The Worlds Most Fascinating Sphere

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The Worlds MostFascinating Sphere
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Myths Misconceptions

• Dimples like a snow tire
• Dimples increase drag
• Dimples create lift
• Put over spin on the ball for more distance

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I want to see the effects!
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• I History

II. Theory
IV. Results
III. Research
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HISTORY
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Feathery 1400s - 1880s
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Gutta-percha 1850s-1900s
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Hand Hammered Gutta-Percha
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Typical Ball Today

• 300-400 dimples
• USGA standards
• Diameter no less
• than 1.680 inches
• Weight no more
• than 1.620 ounces
• Spherically Symmetrical

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THEORY
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Aerodynamic Forces on a Body
p
t

• Pressure p - acts normal
• Shear stress t - acts tangential

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Resultant Force, R

• Parameters
• U8, velocity
• d, diameter (r, radius)
• v, rotational velocity
• r8, density of air
• µ8, viscosity of air
• k, surface roughness
• R (U8,d,v,r8, µ8, k)

U, velocity of ball
R, resultant force
g( , , )
CR g(Re, , ?)
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Lift and Drag Coefficients
Lift

• CL g1(Re, , ?)
• CD g2(Re, , ?)
• CL
• CD

U, velocity
Resultant
Drag
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Reynolds Number (Re)

• Inertial forces / viscous forces
• Re
• Re Values 104 105 106
• Golf Ball Re 60,000 - 220,000
• Determines Laminar or
• Turbulent Flow

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Laminar Flow
Van Dyke
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Turbulent Flow
Van Dyke
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Flow Similarity

• Validates Wind Tunnel Testing
• Flows dynamically similar if
• Bodies are geometrically similar
• Similarity parameters the same
• Reynolds Number (Re)
• If dynamically similar we know
• Streamline patterns the same
• Lift and Drag Coefficients are the same

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Types of Flow

• Inviscid - neglecting friction
• Viscid - including friction

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Inviscid Flow

• Bernoullis Equation
• p 1/2 r U2 constant
• p pressure
• - r density
• U velocity
• NO lift, NO drag

U8 170 mph
3/2 U8, highest velocity 255 mph
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Viscid Flow

• Friction / Shear stress - t
• Velocity gradient
• Friction occurs in the boundary layer

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Boundary Layer
b
Ball surface
Ub 255 mph
a
Ua 0
Boundary Layer (thickness greatly exaggerated)

• Zero velocity relative to the surface,
  no-slip
• Large velocity gradients exist in the BL

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Boundary Layer - Velocity Profile
255 mph
b
a
Ua 0
Thickness of the boundary layer of golf ball is
1 of its diameter at 100,000 Re
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Pressure Drag - Flow Separation
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Flow Separation - Adverse Pressure Gradient
Flow likes to move from HIGH pressure to LOW
pressure
Adverse Pressure Gradient
Low pressure
High Pressure
Top of the boundary layer
Surface of the ball
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Effect of Re on Flow Separation
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Experimental Drag on a Smooth Sphere
E. Achenbach 1972
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Boundary Layer Transition
Laminar
Turbulent
Van Dyke
Separation Points
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Velocity Profiles
n
Top of the Boundary Layer
Surface
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Experimental Drag on a Smooth Sphere
Golf Ball Re Range
E. Achenbach
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Effect of Surface Roughness on Critical Reynolds
Number
Golf Ball
E. Achenbach 1973
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Comparison with Golf Ball Critical Reynolds Number
Golf Ball
P W Bearman and J K Harvey 1976
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Magnus Effect

• Berlin, Germany 1852
• A force is created by a spinning symmetrical body
• Occurs in baseball, tennis, soccer, table tennis,
  cricket, external ballistics (spinning bullets)

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The Creation of Lift Pressure Imbalance
U v
U
v
-v
U
Swirling Boundary Layer
U - v
Non-lifting Flow
Lifting Flow
Spin is Key!

• Higher-than-normal velocity on the top lower
  pressure
• Lower-than-normal velocity on the bottom higher
  pressure
• Pressure imbalance Lift force

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The Creation of Lift Momentum
U8
Ball not spinning Wake
Ball Spinning Wake
Non- Symmetric Separation Points
Symmetric Separation Points
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Asymmetrical Separation Points
delayed
advanced
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RESEARCH

• The main goal of my investigation was to learn
  the effects of spin and dimples on the
  aerodynamics of golf balls and employ flow
  visualization to see the effects.

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Georgia Tech Research InstituteWind Tunnel

• Closed-return type
• re-circulating air
• Max speed 200 ft/s

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Test Section 30 H x 43 W x 90 L
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Wind Tunnel Balance
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Apparatus Assembly
Tunnel floor
Tunnel floor
Balance plate
Balance plate
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Models

• 5 balls
• (3) Dimpled
• (1) Smooth
• (1) Rough
• 8 inches diameter
• Stereolithography Apparatus (SLA)
• Styrofoam covered with fiberglass cloth

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Dimpled Balls

• 332 circular dimple pattern from Titleist
• Constant dimple diameter 0.151 in.
• Variable dimple depth
• Too Shallow (TS) 0.0079 in
• About Right (AR) 0.0119 in
• Too Deep (TD) 0.0159 in
• Paint radius
• rounding effect
• significant aerodynamic feature

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Tests

• 6 days
• Measuring
• CL, CD

• Velocity 14 mph 80
• Ball Rpm 200-1500 dimple, rough
• 200-800 smooth

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Vibration Video
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RESULTS
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Flow Separation - Smooth Sphere
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Flow Separation - Dimpled Sphere
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Separation Comparison
Early Separation bigger wake more drag
Delayed Separation smaller wake less drag
Smooth Ball
Dimpled Ball
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Smooth and Rough Spheres with Smoke Video
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Dimpled Ball with Smoke Movie
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Conclusion
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ACKNOWLEDGEMENTS

• John Spitzer - USGA, wind tunnel grant
• Charlie Novak - Lockheed Martin, LSA machine
• Dean McCallister - Delta Sigma Corp, design
• Steve Aoyama - Titleist, ball pattern
• Bob Englar - GTRI, joint endeavor
• Dr. Adams, data analysis
• Dr. Peterson, advisor
• Dr. Cavagnaro, aerodynamics