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

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 = -------------

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 noticed @ low v rubbing of layers of air adjacent to projectile  with: flow v, surface size, surface roughness secondary concern

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

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

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

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

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

 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

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

FIG K.9 page 424

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