F D = ½ C D A ρ v ²
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FD = CD A vCD coefficient of drag, indicates how streamlined a projectile is (low number:very streamlined)A is the frontal area of projectile facing the flow (rho) is the air density (less in warm air and at higher altitude)v means if v doubles, drag quadruples
TERMINAL VELOCITYVterminal 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 heavierbadminton bird compared with tennis ball volleyball compared with soccer ball
STREAMLININGAchieved by:1. decreasing area size facing oncoming airflow2. tapering leading side air not abruptly moved Effects of Streamlining:A. more laminar flow past body with less wakeB. less turbulence behind body less difference in pressure zones between front and tail of bodysee FIG 13.1 on page 432
DRAFTINGFor 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 savedXC Skiing @ 1 meter behind = 23% energy saved90% of all resistive forces in Cycling are DRAGFIG 13.2 on page 433
FLUID LIFT FORCE on AIRFOILSFL (Lift Force) always perpendicular to direction of the oncoming air flowLift can be upward, downward, lateral due to difference in pressure zones on opposite sides of projectileBernoullis Principle: flow v = pressure zone / flow v = p zoneFL affected by Projection and Attack
Angles Affecting LIFTPROJECTION angle between horizontal (e.g. ground) and C of G of projectile FIG 13.5 on page 436
Angles Affecting LIFTATTITUDE angle between horizontal and long axis of projectile FIG 13.6 on page 437
Discus descending to ground from right to left Attitude 30 Projection 45 Attack ??
Angles Affecting LIFTATTACK angle between projectiles long axis and projection FIG K.9on page 424 FIG 13.8on page 438
Above FIG 13.8 at apex of flight page 438Attack below from page 424
Center of Pressure (CP)The point on a projectile where the both the Lift and Drag Forces actchanges as the Attack changesCG and CP co-linear = LIFTCG and CP out of line = Torque pitch DragCP in front of CG = Stall leading side pitch up see FIG 13.9 on page 439
MAGNUS EFFECTLift due to the spin on a spherical projectile Projectile has a Boundary layer of air that moves in the direction of the spin Projectiles Boundary layer of air interfaces with on coming air flow High and Low pressure zones develop due to difference in air flow velocities [Bernoulli]
Back Spin Top SpinBottom of ball moving toward the direction of the balls flighthigher flow on top = pressurelower flow on bottom = pressure lift UPWARD Top of the ball moving toward the direction of the balls flightlower flow on top = pressurehigher flow on bottom = pressure lift DOWNWARD
Back Spin: top of ball moves backwards, away from balls flight path Back Spin produces Lift Force in what direction?
Top Spin: top of ball moves forwards in the direction of balls flight path Top Spin produces Lift Force in what direction?
Basic Biomechanics Susan J. Hall page 531
Floater Serve / Knuckleball Pitchall 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