John Kallend Ph.D.

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John Kallend Ph.D. Professor, Department of Mech
anical, Materials and Aerospace Engineering Il
linois Institute of Technology
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Physics and Skydiving?You must be kidding!
Gravity Laws of motion Aerodynamics Air densi
ty, pressure, temperature Design of Equipment and
Instruments
Materials for equipment.
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Deflecting air forwards causes the skydiver to
move rearwards (Newtons 3rd law).
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Forward motion is achieved by deflecting air
backwards
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Twisting the body deflects air to the side and
allows the skydiver to turn and steer.
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A modern parachute has two surfaces and is
inflated by air entering the front. When
inflated it has the shape of a wing. It flies
forward three feet for every foot it descends.
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The parachute flies forward at around 30mph, and
descends at 10mph. It is fully steerable, like a
glider.

Control lines attached to the canopy pull down
the rear to (a) deflect air downwards and (b)
increase drag. This slows the jumper down for
landing.
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FREEFALL!HOW FAST DO YOU GO?What is Terminal
Velocity?
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Fall rate is controlled by the balance between
gravity and air resistance
Drag 0.5 ? A Cd v2
Gravity mg
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Drag 0.5 ? A Cd v2
? is the density of the air (1.23kg/m3 at sea
level) A is the frontal area of the object Cd is
the drag coefficient which measures how
streamlined and slippery the object is
v is the velocity
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Forces Acting on 70Kg Skydiver
Terminal Velocity
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Fall rate is controlled by the balance between
gravity and air resistance
Drag 0.5 ? A Cd v2
Gravity mg
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Velocity vs Time after Jumping from 4,300m
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Distance vs Time after Jumping from 4,300m
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How to Change Fall Rate
1. Change Cd (body position, jumpsuit)
2. Change mass (weight vest, tandem)
3. Change area presented to the wind
4. Change air density (altitude)
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The skydiver can control fall rate by changing
frontal area and drag coefficient
Large area exposed to wind, high Cd terminal vel
ocity 110
to 130 mph,
Small frontal area, low Cd, terminal velocity 3
00mph
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Air density varies with altitude
?(h) ?(0) e- 0.0000306h
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Terminal velocity increases as air density
decreases
So you go slower the farther you fall!
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Hollywood SkydivingClips from Point Break
SPOT THE PHYSICS ERRORS
IIT DOES NOT CONDONE THE USE OF BAD LANGUAGE IN
THE MOVIE CLIPS!

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At 125 mph it takes approximately 5 seconds to
fall 1000ft. It takes about 10 seconds to reach

terminal velocity, which also covers 1000ft.
SO - a jumper leaving a plane at 12,000 feet
will
take 65 seconds to reach the ground.
OR
A freefall lasting 4 minutes must exit the plane
at an altitude of 47,000 ft even if we ignore th
e increase in terminal velocity due to the extre
me altitude (in fact, its 59,000 ft if you accou
nt for this).
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Ever feel left behind?
In a 125mph freefall, a skydiver who leaves 1
second late will be left 180 ft behind his or her
partner(s) A jumper who waits 8 seconds will be
1,440 feet behind (about the height of Sears
Tower).
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HOW ABOUT THOSE DRAMATIC RESCUES?
Two skydivers holding on to each other will
fall at about 1.4 times the speed of a solo
jumper (175mph or 260 ft/sec). The parachute ta
kes about 2 seconds to slow you
down, so the deceleration is 260/2 130 ft/sec2
which is 4g. If the person weighs 140lb they
will have to be able to hold on with a force of
700 pounds! Not very likely!
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Projectile Motion !
v
vy
?
Dx
?
vx
Dy
D
mg
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D - k v2 -k (vx2 vy 2 )
Dx - k (vx2 vy 2) vx / ? (vx2 vy 2 ) m d
vx/dt - k vx ? (vx2 vy 2 )
Similarly m dvy/dt - k vy ? (vx2 vy 2 )
-mg
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Avoiding Mid-Air Collisions
2-d Model
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Thank you for your attention.
Physics Rules!