F D = ½ C D A ρ v ²

2. 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

3. 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 sooner than heavier • badminton bird compared with tennis ballvolleyball compared with soccer ball

4. 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

5. 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 = 6.5% energy saved • XC Skiing @ 1 meter behind = 23% energy saved • 90% of all resistive forces in Cycling are DRAG • FIG 13.2 on page 433

6. FLUID LIFT FORCE on AIRFOILS • FL(Lift Force) always perpendicular to direction of the oncoming air flow • Lift can be upward, downward, lateral • 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 

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 Attitude  30°Projection  45°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

16. 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]

17. 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 Back SpinTop Spin

18. Back Spin: top of ball moves backwards, away from ball’s flight pathBack Spin produces Lift Force in what direction?

19. Top Spin: top of ball moves forwards in the direction of ball’s flight pathTop Spin produces Lift Force in what direction?

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

21. 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