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## Using Mathematics: Par for the Course

Ever wonder why a golf ball has dimples? It is a known fact that dimples improve the flight of a golf ball by reducing the drag and helping the ball fly farther. The drag is created by surrounding air flow (an aerodynamic force) as well as gravity. Experiments have shown that dimpled golf balls travel further than those with no dimples, as the latter experience about twice the drag.

So, the big question...what arrangement of dimples is best? Unfortunately, that is an unanswered question. But, mathematical scientists (Arizona State University and the University of Maryland) are using a supercomputer to model air flow around a ball in flight and then study how dimples influence this flow. The goal is to make an improved golf ball, with an optimal dimple size and pattern that maximally lowers drag.

All of this is legal...the United States Golf Association (USGA) regulates the design of golfballs, specifying uniform size and weight specifications, but it does not regulate dimple patterns.

Current dimple patterns are created by simple trial and error, with the flight length of one prototype tested against another. In contrast, the researchers are studying dimple size and patterns based on mathematical equations that model the physics of a golf ball in flight. The situation is not easy, as solving these equations would take more than 15 years of time on the world's fastest computers "just to get a glimpse of the flow around the golf ball for a fraction of a second."

So, the mathematical scientists are creatively developing highly-efficient algorithms and software that can solve these equations on parallel supercomputers, thereby reducing the simulation time from years to about 300 hours.

Their results are amazing...not only modeling the air flow around a golf ball at each precise location but also modeling air flow in an out of every dimple as the golf ball spins through the air.

The next step...using this model and same mathematical equations to compare different dimple designs....but the researchers add that this will probably take several years.

Source: ScienceDaily, December 1, 2008