A golf ball can be driven great distances down the fairway. How is this
possible? Is the drive only dependent on the strength of the golfer or
are other factors at play? As we will see, the aerodynamic forces play a
key role in the flight of the golf ball. We will start by looking at the
history of the golf ball, show why a golf ball has dimples, then explain
how lift is formed by the spin imposed on the golf ball.
We will also look at how experimental tests can be
performed using a spinning ball in a wind tunnel.
History of the Golf Ball
The early golf ball, known as a featherie, was simply a leather pouch
filled with goose feathers. In order to obtain a hard ball, the pouch was
filled while wet with wet goose feathers. Since people believed a smooth
sphere would result in less drag (and thus fly farther),
the pouch was stitched inside out. Once
the pouch was filled, it was stitched shut. Therefore there were a few
stitches on the outside of the ball. The ball was then dried, oiled, and
painted white. The typical drive with this type of ball was about 150 to
175 yards. Once this ball became wet, it was totally useless.
In 1845, the gutta-percha ball was introduced. This ball was made from
the gum of the Malaysian Sapodilla tree. This gum was heated and molded
into a sphere. This resulted in a very smooth surface. The typical drive
with the gutta-percha ball was shorter than that obtained with the
featherie. However, according to golf legend a professor at Saint Andrews
University in Scotland soon discovered that the ball flew farther if the
surface was scored or marked.
This lead to a variety of surface designs which were chosen more or less
by intuition. By 1930, the current golf ball with dimples was accepted as
the standard design. The modern golf ball consists of rubber thread
wound around a rubber core and coated with dimpled enamel. The dimples
are arranged in rows. The number of dimples is either 336 for an American
ball or 330 for a British ball. The typical drive with a modern golf ball
is about 180 to 250 yards.
Why, then, does a golf ball have dimples? The answer to this question can
be found by looking at the aerodynamic drag on a sphere. There are two
types of drag experienced by a sphere. The first is the obvious drag due
to friction. This only accounts for a small part of the drag experienced
by a ball. The majority of the drag comes from the separation of the flow
behind the ball and is known as pressure drag due to separation. For
laminar flow past a sphere, the flow separates very early as shown in
Figure 1. However, for a turbulent flow, separation is delayed as can be
seen in Figure 2. Notice the difference in the size of the separation
region behind the spheres. The separation region in the turbulent case is
much smaller than in the laminar case. The larger separation region of
the laminar case implies a larger pressure drag on the sphere. This is
why the professor experienced a longer drive with the marked ball. The
surface roughness caused the flow to transition from laminar to
turbulent. The turbulent flow has more energy than the laminar flow and
thus, the flow stays attached longer.
|Figure 1: Laminar Flow
Over a Sphere.
|Figure 2: Turbulent Flow
Over a Sphere.
So, why dimples? Why not use another method to achieve the same affect?
The critical Reynolds number, Recr, holds the answer to this
question. As you recall, Recr is the Reynolds number at which
the flow transitions from a laminar to a turbulent state. For a smooth
sphere, Recr is much larger than the average Reynolds number
experienced by a golf ball. For a sand roughened golf ball, the reduction
in drag at Recr is greater than that of the dimpled golf ball.
However, as the Reyn olds number continues to increase, the drag
increases. The dimpled ball, on the other hand, has a lower
Recr, and the drag is fairly constant for Reynolds numbers
greater than Recr.
Therefore, the dimples cause Recr to decrease which implies
that the flow becomes turbulent at a lower velocity than on a smooth
sphere. This in turn causes the flow to remain attached longer on a
dimpled golf ball which implies a reduction in drag. As the speed of the
dimpled golf ball is increased, the drag doesn't change much. This
is a good property in a sport like golf.
Although round dimples were accepted as the standard, a variety of other
shapes were experimented with as well. Among these were squares,
rectangles, and hexagons. The hexagons actually result in a lower
drag than the round dimples. Perhaps in the future we will see golf balls
with hexagonal dimples.
|Figure 3: Golf Ball
with Round Dimples.
|Figure 4: Turbulent Flow
with Hexagonal Dimples.
How a Golf Ball Produces Lift
Lift is another aerodynamic force which affects the flight of a golf ball.
This idea might sound a little odd, but given the proper spin a golf ball
can produce lift. Originally, golfers thought that all spin was
detrimental. However, in 1877, British scientist P.G. Tait learned that a
ball, driven with a spin about a horizontal axis with the top of the ball
coming toward the golfer produces a lifting force. This type of spin is
know as a backspin.
The backspin increases the speed on the upper surface of the ball while
decreasing the speed on the lower surface. From the
Bernoulli principle, when the velocity increases the pressure decreases.
Therefore, the pressure on the upper surface is less than the pressure on
the lower surface of the ball. This pressure differential results in a
finite lift being applied to the ball.
|Figure 5: Smoke Flow
Over a Spinning Sphere.
The dimples also help in the generation of lift. By keeping the flow
attached, the dimples help promote an asymmetry of the flow in the wake.
This asymmetry can be seen in Figure 5. In this figure, the smoke shows
the flow pattern about a spinning golf ball. The flow is moving from
left to right and the ball is spinning in the counter-clockwise direction. The
wake is being deflected downwards. This downward deflection of the wake
implies that a lifting force is being applied to the golf ball.
Hook and Slice
A hook or a slice can be explained in the same way. If the golf ball is
given a spin about its vertical axis, the ball will be deflected to
the right for a clockwise rotation (as viewed looking down from above) and to the left for a counter-clockwise
rotation. The generation of an aerodynamic force by a spin about the
axis perpendicular to the flight path is known as the Magnus effect. The
Magnus effect is important in most ball games.
In order to eliminate the hook or slice from a golfers game, modifications
were made to the dimpled golf ball. Since we know how the dimples aid in
producing lift, what if we removed the dimples from two sides of the ball
and leave a strip of dimples around the equator. Then if we line up the
ball on the tee such that the dimpled band is in the vertical plane, we
can minimize the side force imparted by a spin about the vertical axis
while still receive the benefits of the backspin. This ball was known as
the Polara or the happy nonhooker. However, the United States Golfing
Association soon became concerned that this ball would "reduce the skill
required to play golf and threaten the integrity of the game." So they
amended the rules to require that a "golf ball be designed to have equal
aerodynamic properties and equal moments of inertia about any axis through
its center." This new rule effectively made the happy nonhooker illegal.
Effect of gravity
During the last part of a golf balls flight, the gravitational forces
become dominant. As the balls velocity decreases due to the drag imposed
upon it, the lift decreases. At some point, the lift will no longer be
greater than the weight and the ball will begin falling to the ground.
The effects of the dimples on a spinning golf ball were measured
experimentally. This was done by placing a model of the golf ball in a
wind tunnel. Several problems occur whenever wind tunnel experiments are
made. The most obvious is how do we keep the model in the center of the
test section? For the spinning golf ball, another basic question must be
answered - How do we make the ball spin? Scientist always seam to have
answers for questions like these. Wires were used to suspend the model in
the tunnel. The diameter of the wire had to be much smaller than the golf
ball in order to minimize any possible interference effects. Also, to
stabilize the ball, two wires had to be used. The first suspends the ball
from the top of the tunnel, while the s econd stabilizes the ball from the
Applying the spin to the ball is a harder problem. To solve this, a
hollow golf ball is used. A small motor and bearing assembly on which the
ball revolves is placed inside the ball. The wires also serve to supply a
voltage to the motor assembly.
Not only do the wires provide support and the necessary voltage for the
motor, they also help in analyzing the forces acting on the ball. The
upper wire is mounted to a strain-gauged arm which measures the lift force
on the ball. It should be noted that since the ball is spinning about the
vertical axis, this force is actually a side force.
The strain gauge is in turn mounted to a rigid support attached to a
wind-tunnel three-component balance. The wind-tunnel balance is used to
measure the drag on the golf ball.
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Last modified: Thu May 7 10:24:14 PDT 1998
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