The Physics of Basketball

1
The Physics of Basketball

• Ulrike Lahaise
• Georgia Perimeter College
• Decatur Campus Symposium 2006

2
Outline

• Little Tidbits
• Intro
• Projectile Motion
• Concepts of Work and Energy
• The Swish
• Lay Up Shot
• Best Launching Angle
• Wilts Problem/Solution
• Observation of Real Play
• The Spin
• The Bounce
• Bibliography

3
Little Tidbits I

• Why was Wilt Chamberlain bad at foul shots?
• 7 ft. 2 in. Philly Warriors 59/60 72/73
  31,419 career points 23,924 reb. in 1045 games
  lifetime avg. 30.1 pts./gm. 22 reb./gm 45.8
  min/game in playing time.
• poor foul-shooting ability, 51.1!
• Hypothesis because he was so tall?
• Angelo Armenti (The Physics of Sports)
• Observation tall players have worse foul shot
  percentage than short players
• Not as bad as Wilts, though!

4
Little Tidbits I

• From The Physics of Sports, edited by Angelo
  Armenti

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Little Tidbits II

• 1980s Nike Commercial
• Mars Blackman Yo Professor, how does Mike defy
  gravity, do you know, do you know, do you know,
  do you know?
• Prof Michael Jordan overcomes the acceleration
  of gravity by the application of his muscle power
  in the vertical plane thus producing a low
  altitude earth orbit.
• Mars A what?
• Prof Do you know what I mean? Do you know, do
  you know, do you know?
• Mars Money, check him out!

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Little Tidbits II

• From The Physics of Sports, edited by Angelo
  Armenti

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Little Tidbits II

• Hang Time - Translation
• Jordan flies in two dimensions horizontally
  and vertically
• less height/distance than the world records
• high jump (around 2 m) only vertical
• long jump (around 9 m) only horizontal
• full force at angle vertical and horizontal
  components combined
• Equally impressive!

8
Intro Projectile Motion (I)

• Two dimensional motion of an object released with
  a certain launching speed/angle
• Neglect air resistance
• Only acceleration of object is Earths gravity
• Split up into horizontal motion component and
  vertical motion component
• Dr. John Evans slides

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Intro Projectile Motion (II)

• Horizontal motion is constant
• Vertical motion is uniformly accelerated
• Vertical position vs. time is a parabola
• Vertical position vs. horizontal position (shape
  of the path) is a parabola, (figure from Peter
  Brancazio)

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Intro Projectile Motion (III)

• Demos and Visuals
• Cutnell Johnson College Physics
• Projectile Motion Simulation (http//www.hazelwood
  .k12.mo.us/grichert)
• R. Nave (HyperPhysics Mechanics)

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Intro Work of a Shot (I)

• How does the player impart speed?
• Players work work force x distance in hand
• Players work change in balls KE
• KE Kinetic Energy energy of motion
• Depends on mass and square of speed
• Can get same increase in KE by varying force or
  distance

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Intro Work of a Shot (II)

• Example Granny (or, in this case, Daisy) Shot
• Underhanded shooting style
• If force is lacking
• make it up with
• distance!

13
The Swish Lay Up Shot (I)

• Ball shot on the run
• maintains same speed and direction as player had
  when shooting (due to its inertia)
• Plus, speed and direction given by players shot
• Image from Worsley School, Alberta, Canada,
  Science Files

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The Swish Lay Up Shot (II)

• Ex. player shoots while running to net
• push ball toward basket?
• Ball has same forward motion as player, likely
  overshoots with additional forward push
• shoot it straight up?
• shoot straight up when 2 3 feet away from net,
  score if launching speed and timing are right

15
The Swish Lay Up Shot (III)

• Ex. player shoots while running crosswise
• Aim at center of basket?
• Ball overshoots, bounces off far edge of rim
• Aim at near side of rim?
• Compensates for balls inertia in same direction
  as players motion best chance of going in

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The Swish Free Throw

• Problem Best Launching Angle (Peter Brancazio)
• given distance infinite of speed/angle
  combinations to center of baskets
• shape of path (trajectory) parabola
• One optimum speed/angle combination
• most leeway (wiggle room)
• Lowest amount of force needed

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The Swish Theory (I)

• entry angle between direction of ball and plane
  of rim 32
• Angle 32
• No leeway, area ball sees its own
• For angles between 32 and 90
• Leeway increases, area ball sees gt its own

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The Swish Theory (II)

• Minimum launching angle for minimum entry angle
• Need specific launching speed to make the shot
• Is smaller for taller players and larger distances

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The Swish Theory (III)

• For launching angle greater than minimum
• More leeway in launching speed ball can make
  basket within range of launching speeds
• Left/right leeway is greater for shorter
  distances and the higher release height

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The Swish Theory (IV)

• Launching angle hard to measure, instead
• distance, L 10 25 ft.
• Any closer, player might bank further shots -
  desperation
• release height below basket, h 1 4 ft.
• Players shoot 1 2 ft. above head including jump
  shots

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The Swish Theory (V)

• Scenario 6 ft player L of 13.5 ft. h 2 ft
• Leeway in launching speed (v) very small!
• Doesnt get larger than 1
• Slightly increases with increasing launching
  angle but not significantly player must be
  accurate
• Leeway in launching angle greater than for v
• largest for angles right around minimum speed
  angle (49.2)
• Between 4 and 11
• Larger shooting distances (L) smaller leeway

22
The Swish Wilts Problem

• Same L and shooting height closer to net (h)
  larger leeway
• Theoretically Taller players have a better
  chance
• Wilts problem according to Peter Brancazio
  Fortunately for the shorter players, most taller
  players tend to develop their rebounding and
  under-the-basket play at the expense of their
  longer-distance shooting skills.

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The Swish Wilts Solution (I)

• Overhand vs. Underhand Shot
• Theoretical calculations by A. Tan and G. Miller
  for avg. NBA player, 6 ft 6 in

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The Swish Wilts Solutions (II)

• Overhand shot
• Lower launching speed less force required ()
• Larger entry angle ball sees larger area when
  entering basket ()
• Larger entry speed higher chance to bounce off
  rim if clean shot missed (-)
• Underhand shot
• Lower entry speed less chance to bounce off rim
  if clean shot missed ()
• Higher launching speed more force required (-)
• Smaller entry angle ball sees smaller area to
  enter (-)
• Can increase launching angle/speed with more
  force

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The Swish Wilts Solution (II)

• Theoretical Prediction Overhand shot preferable
• Experiment Underhand shot more successful
• Ball is evenly balanced between the two hands
• Muscles are more relaxed
• Greater accuracy in the forward direction entire
  arm goes into the swing, less player error when
  aiming
• Types of muscles in overhand shot harder to
  control shot directed with one hand less
  accurate in forward direction

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The Swish Wilts Solution (III)

• Observation Attitude triumphs!
• Underhand shot
• Advocated by former NBA player Rick Barry
• Wilt used it for a while and improved his stats
• Minimizes left/right drift of ball
• Player has more control over shot
• Overhand Shot
• requires movement from the wrist, elbow, and
  shoulder More ways to mess up!
• Overriding plus It looks a lot cooler!

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The Swish Observation (I)

• Players develop kinesthetic, aka muscle memory
• Able to make tiny adjustments to correct shot
• average pro hits 50 under game conditions, gt
  70 when unguarded, best pros 90 when
  unguarded
• Different launching angles for same speed
• 60 yields high arch, 30yields low (or flat)
  arch
• 45 yields furthest distance

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The Swish Observation (II)

• Launching angle high arch vs. low arch
• High arch angle gt minimum speed angle
• Slightly larger leeway in speed, harder to block
  by tall defenders ()
• Harder to launch and aim (-)
• Low arch angle lt minimum speed angle
• youngsters on playground lacking height and
  strength
• Shot aimed directly at rim
• very small leeway in launching speed (-)
• larger launching speed than minimum-speed angle
  (-)

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The Swish Observation (III)

• Launching angle used by pros
• Early days slower, more deliberate play set
  shot most often used
• Set shot a high-arch shot launched from the
  chest or over the head with both feet on the floor

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The Swish Observation (IV)

• Today game is faster and more one-on-one
• Jump Shot most commonly used
• launched while in mid air usually with one hand
• launched quickly with minimum effort
• used even when unguarded rather than set shot
• Theory more leeway (launched higher up)
• In reality players launch it as low-arch shot!
• But slightly higher arch higher accuracy and
  less force
• Players use same launching angle regardless of L
• Theory minimum-speed angle larger for smaller L
• higher-arch shot nearer net gives more leeway

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The Swish Animation

• Make a jump shot every time
• Fear of Physics web site
• http//www.fearofphysics.com/Proj/proj.html
• Using basketball to teach physics and geometry
  concepts
• Basketball Explorations Interactive web site
  developed by a highschool group
• http//library.advanced.org/12006/

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The Spin (I)

• Ball shot with fingertips (and flick of wrist)
• Better control of launching angle
• Ball gets backspin
• Arnold Red Auerbach
• great basketball coach
• backspin makes the shot softer and helps it to
  be lucky
• Peter J. Brancazio Good physics rather than
  good luck!

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The Spin (II)

• Ball strikes surface/rim with specific angle and
  speed
• Can split balls motion into horizontal and
  vertical components
• Certain energy in both types of motion
• Add up to total energy of motion
• Bounce spin shifts some energy of one type to
  other
• Some energy will be lost (shifted to the surface)

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The Spin No Initial Spin

• frictional force opposes the forward, horizontal
  motion
• acts as a torque ball gets forward spin
• forward energy less, spin energy more
• rebound with forward spin, not quite as fast in
  the horizontal direction

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The Spin Initial Top Spin

• if ball spins fast enough, backward motion of
  balls bottom faster than its forward motion
• frictional force opposes the net backward motion
  of the balls skin, acts forward
• Some energy shifted from spin to forward motion
• rebound with less forward spin, more forward
  motion faster, lower angle

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The Spin Initial Back Spin

• ball as whole has forward motion and its bottom
  has forward motion due to spin
• Frictional force opposes both kinds of motion
• spinning and forward motion decrease
• bounce straighter upward, larger angle
• considerable speed loss
• More likely to score
• after hitting rim or backb.

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The Bounce (I)

• Deformation of surface of ball depends on air
  pressure inside
• The more air pressure, the less deformation
• The more energy stored in compressed air inside
• Air stores and returns energy more efficiently
  than material of ball

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The Bounce (II)

• Under inflated ball some energy wasted in
  deformation
• Ball material heats up due to internal friction
• Molecules move across one another ball heats up
• ball will not rebound very high
• Highly pressurized ball more elastic collision
• Floor must be harder than ball!
• soft floor material will flex when the ball hits
  it, ball looses some energy to floor
• Floor heats up

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The Bounce (III)

• Example 4th grade science fair project
• Bounce height of balls measured as function of
  internal air pressure 0 psi, 3 psi, 6 psi, 9
  psi, 12 psi
• Bounce height increased with pressure, highest
  bounce for 9 psi, a little lower for 12 psi
• U of Virginia explanation reasonably hard
  surface used, but it began to dent significantly
  for 12 psi-ball
• 12 psi-ball hard enough to dent floor
• Floor took part in bounce, ball shifted some of
  its KE to it

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Dos and Donts

• Do attempt to score

• Dont travel with ball!

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Bibliography

• The Physics of Sports, collection of articles
  edited by Angelo Armenti Jr.
• The Physics of Basketball by Peter J. Brancazio
• Kinematics of the free throw in basketball by
  A. Tan and G. Miller
• John Evans Introductory Physics Power Point
  Slides http//www.complexsystems.us/
• Cutnell Johnson College Physics
  http//www3.interscience.wiley.com8100/legacy/col
  lege/cutnell/0471151831/concepts/index.htm?newwind
  owtrue
• Projectile Motion Simulation http//www.hazelwoo
  d.k12.mo.us/grichert
• Rod Nave, Georgia State, HyperPhysics
  Mechanics http//hyperphysics.phy-astr.gsu.edu/Hb
  ase/hph.html
• Worsley School, Alberta, Canada, Science Files
  http//www.worsleyschool.net/science/files/physics
  of/basketball.html
• University of Virginia http//howthingswork.virgi
  nia.edu/bouncing_balls.html