a is the frontal area of projectile facing the flow
DESCRIPTION
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 ball volleyball compared with soccer ballTRANSCRIPT
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FD = ½ CD A ρ v²
• 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 (less in warm air and at higher altitude)
• v² means if v doubles, drag quadruples
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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
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STREAMLINING• Achieved by:1. decreasing area size facing oncoming airflow2. 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
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DRAFTING
For given body & wind v, Headwind has a greater effect than Tailwind on the moving body: (run @ 6mps with 2mps wind: H = 8mps, T = 4mps)
Running @ 1 meter behind = ----% energy savedXC Skiing @ 1 meter behind = ----% energy saved90% of all resistive forces in Cycling are DRAGFIG 13.2 on page 433
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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 Bernoulli’s Principle:
flow v = pressure zone / flow v = p zone
FL affected by Projection and Attack
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Angles Affecting LIFT
PROJECTIONPROJECTION
ATTITUDEATTITUDE
ATTACKATTACK
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Angles Affecting LIFT
PROJECTION angle between horizontal (e.g. ground) and C of G of projectile
FIG 13.5 on page 436
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Projection
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Angles Affecting LIFT
ATTITUDE angle between horizontal and long axis of projectile
FIG 13.6 on page 437
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Discus descending to ground from left to right Projection 45° Attitude 30°
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Angles Affecting LIFT
ATTACK angle between projectile’s long axis and projection
FIG K.9 on page 424 FIG 13.8 on page 438
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Above FIG 13.8at apex of flightpage 438
Attack below from page 424
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Center of Pressure (CP)
The point on a projectile where the both the Lift and Drag Forces act
changes as the Attack changesCG and CP co-linear = LIFTCG and CP out of line = Torque pitch DragCP in front of CG = Stall leading side pitch up see FIG 13.9 on page 439
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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 Projectile’s Boundary layer of air interfaces with
on coming air flow High and Low pressure zones develop due to
difference in air flow velocities [Bernoulli]
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Back Spin Top SpinBottom of ball moving
toward the direction of the ball’s flight
higher flow on top = pressure
lower flow on bottom= pressure
lift UPWARD
Top of the ball moving toward the direction of the ball’s flight
lower flow on top= pressure
higher flow on bottom = pressure
lift DOWNWARD
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Back Spin (top of ball moves backwards, away from ball’s flight path)
Back Spin produces upward Lift Force
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Top Spin (top of ball moves forward in the direction of ball’s flight path)
Top Spin produces downward Lift Force
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“Basic Biomechanics” Susan J. Hall page 531
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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