dig., 23(7), Jul 1972, 46-49, 49: Have a good look around the area of the hole in sizing-up long putts, especially at times when grass growth is slow. Take into account a possible speed-up factor around the hole when greens are heavily worn. If foot traffic has been heavy, you could hit a 40-footer far past the hole if you base your stroke on the speed requirement of the first 20 feet.

4.01.01.01., Rosburg, Bob, Diners Club Matches, ABC, Dec 13, 1997, In winter Bermuda greens are frequently overseeded with rye or bent for color, and this changes the green speed. From off the edge of the green, a long putt's distance is harder to judge and the ball might get caught in the overseeded grrass. The best approach is to chip, say with a 7 iron, to get a good roll out of the ball.

4.01.01.01., Stockton, Dave & Barkow, Al, Dave Stockton's Putt to Win: Secrets for Mastering the Other Game of Golf, (New York: Simon & Schuster, 1996), , 41: The firmness of a green is another way to read speed, but this is strictly a matter of feel. On some greens, you can feel the speed just by walking on them. Oakmont is like that -- you're kind of glad you're wearing spikes, so you don't slip and fall. In [42] fact, you can get the feel of a green's speed by how your spikes go into the ground. Is there a certain resistance? Does it feel brittle? Then the green likely will be fast. If you feel you're walking on a cushion, if the green is moist, the green likely will be relatively slow. 50: On hard, fast greens, speed is crucial to success. Putts are not going to break as much as it appears, no matter how softly you roll the ball, because the ball is going to have some pace on it. To counter this I apply some stroke technique. I try to keep the [51] putter very low to the ground during the stroke, even letting it ride on the grass a touch going back. I won't forward press quite as much as normal, if at all, because I don't want to take a chance on popping the ball, having it jump off the face. When a downhiller is really slick, I won't forward press at all, using the loft of my putter to produce a sofetr roll. I might even begin the stroke with my hands slightly back of center so that the loft of the putter kind of deadens the impact.

4.01.01.02., .-- , -- -- PHYSICS, , ,

4.01.01.02., Carlson, John E., The pendulum clock, Physics Teacher, 29(1), 1991, 8-11, 8: simple pendulum, T=2pi x sq root of L/g; but most pendulums are not so simple. More general: T=2pi x sq root I/k, where I (moment of inertia) for a thin rod pivoted at one end is I=ML(sq)/3 and k (torsional constant) = torgue/Theta or LMgsinTheta/2Theta; for small Theta, sinTheta approximately = Theta, so if Theta is kept small, k approx. = LMg/2; therefore, general formula is T=2pi x sq root[2L/3g]; [NOTE: Theta is about the same as sinTheta up to about 15 degrees, where the diff. is about 1%; at 20 deg., diff. 2%; 25 deg., diff. 3%; 30 deg., diff. 4.5%; 35 deg., diff. 6%]. 10-11: two-mass pendulum requires four-step process to calculate T, with five variable {temperature effects, two masses, and two lengths]; 1st calc. temp effects on L using thermal coeffic. of expansion alpha: L(1)=L(ref. of mass 1 at 0 deg. C) x (1 + alpha(1)T); L(2)=L(ref. of mass 2 at 0 deg. C) x alpha(2)T); 2nd, calc moments of inertia: I(1) = [M(1) x L(1)(sq)] / 3 and I(2) = [M(2) x L(2)(sq) / 12] + [M(2) x [L(1) - L(2)/2](sq)]; 3rd, calc torsional constants k: k(1) = M(1) x g x L(1) / 2; k(2) = M(2) x g x [L(1) - L(2)/2]; and 4th calc. T: t = 2pi x sq root[ (I(1) + I(2)) / (k(1) + k(2)) ] -- very tedious without a computer.

4.01.01.02., Edge, R.D., Two-dimensional collisions using s, Physics Teacher, 27(3), 1989, 207-209,

4.01.01.02., Golf Magazine , Golf Magazine's Handbook of Putting, (New York: Harper & Row, 1973; London: Pelham, 1975), , 127: on a wet green, the ball will slide more [because there is less linear friction converting linear motion to angular motion making the ball roll; so, to the extent the ball is not engaging the friction of the grass tips the putt is less affected by grain, and to the extent the putt has less friction and so rolls faster it will be less affected by the break or slope over the segment of the putt where the speed is higher, although as ball slows down near hole the reggular slpe effect will take over, but still then the slope effect will be resisted a bit by water pressure keeping ball uphill a bit -- not likely too much of an effect. Also note that wetness might generally slow the putt overall, especially as it nears hole -- blasted along at first then dramatically dying out -- and in the dying phase there is more opportunity for gravity to work; altogether, a somehwat confused and complicated set of effects] A hairy green (one that hasn't been cut recently) will have the same effect as a wet one. 128: Play the ball with a firm left wrist and play the ball up a bit for upswing overspin -- both for a firmer, truer roll that holds the line well. Also, Bermuda holds the moisture longer than bent grass.

4.01.01.02., Head, James, Faith in physics: Building new confidence with classic demonstration, Physics Teacher, 33(1), 1995, 10-15,

4.01.01.02., Holmes, Brian W., Putting: How a golf ball and hole interact, Am. J. Physics, 59(2), Feb 1991, 129-136, Study analyzes the physics of an American ball rolling at a 4.25-inch diameter hole as a function of initial velocity and impact paraemeters, concluding a ball must roll at 1.626 m/s or less (64.016 inches per second) to stay in the cup; a smaller British ball is easier to sink than the American ball; a ball with a larger moment of inertia is harder to sink; and any bounces and skids lower the maximum speed that allows that putt to sink. In passing, author notes that the greater moment of inertia makes the ball easier to kick past the hole and 10% more moment of inertia translates to about 1% decrease in maximum allowable speed for dropping; that a ball dropped onto the surface of a green rebounds in general about 10% of the initial drop height; that the effective radius of the hole runs from 100% actual size at 0 m/s to 50% size at 1.23 m/s to 0% size at 1.626 m/s in an uneven curving arc; and that in practice balls fall even though outside the computer-generated boundary, probably due to losses of energy from initial conditions from bouncing and skidding en route. Ball has a veloc. at point it reaches rim (V(0)) and a min. veloc. for the ball to roll on the rim (V(m)). There is also a capture veloc (V(c)) and a max. veloc. (V(max)) above which the ball will skip over the hole even if it hits dead center. In this scheme, V(m) = 0.457 m/s [18 ips, 1.5 fps, 3.4 rev/s]; V(c) = 1.313 m/s [51.7 ips, 4.3 fps, 9.8 rev/s]; V(max) = 1.626 m/s [64.0 ips, 5.3 fps, 12.1 rev/s]; V(max) smaller British ball = 1.653 m/s (easier to sink) [65.1 ips, 5.4 fps, 12.3 rev/s]; when the veloc of the ball upon reaching the rim is less than V(m), the ball rolls on the rim a bit; when V(0) < V(c), the ball will drop in the hole without hitting the back rim; V(c) declines as the ball's path across the hole moves out toward the side edge and coincides with V(m) at about 0.5 to the side of the center at a velocity of about 0.6 m/s.

4.01.01.02., Holmes, Brian W., Putting: How a golf ball and hole interact, Am. J. Physics, 59(2), Feb 1991, 129-136, The capture region where V(0) > V(m) and V(0) < V(c) extends from initial velocities of 0.457 m/s to 1.313 m/s a the center of the hole and from 0 off center to 0.5 off center with the velocity range converging over this cup range from 1.313 at center to 0.6 at 0.5 off center at the top and from 0.457 to 0.6 along the bottom; roughly speaking, these putts act like center cut or dead in the heart putts, the ball rolling over the edge and dropping to the bottom of the cup without hitting the back edge of the hole. A second sink region is one where the ball hits the back edge after falling at least one-half (or more) of a ball diameter, either by flying over the edge to the back edge or by rolling some along the rim as it sinks. These balls hit the back edge and then sink. The range extends from the max. velocity at which even a center-cut ball flies over the back edge, 1.626 m/s, to initial velocities above V(c), or 1.313 m/s at the center of the hole and dropping to 0.6 m/s at 0.5 off center and thereafter increasing back up to the max. velocity just short of .84 off center (1/2 a ball). There are nine (9) patterns of interaction between the ball and hole: 1. balls that roll on the front rim before they are captured flying=CF1; 2. balls that lose contact with the surface as soon as they reach the front rim and that are captured before striking the opposite rim=CF2; 3. balls that are captured flying after striking the opposite rim=CF3; 4. balls that lose contact with the surface when they first encounter the front rim and that are then captured after striking the rim a second time=CF4; 5. balls that are captured rolling and that never lose contact with the rim=CR1; 6. balls that are captured rolling after undergoing ballistic motion [losing contact with ground]=CR2; 7. balls that escape rolling without losing contact with the rim=ER1; 8. balls that escape rolling [jump out and roll away] after striking the opposte rim=ER2; and 9. balls that strike the opposite rim and escape flying [bounce out].

4.01.01.02., Holmes, Brian W., Putting: How a golf ball and hole interact, Am. J. Physics, 59(2), Feb 1991, 129-136, CF3 balls that pop and drop, hitting the opposite rim and then dropping [rammed in], are those that exceed the capture speed but are less than the maximum speed. At the center of the hole, this range is from 1.313 to 1.626 m/s or the V(c) and V(max) points. Both these lines decline steadily as the path moves out to the edge, maintaining the same separation and thus defining a band for pop and drop sinkers. The band runs from 1.313 to 1.626 m/s at 0% out down to about 0.65 m/s at anywhere between 60% and 75% out; beyond 75% out, the only way for a ball to drop is to topple in or go in as a ringer, and this is really closer to anything beyond 60% out. CF4 balls that hit the back rim, jump up, bounce down on the rim again, and then fall (hop & drop) begin when the plunkers CF2 get too far out and when the topplers CF1 are going a little too fast, but it is a very small region: between 50% out and about 65% out, above about 0.5 up to a max of 0.7 m/s. They are sort of pop & drop balls that hit between 50% and 65% out but are a little closer to the center than pop & drop balls in the area 65% to 75% out at comparable speeds 0.5 to 0.7 m/s. This area is really a minor expansion of the pop & drop zone. In fact, this capture zone is a little braoder than appears by claculation alone, because balls above the maximum speed but within the 50% area still occasionally drop back in up to about 1.75 m/s at dead center and maybe 0.2 m/s more than expected above the whole CF3 top range due to bouncing and skidding of the ball as it hits the rim, killing some of its excess speed.

4.01.01.02., Holmes, Brian W., Putting: How a golf ball and hole interact, Am. J. Physics, 59(2), Feb 1991, 129-136, Most balls that contact the hole at 75% out or closer in but miss do so by jumping the hole above the maximum speed. A very few jump the hole and then roll off, but really, it is the same phenomenon. Ball paths farther out then 75% that miss will either jump the hole or lip out. Lip-out balls are those ER1 balls between 75% and 100% out that are above V(max) and below V(m), which cross at 75%; thus, so long as the ball stays below V(m) it will not fly the hole, but above V(max) and 75% out it will definitely miss. Bteween 75% and 100%, V(max) drops from 0.65 m/s to 0, while V(m) increases sharply from 0.65 m/s to 1.626 m/s and above. So, essentially, unless you care to categorize misses, everything exceeding about 0.65 m/s at 75% out, 0.5 m/s at 80% out, 0.4 m/s at 85% out, 0.3 m/s at 90% out, and 0.2 m/s at 95% out will miss.

4.01.01.02., Holmes, Brian W., Putting: How a golf ball and hole interact, Am. J. Physics, 59(2), Feb 1991, 129-136, Defining the point where the center of the ball's path enters the hole as a % of the hole's width/radius out of the center (100% or more=completely out of the hole; 0%=dead center), a graph of initial ball velocity at the front rim versus path shows that center-cut putts drop at any velocity above 0 up to a maximum of 1.626 m/s; as the path moves out to the edge of the hole, the point at which balls fall in and stay in declines more or less steadily to 0 at the very edge of the hole, so that, for example, when the trajectory crosses 1/2 way out of center, the range of drop speeds must be about 1.3 m/s or less, and 3/4 the way out of center, the range of drop speeds must be even slower, about 0.5 m/s or less. CF1 balls topple in at speeds under about 0.5 m/s out to about 65% off center, then the topple-in speed starts to drop to about 0.3 m/s at 90% out, then drops rapidly to 0 m/s at 100%; however, while the topple-in speed drops above 65% out, balls continue to fall in as CR1 balls that slip around and down the rim, ringing around to the bottom of the hole; these ringer putts start at about 65% out to perhaps 90% out, but the drop speed at first increases from just over 0.5 m/s at 65% up to 0.65 m/s at 75% then declines rapidly to just above 0.3 m/s at 90% out; beyond 90%, ringers don't stay in the hole. CF2 balls are those that plunk in the hole without hitting the back or running along the rim; plunkers drop on a path at the center between speeds of 0.457 and 1.313 m/s; as the path changes mre to the outer edge, the top speed declines steadily down to about 0.65 m/s at 60% out and the bottom speed stays close to 0.5 m/s from 0% to 50% and then between 50% and 60% curves up to 0.65 m/s. A minor point is CF4, balls that hit the back rim, jump up, hit the rim, and fall (hop & drop). These balls begin when the plunkers get too far out and when the topplers are going a little too fast, but it is a very small region: between 50% out and about 65% out, above about 0.5 up to a max of 0.7 m/s.

4.01.01.02., Holmes, Brian W., Putting: How a golf ball and hole interact, Am. J. Physics, 59(2), Feb 1991, 129-136, Looking at the hole as a shape that shrinks the faster the ball is going when it reaches the hole, one can graph the effective size of the hole versus ball speed, to see that the as the ball goes faster from 0 up to a maximum of 1.626 m/s, the effective size of the hole decreases or shrinks. At just over 0 m/s, the hole is 100%; at 1.626 m/s the hole has shrunk to 0%. The effective size of the hole may be considered the same as the chance or probability the ball will drop. At a ball speed at the hole of 0.5 m/s, the ball has a hole a little over 75% its original size, and so will drop if its path is inside the 75% section of the hole; otherwise, it will miss. The hole shrinks to half its original size at a ball speed of 1.23 m/s at the hole. Any ball speed much above this has only a slim chance of dropping.

4.01.01.02., Holmes, Brian W., Putting: How a golf ball and hole interact, Am. J. Physics, 59(2), Feb 1991, 129-136, 131: when the ball hits the back of the rim, the maximum speed for capture depends somewhat on the kind of bounce the ball gets, and the better the bounce back the more likely the ball will drop. This bounce back along the original path of the putt tends to overcome the forward linear and angular momentum of the ball, which is tending to make the ball jump over the back rim. The combination of the influences may make the ball bounce back and drop, bounce up and fall back onto the rim, bounce and roll over the back rim, or bounce up and fly over the back rim. The bounce is determined by the construction of the ball and the compactness of the dirt or turf at the back rim. If this combination were tested by dropping a ball down onto such dirt or turf, the coefficient of restitution would be the square root of the ratio of the bounce to the height of the drop. Thus, if a given golf ball were to bounce back 10% of the way, the square root of 0.1 is about 0.3. A cup with a 0.3 coefficient of restitution will allow capture of balls above the maximum speed of 1.626 m/s, and calculations predict capture at just above 1.9 m/s, quite a large increase in capture speed (about 15%). However, this is a little unrealistic, because a golf ball dropped on the green itself only rebounds about 10% [no by my experience; a ball dropped from 4 ft bounces only about two inches, roughly 4%, or 0.04 for a coeffic of 0.02, not 0.3 -- a big difference], and the back of the cup will be hit somewhat obliquely as the ball drops and spins forward, so it is unlikely the back-rim bounce will increase the maximum capture speed very much. Still, it is interesting to note the counter-intuitive fact that a hole line all the way to the top with hard plastic makes it easier to hole putts than one with the liner sunk down into the hole a few inches, with the ball hitting softer turf at the back of the hole. In the same way, a ball that skids when it hits the back has less forward momentum and so is more likely to drop.

4.01.01.02., Holmes, Brian W., Putting: How a golf ball and hole interact, Am. J. Physics, 59(2), Feb 1991, 129-136, 131: Balls with greater moments of inertia are harder to sink. A uniform solid sphere has I = 2/5 x m x R(ball)(sq), but golf balls are not uniform, and the I varies with the deisgn. Wound balls have smaller moments of inertia than two-piece balls. In a race down an inclined plane, a wound ball usually defeats a two-piece ball. According to Inertia Dynamics, Inc., I / [mR(ball)(sq)] for several balls was measured as follows: Wound(1) = 0.375; Wound(2) = 0.380; Two-piece(1) = 0.391; Perfect solid sphere = 0.400; Two-piece(2) = 0.412; Two-piece(3) = 0.413; Two-piece(4) = 0.415. Thus, in general, a wound ball is easier to sink. The computer model predicts that a higher moment of inertia makes a ball harder to capture. It is easy to see why thus is so: the greater angular momentum of such a ball results in a bigger kick out of the hole when it strikes the opposite rim. We find that wound ball (1) with a moment of inertia of 0.375 mR(b)(sq) will be captured at speeds up to 1.638 m/s, whereas the two-piece ball (4), with a moment of inertia 0.415 mR(b)(sq), will be captured at speeds up to 1.620 m/s. That is, increasing the moment of inertia by about 10% decreases the maximum capture speed by about 1%.

4.01.01.02., Karios, Frank G. & Mamola, Karl C., Apparatus for teaching physics: Wilber-force , demonstration size, Physics Teacher, 31(5), 1993, 314-315,

4.01.01.02., Kugler, Peter Noble & Tuvey, Michael T., Information, Natural Law, and the Self-Assembly of Rhythmic Movement, (Hillsdale, NJ: L. Erlbaum Assocs., 1987), ,

4.01.01.02., Masuda, M. & Kojima, S., Kick back effect of club-head at impact, In Cochran, A.J. & Farrally, F.R., eds., Science and Golf II: Proceedings of the 1994 World Scientific Congress of Golf, St. Andrews, Scotland, (London: E. & F.N. Spon, 1994), 284-289,

4.01.01.02., Mitchell, Jr., Walter E., Speeding up the Foucault , Physics Teacher, 28(6), 1990, 362,

4.01.01.02., Palmer, Arnold & Dobereiner, Peter, Arnold Palmer's Complete Book of Putting, (New York: Atheneum, 1986), , 68; course of putt, not a roll but For about 20 percent of its travel the ball will actually be airborne, skidding above the grass with some backspin before skipping two or three times and then settling into an unbroken roll. During the roll phase, the ball rides on top of the blades of grass, and as it loses its forward momentum, it settles down onto the solid surface of the green, all of which will be clearly discernable in the dusty turf (you can observe the same pattern when putting on greens from which the early morning dew has not been swept). it makes no difference to this pattern whether you strike the ball on the upswing or the downswing, or even if you deliberately make contact high on the ball with a half-topping stroke in an attempt to get the ball rolling smoothly [69] right from the start.

4.01.01.02., Pelz, Dave & Mastroni, Nick, Putt Like the Pros: Dave Pelz's Scientific Way to Improve Your Stroke, Reading Greens, and Lowering Your Score, (New York: Harper Collins Publishers, 1989), , ch 16, 163-176, Putter physics, or, what makes a wand magic

4.01.01.02., Peters, R.D. & Shepherd, J.A., A with adjustable trends in the period, Am. J. Physics, 57(6), Jun 1989, 535-539,

4.01.01.02., Weber, Arthur P., Green speed physics, USGA Green Sec. Rec., 35(2), Mar 1997, 12-15,

4.01.01.02., Whitaker, Robert J., A note on the Blackburn , Am. J. Physics, 59(4), Apr 1991, 330-333,

4.01.01.03., .-- , -- -- MAXIMUM / -- OPTIMUM -- SPEED, , ,

4.01.01.03., Cochran, Alastair & Stobbs, John, Search for the Perfect Swing: The Proven Scientific Aproach to Fundamentally Improving Your Game, (Chicago, IL: Triumph Books, 1968), , 141: For a normal hole the just-fall-back-in speed corresponds to an overshoot distance of only five or six feet. For a double-size hole, the width is doubled but also the depth from front to back si doubled, and this results in a just-fall-back-in speed that corresponds to an overshoot distance of twenty to twenty-five feet on an average green. This is a maximum speed four or five times higher than the standard hole. [NOTE: what is speed at hole here? If max. speed sends ball 6 feet past hole, then a speed that sends ball only 1.5 feet (18 inches) past the hole should be about one-fourth the max. speed; if the max. speed is about 60 ips, the the optimum speed ought to be about 15 ips, but I think this is a little low? Maybe not ... maybe this is just about the right opt. speed at the hole]

4.01.01.03., Crafter, Jane, How to find your holing speed, Golf Dig., 44(11), Nov 1994, 54-59, 54: holing speed or optimum speed is one that carries the ball 9 inches past the cup; practice swinging the putterhead as the first step to achieving holing speed; 55: Drill: fishing sinker pendulum; tie a weight on a strig and wrap the end of the stirng around your index finger so the weight hangs behind the shaft of the putter; swing the putter back and forth with a smooth and even stroke that synchronizes with the swinging weight; if you get jerky or lose rhythm, the stroke will fall out of synchronization with the pendulum weight; 56: to keep left wrist firm, keep right wrist firm: maintain right wrist cock throughout stroke; Drill: place a ball between inside of right wrist and shaft and putt while keeping ball in place; Impact: This sounds obvious, but the most solid putts occur when the middle of the putterface contacts the middle of the ball. In other words, a level hit -- one that produces the minimum of backspin or overspin -- is best. I've never been a believer in trying to hit down or up on putts. That's way too difficult to reproduce on a consistent basis. Drill; stack 2 quarters behind the ball and place the putterhead on the quarters; make the stroke by missing the quarters. Consistent strikes lead to consistent distance. 57: Path: straight back & through; Drill: board outside ball to practice not taking putter outside back; board inside ball to practice not taking putter inside back; two boards 1 putter width to practice straight strokes. 58: [Y]ou want the ball to be running at the hole as if it will finish about nine inches past. That gives it the best chance of going in. Any slower and it may veer off; any faster and you have to hit the middle of the cup for the ball to go in. If it doesn't, you'll lip out. Drill: place tee 9 behind hole; place 4 balls in line 4', 5', 6' and 7' away and putt in order, trying to stop them at tee; forget hole, let hole get in the way.

4.01.01.03., Crampton, Bruce, How to putt confidently, Golf Dig., 24(8), Aug 1973, 34-37, 37: mallet for livelier feel; handle under heel pad of left hand; thumbs straight up and down handle; palms parallel; slightly opem stance with right slightly more forward toward lie than left; well-balanced; eyes over line and slightly behind ball; Be sure you're looking at the back of the ball. That's where the putter is going to make contact. Too many people look at the top of the ball. [RFloyd says same]; ball inside left foot; hands lead clubead; thumbs next to crease of left trousers leg; The key to putting is hiiting the ball solidly.; arms-shoulder putter; not stiff but preserve triangle in stroke up to 10-15' range; left hand dominates stroke: initiates & guides; avoid quitting w/ left hand: If you can extend your left hand toward the target, you will make more putts.; hands behind ball or left wrist breakdown causes hitting up weakly; keep stroke low; short putts may end up on the ground; up-down tapping of putterhead to start with slight forward press; keep body still; Constantly remind yourself to keep your backstroke as short as possible to avoid easing up on the putt coming through the ball.; on longer putts keep grip pressure light for touch and speed; But on the shorter putts, where it is crucial to be more accurate and the stroke is more compact, it is important to maintain uniform pressure. If you grip the club lightly at address you've got to tense a little to take it away. This will change the angle of the club. So grip the club a little firmer on the short ones ... not rigid, but firm. Then you can draw it back without changing that grip pressure.; choke down for shorter putts; commit stroke mechanics to muscle memory so you don't have to think about mechanics while playing; speed: My thought is that you strike the ball just hard enough so it will hit the back of the cup lightly. This will allow you to use all the hole; if the ball is slightly off-line it can still topple in.; need touch and feel for speed control: don't do heavy work w/ hands before playing.

4.01.01.03., Daish, C.B., The Physics of Ball Games, (London, English Universities Press, Ltd., 1972), , 115: a study of high speed film of professional golfers at 2m, 6m and 15m putts showed velocity profiles as follows: 2m: from 150ms to 0ms, the velocity increased from 0.75 m/s to 3 m/s at impact, then fell during impact [0.5 ms] to 2.5 m/s and then by 75 ms declined to 2 m/s; for the 6m putt over the same times: from 1.2 m/s to 4.5 m/s at impact, down to 3.25 m/s during impact and thereafter to 2.75 m/s; the 15m putt: from 2 m/s to 7 m/s then down to 5.5 m/s during impact then down to 5 m/s

4.01.01.03., DeMattia, Connie, Golf Digest basics: From our schools: The short putts: Achieve a straight, square path, Golf Dig., 49(1), Jan 1998, 136, 136: While distance control is crucial on longer putts, short ones -- those from eight feet in -- don't require the putt to roll a precise distance. Direction is of far greater importance. If the ball tracks on a precise line, it can find the bottom of the cup even if struck a bit too firmly. Line the face up square and make a straight stroke back making sure not to rotate the clubface and make a straight stroke through. A longer stroke would require you to swing the club to the inside eventually, but all you need for short putts is a straight-back path.

4.01.01.03., Dennis, Larry, Die putts at the hole -- and you're dead: New tests prove you'll make more putts hitting them harder, Golf Dig., 28(7), Jul 1977, 52-55, Pelz, Pres. of Preceptor Golf Ltd.; 53: A green is not a billiard table. Pelz's true-roller putting data for 17-inch rule from eastern seaboard courses at various latitudes w/ bent & bermuda and all putts were 12-foot putts: COURSE [grass, condition], Best Speed Dist. Past Hole--Best % [Dying Speed %]: WESTCHESTER CC, RYE, NY [bent, freshly mowed, early am]: 5-20--95% [40%] [bec. of footprints, ie, late afternoon: 15-20--60%]; SEDGEFIELD CC, GREENSBORO, NC [bent, early am]: 10-15--75% [20%] [bec. of footprints, ie, late afternoon, 40--50%]; PINEHURST, NC [bent mixed w/ poa ann., freshly mowed]: 24--70% [10%]; CONGRESSIONAL CC, WASHINGTON, DC [bent, immed. after 1976 PGA Championship]: 12-15--95% [50%]; COLUMBIA CC, CHEVY CHASE [bent]: 15--90% [30%]; BELLE HAVEN CC, ALEXANDRIA, VA [poa ann., spring]: 40--30%; SAME [bent, Fall, September]: 20--65% [--]; INVERRARY CC, LAUDERHILL, FL [bermuda]: 20-30--70% [0%]; LONG BOAT KEY, SARASOTA, FL [bermuda]: 30--75% [10%]; 54: going faster, putts begin to lip out, but The dropoff is not as great on the bent greens, however, because more of those putts have a tendency to hit dead center in the back of the cup and stay in. Pelz: Florida golfers should be better than Northern golfers because they hit the ball harder; Nicklaus did not win a Florida tournament until 9th yr on tour; Julius Boros, who grew up on the bent grass greens of Connecticut, was on the tour for 17 years before he won in Florida. [See also George Archer's comments in his Stroke that Won the Masters article and Ray Floyd, From 60 Yards In, for similiar although varying comments.] 54: You will make fewer putts on a poorer quality green, and even to make your best percentage you must hit the ball harder than on a good green.

4.01.01.03., GCM, Note, , , From Cochran & Stobbs: 141: For a normal hole the just-fall-back-in speed corresponds to an overshoot distance of only five or six feet. For a double-size hole, the width is doubled but also the depth from front to back si doubled, and this results in a just-fall-back-in speed that corresponds to an overshoot distance of twenty to twenty-five feet on an average green. This is a maximum speed four or five times higher than the standard hole. [NOTE: what is speed at hole here? If max. speed sends ball 6 feet past hole, then a speed that sends ball only 1.5 feet (18 inches) past the hole should be about one-fourth the max. speed; if the max. speed is about 60 ips, the the optimum speed ought to be about 15 ips, but I think this is a little low? Maybe not ... maybe this is just about the right opt. speed at the hole. Does this speed of 15 ips send the ball 18 inches past the hole or not?]

4.01.01.03., Golf Magazine , Golf Magazine's Handbook of Putting, (New York: Harper & Row, 1973; London: Pelham, 1975), , 124: Pay particular attention to the area around the cup. There may be spike scuffs, footprints, or ragged edges that could seriously hamper the line of your putt. Since the ball is traveling slowly near the cup, it is subject to the slightest imperfections on the green. When such imperfections exist, it is usually a good idea to putt more firmly, hoping that the ball will be able to resist the rough spots. That is, hit the ball harder and don't allow for as much break. Irregular greens are next to impossible to read, so it's hard to determine the exact break (or bounce) you're going to get. Even if you do have the ball breaking toward the hole, if it's moving too slowly the ball will be easily knocked off line by one bump or another. On this kind of green, it's best to take your chances of banging the ball at the hole, never giving up the cup unless the break is so severe as to dictate it.

4.01.01.03., Kostis, Peter, Control your speed to improve your putting, Golf Dig., 44(3), Mar 1993, 90-96, 92: This is a fact: To give your ball the best chance of going into the hole, it has to be rtaveling at a speed that will carry it 18 to 24 inches past the cup. 94: [T]hat's true for every putt, whatever its length. A 45-foot putt that goes 2 feet past and a 3-foot putt that goes 2 feet past are equal in terms of aggressiveness. Both were traveling at the same speed when they reached the hole, so both were the same in terms of aggressiveness. [very good point about ball speed at hole]

4.01.01.03., Lampert, Lawrence D., The Pro's Edge: Vision Training for Golf, (Boca Raton, FL: Saturn Press, 1998), , 57: a 20' level putt on a medium fast green takes about 4.2 seconds; uphill about 3 secs.; downhill about 5 to 5.2 secs.

4.01.01.03., Leadbetter, David & Huggan, John, David leadbetter's Fault's and Fixes, (New York: Harper Collins, 1993), , 109: Always try to hit a putt firmly enough that, should it miss, the ball will finish about 18 inches past the hole. That's the optimum speed for the ball to hold its line, yet still fall in if it catches any part of the cup.

4.01.01.03., Mahoney, J.F., Theoretical analysis of aggressive golf putts, Res. Q. for Exercise & Sport, 53(2), Mar 1982, 165-171, The study proposes a method to judge the efficacy of aggressive putts for misses of line or speed. A rolling ball dropping in a cup is modelled to calculate speeds that allow the ball to drop, and then a level putt is modelled as rolling a ball at a square area (not a hole) of a certain arc-width along a straight radial line from the ball, with radial lines from the ball intersecting the left and right sides of the target's arc. Based on the sppeds that allow the ball to drop in a trough, he defines four distance zones with three arcs radially from the ball at the front of the target, back of the target, and a range past the target, with the zones being are either too short to reach the target, target-high, beyond the target but at a speed that would have allowed the ball to drop, or too far beyond the target for the ball to have dropped. The two defines geometrically nine regions: a success zone where balls end either in the target or at a distance beyond the target such that the ball would have fallen in a trough the same width as the target; short of this but on an acceptable line to enter the success zone; beyond the success zone but on line; and 3 pairs of zones the same distance radially from the ball on either side of these three zones: too short/weak and pulled or pushed off line; the success distance but pushed or pulled off line; and too strong/hard and pushed or pulled off line. Formulas define the extent of the error of line and speed as a percentage of the nearest line and speed that would have succeeded. The formulas are recast for a tilted slope to judge uphill or downhill putts. Putts straight uphill and downhill are only straight when they roll directly at the hole; any deviation means the putt runs laterally on a slope and so will break away from the hole going up or to the hole going down. The math indicates that the maximum relative energy that can be tolerated favors downhill putts versus uphill, contrary to belief. Also a ball moving with less friction has more favorable energy .

4.01.01.03., Middlecoff, Cary & Michael, Tom, Master Guide to Golf, (Englewood Cliffs, NJ: Prentice-Hall, 1960), , 137: When the green is fast and you want to make the next putt if you miss this one, play the full apparent break, i.e., let the ball reach the hole travelling quite slowly. But if the green is slow or oyu're in a match-paly situation in which you'll lose the hole anyway unless you sink the putt, you can risk a firmer stroke to make the ball hew to the line.

4.01.01.03., O'Brien, G., Putting ills cured, Golf World, 7(31), Jan 8, 1954, 10, 10: Stroke the ball with enough impact to roll it some ten inches beyond the cup.

4.01.01.03., Palmer, Arnold & Dobereiner, Peter, Arnold Palmer's Complete Book of Putting, (New York: Atheneum, 1986), , 58: Toward the end of a busy day when there has been heavy traffic on the course, [59] it is common to see a putt heading on perfect line for the target lurch sideways like a drunken sailor in the last foot or so of it travel and miss the hole comfortably. The rapr putters score because the putt is traveling at a fair lick as it reaches the hole and is therefore much less likely to fall away from its target line. That line has to be true, of course, because the target is effectively only two balls wide. The margin for error is considerably reduced because, whereas the stroked putt will topple into the side of the hole, the rapped putt on that line will invariably jump over the edge of the hole. Most rap putters aim to putt the ball to a precise spot about eighteen inches behind and dead on line with the center of the hole.

4.01.01.03., Pelz, Dave & Mastroni, Nick, Putt Like the Pros: Dave Pelz's Scientific Way to Improve Your Stroke, Reading Greens, and Lowering Your Score, (New York: Harper Collins Publishers, 1989), , ch 13, 125-135

4.01.01.03., Rodgers, Phil & Barkow, Al, Play Lower Handicap Golf, (South Norwalk, CT: Golf Digest, 1986), , 92: Do everything you can to determine the line of a putt, set up to hit the ball on that line, then concentrate ONLY on hitting the ball the correct distance. [wrong way around] The key to hitting putts the correct istance is in the pace of the stroke. Watch a good putter practice 10-footers, and you'll see that he swings the putter back and through at the same speed every time. He is very conscious of how far he is hitting the ball, and every stroke is the same size. 93: Then there are the players who are aiming all the time and not paying enough attention to distance. They tend to be inconsistent. ... There was another survey done on putting. Ten of the best putters in the game were tested, and it was found they had very little in common as far as stroke path. Some swung the putter insie to out, some a little inside to sqaure, some straight back and through. But the one thing they all did was stroke the ball within a thousandth of a second at 32 feet per second, which is the force of gravity. They all swung the putter back and through at the same time. [give that physicist the Nobel Prize for Fiction!] [seconds/ feet per second, and force not acceleration due to the force of gravity?]

4.01.01.03., Soley, Clyne, Putting: How well should you putt? It depends on your handicap, as shown by the results of over 3, 500 rounds of golf, Golf Mag., 30(2), Feb 1978, 104-105, 105: It has been documented mathematically by Dr. Alastair Cochran in The Search for the Perfect Swing that a putt destined to travel four feet or more beyond the cup will not drop, even if it is dead center. This principle was confirmed in my study employing a putting machine. On a green slightly faster than normal the critical distance beyond the hole was 4 1/2 feet. At that speed the ball hit the back of the hole, hopped up and remained on the edge. So the never up, never in axiom becomes meaningless unless the putt is struck softly enough to travel no more than about four feet beyond the hole. [Note: distance ball rolls past the hole depends on speed at hole and on speed of green, so one cannot say that the maximum speed at the hole is one that rolls the ball X feet past the hole; instead, the ball at max speed V will roll X+ on fast greens, X on medium greens, and X- on slow greens. On a slow green, the max speed will not roll the ball too far past the hole, say 2.5 feet, whereas on a fast green, the same speed at the hole will roll the ball 4.5 feet past the hole. Therefore, in finding the max speed for green conditions before a round, assess green speed and smack a few ball near the hole dead center to get the ball to skip the hole, and see how far past it goes.]

4.01.01.03., Stockton, Dave & Barkow, Al, Dave Stockton's Putt to Win: Secrets for Mastering the Other Game of Golf, (New York: Simon & Schuster, 1996), , 151: What is one myth about putting? Never up, never in. I'll grant you, if you're short on a putt it's never going in, but if you [152] are only an inch short it's unlikely you'll three-putt. And if you eliminate three or four three-putt greens per round, all of a sudden your handicap goes down and you haven't even sunk any long putts. Constantly going well past the hole is far worse than coming up a few inches short every now and then.

4.01.01.03., Templeton, H.A., Vector Putting: The Art and Science of Reading Greens and Computing Break, (Fort Worth, TX: Vector Golf, Inc., 1984), ,

Putting Academy
eMail
PZ Radio
Oldtime Music
© 1999-2007 Geoff Mangum
Solution Graphics
 



The intelligent golf search engine.