A Physicists Approach to Springboard Diving

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A Physicists Approach to Springboard Diving

• Edward N. Roberts
• University of the South, Sewanee
• March 6th 2002

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A Question Posed to Physicists

• Is it possible for a somersaulting springboard
  diver to initiate a twisting motion without any
  torque being applied to their body? That is, can
  a diver begin to twist after having left the
  diving board?

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Answer

• Yes
• Physics Department at Cornell University
• Interestingly 56 of those asked the question
  answered incorrectly.
  

Frohlich, Cliff Do springboard divers ...,
Am.J.Phys.47(7), July 1979.
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Laws of Physics applicable to the sport of Diving

• Center of Mass
• Angular Velocity
• Moments of Inertia
• Principle of Acceleration
• Many more...

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Laws of Physics applicable to the sport of Diving

• Why even talk about the physics of Diving?

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Terminology used in Diving

• The Approach
• The Hurdle
• Categories of dives
• Forward
• Back
• Reverse
• Inward
• Twister

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Terminology used in Diving

• Four positions of dives
• Straight
• Pike
• Tuck
• Free

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Flight of a Dive

• Rotation around Center of Mass
• Parabolic Flight of Dives
• What can be determined from this?

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Flight of a Dive

• Equations of Motion

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Parabolic flight of a dive
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Parabolic flight of a dive
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Conservation of Angular Momentum

• Conservation of Angular Momentum Equation

• Angular Velocity Equation is

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Moments of Inertia

• Moments of Inertia must be determined
• Assumptions
• Rigid Body
• Density Distribution equally
• 14 Separate parts
• Represent simple Geometric shapes

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Calculation of the Inertia
Thin Rod Cylinder
Sphere
Solid Cylinder
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Calculation of the Mass Chart
Stanley Plagenhoef, Patterns of Human Motion
(Englewood Cliffs, NJPrentice-Hall, 1971),
chapter 3
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Calculation of the Mass
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Calculation of the Inertia

• The Parallel-Axis Theorem
• Relates the moment of inertia about an axis
  through the center of mass of an object to the
  moment of inertia about a second parallel axis.
  

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14 Separate parts diagramExample Calculation
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14 Separate parts diagramExample Calculation
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Calculation of distance from Axis of Rotation
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Calculation of distance from Axis of Rotation
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Videopoint Calculation of ?

• Center of Mass used as the origin
• Plotted the rotation of the head around the
  center of mass

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Example of Tuck ? calculation
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Conservation of Angular Momentum
Calculated moment of Inertia for the straight
position I 15.7 kgm2 ? 115 /s
2.01 rad/s L 31.5 kgm2/s

• Calculated moment of Inertia for the tuck
  position
  
• I 5.30 kgm2 ? 560 /s 9.60 rad/s
  L 50.9 kgm2/s

• 31.5 kgm2/s 50.9 kgm2/s

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Mechanics of Somersaults

• Angular Velocity
• Throwing of arms
• Leaning
• Equal and opposite forces

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Mechanics of a Twist

• Three types of Twists
• Torque Twist
• Cat Twists or Zero Angular Momentum Twist
• Torque-free Twist

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Torque Twist

• The simplest form of a twist
• Equal and opposite force
• Unable to be controlled

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Cat Twists

• Why does a cat when dropped land on its feet?
• Conservation of Angular Momentum
• How does a cat perform this?
• How a diver can do the same twist.

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Torque-free Twist

• Type of twist which divers perform
• How a torque-free twist occurs
• Possession of Angular Momentum
• Not on the board and can twist
• Can be controlled

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Tilt of a Torque-free Twist
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My Experiments

• Three Camera Angles
• Timing of each camera Angle.

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Picture of the Overhead Camera
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Results of Torque-free Twist
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Torque-free Twist
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Torque-free Twist
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My experiments

• Diving Board considered a cantilever
• -lever arm the distance from the fulcrum to the
  end of board
  
• Setup for how this was done
• Results

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Lever Arm changing Data
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Conclusion

• Divers are able to twist without the diving
  board
  
• Increasing relationship between the Lever Arm and
  height received
  
• Questions???