# A little lesson in projectile motion, from the R&A's Dawson

A lot of insiders were wondering what new math R&A Chief Executive Peter Dawson was using when he spoke up about changes to Royal St. George's for this year's British Open, which starts Thursday. It was confusing, but as it turns out, it is right.

Dawson is quoted in a piece by John Huggan on CBSSports.com, suggesting the difficult contours on some of Royal St. George's fairways lead to bounces that take the ball careening somewhat unfairly off line. He says, in part, "We were aware that a very low percentage of the field were able to hit those three fairways eight years ago. That was because of the severe contours on all three. And, I also think, because players tend to hit the ball so much higher these days. It's coming down more steeply, so it is more likely to go sideways on landing."

While I'm not sure that the best players best drives are designed to land "steeply," it is true that the trajectories are higher than in the days of persimmon drivers and wound balls. Generally speaking, the best drives land at an angle of less than 40 degrees, which should help produce more roll (although a much lower shot will yield an even flatter landing angle and will produce the most roll, provided there's not something to stop that roll, like a bunker or burn or sheep). Here's how I explained the concept of "angle of descent" back in 2006.

But here's the bit that justifies Dawson's explanation of projectile motion. Basically, a projectile like a golf ball has two velocity components, a horizontal one and a vertical one, as Martin Brouillette, professor of mechanical engineering at the University of Sherbrooke and a member of the Golf Digest Technical Panel explains: "Assuming two cases with the same landing velocity but with different landing angles, the case with the steeper landing angle has a smaller horizontal velocity component, therefore a greater vertical velocity component. This greater vertical velocity component, upon interacting with a tilted landing surface, is more likely to produce a greater sideways velocity component."

For those whose last science class was in high school, here's a translation: When the ball bounds off the the fairway from a steep landing angle, more of its energy (velocity) is given toward going up, not forward. Since the ball has more energy going up when it hits a wildly tilted fairway like some of those at Royal St. George's, it's going to direct more of its energy toward whatever direction the tilt is sending it. A low shot (remember Tiger Woods' infamous stinger, used so effectively in his 2006 British Open victory that he went the entire championship using the driver only once?) yields a landing angle with more energy going forward and thus could (theoretically) reduce the negative effect of an awkward landing angle in the fairway. Of course, a ball that's rolling over those awkward angles is going to be dramatically affected; one that's flying by those humps and bumps won't be bothered by them at all.

A lot to think about if you're a competitor heading to the first tee tomorrow at Sandwich, no?

--Mike Stachura
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