Why are Golf Balls Dimpled?

So Why are Golf Balls Dimpled? Who knows, i guess someone somewhere down the line started
making them like that and everyone just started using them! Not quite, but close enough!
In a way, the reason why golf balls have dimples is a story of natural selection. Originally, golf
balls were smooth; but golfers noticed that older balls that were beat up with nicks, bumps and
slices in the cover seemed to fly farther. Golfers, being golfers, naturally gravitate toward anything
that gives them an advantage on the golf course, so old, beat-up balls became standard issue.

At some point, an aerodynamicist must have looked at this problem and realized that the nicks and
cuts were acting as “turbulators” — they induce turbulence in the layer of air next to the ball
(the “boundary layer”). In some situations, a turbulent boundary layer reduces drag.

The dimples, paradoxically, do increase drag slightly. But they also increase what is called the
“Magnus lift”, that peculiar lifting force experienced by rotating bodies travelling through a medium.
Magnus lift is present because a driven golf ball has backspin. The same Magnus effect can cause a
ball to hook or slice if it has sideways spin.

impetus trajectory

Contrary to simple ideas of trajectories in a vacuum, golf balls do not travel in inverted parabolas. They follow what is called an “impetus trajectory”. This is because of the combination of drag (which reduces horizontal speed late in the trajectory) and Magnus lift (which supports the ball
during the initial part of the trajectory, making it relatively straight). The trajectory can even curve upwards at first, depending on conditions!

A golf ball leaves the tee with a speed of about 70 m/s and a backspin of at least 50 rev/s. The
Magnus force can be thought of as due to the relative drag on the air on the top and bottom
portions of the golf ball: the top portion is moving slower relative to the air around it, so there is
less drag on the air that goes over the ball. The boundary layer is relatively thin, and air in the
not-too-near region moves rapidly relative to the ball. The bottom portion moves fast relative to
the air around it; there is more drag on the air passing by the bottom, and the boundary (turbulent)
layer is relatively thick; air in the not-too-near region moves more slowly relative to the ball. The
Bernoulli force produces lift. (Alternatively, one could say that “the flow lines past the ball are
displaced down, so the ball is pushed up.”)

A difficulty comes near the transition region between laminar flow and turbulent flow. At low
speeds,the flow around the ball is laminar. As speed is increased, the bottom part tends to go
turbulent first. But turbulent flow can follow a surface much more easily than laminar flow.
As a result, the laminar flow lines around the top break away from the surface sooner than
otherwise, and there is a net upward displacement of the flow lines. The Magnus lift becomes
negative.

dimples vs. smooth

The dimples aid the rapid formation of a turbulent boundary layer around the golf ball in flight, giving more lift. Without them the ball would travel in more of a parabolic trajectory, hitting the ground sooner (and not coming straight down). This was discovered by accident in the early days of golf when golfers noticed that old roughened golf balls went farther.

Despite the drag, a dimpled golf ball can even go farther in air than it would in vacuum given the same initial velocity and low angle. However, a golf ball shot at 45° and 70 m/s in vacuum would go 500 metres to the first bounce, which exceeds all records!

References:

Lord Rayleigh, “On the Irregular Flight of a Tennis Ball”, Scientific Papers I, pg 344.
R. Watts and R. Ferver, “The Lateral Force on a Spinning Sphere Aerodynamics of a Curveball”, Am. J. Phys. 55, 40 (1986).
Steve Haake, “Physics and Golf? You must be joking!” Physics World 10, 76 (1997).
Journal of Applied Physics 20, 821 (1949) by Davies.
American Journal of Physics 56, 933 (1988) by McPhee and Andrews.
“The Physics of Golf” by Theodore P. Jorgensen