Physics Of Volleyball (2023)

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Physics Of Volleyball – Optimizing The Serve

One way to optimize a volleyball serve is to minimize the time the ball spends in the air. This in turn minimizes the reaction time of the opposing team, making it more difficult for them to return the shot. In this analysis of the volleyball physics, we will look at ways to minimize the time the ball spends in the air, after the serve is made.

To set up this physics analysis we must first define the different variables in the problem. The schematic below shows a top view of a volleyball court, with labels given as shown.

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La is the distance from the serve location (behind the end line) to the net, along the direction the volleyball is served

Lb is the arbitrary distance from the net to where the ball lands on the other side of the court, along the direction the volleyball is served

d is the distance beyond the net where the ball lands

α is the angle the volleyball trajectory makes with the side line

The following schematic shows a view of the volleyball trajectory, between the point of serve and the point at which the volleyball lands on the court.

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g is the acceleration due to gravity (equal to 9.8 m/s2 on earth)

H is the height of the net

hmax is the maximum height reached by the ball

ho is the initial height of the ball at the serve location

V is the initial serve velocity of the ball

θ is the initial angle the ball makes with the horizontal (and above it)

Point A is the serve location

Point B is the location just above the net, through which the ball passes

Point C is the location on the court where the ball lands

The coordinate system xy is defined with the positive x and y axes pointing in the directions shown. For convenience, the origin of this coordinate system is at point A.

The physics behind this analysis is of a kinematic nature, since we are only concerned with the motion of the ball. This optimization problem is an interesting application of projectile motion. To simplify this analysis we shall assume that air resistance and aerodynamic effects acting on the volleyball can be ignored.

From the equations for projectile motion, we have

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Where x and y denotes the position of the ball at any point in its trajectory, and t is time, in seconds.

Combine equations (1) and (2) to remove the time variable t and we get

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This is the equation of a parabola in terms of x and y. This equation has the general form:

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The variables a and b can be solved for in terms of the parameters La, Lb, ho, and H. They can be solved using two simultaneous equations based on the coordinates of points B and C, relative to the coordinate system xy (with origin at point A).

The coordinates of point B (relative to xy) is (La , Hho)

The coordinates of point C (relative to xy) is (La+Lb , -ho)


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The coordinates (x,y) for points B and C can be substituted for x and y in the general parabola equation given by

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We can then solve for a and b in terms of the parameters La, Lb, ho, and H. These can then be used to solve for the initial velocity V and initial angle θ of the volleyball using the following equations:

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The time that the ball is airborne (i.e. the time we wish to minimize) is given by

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Upon analysis of the results we find that we can minimize the time by doing three things:

(1) Get the ball just over the net

(2) Make Lb as large as possible (serve the ball so that it lands near the end line)

(3) Make ho as large as possible (with a jump serve)

Points (1) and (2) make sense since a shallower trajectory means the ball reaches a lower maximum height hmax, which means the ball spends less time in the air. However, if the ball lands close to the net (with small Lb), then the ball requires a high arc. This means that the ball is airborne for a longer period of time.

Point (3) makes sense since serving the ball at an ho as large as possible (with a jump serve), enables the ball to start its downward trajectory sooner (since hmax is reached sooner). This also decreases the time the ball spends in the air.

To get an idea of how much time the ball spends in the air, let's say we have d = 9 m, ho = 3.0 m, and H = 2.4 m. The time the ball spends in the air is t = 0.86 seconds.

A volleyball player can put the above three points into practice by practicing jump serves which (1) barely get the ball over the net, and (2) land as close as possible to the end line. The picture below shows an example of a jump serve.

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Source: Author:

In addition, serving the ball at a cross-court angle α does not change the time the ball spends in the air (for a given d, ho, and H). It only affects the horizontal speed of the ball (Vcosθ). So, the greater the angle α, the greater the ball speed. This can be advantageous since a higher serve velocity V can make it more difficult for the opposing team to return the shot.

The analysis shown previously allows us to predict the primary kinematic behaviour of a volleyball serve, subject to the assumption that air drag and aerodynamic effects can be ignored. However, these effects can in fact be significant and must be accounted for in order to make the model prediction as accurate as possible. In the next section we will discuss these effects in greater detail.

The Magnus Effect And Air Resistance

The airborne time of the volleyball can be reduced even more by putting top-spin on the volleyball. This causes the ball to experience an aerodynamic force known as the magnus effect, which "pushes" the ball downward so that it lands faster. This complicates the physics analysis. The figure below illustrates the magnus effect.

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Source: Author:

As the ball spins, friction between the ball and air causes the air to react to the direction of spin of the ball.

As the ball undergoes top-spin (shown as clockwise rotation in the figure), it causes the velocity of the air around the top half of the ball to become less than the air velocity around the bottom half of the ball. This is because the tangential velocity of the ball in the top half acts in the opposite direction to the airflow, and the tangential velocity of the ball in the bottom half acts in the same direction as the airflow. In the figure shown, the airflow is in the leftward direction, relative to the ball.

Since the (resultant) air speed around the top half of the ball is less than the air speed around the bottom half of the ball, the pressure is greater on the top of the ball. This causes a net downward force (F) to act on the ball. This is due to Bernoulli's principle which states that when air velocity decreases, air pressure increases (and vice-versa).

As a result, by putting enough top-spin on the volleyball, the airborne time can be further reduced by as much as a tenth of a second. The following paper by D. Lithio and E. Webb explains the details of a volleyball serve and include mathematical models which account for the effects of air resistance (drag) and top-spin:

Optimizing A Volleyball Serve, Dan Lithio, Hope College, and Eric Webb, Case Western Reserve University, October 14, 2006.

This paper is very informative for those wishing to see the full analysis of the physics of volleyball, with regards to optimizing the serve.

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How is physics used in volleyball? ›

Gravitational force impacts every aspect of volleyball; whether you are serving, passing, or hitting. Gravity will effect every contact with the volleyball. When some one is going to serve, the server uses upward and forward force on the volleyball, while gravity is using a downward force.

What energy is in volleyball physics? ›

Energy of motion is called kinetic energy. A volleyball's kinetic energy enables the ball to do work when it strikes a net and forces the net to deform. net gains elastic potential energy. This gives the net the ability to do work on the ball, stopping its motion and forcing it to move in the opposite direction.

What is projectile motion in physics in volleyball? ›

Projectile Motion describes the motion of the ball. Whether it's a serve, set, or dig, a volleyball will always travel in a parabolic motion. This is because the only force that acts on the ball after the ball is given an initial force is gravity assuming that there is no air resistance.

What is the mechanics of the game volleyball? ›

To start, flip a coin to determine which team serves the ball first. Then the two teams will rally—or hit the ball back and forth over the net—until a fault occurs. There is a maximum of three hits per side. The objective is to score points by sending the ball over the net, grounding it into the opponent's court.

What is Bernoulli's principle in volleyball? ›

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.

What Newton's laws does volleyball use? ›

Newton's third law of motion states that for every action there is an equal and opposite reaction. This means that if something is pushed or pulled, it will also move in the opposite direction. In the same way, when a ball is hit in volleyball, it must ricochet off the ground back to its player.

How is velocity used in volleyball? ›

Speed and quick feet help players immediately react to whatever direction the ball is hit, preventing it from touching the floor. Hitting, blocking, setting, and digging skills will all improve when a player is able to quickly move around the volleyball court.

What is momentum in volleyball? ›

The term “momentum” here refers to a condition in which psychological factors cause a player or team to achieve a higher (or lower) than normal performance over a period of time due to a positive correlation between successive outcomes.

What energy does a volleyball player spiking a ball? ›

So let's start valuable player spiking a ball. So that action is causes causes the ball to move. And that is therefore kinetic energy.

What plane of motion is volleyball in? ›

Heidens also teach force absorption and production in the frontal (lateral) plane. Most of volleyball consists of lateral movements, so if a player is strong side-to-side, not only will it reduce injury risk but she will be more confident moving sideways and will thus do it more.

What is acceleration in volleyball? ›

Acceleration occurs when there is an increase in velocity. This can be achieved in volleyball by a few tricks. Acceleration that occurs without the aid of the player happens because of the downward force of gravity. A player can also create top spin on the ball to make the ball accelerate towards the ground.

What is Magnus effect in volleyball? ›

In brief, the Magnus effect is the trajectory deflection of spherical ball spinning in the air, caused by a force transverse to both the linear and angular velocities.

What are the 3 fundamentals in volleyball? ›

The following are described: serving, passing (forearm underhand passing), setting (overhead passing), attack options (hitting/spiking), blocking (from attack and defend positions), and defensive skills (rolling & sliding).

Why is the libero not allowed to serve? ›

Why The Change To Allow Serving? The original concept behind the libero position was that they were strictly a defensive position that was created to sustain rallies by improved digging and better passing. They were not to be included in virtually any offense.

What are three basic concepts of volleyball? ›

  • Games are played to 25 points and a team must win by 2 points.
  • Each team is allowed 6 players on the court.
  • Rally scoring - a point is scored on every serve.
  • ex. ...
  • Each team has up to 3 hits to get the ball over the net. ...
  • One person may not strike the ball two times in a row.

What is Bernoulli's law in physics? ›

Bernoulli's principle states the following, Bernoulli's principle: Within a horizontal flow of fluid, points of higher fluid speed will have less pressure than points of slower fluid speed.

What causes a volleyball to float? ›

As the air surrounding the volleyball transitions from laminar to turbulent flow, also known as the drag crisis, the erratic movement of the trailing air causes lift in the ball at random locations, leading to random movement of the ball.

Does volleyball use projectile motion? ›

Volleyball is a sport made up entirely of projectile motion. For example: when a ball is set in volleyball, it will follow some form of a parabolic path until it is hit again by another player. After the ball leaves the setter's hands, it becomes a projectile following the parabolic path.

What forces are used in volleyball? ›

The action force of a spiked ball meets the reaction force of a player's block. A team scores a point when the action force of a spiked ball meets the reaction force of the opposing team's court.

What is blocking in volleyball physics? ›

Blocking allows a portion of the court of be taken away from the hitter and allows the defense to play more court because that area is shut off. To overcome a successful block, the players hands and arms have to penetrate and seal the net creating a wall for the hitter to work around.

What law of motion is hitting a ball? ›

A bat hits a baseball with of force. How much force does the baseball exert on the bat? Explanation: Newton's third law states that when object A exerts a force on object B, object B exerts a force equal in magnitude but opposite in direction on object A.

What is the fastest speed of a volleyball? ›

The fastest possible serve has a starting angle of 0.111 radians, a starting velocity of 26.162 m/s, and takes 0.900 seconds.

What is stability in volleyball? ›

It's important to point out that a volleyball player has to focus on stability. In other words, athletes need to keep their feet firmly on the ground during the game. Obviously, if a defensive player has a strong and stable body he/she will be able to resist most of the opponent team's attacks perfectly.

What are the biomechanical principles of a volleyball spike? ›

The 4 key components consist of approach/take-off, jumping height, arm swing and hit. In order to generate the greatest amount of power when spiking, a volleyball player needs to be able to summate these forces as one to make them in to one flowing movement.

What is summation of forces in volleyball? ›

This is the principle of force summation where all body parts are used in sequence starting from large muscles first like quads and then sequencing the muscle groups down to smaller muscles like wrist extensors. This would help the player generate more force to get the ball over the net and further into the court.

Why is spiking so hard in volleyball? ›

A spike is a very complex skill and it takes a lot of patience and perseverance to master in it. The spike requires quickness, agility, explosive power, strength, hand-eye coordination and whole- body coordination.

What muscles help you spike a volleyball? ›

During the spike, the anterior deltoid and supraspinatus functioned together to elevate and place the humerus throughout all phases. During cocking the infraspinatus and teres minor acted together to rotate the humerus externally.

What type of movement is a volleyball spike? ›

The volleyball spike is a complex motion that can be characterized in 4 phases [2]: approach phase, arm cocking phase, acceleration phase and follow through phase. From the moment of take-off until striking the ball, energy and (angular) momentum of the total body are conserved physical quantities.

What are movement sequences in volleyball? ›

Volleyball can be characterized by movement patterns including first-step quickness, multiplanar movement (movement in all directions), level changes (up and down movement), deceleration (slowing down movement), and high-levels of force production (producing movement quickly).

Is there air resistance in volleyball? ›

The ball however does have air resistance when in the air. Its much easier to hit a volleyball than many other things such as bowling balls, basketballs, and soccer balls because volleyballs have less inertia. Also the gravitational force of the earth impacts every part of volleyball.

How does Newton's first law affect volleyball? ›

Volleyball fits in with the Newtons First law

The force of the servers hand applying pressure to the ball to make the ball go up ward will make the ball stay in motion till the server then hits the ball. The ball remains in motion until it reaches the opposing team, hits the net, and or hits the ground.

What is the hardest skill in volleyball? ›

Setting might look like a piece of cake, but it is the hardest position in volleyball for many reasons. One reason is that as a setter, it is their job to get the second ball up to one of their hitters, even if the first pass was not any good.

What is the most attacking skill in volleyball? ›

An arm swing is a key element of an attack in the game of volleyball. A volleyball player should aim to make a fast arm swing to carry out a powerful attach hit and land the ball on the opposite side of the court successfully.

What is the strongest role in volleyball? ›

The setter is considered to be the most important position in volleyball. The setter on the team is the leader. Just like a quarterback in football, a setter in volleyball is in charge out on the court.

What is the most fundamental play in volleyball? ›

1. Bumping — Bumping, otherwise known as forearm passing, is one of the most essential volleyball skills for all positions. It's the way you keep the ball in play and set your team up for success.

What is the easiest skill in volleyball? ›

By far one of the most basic skills in volleyball is passing, also known as bumping. This is when a player contacts the volleyball with their forearms and redirects the ball to one of their teammates.

What is the 3 first name of volleyball? ›

The Origins. William G. Morgan (1870-1942), who was born in the State of New York, has gone down in history as the inventor of the game of volleyball, to which he originally gave the name "Mintonette".

What happens if a libero attacks? ›

The referee will use the illegal attack signal for any attack faults associated with the libero. Replacement of players: The libero is allowed to replace any player in a back-row position only.

Why is the libero always short? ›

A libero (LEE'-beh-ro) in indoor volleyball is a back-row defensive specialist. Since they only play in the back row, those players are often shorter than the front-row blockers and hitters but have impeccable ball-control skills.

Why can't libero be captain? ›

In volleyball, Rule 5 was revised to allow the libero to be either the team or game captain. The Commission reasoned that, although the libero frequently enters and leaves the court, same as a team captain in many cases, there is no reason to not allow the libero to be captain.

What are 3 important facts about volleyball? ›

Volleyball was invented by William G. Morgan in 1895, but it did not become an Olympic sport until 1964. A single player may jump as many as 300 times in a volleyball match. The record for most consecutive passes in volleyball is 110, achieved in the United States, in Raleigh, North Carolina, on February 5, 2010.

What are the 5 components of fitness in volleyball? ›

Fitness Components for Volleyball
  • Core and Shoulder Strength. Core strength – strength in the abdominal muscles, obliques and hips – is crucial for all volleyball players because it provides stability for all the twisting, turning and stretching movements of the game. ...
  • Lower-Body Strength. ...
  • Speed. ...
  • Lateral Movement.
Feb 8, 2013

How does physics play a role in sports? ›

Understanding the physics of motion can affect all areas of sports, from helping athletes move faster, to preventing injuries, planning more efficient trainings, and developing aerodynamic equipment and clothing.

How is physics used in games? ›

Modern video games use physics to achieve realistic behaviour and special effects. Everything from billiard balls, to flying debris, to tactical fighter jets is simulated in games using fundamental principles of dynamics.

How do athletes use physics? ›

Overall, the principles of physics can describe certain phenomena and influence various facets of sports, from helping athletes move faster and hit harder, to training more efficiently, to preventing injuries, to strengthening their mindset, to designing aerodynamic clothing and devices.

How does the force of gravity influence the movements in volleyball? ›

Gravity impacts the movement of the volleyball throughout the entire game. For example, when a player serves the ball, it starts to descend once it crosses the net because gravity is forcing it downwards. There are several techniques that can be used to help gravity bring the ball down faster.

What sport has the most physics? ›

Of all sports, ice hockey is possibly the one with the widest array of physics elements in it. The game provides many examples that can bring physics to life in the classroom.

What sports use gravity? ›

- Some athletes use gravity in their sports, for example ski jumpers, divers and cyclists. - Some athletes have to overcome the force of gravity, for example high jumpers, shot putters and weight lifters.

How is physics related to exercise? ›

An understanding of how physics interacts with human movement is essential in the testing and application of proper exercise methods. Gravity, inertia, velocity, acceleration, friction, momentum, work, power, and torque are all aspects of physics that must be considered in proper exercise application and measurement.

What games has the most realistic physics? ›

The most satisfying physics in PC games
  • Grand Theft Auto V. ...
  • Kerbal Space Program. ...
  • Just Cause 4. ...
  • Crayon Physics Deluxe. ...
  • Totally Accurate Battle Simulator. ...
  • Besiege. ...
  • Line Rider. ...
  • Human Fall Flat.
Mar 27, 2020

What are some examples of game physics? ›

Common examples in platform games include the ability to start moving horizontally or change direction in mid-air and the double jump ability found in some games. Setting the values of physical parameters, such as the amount of gravity present, is also a part of defining the game physics of a particular game.

Do games need physics? ›

Unless you're making a text-only game, you'll need to apply some form of Newtonian physics to pretty much every action that occurs on the screen. Computer and video games apply the laws of physics so that objects "behave" as they do in the normal world.

What sport uses the most power? ›

Weightlifting and gymnastics were the two highest rated sports for strength and power. That makes sense. The strength sports ranking list by the expert panel from ESPN provides an alternative list. The ratings are still being recorded (this list is from December 2019), so the list order may change over time.

How do Newton's laws apply to sports? ›

Newton's Third Law of Motion states that for every action there is an equal and opposite reaction, meaning that the larger player experiences a force from the smaller player pushing back on the bigger player, even if the smaller player is not trying to do so, slowing the bigger player down.

How is kinetic energy used in sports? ›

When you hit a ball with a bat or racquet, work is done. A runner does work when they accelerate and acquire kinetic energy. Once that kinetic energy is achieved, work continues to be done just to overcome friction and maintain speed. Energy comes from the food they eat.

How does acceleration work in volleyball? ›

Acceleration occurs when there is an increase in velocity. This can be achieved in volleyball by a few tricks. Acceleration that occurs without the aid of the player happens because of the downward force of gravity. A player can also create top spin on the ball to make the ball accelerate towards the ground.

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