Posted for Philip Ball

Searching for the perfect putt to improve your golf handicap? It’s all just a matter of finding the right physics, according to Robert Grober of Yale University. In a preprint paper he says that the mechanics of a putting stroke for top golfers can be understood by assuming that the motion is that of a pendulum, driven by the force of the golfer’s body movements to oscillate at twice its natural frequency.

A putting stroke clearly looks like a simple pendulum swing. But it is a driven pendulum, propelled by muscle power rather than swinging passively under gravity. This force first creates a backswing, then a downswing to strike the ball. Grober has studied footage of some leading golfers, and finds that the movement has some constant characteristics: the putting head is moving at constant speed (not accelerating) when it hits the ball, the total duration of the stroke doesn’t really change much as the intended length of the putt increases, and the ratio of the duration of the backswing to that of the downswing is usually around 2.

All this, he says, can be understood if the club’s motion is that of a pendulum driven as indicated above. There’s no suggestion that golfers know any of this – they have apparently been led by experience and intuition to this type of movement.

But why does it make for a good putt? Grober thinks it is because the results are relatively insensitive to the driving force. That’s to say, because the motion is basically resonant, being governed by the mechanics of pendulum motion, variations in how the golfer controls the driving force throughout the putt don’t alter very much the velocity of the club head. What matters, at least in terms of the length of the putt, is how big the backswing is, not what comes after. This means that there’s less scope for error: even if you don’t apply quite the same force, the resulting stroke is much the same.

How do you develop a stroke like this? Grober explains: “one can get a feel for this tempo by continuously and repeatedly swinging the club back and forth at resonance, in exactly the same manner one would swing a pendulum. The duration of the actual stroke is exactly the amount of time it takes for this pendulum like motion to swing the putter half a cycle”. Now you know.

Image: by DeaPeaJay via Flickr under attribution-share alike 2.0 generic