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The Aerodynamics of Baseball April 18, 2009

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Outline Background Basic Physics of Flight Fly Ball Pitched Ball Questions

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Why NASA? Computational Fluid Dynamics Glenn Research Center

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Why NASA? Educational Outreach Beginner’s Guide to Aeronautics Glenn Research Center

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Why NASA? Glenn Research Center

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Physics of Flight Objects Respond to External Forces Newton’s Laws of Motion Glenn Research Center

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Forces A Force is a Push or a Pull A Force is a Vector Quantity Vectors: Velocity, Acceleration, Displacement, Force Scalars: Temperature, Pressure, Density, Mass Volume, Length, Area, Kinetic Energy, … Magnitude (Size) Direction VectorsScalars Magnitude only Glenn Research Center

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Forces in Flight Flight Velocity Weight Lift Drag Aerodynamics Center of Gravity Center of Pressure Glenn Research Center

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Weight Glenn Research Center W = m g Baseball Rule Book Weight = 5 oz (actually 5/16 lb) Diameter = 2.875 to 3 inches

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Motion in Flight Flight Velocity Weight Neglect Aerodynamics Glenn Research Center F = m a a = F m v = g t + v 0 d = g t + v t + d 0 0 2 2 Newton’s 2 nd Law F = W = m g (constant mass) = g

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V L V = V cos (a) Lo a U = V sin (a) oL

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HitModeler http://www.grc.nasa.gov/WWW/K-12/airplane/hitmod.html

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Fly Ball Results Glenn Research Center SpeedAngleDistanceDragLocationTempPress 10045 --- 0 Wind - 669

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Properties Glenn Research Center Air Nitrogen N 78% Oxygen O 21% Traces - CO - H O - … Mixture of Gases 2 2 2 2 Molecules in constant motion Collide with each other and container Mass (m) -> Density Momentum (m V) -> Pressure Kinetic Energy (m V ) -> Temperature 2 Viscosity, Compressibility

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Aerodynamic Drag Velocity V Aerodynamic Drag Sir George Cayley Glenn Research Center 2 2 D = Cd V A F ~ V A Shape - Inclination - Viscosity Size - Area A Air Density Viscosity Shape Modern Drag Equation 2 Cd = Coefficient contains effects of Shape – Viscosity Dynamic Pressure depends on state of the gas (pressure & temperature) V 2 2 =

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Motion in Flight Include Aerodynamic Drag Glenn Research Center Problem #1 Solution: Slight rotation of the ball pins the separation point Time Drag Flow past a ball is highly unsteady and can become chaotic

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Motion in Flight Include Aerodynamics Glenn Research Center Problem #2 Drag Coefficient for a Spinning Ball Depends on Viscosity & Surface Details Re x 101.010.0 Reynolds Number = Re = Viscous Force Inertial Forces = V d Cd,5,3,1 Smooth Ball Baseball -5 Cd =.3 Baseball

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Motion in Flight Include Aerodynamic Drag Glenn Research Center V = a t + V 0 Problem #3 F = W - D = m a Can’t use simplified Newton’s 2 nd Law D = function of V 2 Must Solve: dV 2 W C V A dt 2 m = - 2 d dV dt = F m

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HitModeler http://www.grc.nasa.gov/WWW/K-12/airplane/hitmod.html

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Glenn Research Center SpeedAngleDistanceDragLocationTempPress 10045 --- 0 Wind - 669 10045Cleve60290.3378 Fly Ball Results

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Glenn Research Center SpeedAngleDistanceDragLocationTempPress 10045 --- 0 Wind - 669 10045Cleve60290.3378 10045Cleve80290.3385 Fly Ball Results

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Glenn Research Center SpeedAngleDistanceDragLocationTempPress 10045 --- 0 Wind - 669 10045Cleve60290.3378 10045Cleve80290.3385 10045Cleve32290.3370 Fly Ball Results

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Glenn Research Center SpeedAngleDistanceDragLocationTempPress 10045 --- 0 Wind - 669 10045Cleve60290.3378 10045Cleve80290.3385 10045Cleve32290.3370 10045Cleve60280.3384 Fly Ball Results

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Glenn Research Center SpeedAngleDistanceDragLocationTempPress 10045 --- 0 Wind - 669 10045Cleve60290.3378 10045Cleve80290.3385 10045Cleve32290.3370 10045Cleve60280.3384 10045Cleve6029+5.3410 Fly Ball Results

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Glenn Research Center SpeedAngleDistanceDragLocationTempPress 10045 --- 0 Wind - 669 10045Cleve60290.3378 10045Cleve80290.3385 10045Cleve32290.3370 10045Cleve60280.3384 10045Cleve6029+5.3410 10045Cleve6029 -5.3338 Fly Ball Results

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Glenn Research Center SpeedAngleDistanceDragLocationTempPress 10045 --- 0 Wind - 669 10045Cleve60290.3378 10045Cleve80290.3385 10045Cleve32290.3370 10045Cleve60280.3384 10045Cleve6029+5.3410 10045Cleve6029 -5.3338 10045Denver6024 0.3404 Fly Ball Results

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Aerodynamic Lift Velocity V Aerodynamic Lift Sir George Cayley Glenn Research Center 2 2 L = Cl V A F ~ V A Shape - Inclination - Viscosity Size - Area A Air Density Viscosity Shape Modern Lift Equation 2 Cl = Coefficient contains effects of Shape – Spin - Viscosity Dynamic Pressure depends on state of the gas (pressure & temperature) V 2 2 = Spin

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Flow Moving with ball

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Aerodynamic Lift Velocity V Ideal Lift Glenn Research Center 2 L = Cl L ideal L ideal = N d d s V Size - Diameter d Air Density Viscosity Shape Lift Equation Cl = Coefficient contains effects of Shape - Viscosity Spin - s Aerodynamic Lift Cl =.15 N = numerical factor

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Ideal Trajectory

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http://www.grc.nasa.gov/WWW/K-12/airplane/foilb.html

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Some Curve Ball Results Glenn Research Center A) 100 mph fast ball crosses plate in.44 sec drops almost 3 feet from the pitcher’s hand B) Curve ball (80 mph – 2000 rpm – axis vertical – Cleveland).54 sec - 20 inches side-to-side - drops 4.5 feet C)Same as B except Hot Day (90 degrees) – loses 1.1 inch Same as B except Cold Day (34 degrees) – adds 1.2 inch D) Same as B except axis horizontal – no side-to side ball drops 3 feet or 6 feet depending on orientation No rising fastball (would need about 5000 rpm) E) Changing axis between B & D gives large variation

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Some Curve Ball Results Glenn Research Center A) Curve ball (80 mph – 2000 rpm – axis vertical – Cleveland).54 sec - 20 inches side-to-side - drops 4.5 feet B) Same as A except Denver (25 in Hg vs 29 in Hg) loses 3.1 inches side-to-side Denver is a bad place to pitch and a good place to hit! C)A 100 mph fastball crosses the plate at 94 mph in Cleveland, 96 mph in Denver

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Conclusions Glenn Research Center A) Aerodynamics has a big effect on the game of baseball B) Understanding these effects explain observations about different ballparks and different pitchers / hitters at various times during the season and post-season C) Software is available for you to learn some more about baseball and aerodynamics. You can play on-line or download the software (Java source is supplied). Search on “ NASA Baseball” D) GO TRIBE !!

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Advertisements Glenn Research Center A) May 13 and May 28 - WKYC Weather Days B)June 27 – 28 NASA Days with the Tribe special Kid’s events and exhibits C)GO TRIBE !! Questions?

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Backups

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Time Drag Drag of a smooth ball ---- Knuckle Ball

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Glenn Research Center SpeedAngleDistanceDragLocationTempPress 10045 --- 0 Wind - 669 10045Cleve60290.3378 10045Cleve90290.3387 10045Cleve35290.3370 10045Cleve60280.3384 10045Cleve6029+5.3417 10045Cleve6029 -5.3338 10045Denver6024 0.3405 Fly Ball Results

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