Transcript BIOMECHANICS APPLICATIONS

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
 Vdrag +
Vheadwind
Tailwind
 Vdrag
- Vtailwind
 flow velocity acting
on body
 body v = 20mps

 flow velocity acting
on body
 body v = 20mps

 Vheadwind = 5mps
 Vtailwind = 5mps
 Vres = 25mps (20 + 5)
 Vres = 15mps (20 - 5)
Skin Friction
most noticed @ low v
 rubbing of layers of air
adjacent to projectile
  with: flow v,
surface size, surface
roughness
 secondary concern

Profile Drag

 with area exposed to
approaching air flow
 with projectile v
 lead side =  pressure
 trail side =  pressure


main source of Drag
DRAG: Profile & Skin Friction
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
Profile Drag
increases from
a to c as more
AREA is exposed
to oncoming
airflow
AREA
a: minimal
b: moderate
c: too large
FIG K.10 pg 424
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 a LOW pressure zone
 low flow velocity creates a HIGH 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
Newton’s 3rd Law:
Action/Reaction
Difference in Pressure Zones
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