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In air flow that can highly affect

the early stages of studying physics, students generally look at a simplified version
of projectile motion. Obviously, this cannot predict certain movements of objects
in the air. There are unaccounted properties such as magnus force and air flow that
can highly affect the movement of the projectile. When looking at “ball” sports
(E.g. Baseball, Soccer, Tennis, and Volleyball), having a greater understanding
of the concepts behind projectile motion can be a key tool in improving one’s


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the sport of volleyball, the main goal is win a best of five match with each
game to 25 points. This is generally achieved by teams making the least amount
of errors possible. There is little that one can control during the play of the
game, but one of the major things a player can influence directly is the serve.
The server alone is responsible for how plays on the opposing side are started
so providing a good service is an effective strategy to help one’s team win the
game. An effective serve is one that the opposing team struggles to receive.
This could be a well-placed and/or fast serve that leaves one little time to
react. By serving like this, one’s team has the greater potential of either get
a point by the unreturned serve or setting up a hard ball for the opposing team
to return, forcing them to return an easy-to-hit ball back. When one can
understand some of the properties of physics behind a serve, one should be able
to optimize their serve to increase their likelihood of winning.

Rulings, and Dimensions of the Court

A serve is the way to initiate the game of Volleyball.
Servers will toss the ball up whilst sending their hands up and back. Servers
will then shift their weight forward and swing their hands through the middle
of the ball and towards their target as shown in figure 1. Servers must serve
from out of the court before stepping inside the court to join the play. The
serve is legal if the ball was hit with only one part of the arm, passes the
vertical plane created by the antennae on the net, and if the ball lands within
the opposite side of the court. The court dimensions are shown in figure 2


the past whilst looking at the flight of a projectile, students generally only
look at problems with only gravity because it simplifies the problem
drastically. When one accounts for air in projectile motion, the problem gets
more complex. For example, if a volleyball is spinning on its horizontal axis
clockwise towards a wind stream there is an additional downward force acting on
the ball besides gravity and vice versa if it is spinning counter clockwise it
will have an additional upwards force working against gravity. What happens when
a volleyball is spinning clockwise is that the bottom side of the ball is spinning
with the Windstream and the top side is spinning against it. This causes the
air on bottom of the ball to curve up towards the back with the shape of the
ball and the air on the top of the ball comes to halt due to the opposing spin.
What the deflected air creates is a sort of “air force” that points upwards and
due to Newton’s third law, an equal and opposite force is also there pushing
down which we can call the magnus force. This is shown in figure 3. Magnus Force at its simplest form
can modelled with




Where  is angular velocity,  is the linear
velocity, and  is the spin of the
ball as a function of its of its own velocity. This additional force can cause
a volleyball or any ball for that matter to hit the ground faster, or stay in
the air longer depending on the spin applied.



looking at a volleyball travelling through air it is important to understand
how the air behaves whilst the ball is moving. When air moves past a ball
moving through the air smoothly one can call this laminar flow. When the air
interacts with the surface of the ball, friction between the two create a
boundary layer of air around the ball. Drag forces holds this boundary layer of
air on the surface of the ball. When the ball reaches a certain velocity, this
boundary layer will begin to break off behind the ball due to a decrease in
drag thus causing a behavior known as turbulent flow. Determining whether the
air flow will be turbulent or laminar is calculated through Reynolds Number.
Reynold’s number is calculated by,



an object hits a high enough Reynold’s Number, the flow will become turbulent
as shown in the figure below. Reynold’s number is heavily affected by the
velocity at which the volleyball travels through the air.


a volleyball moves through the air without spinning, the object does not
experience the magnus effect. The object is still subjected to gravity, lift,
and drag. As previously stated when the air flow goes from laminar to
turbulent, the drag force is heavily reduced on the ball. This phase is what is
known as drag crisis. During this drag crisis, the boundary layers of air
around the ball break off from the ball to create erratic air movements behind
the ball. These erratic movements from the behind the ball to generate lift
forces to move the ball side to side creating a knuckle ball effect. This can
seemly be created by hitting a volleyball with no spin at a specific range of


of volleyball serves cannot be defined by simplified kinematics. Volleyballs (or
balls in general) in flight are heavily affected by the air in which they
travel. The Magnus effect heavily affects the trajectory of serves due the
magnus forces created due to the deflection of air even causing some serves to
move in z directions depending on its axis of rotation when spinning. If a
volleyball is not rotating but it served in the air, it is not subject to this
magnus effect, but the ball may still follow an unpredictable zig zag motion
(also known as a float serve) due to turbulent air flow acting on the ball. By
controlling spin on the ball, one can make their serve more difficult to return
by either making their serves hit their opponents side of the court faster or
by making their serves trajectory harder to predict.





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