The Physics of a golf Ball

The first written reference of golf was in 1457. Golf balls have had extraordinary changes since that time; they’ve gone from leather pouches to dried gum to today’s dimpled balls. These dimples help decrease the drag and increase the lift.

Different forces are applied to the golf ball when struck by the club. Golf clubs have grooves to create backspin. And then there are different variables that affect how a golf ball will travel, these include: lie angle and the shaft length.A golfer must never forget about “the wind factor”. And last but not least , a golfer must flat-out use his own judgment in the game of golf.The game of golf has a science all of it’s own, and even the best players have days when the simplest of strokes proves a frustrating challenge.

Golf has been an extraordinary sport for quite a while. In-fact, the first written reference of golf dates back to 1457. Since that time it has been a developing sport that has turned into a multi-billion dollar industry. With all the money, energy, and time (the sandpit in my situation) that has been exhorted to the game of golf, you’d think it would be a cakewalk rather than a mystery. Surprisingly enough, the average golfer knows next to nothing about the physics of golf. Here’s an inside look at what happens from the time the golfer steps on the tee too the time that the ball falls into that “ooh” so far away black hole.

With like anything else, the game of golf has gone through ratification due to science and technology. Up until 1848, a spherical leather pouch was filled with wet goose feathers. The pouch was stitched with linen thread, turned inside out so that the stitching was on the inside. The ball dried to become very hard.

It was then oiled and whitened. An acceptable average drive with these balls was from 150 to 175 yards—and they became useless when wet. Therefore, the Gutta-percha ball arrived on the scene in 1848 to take on the role of smooth, solid, dried gum from the Malaysian sapodilla tree. These “guttie” balls had two negatives; they sometimes broke into pieces as some modern solid balls have been known to do and they did not fly as well as the feather balls. None the less, as these balls were used their surfaces became roughened. Players soon realized, however, that cut-up balls flew further and the concept of dimples was born.

But why are dimples purposely molded into the modern day golf ball? This question deals with the way that air affects the flight of a spinning object (or aerodynamics if you will) – and that’s the bottom line. Moreover, two simple principles will be discussed in great detail hereafter: lift and drag. Let’s not run faster than we are able though. Before we get on a rampage let’s look at what experience has taught us about a spinning ball.

A British scientist in 1887, Professor P.G. Tait owns all the credit to the findings concerning the importance of spin on the flight of a golf ball. He relates that in his youth he was taught that “all spin is detrimental” and he practiced assiduously to master the art of hitting a ball almost free of spin. After many complex and frustrating experiences, Professor Tait states clearly that, a ball driven with spin about a horizontal axis with the top of the ball coming toward the golfer, has a lifting force on it which keeps the ball in the air much longer than would be possible without spin.

Professor Tait did all his work with gutta-percha balls, which means that he did not consider the effect of the roughness of the surface of the ball on its motion through the air.
In between the time that the golfer (if that’s what we want to call him) step’s up to the tee and the time that he cusses, there are two complicated forces that must be understood. The club comes into contact with the ball and they move together for about of an inch. Then, after half a thousandth of a second, the ball shoots off into the distance at about 160-mph. There are two components of force acted between the golf ball and the lofted club: one normal to the face of the club and one parallel to it.

Another worthy way of putting all this is “hitting the sweet spot” with the perfect club.Obviously, the club affects the way the ball flies through the air. The loft of the club determines the angle at which the ball is launched. Smaller lofts, 10 degrees or so, are what golfers use to drive the ball to achieve great distances. On the other hand, a higher loft of 45 degrees and above launch the ball more steeply and does not travel as far.

Interestingly enough, not only does the loft of the club affect the launch angle; it also influences the velocity of the ball and the spin with which it leaves. This is where the two influent forces are affected: by the loft of the club. The force normal to the club generally affects the velocity (speed and direction), while the parallel (or tangential) force rotates the ball or gives what we call backspin. The normal force rises to approximately 2,000 lbs. (9 kN) during the half-millisecond of impact.

The tangential force is a little more complicated, acting downwards on the ball before briefly reversing direction and acting upwards just at the end of impact. The clubs also have grooves that act to grip the ball and increase the ability to create backspins.As previously stated, when a golf ball is struck it administers it’s own backspin, which makes it act like an airplane wing. Now things start to happen when the golf ball is inclined to create an angle of attack from the lofted club. The ball deflects the airflow downward creating an upward reaction force (Newton’s 3rd Law).

And this is lift! The same Bernouilli principal that governs the airplane wing. The flow of air over the top of the ball produces a low-pressure region. The low pressure resulting from the increase in speed of the air over the top side of the ball in conjunction with the high pressure below the ball produces the lift of the ball. But how do the dimples periodically help increase the Magnus lift? Before understanding this question, we must grasp the concept of the second main element of aerodynamics spoken about – drag.

Visualize with me again if you would: golfer swings with all he’s got and right before he swears he’ll never golf again, the ball is undergoing a lot of pressure. The ball will be influencing pressure once it hits the bottom of the pond, however, that’s not the pressure I’m speaking about. The air hits the front of the ball in its flight, creating a high pressure area, and splits around to the sides. But it is traveling to fast and separates from the surface leaving a low pressure area behind. This combination of high pressure in front and low pressure in back is the main source of the balls drag. When the surface of the ball is covered with dimples, a thin layer of air next to the ball (aerodynamicists call it the boundary layer) becomes turbulent.

Here’s the good part: a turbulent boundary layer has better tires. It stirs the air up a bit. It can better follow the curvature of the ball’s profile. It travels farther around the ball before separating, which creates a much smaller wake, and much less drag. In fact, a dimpled ball has only about half the drag of a smooth one.

The aerodynamic lift and drag on a spinning golf ball have at least three variables to consider, the speed of the ball through the air, the rate of the spin of the ball (which averages from 3,000rpm to 10,000rpm), and the surface texture of the ball. This means that both the lift and drag forces vary throughout the flight of the ball. The dimples aid the rapid formation of a turbulent boundary layer around the golf ball in flight, giving more lift. Without ‘em, the ball would travel in more of a parabolic trajectory, hitting the ground sooner (and not coming straight down).

But, golf balls do follow an ‘impetus trajectory’. This is because the drag force decreases at the end of its flight. The spin of
the ball also drops off through the flight and so its lift decreases. The end result is a
* *
(golfer)* *
* * *-- trajectory
O/ * *
|* *
-/ -T----------------------------------------------------------ground
trajectory that looks like the one shown above.

In the game of golf, it’s extremely important to consider the environmental conditions. Wind can be one of them frustrating challenging factors that can affect your game of golf. It’d be irrelevant to examine the different velocities that must be considered when wind approaches the golf course. Our focus has been on the golf ball itself. However, if we remember how lift and drag depend on velocity of the ball through the air, we realize at once that a ball hit against the wind will have greater lift and more drag and one hit with the wind will have a smaller lift and less drag. But a smart golfer must realize the strength and direction of the wind.

Understanding the physics of a modern day golf ball will not alone save you from an embarrassing round of golf. Perfection comes with experience and getting a feel of each course that awaits you. I do believe that a thorough understanding of the physical principals underlying the various aspects of the flight of the golf ball will help the golfer to make the correct judgments and thereby improve his game.
Bibliography:
Sources
Haake, S. (1997) The Physics of Golf.Science Spectra.

Jorgensen, T.P. (1994) Aerodynamic Forces.The Physics of Golf.
www.kent.wednet.edu (1995) The physics of Golf
Why do golf balls have dimples?