Aerodynamic Drag Force Air resistance fluid resistance motion

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

Headwind • Vdrag + Vheadwind Tailwind • Vdrag - Vtailwind • flow velocity acting on body • body v = 20 mps • Vheadwind = 5 mps • Vres = ------- • Vtailwind = 5 mps • Vres = ------

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

STREAMLINING Ø Achieved by: 1. decreasing size of area facing oncoming airflow 2. tapering leading side - air is not abruptly moved Ø Streamlining results in: A. more laminar flow past body with less “wake” B. less turbulence behind body less difference in pressure zones

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

Drag Factors FDrag = ½ CD A ρ v² Ø Skin Friction and Profile Drag Ø CD coefficient of drag, indicates how streamlined a projectile is (low number = very streamlined) Ø A is the frontal area of projectile facing the flow Ø ρ (rho) is the air density (density less in warm air and at higher altitude) Ø v² means if v doubles, drag quadruples

Profile Drag increases from a to c as more AREA is exposed to oncoming airflow AREA a: -----b: -----c: -----

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

flow v on top p zone on bottom upward Flift flow v on top p zone on bottom downward Flift

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

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) ρ ( air density) A (area of pressure) v² (air flow velocity)

FIG K. 9 page 424

http: //www. grc. nasa. gov/WWW/K-12/airplane/incline. html LIFT and DRAG: Effects of Inclination of an AIRFOIL