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 sooner than heavier

badminton bird compared with tennis ballvolleyball compared with soccer ball

STREAMLINING

• Achieved by:Achieved by:1. decreasing area size facing oncoming airflow2. tapering leading side air not abruptly moved

• Effects of Streamlining: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 = 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

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

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 right to left Attitude 30° Projection 45° Attack ??°

Angles Affecting LIFT

ATTACK angle between projectile’s long axis and projection

FIG K.9 on page 424 FIG 13.8 on page 438

Above FIG 13.8at apex of flight

page 438

Attack below from page 424

Center of Pressure (CP)

The point on a projectile where the both the Lift and Drag Forces act

changes 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 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 Lift Force in what direction?

Top Spin: top of ball moves forwards in the direction of ball’s flight path

Top Spin produces Lift Force in what direction?

“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