Watch professional golfers putt and you’ll eventually notice three common features about their style, says Robert Grober, an expert on the physics of golf at the Yale University.

First, the putter head always moves at a constant speed when it hits the ball. Second, the length of time the putting stroke takes has little impact on the speed of the ball (and therefore the length of the putt). And finally, a professional golfer’s backswing takes about twice as long as the downswing.

Grober has used these observations to construct a mathematical model of a putting swing and to explore other properties of such a system.

It turns out that the model that best accounts for this behaviour is a simple pendulum driven at twice its resonant frequency.

That explains a number of other observations about professional golfers, says Grober. For example, a common putting tip is that longer backswings equate to longer putts. This model has exactly this characteristic: the length of the backswing is proportional to the speed of the club at impact.

It is also relatively straightforward to get a sense of the tempo of the required putt by swinging the club back and forth in resonance, like a pendulum. The duration of the actual stroke is exactly half the length of the putter cycle (i.e. from the address position moving backward, to the address position moving forward). “In fact, one often observes golfers instinctively doing this before they hit a putt,” says Grober.

So now the secret is out. Make a careful note for next time you’re out on the links.

Ref: arxiv.org/abs/0903.1762: Resonance in Putting