A is the frontal area of projectile facing the flow FD = ½ CD A ρ v² 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

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 ball volleyball compared with soccer ball

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

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

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 

Angles Affecting LIFT PROJECTION  ATTITUDE  ATTACK 

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

Projection

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

Discus descending to ground from left to right Projection  45° Attitude  30°

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

Attack  below from page 424 Above FIG 13.8 at apex of flight page 438

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

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]

Back Spin Top 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

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

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

“Basic Biomechanics” Susan J. Hall page 531

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