Physics of Flight Objects Respond to External Forces Newton’s Laws of Motion Glenn Research Center
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
Forces in Flight Flight Velocity Weight Lift Drag Aerodynamics Center of Gravity Center of Pressure Glenn Research Center
Weight Glenn Research Center W = m g Baseball Rule Book Weight = 5 oz (actually 5/16 lb) Diameter = 2.875 to 3 inches
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
Fly Ball Results Glenn Research Center SpeedAngleDistanceDragLocationTempPress 10045 --- 0 Wind - 669
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
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 =
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
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
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
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
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
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
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
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 !!
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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