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The Laws of Physics On the Green

While golf is a game, researchers still wrestle with serious challenges in the drive to improve equipment. One test for designers is the critical physical concept, the moment of inertia, which measures how difficult it is to make a body rotate around an axis. Alan Hocknell, Callaway’s vice president of innovation and advanced design, describes the concept in relation to a spinning figure skater. Arms extended, the skater has a greater moment of inertia and spins more slowly. Arms pulled tight to the body, the skater has a lesser moment of inertia, and spins more rapidly.

Golf-club designers aim for a larger moment of inertia. While skaters may want to spin more rapidly, golfers want to hit straight through a golf ball. But a golfer’s swing and the impact of hitting a round ball can, in effect, twist, spin, or turn the club, leading to a wayward shot.

Given the laws of physics, the challenge is to design a club that holds steady and resists rotation. That was part of a task Callaway gave Hocknell and Cackett in 2001: Using any materials and shape, design the ideal driver (the club with a large head used for long tee shots.) Golf authorities regulate the dimensions and volumes of clubheads, so within those parameters, Hocknell and Cackett studied hundreds of possibilities, in the firm’s “Virtual Test Center,” using computer simulations of club and ball actions, down to the bounces of simulated shots. Their solution was a driver made of composite materials with a square clubhead, an idea that evolved into Callaway’s popular FT-i driver, which has a titanium face and a graphite epoxy body.

The team realized that light, composite materials would save weight, and let them distribute the clubhead mass broadly, including the corners of the clubhead. In this way they created a clubhead with a greater moment of inertia, less prone to unfortunate twists and turns. Just as a figure skater spins more slowly with arms extended, a golf clubhead rotates more slowly with its mass spread to its far corners. After all, golfers rarely deliver the clubhead to the ball in exact alignment with their intended target. A clubhead that is angled and not “square” at impact will hook or slice the ball, and a club with uneven mass distribution—concentrated near the face—will enhance this tendency.

The team discovered more benefits to their design. One of golf’s most counterintuitive physical phenomena is the gear effect. For example, a ball hit on the “toe” side of the driver—its far end—will have sidespin, as if the clubhead and ball were meshed gears. For this reason, a driver face bulges slightly outwards, to limit sidespin. But a big moment of inertia also limits the gear effect, straightening all shots.

As both pro and amateur golfers know, club-design variables complicate matters. If a club’s center of gravity is further away from the face—like that of a hefty driver—it will enhance the gear effect. Design, in essence, is a complex process of balancing these factors to best allow for longer, straighter drives.

“The main benefit,” says Cackett, “is that with the persimmon driver of 20 years ago, if you didn’t hit it close to the center, you were going to see a lot of curvature in your shot—it was going to be a big snap hook or a slice. People feared hitting the driver back then. It was not an easy club to hit. And today it’s perhaps the most enjoyable club to hit, because it’s so much more forgiving. You can hit it off-center and still get a really good result.”

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Rensselaer (ISSN 0898-1442) is published in Spring, Summer, Fall, and Winter by the Office of Strategic Communications and External Relations, Rensselaer Polytechnic Institute, Troy, NY 12180-3590. Opinions expressed in these pages do not necessarily reflect the views of the editors or the policies of the Institute. ©2008 Rensselaer Polytechnic Institute.