The Physics of Football

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The Physics of Football
Stratton Matthews Professor Hopkins Physics 001
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Norman Einstein?

• In the 2004-2005 NFL season, head coach Bill
  Belichick accomplished a feat that many thought
  to be impossible in todays game. He led his New
  England Patriots to 3 Super Bowl wins in 4 years,
  making them the most current dynasty in history.
  
• After the most recent win, many critics were
  calling Bill a genius coach. Well, in the words
  of Joe Theismann, former Quarterback of the
  Washington Redskins,
• Nobody in football should be called a genius. A
  genius is a guy like Norman Einstein.

thanks Joe
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Physics In Football

• While Joe may not have been the sharpest tool in
  the shed, he was somewhat correct. The genius
  in football isnt the coach, but rather the
  concepts the coach teaches. The concepts that
  will be examined in this presentation are
• The Dimensions of a Pass
• The Force of a Tackle
• The Momentum of a Collision

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Passing a 2D technique(Wait for Clip to Play)
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Passing a 2D technique

• Like that pitch and catch in the last slide? Im
  sure the coach did too.
• While he may not have been thinking about it, the
  quarterback in the last slide was quickly
  calculating physics in his head. After he
  snapped the ball, he knew his throw had to be
  quickly delivered to his teammate across the
  field. Well, the basic principle behind his
  common-sense thinking involved physics.

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Passing a 2D technique

• The physics behind the quarterbacks thinking is
  called 2-Dimensional Motion. 2D motion in
  physics is pretty much breaking down the path of
  a projectile into two vectors.
• For example, assume the quarterbacks pass looked
  something like this (the red line represents the
  path of the ball)

2 Dimensional Motion would break down the path of
the ball into two separate motions. The first
motion would be horizontal (from one side of the
picture to the other), and the other motion would
be vertical (up and down on the picture).
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Passing a 2D technique

• A graphic of this break down would look something
  like this

Notice how the horizontal motion continues in the
same direction, while the vertical motion changes
halfway. Thats because the force exerted on the
football in the vertical direction has been
counteracted the entire time by the force of
gravity. Halfway across its path, the ball
experiences more force from gravity then it does
from the throw. Therefore, the ball begins to
fall downward.
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Passing a 2D technique

• All of the motion that the ball encounters can be
  calculated using simple formulas. A quarterback
  would use these formulas to determine
• How to reduce the time the ball spends in the air
• How to throw the ball as far as possible

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Passing a 2D technique

• How to reduce the time the ball spends in the air
• The formula used to determine the amount of time
  the ball spends in the air is t (2V /g),
  where t is total time in the air, V is the
  velocity in the vertical direction, and g is the
  acceleration due to gravity.
• Using this formula, a quarterback can determine
  that the best way to reduce the time the ball
  spends in the air, is to reduce the velocity he
  puts on the ball in the vertical direction. He
  can then conclude that he should exert most of
  his force in the horizontal direction if he wants
  the ball to reach its destination as quickly as
  possible.

y
y
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Passing a 2D technique

• How to throw the ball as far as possible
• To determine how to throw the ball as far as
  possible is a little complicated. The main
  formula used to determine how to throw the ball
  as far as possible is x V t, where x is
  the distance in the horizontal direction, V is
  the velocity in the horizontal direction, and t
  is the total time in the air.
• At first glance it seems as though distance is
  only dependant on the velocity in the horizontal
  direction. While a quarterbacks dream may be to
  only have to throw the ball horizontally to get
  it as far as possible as fast as possible, it is
  not reality.
• Recall the formula for the time the ball spends
  in the air t (2V /g). If we substitute that
  formula into the original formula for t, then
  we see that distance traveled is dependant on
  both the horizontal and vertical velocity.

x
x
y
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Passing a 2D technique

• So how do you throw the ball as far as possible?
• The answer lies in Trigonometry. The quarterback
  would need to throw the ball so that the maximum
  product of the velocity in the horizontal
  direction and the velocity in the vertical
  direction would be achieved.
• The easiest way to explain this is to say that
  when the angle of release for the football
  increases, its velocity in the vertical direction
  increases, while the velocity in the horizontal
  direction decreases. Likewise, when the angle of
  release decreases, the balls velocity in the
  horizontal direction increases, while the
  velocity in the vertical direction decreases.
• Therefore, to get the largest product of both
  velocities, would be to have the angle of release
  right in the middle. The series of pictures
  below helps describe this nonsense. In the
  first picture, the angle of release is small, so
  the ball travels faster, but also a shorter
  distance. In the second picture, the angle of
  release is large so the ball travels extremely
  high, but does not travel as far. In the last
  picture, the angle of release is between zero and
  ninety degrees, (45), and results in the furthest
  possible throw.

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Passing a 2D technique

• IN A NUTSHELL
• To get the ball from point A to point B as fast
  as possible, throw it as hard as you can on a
  straight line (an angle of release of zero).
• To throw the ball as far as you can, throw it as
  hard as you can on a 45 degree angle.

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MOVING ON
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The Force of a Sack

• The force of a sack can be calculated easily with
  physics. Its a lot easier to calculate then
  passing a ball. The formula used to calculate
  the force behind a sack would be the infamous
• F ma
• Pretty much, what this formula says is, the
  bigger you are and the faster youre moving, the
  harder you hit.

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The Force of a Sack

• Just for fun, lets calculate how much force
  William The Fridge Perry hit with.
• The Fridge, in his prime, weighed about 370
  pounds, roughly 170 kg. If he ran as fast as the
  average Defensive Lineman, then he by the time he
  reached a quarterback, he was accelerating at
  about 6 m/s. Using the formula F ma, we can
  conclude that Refrigerator Perry hit with a force
  of about
• 1020 N.
• Getting hit by The Fridge, is therefore
• comparable to having a baby elephant
• dropped on you.

2
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Sometimes, its the defenders who get knocked
over(wait for clip to play)
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Momentum of arunning back

• In the previous clip, Greg Jones, current running
  back for the Jacksonville Jaguars, rumbled over
  Sean Taylor, current safety for the Washington
  Redskins.
• To calculate how this happened, we use the
  formula for momentum

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Momentum of arunning back

• Greg Jones, RB
• (the guy running with the ball in the clip)
• Height 6-1
• Weight 250 lb (113 kg)
• Velocity at time of impact approx. 7m/s
• Velocity after impact approx. 5m/s

• Sean Taylor, FS
• (the guy getting run over in the clip)
• Height 6-2
• Weight 232 lb (105 kg)
• Velocity at time of impact 0
• Velocity after impact ??

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Momentum of arunning back

• To figure out just how fast Sean Taylor was
  knocked backwards, we use the Conservation of
  Momentum equation.

(113)(7) (105)(0) (113)(5)
(105)(x) 791 565
105x 226 105x
x 2.15 m/s
Sean Taylor was therefore sent back at 2.15
meters per second, after receiving the hit from
Greg Jones. Ouch.
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In conclusion

• Football players are amazing specimens. Theyre
  bigger, faster, and stronger than most people.
  Weve discovered that The Fridge can hit you as
  hard as a falling baby elephant, and Greg Jones
  can knock a 230 pound man backwards at 2m/s.
• Also, its become quite clear that quarterbacks
  really are the smartest players in the game.
• However, as smart as they are, they should leave
  the genius thinking up to guys like Norman
  Einstein.

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Bibliography

• Einstein Picture
• http//www.paranormal.lublin.pl/foto/einstein2.jpg
  
• Football Catch Movie
• http//www.benton.k12.in.us/bc/sport/ftblV/ftbl200
  0.html
• Football Tackle Movie
• http//www.wisecountysports.com/AlumniGame2004/Hom
  e.html
• William Perrys Picture
• http//images.sportsline.com/u/photos/football/nfl
  /img5827407.jpg
• Greg Jones (RB) Runs Over Sean Taylor (FS) Movie
  http//www.fsukxaz.com/ToddsNolePage.html
• Momentum Formula Picture
• http//en.wikipedia.org/wiki/Momentum
• All Football Player Statistics
• http//www.nfl.com
• Greg Jones Picture
• http//media.theinsiders.com/Media/NFL/92104_Greg_
  Jones.JPG
• Sean Taylor Picture
• http//media.theinsiders.com/Media/College_Footbal
  l/92104_Sean_Taylor.JPG
• All Physics Information was either taught to me
  or received from
• http//www.howstuffworks.com/physics-of-football.h
  tm