Projectile Motion in Punting
The Science of Punting
The art of punting is critical to any team's success in the game of American football. As any fan knows, the goal of the punter is to kick the ball as far as possible in order to maximize the opposing team's distance to their end zone. Some professional punters have been known to kick the ball up to 120 feet in the air at a speed of 90 miles per hour. In order to determine how such incredulous feats are obtained, one must look at the science that goes into the act of punting
Punting can be viewed as an example of projectile motion. As in mostly all projectile motion problems, the ball is directly affected by Earth's gravitational pull. As the ball soars through the air, gravity slowly pulls it back down to the ground, resulting in an arched path known as a parabola. Parabolas have been studied for thousands of years by renown physicists, such as Galileo Galilei, Isaac Newton, and Albert Einstein. They determined that to find the overall distance traveled by a projectile under influence of gravity, one can use the equation sin(2θ) X v²/g where v is the initial speed of the projectile, g is gravity, and θ is the angle from which the projectile begins its path.
Maximizing Punt Efficiency Using Projectile Motion
In the case of punting, this equation can be made simpler. Firstly, gravity will always remain at a constant acceleration of -9/8 m/s^2. Secondly, the v variable, velocity, will depend on how hard the punter kick the ball and usually can not be manipulated for strategic purposes. With this in mind, the most important variable a punter can use to his advantage would be θ in order to maximize the distance of his punt. From the equation above, it can be inferred that the distance the ball travels will be the greatest when sin(2θ) is maximized. The largest possible output value of sin θ is 1, which is at 90°. So when sin(2θ) = 90, sin(θ) = 45. Therefore, the optimal launch angle for a punter looking to achieve maximum distance would be 45°.
However, in the game of football, the punter may not necessarily want to kick the ball as far as possible. Instead, he may opt to obtain maximum height in order to give his teammates more time to get down the field and defend against the ensuing punt return. To determine this, one must look at the formula for peak height in a parabola, which is (sin(θ))² X v²/2g. As in the previous example, the key variable here is θ. Since the greatest output for sin(θ) is 1 with an input angle of 90°, the highest possible arch a punter could obtain is 90°. However, this would not be ideal, as the punter would not succeed in pushing the opposing team farther down the field. With this in mind, the average NFL punt angle is in the range of 55-60°. So when a punter desires to get the most hang time possible, he'll try to launch his punt around 70°.
Of course, other variables also play a role in the effectiveness of the punt. For example, the velocity is dependent on the punter's leg strength. To increase height, he will also want to increase velocity in order to keep the ball in the air longer before gravity pulls it back down. However, there is not much a punter can do to effect this other than kicking as hard as he can. The other variables, time and displacement, are dependent on the velocity and θ angle.
Another factor to keep in mind is air resistance. Air resistance is dependent on the density of the air. Lower density translates to lower air resistance. The density of the air also decreases with height. This means that in regions with high altitude, there will be less air resistance acting upon the ball, resulting in a higher kick. This gives teams who play in regions of high altitude, such as Denver and Arizona, an advantage when punting the ball.
Maximizing height also means maximizing the ball's time in the air. To determine how effective a punter is, one can look at the average hang time of his punts. Below is a table showing the top five average hang times in the 2014 NFL season.
In the video provided below, researches from the National Science Foundation use high speed cameras to study the projectile motion of former NFL player Craig Hentrich's punts.
Citations:
“How Should You Launch a Ball to Achieve the Greatest Distance?” Scientific American, Springer Nature, 9 Nov. 2010,
(www.scientificamerican.com/article/football-projectile-motion/)
McGuinness, Gordon. “Specialists Week - Punters.” Pro Football Focus, 22 July 2015, (www.profootballfocus.com/news/specialists-week-punters.)
“Science of NFL Football: Projectile Motion & Parabolas.” Science360, National Science Foundation,
The art of punting is critical to any team's success in the game of American football. As any fan knows, the goal of the punter is to kick the ball as far as possible in order to maximize the opposing team's distance to their end zone. Some professional punters have been known to kick the ball up to 120 feet in the air at a speed of 90 miles per hour. In order to determine how such incredulous feats are obtained, one must look at the science that goes into the act of punting
Punting can be viewed as an example of projectile motion. As in mostly all projectile motion problems, the ball is directly affected by Earth's gravitational pull. As the ball soars through the air, gravity slowly pulls it back down to the ground, resulting in an arched path known as a parabola. Parabolas have been studied for thousands of years by renown physicists, such as Galileo Galilei, Isaac Newton, and Albert Einstein. They determined that to find the overall distance traveled by a projectile under influence of gravity, one can use the equation sin(2θ) X v²/g where v is the initial speed of the projectile, g is gravity, and θ is the angle from which the projectile begins its path.
Maximizing Punt Efficiency Using Projectile Motion
In the case of punting, this equation can be made simpler. Firstly, gravity will always remain at a constant acceleration of -9/8 m/s^2. Secondly, the v variable, velocity, will depend on how hard the punter kick the ball and usually can not be manipulated for strategic purposes. With this in mind, the most important variable a punter can use to his advantage would be θ in order to maximize the distance of his punt. From the equation above, it can be inferred that the distance the ball travels will be the greatest when sin(2θ) is maximized. The largest possible output value of sin θ is 1, which is at 90°. So when sin(2θ) = 90, sin(θ) = 45. Therefore, the optimal launch angle for a punter looking to achieve maximum distance would be 45°.
However, in the game of football, the punter may not necessarily want to kick the ball as far as possible. Instead, he may opt to obtain maximum height in order to give his teammates more time to get down the field and defend against the ensuing punt return. To determine this, one must look at the formula for peak height in a parabola, which is (sin(θ))² X v²/2g. As in the previous example, the key variable here is θ. Since the greatest output for sin(θ) is 1 with an input angle of 90°, the highest possible arch a punter could obtain is 90°. However, this would not be ideal, as the punter would not succeed in pushing the opposing team farther down the field. With this in mind, the average NFL punt angle is in the range of 55-60°. So when a punter desires to get the most hang time possible, he'll try to launch his punt around 70°.
Of course, other variables also play a role in the effectiveness of the punt. For example, the velocity is dependent on the punter's leg strength. To increase height, he will also want to increase velocity in order to keep the ball in the air longer before gravity pulls it back down. However, there is not much a punter can do to effect this other than kicking as hard as he can. The other variables, time and displacement, are dependent on the velocity and θ angle.
Another factor to keep in mind is air resistance. Air resistance is dependent on the density of the air. Lower density translates to lower air resistance. The density of the air also decreases with height. This means that in regions with high altitude, there will be less air resistance acting upon the ball, resulting in a higher kick. This gives teams who play in regions of high altitude, such as Denver and Arizona, an advantage when punting the ball.
Maximizing height also means maximizing the ball's time in the air. To determine how effective a punter is, one can look at the average hang time of his punts. Below is a table showing the top five average hang times in the 2014 NFL season.
In the video provided below, researches from the National Science Foundation use high speed cameras to study the projectile motion of former NFL player Craig Hentrich's punts.
Citations:
“How Should You Launch a Ball to Achieve the Greatest Distance?” Scientific American, Springer Nature, 9 Nov. 2010,
(www.scientificamerican.com/article/football-projectile-motion/)
McGuinness, Gordon. “Specialists Week - Punters.” Pro Football Focus, 22 July 2015, (www.profootballfocus.com/news/specialists-week-punters.)
“Science of NFL Football: Projectile Motion & Parabolas.” Science360, National Science Foundation,
(science360.gov/obj/tkn-video/fc729ef0-22ee-4f61-bb2a-b6c07685fb02/science-nfl-football-projectile-motion-parabolas)
Desonie, Dana. “Pressure and Density of the Atmosphere.” CK-12, CK-12 Foundation, 29 Aug. 2016,
Desonie, Dana. “Pressure and Density of the Atmosphere.” CK-12, CK-12 Foundation, 29 Aug. 2016,
(www.ck12.org/earth-science/pressure-and-density/lesson/Pressure-and-Density-of-the-Atmosphere-MS-ES/)
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