1. Aerodynamic Drag Force
Air resistance (fluid resistance)
motion of the air flowing past projectile
equal to projectile’s velocity BUT in the opposite direction of projectile’s motion

2. Headwind Tailwind Vdrag - Vtailwind Vdrag + Vheadwind Vtailwind = 5mps
 flow velocity acting on body
body v = 20mps
Vtailwind = 5mps
Vres =
Vdrag + Vheadwind
 flow velocity acting on body
body v = 20mps
Vheadwind = 5mps
Vres =

3. Skin Friction Profile Drag
 with area exposed to approaching air flow
 with projectile v
lead side =  pressure
trail side =  pressure
main source of Drag
most low v
rubbing of layers of air adjacent to projectile
 with: flow v, surface size, surface roughness
secondary concern

4. STREAMLINING Achieved by:
1. decreasing size of area facing oncoming airflow
2. tapering leading side - air is not abruptly moved
Streamlining results in:
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

5. Mass of Projectile and Drag Effect
a = F m
a in this case stands for deceleration [negative a]
deceleration = F m
deceleration inversely proportional to projectile m

6. Drag Factors FDrag = ½ CD A ρ v²
Skin Friction and Profile Drag
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 (density less in warm air and at higher altitude)
v² means if v doubles, drag quadruples

7. AREA a: ---------- b: ---------- c: ----------
Profile Drag increases from a to c as more AREA is exposed to oncoming airflow
AREA a: b: c:
FIG K.10 pg 424

8. high flow velocity creates ------- pressure zone
FLUID LIFT FORCE
FL (Lift Force) always perpendicular to direction of the oncoming air flow
Lift can be upward, downward, lateral
FL due to difference in pressure zones on opposite sides of projectile
Bernoulli’s Principle:
high flow velocity creates pressure zone
low flow velocity creates pressure zone

9.  flow v on top  p zone on top  p zone on bottom upward Flift
 flow v on top  p zone on top  p zone on bottom downward Flift

10. 8-May-2001 National Post from “New Scientist” David Anderson disputes Daniel Bernouilli’s Principle

11. LIFT : DRAG
Maximize LIFT FORCE by creating an optimal angle of attack or shaping projectile like an airfoil
Minimize DRAG FORCE with a moderate ATTACK 
FL = ½ CL A ρ v² CL (lift coefficient) A (area of pressure) ρ ( air density) v² (air flow velocity)

12. FIG K.9
page 424

14. Effects of Inclination of an AIRFOIL
LIFT and DRAG:
Effects of Inclination of an AIRFOIL