A Yale physicist with a lifelong passion for golf has figured out a better way to putt on a slope. Thanks to the geometry of the game, he says, there’s a magic spot just uphill of a hole. The trick is to line up the putt not only from where the ball is actually lying, but also from several equidistant points nearby. Do that and the sweet spot will reveal itself.
There are countless mental tricks golfers use to sink putts on a tilted green.
“Many golfers use a mental image of pouring a bucket out on the green and visualize where the water would flow,” says Mark Broadie, a professor at the Graduate School of Business at Columbia University who developed a new statistic for measuring putting performance recently adopted by the PGA Tour.
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Robert Grober, an experimental physicist at Yale University, imagines the ball sitting on a circle centered at the hole. At the 12 o’clock position, the ball travels directly downhill along a straight line to find the hole. But a ball hit from, say, 4 o’clock, must roll uphill along a curve to reach the hole. Grober calculated these curves from different points on a circle, treating the green as a tilted flat surface and taking into account the pull of gravity and the resistance of the grass.
“He did a better and more careful analysis than other people have done in the past,” says Broadie.
These curves can’t be calculated on the fly by golfers on the links — players have to rely on instincts, not computers. But every curve can be achieved by aiming along a straight line at a particular area just uphill of the hole. The trick is to find that spot. Grober drew these straight lines from different points along the circle and found that they come together at almost exactly the same place.
“No one is used to thinking about all of these putts having the same target line,” says Grober, who reported his results online at arXiv.org on June 9.
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After aiming a putt, a golfer can check his or his intuition, Grober says. All it takes is a few steps to the left and right along a 30-degree arc. If the same spot pops out from different points on the arc, it’s likely to be a winner.
“If you’re relatively close to the hole, within 10 feet or so, this works pretty well,” says Grober, who ties strings to stakes at actual golf courses to visualize these lines of sight and demonstrate that this technique works in the real world. “When you show people, they’re pretty shocked.”