1. 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

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 ball volleyball 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: 6mps with 2mps wind: H = 8mps, T = 4mps)
1 meter behind = ----% energy saved
XC 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 left to right Projection  45° Attitude  30°

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

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

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

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

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