THE MOATAH FLOAT..AHHH
The high-speed top-spin serve is daunting, but at least it is predictable.
Anyone who has had to face a typical jump serve knows how the ball
behaves. It dives. The faster it is coming or spinning the quicker it
plummets toward your feet or drops behind your shoulder. The physics of
the jump serve is straight forward. As the ball rotates with top spin it
drags more air under the ball, which must move faster than the air on top
to get by in the same amount of time.
Bernoulli’s Principle states that faster air has lower pressure so more air
pressure on top and less on the bottom forces the ball down. A player has
less time to react to a jump serve but one can still develop intuitive
responses to the predictable flight path.
By contrast, the physics of float serve guarantees that you cannot know
where it is going to go. A non-rotating ball is subject to the unpredictable
interactions between drag, lift, and a narrow window of opportunity called
the “drag crisis.” With a better understanding of the details of these
forces we can begin to improve our intuition of how to manipulate the two
things we can control on a float serve; the contact speed and angle. Once
it leaves our hand we trust physics to take over to generate the ace for
us.
Air moving past a sphere travels in a ‘laminar flow’ as the speed of the
moving air increases from zero. Friction between the ball and the moving
air causes a boundary layer of air to form close to the surface.
At very low speeds the air that touches the ball does not move at all (with
respect to the ball), from the leading edge to trailing point. As it rubs
against the next layer the air is slowed down. The thickness of a
boundary layer is measured by how far away from the surface the air
speed is the same as the air before it contacts the ball (the straight lines
in figure 1). The “drag coefficient” is a measure of how tenaciously the air
sticks to the surface of the ball. When the ball is moving faster through
the air is more difficult for the air to hold on the trailing edge. As these
molecules lose their hold the ball becomes less sticky and the drag
coefficient decreases.
Eventually there comes a speed where the boundary layers are no longer
able to hold together at all and they break away, somewhere along the
trailing edge of the ball. This state is called “turbulent flow.” (see figure 2)
After the ball is fully into the turbulent state, the drag is significantly
reduced. The transition from laminar to turbulent flow is known as the
“drag crisis.” There are many factors that contribute to determining at
what speed a particular ball will suffer this dramatic change. The size and
shape of the ball, the smoothness of its surface, the air it travels in as
well as the weather all interact in a complicated way that cannot be
predicted, only measured, in a wind tunnel. Physicists have combined
many of the factors that contribute to this change of state into a single
figure they call the “Reynolds Number.” The Reynolds Number (Re)
accounts for the mass density and viscosity of air (which depend mostly
on temperature), the diameter of the ball, and the speed of air passing
over its surface in the following relationship.
While all of these factors can change from day to day or from ball to ball
it is the speed that makes the biggest difference from one serve to the
next. The velocity at which a sphere reaches true turbulent flow is called
the “critical speed.” For a typical volleyball the Reynolds number at the
critical speed can vary from 170,000 to 300,000. Numbers like those are
hard for me to feel intuitively so for practical purposes I will instead refer
to the ball speeds they represent, which gives us a range between 10
meters per second and 25 m/s, respectively. Since the slowest you can
serve a ball from the baseline and expect to get it over the net is about
12 m/s and the best pros can launch a jump serve around 30 m/s this is
the range in which a float serves must exist.
When the scientist in me looks at the graph below I see a world of
information about the physics of a sphere in flight. As a volleyball player I
am struck by one thought: My opponents are in big trouble next time I
step up to serve.
Figure 3 describes the results of wind tunnel tests done in Japan back in
2010 on the aerodynamics of a new volleyball designed by Molten. The
graph shows the relationship between the drag on a sphere and the speed
of air moving across it, specifically in the range we are interested in.
Takeshi Asai and his colleagues from various universities around Japan
found that a perfectly smooth sphere (thick dashed line, above) went
through an abrupt drag crisis in the neighborhood of 25 m/s going from a
very high drag coefficient to a very low one. The conventional volleyball
they tested, a Molten MTV5SLIT (thin dashed line above), finished with a
similarly low drag but with a critical speed significantly lower than the
reference sphere. Their newest ball, a Molten V5M5000 with the
honeycomb patterned surface, began with similar characteristics to the
standard ball but had lower critical speed and higher final drag. Though
they did not publish the details, the Japanese engineers also tested the
new Mikasa MVA200 dimpled ball and found it had a critical speed slightly
lower than the conventional ball.
In order to explain my new-found serving confidence let’s take a look at
how drag coefficient tells us what forces will be acting on the ball after it
leaves our hands. The force exerted on the ball due to drag is dependent
on a number of things.
The most important thing to notice is that the drag force goes up as the
speed squared. That means that twice as much speed turns into four
times as much drag! Now if we rearrange Newton’s second law (F = ma;
force equals mass times acceleration) we see that the acceleration (well,
really the deceleration) of the ball is
Taking a look at figure 3 again imagine that we strike the ball hard so
that it starts with a higher medium speed, say 22 m/s. Drag will cause
the ball to slow down (moving your finger along the solid line from right
to left) until it reaches the critical speed. At that moment (hopefully just
as it crosses the net) the drag suddenly increases dramatically, the ball
seems to fall out of the sky, and your opponent curses while diving to the
sand.
The variability of air friction during flight alone would be enough to make
for an effective serve but there is more. Drag is not the only force in play
during the drag crisis and turbulent flow. The same wind tunnel tests
done by Asai and his team also showed forces perpendicular to the
direction of travel, which scientists call ‘lift’. Unlike an airplane wing, a
volleyball is radially symmetric so lift can be in any direction around the
ball at a right angle to the path of its flight.
While in laminar flow the boundary layer is uniform and so there are no
lift forces measured on the smooth sphere or either type ball. Figure 5
below is a comparison of lift forces to Reynolds number for the Molten
balls. During the wind tunnel tests the balls experienced a sharp,
unpredictable sideways force at the drag crisis and then a small but
steady lift under turbulent flow.
The collapse of the boundary layer at the beginning of the drag crisis
causes a chaotic swirling of air in the wake of the ball as each small
vortex breaks free from the surface. At Peking University in China, Wei
Qing-ding and his team believe that the random nature of the creation of
these vortices causes the separation line (a ring around trailing side
represented by the dashed line in figure 2) to form off-axis to the flow,
which probably accounts for the lift we see at higher speeds. Asai
speculates that the orientation of the ball panels controls the direction
and force of deflection.
One guy I play with is convinced that striking near the valve affects the
direction a float serve will drift. Regardless of the cause, it is clear that
even if you hit the ball fast enough that is stays in turbulent flow, the
effect of lift will cause the ball to veer left or right, float long, or add to
the downward effect of gravity.
And my favorite zig-zag serve? Wei also found that early in the drag crisis
there is a narrow range of velocities where the boundary layer can shed
vortices from alternating sides (see Figure 6) causing the lift force to
switch back and forth from one side to the other.
When you put all these factors together the result is an unpredictable
serve? But just how unpredictable is it?
Asai and company used an impact-type ball ejection device to launch nonrotating volleyballs with precise contact speed and angle to answer this
very question. They ran tests on the two styles of Molten balls and the
Mikasa dimple ball. Each was served twenty times and with three different
panel orientations. The very tightest landing zone they achieved was one
meter wide by two meters long (area A in figure 7 below) for the
honeycomb ball struck on the main panel. Most other balls and
orientations resulted in a possible area about 1.5 m by 4m (B). The
Mikasa ball, struck perpendicular to the panels, could be expected to land
anywhere inside an oval five meters long! And that is with no wind.
Now that we know what happens to the ball in a float serve, and have
some idea of why it moves around during its flight, how do we make it
happen? Let’s quickly review the physics.
1. Volleyballs experience a drag crisis (a jump from low to high drag) as
they slow down. The speed at which this happens is dependent on ball
type and air conditions. Smoother balls have a higher speed drag crisis.
Higher air temperature equals a lower critical speed.
2. During higher speed turbulent flow a volleyball will experience both
drag and perpendicular lift which increases as the square of the velocity.
3. The unpredictability of a float serve is from 1 to 5 meters of landing
area.
4. All of the effects listed above ONLY occur with a non-rotating ball.
What should we do when we step up to the line to serve?
1. Eliminate rotation! Even the smallest tumble reduces lift and restricts it
to the direction of rotation. Spinning also forces the state of turbulent
flow, keeping drag coefficient in the region above the drag crisis.
2. Assess your equipment for the best way to get your ball to pass
through the drag crisis.
a. Smooth balls can be served faster than rough balls
b. Bigger, lighter balls can be served faster than smaller heavier balls
c. Off-panel contact may result in more movement.
3. Assess how the conditions will affect movement
a. A headwind can be served into faster to get more lift and drag but a
tail wind can be served slower and closer to the drag crisis.
b. Standing back from the service line gives more time for lift and drag to
move the ball around but slower serves from the baseline are easier to
control when targeting the critical speed.
c. Serve slower when it is hot and faster when it is cold if targeting the
critical speed.
4. Choose your ball trajectory to account for the range of movement.
a. Higher arc serves start and finish faster because of gravity.
Perpendicular movement may be a bit greater as the ball is falling down
from a height but drag only slows the ball down without changing its
trajectory. Flat serves are easier to manipulate because they rely almost
entirely on contact speed.
b. Aim inside the lines. Float serves are supposed to move. Target your
landing spot at least 1 meter from the sidelines and 2 meters from the
net or baseline.
5. Eliminate rotation!! It bears saying again. In my experience the harder
I strike the ball the more difficult it is to hit it just right. The closer I stand
to the baseline the softer I can make contact and the more precisely I am
able to target the center of the ball.
Since researching this article my float serve is generating many more
aces. I am better able to see the changes in ball movement. Slowly my
intuition for how the wind and feel of the ball and my position will
combine to create the most unpredictable results. Now I just have to stop
watching my beautiful float serve and hustle into my defensive ready
position.