FD =

1
FD ½ CD A ? v²

• CD coefficient of drag, indicates how streamlined
  a projectile is (low numbervery streamlined)
• A is the frontal area of projectile facing the
  flow
• ? (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
  ballvolleyball 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 (run _at_
  6mps with 2mps wind H 8mps, T 4mps)
• Running _at_ 1 meter behind ---- energy saved
• XC Skiing _at_ 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
• Bernoullis 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 right to left
Projection ? 45 Attitude ? 30 Attack
? ??
11
Angles Affecting LIFT

• ATTACK ? angle between projectiles long axis
  and projection ? FIG K.9 on page 424 FIG
  13.8 on page 438

12
Attack ?below from page 424
Above FIG 13.8at apex of flightpage 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

14
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15
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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
• Projectiles 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
  balls flight
• higher flow on top ? pressure
• lower flow on bottom ? pressure
• ? lift UPWARD

• Top of the ball moving toward the direction of
  the balls flight
• lower flow on top ? pressure
• higher flow on bottom ? pressure
• ? lift DOWNWARD

18
Back Spin (top of ball moves backwards, away from
balls flight path)Back Spin produces upward
Lift Force
19
Top Spin (top of ball moves forward in the
direction of balls 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