When it comes to improving your golf game, you can spend thousands of dollars buying the latest titanium-induced, Tiger-promoted golf clubs; taking private lessons from the local "I used to be on the Tour" pro; or trying every slice-correcting, swing-speed-estimating, GPS-distance-guessing gadget. But, in the end, it’s about getting that little white sphere to go where you intended it to go. Don't worry, there are many very smart people trying to help you by designing the ultimate golf ball. Of course, they are also after a slice of this billion dollar industry, as any technological advancement that can grab a few more market share points is worth the investment.

In fact, the golf ball wars can get nasty. Earlier this month, Callaway Golf won a court order permanently halting sales of the industry's leading ball, Titleist's Pro V1, arguing patent infringements involving its solid core technology which Callaway acquired when it bought Spaulding/Top Flite in 2003. Titleist disagrees with the decision and will appeal, but in the meantime has altered its manufacturing process so that the patents in question are not used.

The challenge for golf ball manufacturers is to design a better performing ball within the constraints set by United States Golf Association. The USGA enforces limits on the size, weight and initial performance characteristics in an attempt to keep the playing field somewhat level. Every "sanctioned" golf ball must weigh less than 1.62 ounces with a diameter smaller than 1.68 inches. It also must have a similar initial velocity when hit with a metal striker, and rebound at the same angle and speed when hit against a metal block. So, what is left to tinker with? Manufacturers have focused on the internal materials in the ball and its cover design.

Today's balls have 2, 3 or 4 layers of different internal polymer materials to be able to respond differently when hit with a driver versus, say, a wedge. When hit with a driver at much higher swing speed, the energy transfer goes all the way to the core by compressing ball, reducing backspin. During a slower swing with a club that has more angle loft, the energy stays closer to the surface of the ball and allows the grooves of the club to grab onto the ball's cover producing more spin. When driving the ball off of the tee, the preference is more distance and less loft, so a lower backspin is required. For closer shots, more backspin and control are needed.

The Science of Dimples

Which brings us to the cover of the ball and all of the design possibilities. Two forces affect the flight and distance of flying spheres, gravity and aerodynamics. Eventually, gravity wins once the momentum of the ball is slowed by the aerodynamic drag. Since all golf clubs have some angular loft to their clubface, the struck ball will have backspin. As explained by the Magnus Force effect, the air pressure will be lower on the top of the ball since that side is moving slower relative to the air around it. This creates lift as the ball will go in the direction of the lower air pressure. Counteracting this lift is the friction or drag the ball experiences while flying through the air.

Think about a boat moving through water. At the front of the boat, the water moves smoothly around the sides of the boat, but eventually separates from the boat on the back side. This leaves behind a turbulent wake where the water is agitated and creates a lower pressure area. The larger the wake, the more drag is created. A ball in flight has the same properties.

The secret then is how to reduce this wake behind the ball. Enter the infamous golf ball dimples. Dimples on a golf ball create a thin turbulent boundary layer of air molecules that sticks to the ball's contour longer than on a smooth ball. This allows the flowing air to follow the ball's surface farther around the back of the ball, which decreases the size of the wake. In fact, research has shown that a dimpled ball travels about twice as far as a smooth ball.

See video of simulated air flow around a golf ball

So, the design competition comes down to perfecting the dimple, since not all dimples are created equal! The number, size and shape can have a dramatic impact on performance. Typically, today's balls have 300-500 spherically shaped dimples, each with a depth of about .010 inch. However, varying just the depth by .001 inch can have dramatic effects on the ball's flight.

Regarding shape, these traditional round dimple patterns cover up to 86 percent of the surface of the golf ball. To create better coverage, Callaway Golf's HX ball uses hexagon shaped dimples that can create a denser lattice of dimples leaving fewer flat spots. Creating just the right design has traditionally been a trial-and-error process of creating a prototype then testing in a wind tunnel. This time-consuming process does not allow for the extreme fine-tuning of the variables.

Simulation Solution

At the 61st Meeting of the American Physical Society's Division of Fluid Dynamics this week in San Antonio, a team of researchers from Arizona State University and the University of Maryland is reporting new findings that may soon give golf ball manufacturers a more efficient method of testing their designs. Their research takes a different approach, using mathematical equations that model the physics of a golf ball in flight. ASU's Clinton Smith, a Ph.D. student and his advisor Kyle Squires collaborated with Nikolaos Beratlis and Elias Balaras at the University of Maryland and Masaya Tsunoda of Sumitomo Rubber Industries, Ltd. The team has been developing highly efficient algorithms and software to solve these equations on parallel supercomputers, which can reduce the simulation time from years to hours.

Now that the model and process is in place, the next step is to begin the quest for the ultimate dimple. In the meantime, when someone asks you, "What's your handicap?" you can confidently tell them, "Well, my golf ball's design does not optimize its drag coefficient which results in a lower loft and spin rate from its poor aerodynamics."

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"Rotate it like Ronaldo" just doesn't have the same ring to it as "Bend it like Beckham", but the curving free kick is still one of the most exciting plays in soccer/football. Starting with Rivelino in the 1970 World Cup and on to the specialists of today, more players know how to do it and understand the basic physics behind it, but very few can perfect it. But, when it does happen, by chance or skill, it is the highlight of the game.

But let's take a look at this from the other side, through the eyes of the goalkeeper. Obviously, its their job to anticipate where the free kick is going and get to the spot before the ball crosses the line. He sets up his wall to, hopefully, narrow the width of the target, but he knows some players are capable of bending the ball around or over the wall towards the near post. If you watch highlights of free kick goals, you often see keepers flat-footed, just watching the ball go into the top corner. Did they guess wrong and then were not able to react? Did they guess right but misjudged the flight trajectory of the ball. How much did the sidespin or "bend" affect their perception of the exact spot where the ball will cross the line? To get an idea of the effect of spin, here's a compilation of Beckham's best free kick goals (there's a 15 second intro, then the highlights) :

Researchers at Queen's University Belfast and the University of the Mediterranean in France tried to figure this out in this paper. They wanted to compare the abilities of expert field players and expert goalkeepers to accurately predict if a free kick would result in an on-target goal or off-target non-goal. First, a bit about why the ball "bends". We can thank what's called the "Magnus Force" named after the 19th-century German physicist Gustav Magnus. As seen in the diagram below, as the ball spins counter clockwise (for a right-footed player using his instep and kicking the ball on the right side), the air pressure on the left side of the ball is lower as the spin is in the same direction as the oncoming air flow. On the right side of the ball, the spin is in the opposite direction of the air flow, building higher pressure. The ball will follow the path of least resistance, or pressure, and "bend" or curve from right to left. The speed of the spin and the velocity of the shot will determine the amount of bend. For a clockwise spin, the ball bends from left to right.

The researchers showed the players three different types of simulated kicks, a kick bent to the right, a kick bent to the left and a kick with no spin at all. They showed the players these simulations with virtual reality headsets and computer controlled "kicks" and "balls" which they could vary in flight with different programming. The balls would disappear from view at distances of 10 and 12.5 meters from the goal. The reasoning is that this cutoff would correspond with the deadline for reaction time to make a save on the ball. In other words, if the keeper does not correctly guess the final trajectory and position of the ball by this point, he most likely will not be able to physically get to the ball and make the save.

The results showed that both the players and the keepers, (all 20 were expert players from elite clubs like AC Milan, Marseille, Bayer Leverkusen, Schalke 04), were able to correctly predict the result of the kicks with no spin added. However, as 600 RPM spin, either clockwise or counter-clockwise, was added to the ball, the players success declined significantly. Interestingly, the keepers did no better, statistically, then the field players. The researchers conclusion was that the players used the "current heading direction" of the ball to predict the final result, rather than factoring the future affect of the acceleration and change in trajectory caused by the spin.

Just as we saw in the Baseball Hitting post, our human perception skill in tracking flying objects, especially those that are spinning and changing direction, are not perfect. If we understand the physics of the spinning ball, we can better guess at its path, but the pitcher or the free kick taker doesn't usually offer this information beforehand!

Craig, C.M., Berton, E., Rao, G., Fernandez, L., Bootsma, R.J. (2006). Judging where a ball will go: the case of curved free kicks in football. Naturwissenschaften, 93(2), 97-101. DOI: 10.1007/s00114-005-0071-0