History and brief overview of soccer ball sizes

A soccer ball’s size was initially the exact shape and size of the pig’s bladder it was made from! Moreover, until Charles Goodyear patented vulcanized rubber in 1836 this remained the case. The first ‘rubber’ football made in 1855, followed by the first ‘inflatable rubber bladder’ in 1862. These being roughly equivalent to a modern day Size 4 or 5.

However, as history naturally advanced, the ‘beautiful game’ became more popular and more and more people – from children to women wanted to play the game, so the originally inspired Soccer ball changed and different sizes of Soccer ball emerged. In this article, I will take a look at the standard size(s) of football now in existence and the typical demographics that they are used by. 

Soccer Ball Size 1

• Size: 18 – 20 inches (circumference)
• Age recommendation: 3 and under.

The smallest officially recognized Soccer ball size available to buy, this ball is ideal for male or females in their infancy. Either just for kids’ fun, as a great way to start to develop eye and foot coordination, or as a way to check whether you might have the next Lionel Messi or Mia Hamm as part of your family! This size of football is an ideal size for an early introduction into the game of Soccer. 

Other notable uses of this size of ball are that the more experienced player can use it to perfect their ‘touch’, technique and overall ball control as a smaller sized ball is much more difficult to control. (Of course if you’re a budding Diego Maradona, feel free to try using a tennis ball or even a golf ball!) 

Final fact about a Soccer ball size one is it is often sold by Soccer club souvenir shops with their logo and team crest on them so they can also make a great birthday treat.

Soccer Ball Size 2

• Size: 20 – 22 inches (circumference)
• Age recommendation: 3 – 5 years old.

A small step up from the Size one ball, the Size 2 ball is also used for introducing would be young players into the game. It can nevertheless also be used as a practice ‘skills’ ball and indeed is better in this respect as it has a reasonable weight of between 250 to 280 grams. So it is no longer a toy. Though clubs and companies do use this size of ball both for souvenirs and or for promotional marketing.

Soccer Ball Size 3

• Size: 22 – 24 inches (circumference).
• Age recommendation: 5 – 8 years old.
• Weight: 300 – 320 grams.

The Size 3 Soccer ball is the smallest ball used in ‘proper’ league matches. Indeed, it is the size of ball from which many children and youth teams (Under 6 onwards) start to play the game officially.

Slightly bigger and heavier than a Size 2 ball, this size of ball is seen as a ‘bellwether ball’ for testing how well a young player may be able to transition to the larger Size 4 and Size 5 balls which are used at professional levels. 

Moreover, it should be noted that though this ball is not the official size for a ‘futsal’ ball and match, it can be used in such and/or on professional training pitches.

Fun Trivia – ‘cocky’ young players at world renowned clubs have often been ‘brought down to earth’ when their Coach or Managers have had enough of their arrogance and ‘show-boating’, how? The ‘cocky’ player is simply thrown one of these balls (which virtually all clubs have lying around) and told to play with that for the rest of the day!

Soccer Ball Size 4

• Size: 25 – 26 inches (circumference).
• Age recommendation: 8 – 11 years old.
• Weight: 350 – 390 grams.

A Size 4 Soccer ball is designed to ready players for the regulation Size 5 Soccer ball which is used in professional matches. Younger players, who do not quite have the power they will have in their legs when they are older, will find it easier to control and move during practices and matches.

Moreover, due to a lighter weight than the Size 5, this ball will give the older youths the option to really start and develop the techniques required for taking a proper ‘set piece’ such as a ‘corner’ or ‘free kick’. This Size 4 ball gives players a few years to adjust as they get older, stronger, and more skilled.

Note. This is also the officially recognized sized ball for any ‘futsal’ tournaments. Futsal now becoming much more popular in itself and also as a way to help players make the step up to a full ‘elevens’ side for it hones skills and encourages tight ball control.

Soccer Ball Size 5

• Size: 27 – 28 inches (circumference).
• Age recommendation: 12 years and older.
• Weight: 300 – 320 grams.

Finally, we come to the common Soccer ball size which is used universally across the world largely from the age of 12 up. From professional leagues and tournaments such as the MLS, EPL, La Liga, La Ligue, and Serie ‘A’ to a whole host of International tournaments including the World Cup, this is the size of ball mandated for use. 

Weighing in at between 410 – 450 grams, this ball is not recommended for younger age groups (though in England you are given a ball this size for your second or third birthday present – boy or girl!) since it is considerably heavier than the balls mentioned. The reason is primarily dual: 

• It is far harder to control due to its weight and size.
• It can cause injuries, as such younger players’ muscles may not be developed enough for the weight and size of the ball.

When used in any ‘official’ matches, Size 5 balls should have the “FIFA Approved” or “FIFA Inspected” stamp. This means they have been tested and certified as to their official size and weight and are in accordance with the laws of the game.

Summary

The above article gives a rough idea of soccer ball sizes, what type of ball should be used at what age and level of play. However, this is by no means ‘set in stone’ – an old soccer adage applies here; ‘if your good enough, you’re old enough’. Wayne Rooney (previously of DC United) made his English Premier League debut at age 16 and I bet he was kicking a Size 5 around quite a few years before it was recommended!

Ball Testing Requirements:

• Spherical
• Made of leather or other suitable material that is weather resistant
• Of a circumference of not more than 70 cm (28 ins) and not less than 68 cm (27 ins)
• Not more than 453 g (16 oz) in weight and not less than 396 g (14 oz) at the start of the match
• The ball shall be inflated to manufacturer’s recommended pressure

For additional information on NFHS, you can visit their web site by clicking here.

FIFA INSPECTED LOGO

The above logo’s are printed on all soccer balls that are either FIFA Approved or FIFA INSPECTED. Only the highest of quality balls can pass the testing requirements.

FIFA Denominations Programme

The testing procedures and designations offer many benefits to those who buy soccer balls (footballs) including guaranteed quality, value for money and better playing performance. Since January 1, 1996 only those outdoor footballs which have been tested and meet the demanding quality criteria, bearing either of the official markings ‘FIFA Approved‘, ‘FIFA Inspected‘ or ‘International Matchball Standard (IMS),’ are allowed to be used in FIFA (Fédération Internationale de Football Association www.fifa.com ) competition matches and competition matches under the auspices of the six continental Confederations.

As of January 1, 2000 the quality testing and certification has also become compulsory for indoor footballs used for international matches under the auspices of FIFA and the Confederations.

FIFA has set out to ensure that the balls used in top matches meet the most exacting standards. It has meant a general upgrading of standards of footballs (soccer balls) throughout the world. 

Testing procedures for the balls submitted for these designations are designed to simulate match conditions. Manufacturers have to submit seven balls if they are applying for “FIFA Inspected” status, and ten samples if they seek the “FIFA Approved” label. All these are put through their paces at EMPA, the Swiss Federal Laboratories for Materials Testing and Research in St.Gallen.

There is another qualification level, too, less demanding than the others. This is the designation “International Matchball Standard”, and for this the applicant footballs (soccer balls) can be sent to any of seven European test institutes which have been selected by FIFA to test and certify the balls for this category, which is free of any royalty fees.

There are a total of seven tests. All footballs are submitted for the first six and only potential “FIFA Approved” candidates for the seventh test, which is a shooting test for shape and size retention, including change of pressure.

However, the criteria for “FIFA Approved” footballs are higher throughout. For example, 25% loss of pressure is acceptable for a “FIFA Inspected” applicant, but only 20% for a “FIFA Approved” ball.

Video:

Testing The Euro Ball

Testing:

• Circumference: The first test – for circumference – requires the first three footballs to be conditioned for at least 24 hours. They are then inflated to a defined pressure and the diameter of the ball is measured in ten exactly defined points. The test is designed to ensure a well-balanced response in play.
• Sphericity: The second test is for sphericity, which ensures the ball’s in-flight stability. The apparatus used is the same as that used for determining the circumference. The conditioned balls are inflated to a test pressure of 1.0 bar and the diameter of the ball is measured at the middle of the 16 panels, with a high degree of accuracy. The difference between the highest and lowest diameter is determined as a percentage of the mean diameter. The mean difference in the highest and lowest diameter of the three footballs in recorded in the test report.

• Rebound: This is important too, to make sure that the ball bounces in a predictable manner, vital in top class matches. The football is dropped, in guided free fall and with a defined velocity, onto a steel surface. With the help of a video camera, the height of rebound at the lower side of the ball can be determined.
• Water absorption: It is important that a football does not become too heavy when wet. The conditioned footballs are placed in a receptacle filled with 2 cm of water. After being compressed a number of times, with a pneumatic position to simulate playing conditions, the ball is removed, wiped dry and reweighed. Its increase in weight is expressed as a percent of the original weight of the ball, defining precisely the amount of water that has been absorbed.
• Weight: Weight is vital, because it ensures a consistent playing response when the ball is struck. Football samples are inflated and weighed in a standard atmosphere, with a wind protected electronic balance. The mean weight as well as the single values of the three fallouts are recorded in the report.
• Loss of Pressure: The football should not lose pressure over time, thereby remaining playable. The balls are inflated to a defined pressure, then left in a standard atmosphere for a certain period of time, after which the pressure is measured again.

• Shape and Size Retention (“FIFA Approved” only): This test is designed to ensure that the footballs last, even in the most challenging situations. The footballs are inflated to a defined pressure. Two rotating cylinders accelerate the balls to a specific velocity, so that they hit a steel panel at a consistent speed and angle. The footballs are examined after 2000 shots and the increase in circumference and deviations on sphericity are measured. The testing procedures and designations offer many benefits to those who buy footballs including guaranteed quality, value for money and better playing performance.

Detailed FIFA test requirements  

Referees of FIFA and Confederation matches are among the beneficiaries. They simply have to check that the ball carries one of the three marks and that the pressure is correct, rather than having to check weight, circumference and other details before matches.

The testing criteria are indeed tough, but they have been set by the industry itself. Only the best products pass the test, which means that the new standards are worthwhile. Licensees include most of the major leading brands and also manufacturers from India, China, Thailand and Japan, showing that the value put on the FIFA mark is as universal as football itself.

What Players think of the Modern Ball
We look at the effect the Programme has had on the game itself. Has it improved skill levels? Has the job of match officials been made any easier – and have there been any medical benefits or all-round improvements? 10-Dec-1998

Information and articles graciously provided by FIFA. www.fifa.com

Yokohama/Herzogenaurach, December 13th, 2007 – Today, adidas and Cairos Technologies presented the new Goal Line Technology and the adidas intelligent football tested at the FIFA Club World Cup in Japan from December 7 through 16, 2007.  The official match ball of the tournament, adidas Teamgeist II, features a new intelligent technology designed to assist the referee’s decision in determining when and if the ball has crossed the goal line, making it the most accurate football ever produced. 

“The purpose of the adidas intelligent ball and Goal Line Technology is to provide greater transparency during a match and to assist the referee in making quick decisions that can impact the outcome and quality of the game” said Hans-Peter Nuernberg, Senior Development Engineer, adidas Innovation Team.  “We expect the system to perform very well during the FIFA Club World Cup in Japan and we will continue to refine the system so that it is 100% accurate.” 

The intelligent technology implemented in the Teamgeist II uses a magnetic field to provide real-time feedback to a central computer, which tracks the location of the ball on the field and sends the data directly to the referee.  By using a magnetic field and more stabilized and robust components within the ball, the new system is more precise and is not influenced by in-game factors, adverse weather or nearby technical systems.   

“With the complexities and precision needed for Goal Line Technology, it is imperative that the system is tested in a variety of competitive in-game situations,” said Christian Holzer, COO of Cairos technologies.  “The opportunity to test the new technology during such a competitive tournament will supply us with the valuable feedback needed in order to continue refining the system.” 

Since 2003, adidas and Cairos in cooperation with FIFA, have developed the Goal Line Technology, which was first publicly tested in 2005 during the U-17 FIFA World Cup in Peru.  The first system used radio transmissions to correspond with a central computer and a microchip suspended in the ball to determine its location on the field.  The new Goal Line Technology and adidas intelligent ball have been redeveloped since 2005 to address the critical situations in which better accuracy is needed.  

Following the testing during the FIFA Club World Cup in Japan, the results will be evaluated and next steps will be determined by Cairos technologies and adidas as to when the system will be ready to test again publicly.  The new system currently meets all International Football Association Board (IFAB) requirements and the ball has been approved by FIFA for competitive international play.  adidas’ experience in football manufacturing is unsurpassed anywhere in the world and leads the industry in the production of the most innovative footballs since 1963.  The Goal Line technology is a testament to the ongoing commitment adidas has to innovation and the development of new technologies in football and across all sports categories. 

Teamgeist 2

Wawa Aba – African Cup 2008 

Teamgeist 2 AFA

Teamgeist 2 Magnus Moenia Beijing Olympics 2008 –

In 1855, Charles Goodyear designed and built the first vulcanized rubber soccer balls (footballs), which is the world’s oldest football.  The following picture shows the Charles Goodyear ball that was on display at the National Soccer Hall of Fame which was located in Oneonta, NY, USA.

Oldest Soccer Ball (Football) Facts:

• Designed and Built in 1855 by Charles Goodyear
• Made of vulcanized rubber panels glued at the seams  
• Panels are shaped similar to today’s basketball
• The ball was used for a game between the Oneida Football Club, the first organized team in the US, and a team of players from Boston Latin and Boston English Schools. The Oneida club was formed by Gerritt Smith-Miller and came from the students at Dixwell Latin School, where he was a student. Dixwell Latin merged with other schools over time and is a forbear to Noble & Greenough, an independent school located in Dedham, MA. The game was played on Boston Common, where there is a monument to commemorate the game, on November 7, 1863. The ball became the trophy from that game as shown in the picture above.
• The ball was donated by the family of Gerritt Smith-Miller to The Society For the Preservation of New England Antiquities in 1925. 
• It is interesting to note that when James Naismith developed the game of basketball, the first game was played with – a soccer ball! 

Information and pictures obtained from the  National Soccer Hall of Fame which was located in Oneonta, NY, USA.  

What is the oldest football?

In 1855, Charles Goodyear designed and built the first vulcanized rubber soccer balls (footballs), which is the world’s oldest football.

FIFA (Fédération Internationale de Football Association) Laws of the Game

Law 2 – The Ball

Qualities and Measurements

The ball is:

• spherical
• Made of leather or other suitable material
• Of a circumference of not more than 70 cm (28 ins) and not less than 68 cm (27 ins)
• not more than 450 g (16 oz) in weight and not less than 410 g (14 oz) at the start of the match
• of a pressure equal to 0.6 – 1.1 atmosphere (600 – 1100 g/cm 2 ) at sea level (8.5 lbs/sq in to 15.6 lbs/sq in)

Replacement of a Defective Ball

If the ball bursts or becomes defective during the course of a match:

• the match is stopped
• the match is restarted by dropping the replacement ball at the place where the first ball became defective
• If the ball bursts or becomes defective whilst not in play at a kick-off, goal kick, corner kick, free kick, penalty kick or throw-in the match is restarted accordingly

The ball may not be changed during the match without the authority of the referee.

Decision 1

In competition matches, only footballs which meet the minimum technical requirements stipulated in Law 2 are permitted for use.

In FIFA competition matches, and in competition matches organized under the auspices of the confederations, acceptance of a football for use is conditional upon the football bearing one of the following three designations:

• The official “FIFA APPROVED” logo, 
• Or the official “FIFA INSPECTED” logo, 
• Or the reference “INTERNATIONAL MATCH-BALL STANDARD”

Such a designation on a football indicates that it has been tested officially and found to be in compliance with specific technical requirements, different for each category and additional to the minimum specifications stipulated in Law 2. The list of the additional requirements specific to each of the respective categories must be approved by the International F.A. Board. The institutes conducting the tests are subject to the approval of FIFA. National association competitions may require the use of balls bearing any one of these three designations.

In all other matches the ball used must satisfy the requirements of Law 2.

Decision 2

In FIFA competition matches and in competition matches organized under the auspices of the confederations and national associations, no kind of commercial advertising on the ball is permitted, except for the emblem of the competition, the competition organizer and the authorized trademark of the manufacturer. The competition regulations may restrict the size and number of such markings.

For additional information on Football or Soccer Ball Approvals

FIFA has the following Futsal International competition ball requirements:

The ball is: 

• Spherical 
• Made of leather or other suitable material
• Of a circumference of not less than 62 cm and not more than 64 cm 
• Not less than 400 grams nor more than 440 grams in weight at the start of the match 
• Of a pressure equal to 0.4-0.6 atmosphere (400-600g/cm²) at sea level

©2002 FIFA

For the latest laws and additional information on FIFA, you can visit their web site by clicking here.

NFHS , National Federation of State High School Associations Ball Rules

The ball is:

• Spherical
• Made of leather or other suitable material that is weather resistant
• Of a circumference of not more than 70 cm (28 ins) and not less than 68 cm (27 ins)
• not more than 453 g (16 oz) in weight and not less than 396 g (14 oz) at the start of the match
• The ball shall be inflated to manufacturer’s recommended pressure

For latest laws and additional information on NFHS, you can visit their web site by clicking here.

There are many types of soccer balls, footballs or Futbols.  Soccer balls can be categorized by the following types:

Professional Match Soccer Balls

• Developed with top professional clubs to maximize players natural abilities and skills. 
• Approved for use at the highest professional and international levels.
• Pure performance, exact specifications, great accuracy, speed and control.
• Designed for all natural and artificial turf surfaces and all climates.

These soccer balls have been developed for top level international professional matches. They usually have some type of organizational approval such as the FIFA (Fédération Internationale de Football Association) approval logo imprinted on the ball. For information on the ball approvals including ball testing requirements, click here.  At least five layers are used in the construction of the ball and they use the best materials.  For more information on ball materials and construction, go to the Ball Construction Page.  

Professional match balls are the most expensive type of ball since they use the best materials and adhere to strict design and testing parameters. Ball trajectory, shape, balance, bounce, water absorption and velocity are all strictly controlled.

Match Soccer Balls

• High performance range of balls for all playing surfaces. 
• Designed to suit all levels of play and all age groups. 
• Guaranteed to conform to official size, weight, and shape regulations.
• Materials developed for their performance and reliability

Match balls are designed for use in soccer matches. They cost more than practice balls and less than the internationally approved soccer balls (that makes sense). Some type of association approval  such as the National Federation of State High School Associations (NFHS) authentication program, “FIFA Approved” or “FIFA Inspected” is usually imprinted on a match ball. Between four and five lining layers are used in the construction of the ball.

Recreational /Practice/Training /Camp Soccer Balls

• Tough and highly durable balls for extended use.
• Specific materials for use on all playing surfaces.
• Used by coaches for all age groups and all standards

Usually constructed with four or less layers and use a lower quality outer cover such as PVC.  Many practice or camp balls made out of molded material (not stitched together but molded together panels) have been designed to withstand rough surfaces such as concrete or asphalt. 

Practice or camp balls are the least expensive balls when compared with match type soccer balls.

Promotional Balls

These balls are usually made to promote a name brand, organization or event.  Some promotional soccer balls are small in size (size one or two) and not intended for practice or match use.

Indoor Soccer Balls

Many indoor soccer balls consist of a felt type outer covering that is similar to the material used on tennis balls. They have the same size configurations as the outdoor soccer balls.

Futsal Soccer Balls

The main difference between a Futsal ball and a typical soccer ball, is that the bladder is filled with foam. That makes the ball heavier and have less bounce for use on the hard playing surface.  

For information on the FIFA ball laws, click here

Questions about buying Soccer Balls

The following questions are typically asked by people that want to buy soccer balls: What size soccer ball should I buy? 

The first step in purchasing soccer balls is determining the proper size(s) to buy. Many soccer leagues have different size requirements, so be sure to check with your coach or organization to find out which size ball to buy. Soccer balls for match use come in three different sizes which range from size 3 to size 5. For more information on soccer ball sizes

General Soccer Ball Questions:

The following article researching soccer ball physics was first published in Physics World magazine, June 1998 pp25–27.

The Soccer Ball Physics

Bill Shankly, the former manager of Liverpool football club, once said: “Football is not about life or death. It is more important than that.” This month at the World Cup in France, millions of football fans will get that same feeling for a few, short weeks. Then the event will be over, and all that will remain will be a few repeats on television and the endless speculation about what might have happened.

It is this aspect of football that its fans love, and others hate. What if that penalty had gone in? What if the player hadn’t been sent off? What if that free kick hadn’t bent around the wall and gone in for a goal? 

Many fans will remember the free kick taken by the Brazilian Roberto Carlos in a tournament in France last summer. The ball was placed about 30 m from his opponents’ goal and slightly to the right. Carlos hit the ball so far to the right that it initially cleared the wall of defenders by at least a meter and made a ball-boy, who stood meters from the goal, duck his head. Then, almost magically, the ball curved to the left and entered the top right-hand corner of the goal – to the amazement of players, the goalkeeper and the media alike.

Apparently, Carlos practiced this kick all the time on the training ground. He intuitively knew how to curve the ball by hitting it at a particular velocity and with a particular spin. He probably did not, however, know the physics behind it all.

Aerodynamics of sports balls

The first explanation of the lateral deflection of a spinning object was credited by Lord Rayleigh to work done by the German physicist Gustav Magnus in 1852. Magnus had actually been trying to determine why spinning shells and bullets deflect to one side, but his explanation applies equally well to balls. Indeed, the fundamental mechanism of a curving ball in football is almost the same as in other sports such as baseball, golf, cricket and tennis.

Spinning Ball

Consider a ball that is spinning about an axis perpendicular to the flow of air across it (see left). The air travels faster relative to the center of the ball where the periphery of the ball is moving in the same direction as the airflow. This reduces the pressure, according to Bernouilli’s principle.

The opposite effect happens on the other side of the ball, where the air travels slower relative to the center of the ball. There is therefore an imbalance in the forces and the ball deflects – or, as Sir J J Thomson put it in 1910, “the ball follows its nose”. This lateral deflection of a ball in flight is generally known as the “Magnus effect”.

The forces on a spinning ball that is flying through the air are generally divided into two types: a lift force and a drag force. The lift force is the upwards or sidewards force that is responsible for the Magnus effect. The drag force acts in the opposite direction to the path of the ball.

Let us calculate the forces at work in a well taken free kick. Assuming that the velocity of the ball is 25-30 ms^-1 (about 70 mph) and that the spin is about 8-10 revolutions per second, then the lift force turns out to be about 3.5 N.

The regulations state that a professional football must have a mass of 410-450 g, which means that it accelerates by about 8 ms^-2. And since the ball would be in flight for 1 s over its 30 m trajectory, the lift force could make the ball deviate by as much as 4 m from its normal straight-line course. Enough to trouble any goalkeeper!

The drag force, F_D, on a ball increases with the square of the velocity, v, assuming that the density, r, of the ball and its cross-sectional area, A, remain unchanged: F_D = C_DrAv²/2. It appears, however, that the “drag coefficient”, C_D, also depends on the velocity of the ball.

For example, if we plot the drag coefficient against Reynold’s number – a non-dimensional parameter equal to rv D /µ, where D is the diameter of the ball and µ is the kinematic viscosity of the air – we find that the drag coefficient drops suddenly when the airflow at the surface of the ball changes from being smooth and laminar to being turbulent (see right).

When the airflow is laminar and the drag coefficient is high, the boundary layer of air on the surface of the ball “separates” relatively early as it flows over the ball, producing vortices in its wake. However, when the airflow is turbulent, the boundary layer sticks to the ball for longer. This produces late separation and a small drag.

The Reynold’s number at which the drag coefficient drops therefore depends on the surface roughness of the ball. For example, golf balls, which are heavily dimpled, have quite a high surface roughness and the drag coefficient drops at a relatively low Reynold’s number (~ 2 x 10⁴). A football, however, is smoother than a golf ball and the critical transition is reached at a much higher Reynold’s number (~ 4 x 10⁵).

Drag vs Speed

The upshot of all of this is that a slow-moving football experiences a relatively high retarding force. But if you can hit the ball fast enough so that the airflow over it is turbulent, the ball experiences a small retarding force (see right). A fast-moving football is therefore double trouble for a goalkeeper hoping to make a save – not only is the ball moving at high speed, it also does not slow down as much as might be expected. Perhaps the best goalkeepers intuitively understand more soccer ball physics than they realize.

In 1976 Peter Bearman and colleagues from Imperial College, London, carried out a classic series of experiments on golf balls. They found that increasing the spin on a ball produced a higher lift coefficient and hence a bigger Magnus force. However, increasing the velocity at a given spin reduced the lift coefficient.

What this means for a football is that a slow-moving ball with a lot of spin will have a larger sideways force than a fast-moving ball with the same spin. So as a ball slows down at the end of its trajectory, the curve becomes more pronounced.

Roberto Carlos revisited

How does all of this explain the free kick taken by Roberto Carlos? Although we cannot be entirely sure, the following is probably a fair explanation of what went on.

Carlos kicked the ball with the outside of his left foot to make it spin anticlockwise as he looked down onto it. Conditions were dry, so the amount of spin he gave the ball was high, perhaps over 10 revolutions per second. Kicking it with the outside of his foot allowed him to hit the ball hard, at probably over 30 ms^-1 (70 mph).

The flow of air over the surface of the ball was turbulent, which gave the ball a relatively low amount of drag. Some way into its path – perhaps around the 10 m mark (or at about the position of the wall of defenders) – the ball’s velocity dropped such that it entered the laminar flow regime.

This substantially increased the drag on the ball, which made it slow down even more. This enabled the sideways Magnus force, which was bending the ball towards the goal, to come even more into effect. Assuming that the amount of spin had not decayed too much, then the drag coefficient increased.

This introduced an even larger sideways force and caused the ball to bend further. Finally, as the ball slowed, the bend became more exaggerated still (possibly due to the increase in the lift coefficient) until it hit the back of the net – much to the delight of the physicists in the crowd.

Current research into football motion

There is more to football research than simply studying the motion of the ball in flight. Researchers are also interested in finding out how a footballer actually kicks a ball. For example, Stanley Plagenhof of the University of Massachusetts in the US has studied the kinematics of kicking – in other words, ignoring the forces involved. Other researchers, such as Elizabeth Roberts and co-workers at the University of Wisconsin, have done dynamic analyses of kicking, taking the forces involved into account.

These experimental approaches have produced some excellent results, although many challenges still remain. One of the most critical problems is the difficulty of measuring the physical motion of humans, partly because their movements are so unpredictable. However, recent advances in analyzing motion with computers have attracted much attention in sports science, and, with the help of new scientific methods, it is now possible to make reasonably accurate measurements of human motion.

For example, two of the authors (TA and TA) and a research team at Yamagata University in Japan have used a computational scientific approach coupled with the more conventional dynamical methods to simulate the way players kick a ball. These simulations have enabled the creation of “virtual” soccer players of various types – from beginners and young children to professionals – to play in virtual space and time on the computer.

Sports equipment manufacturers, such as the ASICS Corporation, who are sponsoring the Yamagata project, are also interested in the work. They hope to use the results to design safer and higher performance sports equipment that can be made faster and more economically than existing products.

How To Curve A Soccer Ball

The movement of players was followed using high-speed video at 4500 frames per second, and the impact of the foot on the ball was then studied with finite-element analysis. The initial experiments proved what most footballers know: if you strike the ball straight on with your instep so that the foot hits the ball in line with the ball’s center of gravity, then the ball shoots off in a straight line. However, if you kick the ball with the front of your foot and with the angle between your leg and foot at 90° (see left), it will curve in flight. In this case, the impact is off-center. This causes the applied force to act as a torque, which therefore gives the ball a spin.

The experimental results also showed that the spin picked up by the ball is closely related to the coefficient of friction between the foot and the ball, and to the offset distance of the foot from the ball’s center of gravity. A finite-element model of the impact of the foot on the ball, written with DYTRAN and PATRAN software from the MacNeal Schwendler Corporation, was used to numerically analyze these events. This study showed that an increase in the coefficient of friction between the ball and the foot caused the ball to acquire more spin. There was also more spin if the offset position was further from the center of gravity.

Two other interesting effects were observed. First, if the offset distance increased, then the foot touched the ball for a shorter time and over a smaller area, which caused both the spin and the velocity of the ball to decrease. There is therefore an optimum place to hit the ball if you want maximum spin: if you hit the ball too close or too far from the center of gravity, it will not acquire any spin at all.

The other interesting effect was that even if the coefficient of friction is zero, the ball still gains some spin if you kick it with an offset from its center of gravity . Although in this case there is no peripheral force parallel to the circumference of the ball (since the coefficient of friction is zero), the ball nevertheless deforms towards its center, which causes some force to act around the center of gravity. It is therefore possible to spin a football on a rainy day, although the spin will be much less than if conditions were dry.

Of course, the analysis has several limitations. The air outside the ball was ignored, and it was assumed that the air inside the ball behaved according to a compressive, viscous fluid-flow model. Ideally, the air both inside and outside the ball should be included, and the viscosities modeled using Navier-Stokes equations.

It was also assumed that the foot was homogeneous, when it is obvious that a real foot is much more complicated than this. Although it would be impossible to create a perfect model that took every factor into account, this model does include the most important features.

Looking to the future, two of us (TA and TA) also plan to investigate the effect of different types of footwear on the kicking of a ball. Meanwhile, ASICS is combining the Yamagata finite-element simulations with biomechanics, physiology and materials science to design new types of football boots. Ultimately, however, it is the footballer who makes the difference – and without ability, technology is worthless.

The final whistle

So what can we learn from Roberto Carlos? If you kick the ball hard enough for the airflow over the surface to become turbulent, then the drag force remains small and the ball will really fly. If you want the ball to curve, give it lots of spin by hitting it off-center. This is easier on a dry day than on a wet day, but can still be done regardless of conditions.

The ball will curve most when it slows down into the laminar flow regime, so you need to practice to make sure that this transition occurs in the right place – for example, just after the ball has passed a defensive wall. If conditions are wet, you can still get spin, but you would be better off drying the ball (and your boots).

Nearly 90 years ago J J Thomson gave a lecture at the Royal Institution in London on the dynamics of golf balls. He is quoted as saying the following: “If we could accept the explanations of the behavior of the ball given by many contributors to the very voluminous literature which has collected around the game…I should have to bring before you this evening a new dynamics, and announce that matter, when made up into [golf] balls obeys laws of an entirely different character from those governing its action when in any other conditions.”

In football, at least, we can be sure that things have moved on.

Further reading

https://physicsworld.com/a/the-physics-of-football/

C B Daish 1972 The Physics of Ball Games (The English University Press, London)

S J Haake (ed) 1996 The Engineering of Sport (A A Balkema, Rotterdam)

R D Mehta 1985 Aerodynamics of sports balls Ann. Rev. Fluid Mech. 17 151-189

Questions about Pressure and Soccer Balls