The Physics of Skydiving

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The Physics of Skydiving
John Kallend Ph.D. Professor, Department of
Mechanical, Materials and Aerospace
Engineering Illinois Institute of Technology
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Physics and Skydiving?You must be kidding!
Gravity Laws of motion Aerodynamics Air
density, 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?
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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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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
velocity 110 to 130 mph,
Small frontal area, low Cd, terminal velocity gt
300mph
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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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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 the
increase in terminal velocity due to the
extreme altitude (in fact, its 59,000 ft if you
account 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 takes 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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Thank you for your attention.
Physics Rules!