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F D = ½ C D A ρ v ²

F D = ½ C D A ρ v ². C D coefficient of drag, indicates how streamlined a projectile is (low number:very streamlined) A is the frontal area of projectile facing the flow ρ (rho) is the air density (less in warm air and at higher altitude) v ² means if v doubles, drag quadruples.

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F D = ½ C D A ρ v ²

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  1. FD = ½ CD Aρv² • CD coefficient of drag, indicates how streamlined a projectile is (low number:very streamlined) • A is the frontal area of projectile facing the flow • ρ(rho) is the air density (less in warm air and at higher altitude) • v² means if v doubles, drag quadruples

  2. TERMINAL VELOCITY • Vterminal reached when all Fresistive = all Fmotive • as a body falls, it accelerates drag  • drag  as the square of v (v = 4, drag = 16) • Vterminal can also be reached horizontally • light body reaches Vterminal --------- than heavier • badminton bird compared with tennis ballvolleyball compared with soccer ball

  3. STREAMLINING • Achieved by: 1. decreasing area size facing oncoming airflow 2. tapering leading side  air not abruptly moved • Effects of Streamlining: A. more laminar flow past body with less “wake” B. less turbulence behind body less difference in pressure zones between front and tail of body • see FIG 13.1 on page 432

  4. DRAFTING • For given body & wind v, Headwind has a greater effect than Tailwind on the moving body: (run @ 6mps with 2mps wind: H= 8mps, T= 4mps) • Running @ 1 meter behind = ----% energy saved • XC Skiing @ 1 meter behind = ----% energy saved • 90% of all resistive forces in Cycling are DRAG • FIG 13.2 on page 433

  5. FLUID LIFT FORCE on AIRFOILS • FL(Lift Force) always ---------------- to direction of the oncoming air flow • Lift can be ---------, -----------, ------------ • due to difference in pressure zones on opposite sides of projectile • Bernoulli’s Principle: flow v =  pressure zone /  flow v =  p zone • FL affected by Projection and Attack 

  6. Angles Affecting LIFT • PROJECTION • ATTITUDE  • ATTACK

  7. Angles Affecting LIFT PROJECTIONangle between horizontal (e.g. ground) and C of G of projectile FIG 13.5 on page 436

  8. Projection

  9. Angles Affecting LIFT ATTITUDE angle between horizontal and long axis of projectile FIG 13.6 on page 437

  10. Discus descending to ground from right to left Projection  45°Attitude  30° Attack  ??°

  11. Angles Affecting LIFT ATTACKangle between projectile’s long axis and projection  FIG K.9 on page 424 FIG 13.8 on page 438

  12. Attack below from page 424 Above FIG 13.8at apex of flightpage 438

  13. Center of Pressure (CP) • The point on a projectile where the both the Lift and Drag Forces act • changes as the Attack changes • CG and CP co-linear = LIFT • CG and CP out of line = Torque  pitch  Drag • CP in front of CG = Stall  leading side pitch up • see FIG 13.9 on page 439

  14. MAGNUS EFFECT • Lift due to the spin on a spherical projectile • Projectile has a Boundary layer of air that moves in the direction of the spin • Projectile’s Boundary layer of air interfaces with on coming air flow • High and Low pressure zones develop due to difference in air flow velocities [Bernoulli]

  15. Back SpinTop Spin • Bottom of ball moving toward the direction of the ball’s flight • higher flow on top =  pressure • lower flow on bottom=  pressure •  lift UPWARD • Top of the ball moving toward the direction of the ball’s flight • lower flow on top=  pressure • higher flow on bottom =  pressure •  lift DOWNWARD

  16. Back Spin (top of ball moves backwards, away from ball’s flight path)Back Spin produces upward Lift Force

  17. Top Spin (top of ball moves forward in the direction of ball’s flight path)Top Spin produces downward Lift Force

  18. “Basic Biomechanics” Susan J. Hall page 531

  19. Floater Serve / Knuckleball Pitch • all sport balls are not perfectly round in shape • when a ball is projected with little or no spin: 1. the shape causes irregular/shifting air flow past the various sides of the ball 2. high and low pressure zones continually shift around the ball

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