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# Math Research Project: Mathematics in Soccer

This research project investigates mathematical applications to the sport of soccer.

by

Tweet## John Junio

on 29 November 2012#### Transcript of Math Research Project: Mathematics in Soccer

Mathematics in Soccer How Mathematics apply to the sport of soccer

By: John Junio & Ranier Lopez Mathematics in Soccer Equations in Soccer Rules of Soccer "The Magnus Effect" Specifications How Does One "Bend it Like Beckham?" Probabilities Soccer is a sport that uses a variety of mathematical and scientific principles

These principles include geometry, calculus, physics, and probability

Estimation also plays a large role in the sport There are many equations that explain phenomena in soccer that to ordinary people may seem impossible

Speed = Distance/Time

Newton’s Second Law (f = ma)

Friction (F = µFa)

Bernoulli's Principle/Magnus Effect Offsides

the attacking player is in the opponent's half of the field and receives the ball behind the last defender (not including the goalie)

the attacking player has to be involved in the play, either by playing the ball or interfering with a defender or goalkeeper

Penalty Kick

when one attacker is deliberately tackled by a defender in the penalty area; penalty kick is given to attacking team

Kick off

in the center of the circle at the beginning of the game and after every goal scored If you kick the ball with the inside or outside of your foot and make contact with the ball on the lower right/left side of the ball and if kicked hard enough and get lift on the ball, it will slightly spin right, thus making it curve from right to left or left to right

In a match between Brazil and France in 1997, a young player named Roberto Carlos made soccer's most interesting phenomenon through a free kick.

He bent a ball at an angle such that the ball circumvented the four-man "wall" that was blocking him from making a straight shot. Helps explain how Roberto Carlos was able to curve the ball

States that the spinning ball grabs the air and pulls it along the longer path and on one side of the object, the whirlpool’s motion will be only slightly affected and the velocity will be slower because of the shorter path it will take

The motion of the whirlpool on the other side however will be greatly affected by the Magnus Effect, thus it will follow a much longer path and have a greater velocity creating a force perpendicular to the line of motion

Said by some to be a demonstration of Bernoulli's Principle but it is actually different due to the fact that it takes into account the viscosity of the air. Dimensions

Soccer Ball:

Circumference is 27 in

14 to 16 oz

Soccer Field:

The length is from 100 to 130 yards

The width is from 50 to 100 yards

Soccer Goal:

24 ft x 8 ft When a penalty kick is taken it is in favor of the kicker (penalty spot is 12 yards away from goal), but the goalie can change the probability towards him with a couple of different strategies: he can change his posture (make himself look bigger), look at the kicker’s movement which may help determine which side the kicker will kick, and quick reflexes

The kicker’s 75% chance of scoring the penalty kick can then lower to a 45% chance Changing the Rules Number of Players

No Offsides

Changing the Size of the Field

Different Size of the Ball

Different Kickoff Position Bernoulli's Principle Bernoulli's Principle states that as the speed of a moving fluid (liquid or gas) increases, the pressure within the fluid decreases. Data Ranier John Distance Time 10 ft 20 ft 30 ft 0.23s, 0.2s, 0.3s 0.5s, 0.6s, 0.6s 0.5s, 0.4s, 0.45s 0.9s, 1.0s, 1.2s 0.6s, 0.63s, 0.67s 1.4s, 1.3s, 1.37s Averages After averaging the times and using distance over time to calculate the speed, Ranier's average ball kick speed is 35 mph, while John's average ball kick speed is 15 mph

There is a difference between a soccer player's ball kick speed and a non-soccer player's ball kick speed. Results By getting rid of offsides defense would have to permanently stay back to prevent goals from "cherry-pickers"

By changing the number of players on the field:

Less players would make the game slower because there will be more space for the fewer number of players to run making them tired quicker

More players would mean that they will be compacted onto the field, less running for them, too crowded on the field which may make it less entertaining

The larger the soccer field, the more space there is for the players, requiring more running for the players and making it more challenging to score

The smaller the field, the more compacted the players will be, but the players will have less space to move about. Results Continued Having a smaller soccer ball forces you to make quicker adjustments with your feet, ball would not travel as far, game would be slower, opponents would have a harder time taking the ball away, but you would also have a harder time controlling the ball

Having a bigger soccer ball balls takes much more effort to move the ball to where you want it to go, may also be easier for opponents to take the ball away from you, ball will travel farther when kicked, easier time in controlling the ball

If the ball started in the middle of the circle, and both teams had to stay in their boxes then when referee blew the whistle, everybody would run off towards the ball. This would affect the game because the players would have to exert more effort in controlling the ball for their team and will fatigue them faster Data for Soccer Simulation based on Proposed Modifications to Soccer Problems Encountered During the Experiment/Research Sources/Bibliography When the number of players was reduced from 11 to 5:

The average number of goals scored: 1.2

When the number of players on the field was increased from 11 to 17:

The average number of goals scored: 6.8

When the size of the field was widened:

The average number of goals scored: 1.8

When the size of the field was reduced:

The average number of goals scored: 4.6 Some of the ideas that we proposed to research and experiment on were not possible for us to do, due to limited resources and time. http://lc3.littlechute.k12.wi.us/High%20School/Academics/Science%20Department/Janssen/Physics%20Of%20Project/projects/soccerandrewphil/bending.html

http://www.infoplease.com/encyclopedia/science/bernoulli-principle.html

http://www.grc.nasa.gov/WWW/k-12/airplane/straj.html

http://www.unc.edu/~ncrani/aerodynamics1.html

http://tuhsphysics.ttsd.k12.or.us/Research/IB10/BrucFlorShan/index.htm (D) - distance ball bends

(R) - ball's radius

(p) - density of air

(w) - ball's angular velocity

(v) - ball's velocity through the air

(m) - mass

(x) - distance traveled by the ball in the direction it was kicked

Full transcriptBy: John Junio & Ranier Lopez Mathematics in Soccer Equations in Soccer Rules of Soccer "The Magnus Effect" Specifications How Does One "Bend it Like Beckham?" Probabilities Soccer is a sport that uses a variety of mathematical and scientific principles

These principles include geometry, calculus, physics, and probability

Estimation also plays a large role in the sport There are many equations that explain phenomena in soccer that to ordinary people may seem impossible

Speed = Distance/Time

Newton’s Second Law (f = ma)

Friction (F = µFa)

Bernoulli's Principle/Magnus Effect Offsides

the attacking player is in the opponent's half of the field and receives the ball behind the last defender (not including the goalie)

the attacking player has to be involved in the play, either by playing the ball or interfering with a defender or goalkeeper

Penalty Kick

when one attacker is deliberately tackled by a defender in the penalty area; penalty kick is given to attacking team

Kick off

in the center of the circle at the beginning of the game and after every goal scored If you kick the ball with the inside or outside of your foot and make contact with the ball on the lower right/left side of the ball and if kicked hard enough and get lift on the ball, it will slightly spin right, thus making it curve from right to left or left to right

In a match between Brazil and France in 1997, a young player named Roberto Carlos made soccer's most interesting phenomenon through a free kick.

He bent a ball at an angle such that the ball circumvented the four-man "wall" that was blocking him from making a straight shot. Helps explain how Roberto Carlos was able to curve the ball

States that the spinning ball grabs the air and pulls it along the longer path and on one side of the object, the whirlpool’s motion will be only slightly affected and the velocity will be slower because of the shorter path it will take

The motion of the whirlpool on the other side however will be greatly affected by the Magnus Effect, thus it will follow a much longer path and have a greater velocity creating a force perpendicular to the line of motion

Said by some to be a demonstration of Bernoulli's Principle but it is actually different due to the fact that it takes into account the viscosity of the air. Dimensions

Soccer Ball:

Circumference is 27 in

14 to 16 oz

Soccer Field:

The length is from 100 to 130 yards

The width is from 50 to 100 yards

Soccer Goal:

24 ft x 8 ft When a penalty kick is taken it is in favor of the kicker (penalty spot is 12 yards away from goal), but the goalie can change the probability towards him with a couple of different strategies: he can change his posture (make himself look bigger), look at the kicker’s movement which may help determine which side the kicker will kick, and quick reflexes

The kicker’s 75% chance of scoring the penalty kick can then lower to a 45% chance Changing the Rules Number of Players

No Offsides

Changing the Size of the Field

Different Size of the Ball

Different Kickoff Position Bernoulli's Principle Bernoulli's Principle states that as the speed of a moving fluid (liquid or gas) increases, the pressure within the fluid decreases. Data Ranier John Distance Time 10 ft 20 ft 30 ft 0.23s, 0.2s, 0.3s 0.5s, 0.6s, 0.6s 0.5s, 0.4s, 0.45s 0.9s, 1.0s, 1.2s 0.6s, 0.63s, 0.67s 1.4s, 1.3s, 1.37s Averages After averaging the times and using distance over time to calculate the speed, Ranier's average ball kick speed is 35 mph, while John's average ball kick speed is 15 mph

There is a difference between a soccer player's ball kick speed and a non-soccer player's ball kick speed. Results By getting rid of offsides defense would have to permanently stay back to prevent goals from "cherry-pickers"

By changing the number of players on the field:

Less players would make the game slower because there will be more space for the fewer number of players to run making them tired quicker

More players would mean that they will be compacted onto the field, less running for them, too crowded on the field which may make it less entertaining

The larger the soccer field, the more space there is for the players, requiring more running for the players and making it more challenging to score

The smaller the field, the more compacted the players will be, but the players will have less space to move about. Results Continued Having a smaller soccer ball forces you to make quicker adjustments with your feet, ball would not travel as far, game would be slower, opponents would have a harder time taking the ball away, but you would also have a harder time controlling the ball

Having a bigger soccer ball balls takes much more effort to move the ball to where you want it to go, may also be easier for opponents to take the ball away from you, ball will travel farther when kicked, easier time in controlling the ball

If the ball started in the middle of the circle, and both teams had to stay in their boxes then when referee blew the whistle, everybody would run off towards the ball. This would affect the game because the players would have to exert more effort in controlling the ball for their team and will fatigue them faster Data for Soccer Simulation based on Proposed Modifications to Soccer Problems Encountered During the Experiment/Research Sources/Bibliography When the number of players was reduced from 11 to 5:

The average number of goals scored: 1.2

When the number of players on the field was increased from 11 to 17:

The average number of goals scored: 6.8

When the size of the field was widened:

The average number of goals scored: 1.8

When the size of the field was reduced:

The average number of goals scored: 4.6 Some of the ideas that we proposed to research and experiment on were not possible for us to do, due to limited resources and time. http://lc3.littlechute.k12.wi.us/High%20School/Academics/Science%20Department/Janssen/Physics%20Of%20Project/projects/soccerandrewphil/bending.html

http://www.infoplease.com/encyclopedia/science/bernoulli-principle.html

http://www.grc.nasa.gov/WWW/k-12/airplane/straj.html

http://www.unc.edu/~ncrani/aerodynamics1.html

http://tuhsphysics.ttsd.k12.or.us/Research/IB10/BrucFlorShan/index.htm (D) - distance ball bends

(R) - ball's radius

(p) - density of air

(w) - ball's angular velocity

(v) - ball's velocity through the air

(m) - mass

(x) - distance traveled by the ball in the direction it was kicked