John Kallend Ph.D.John Kallend Ph.D.

Professor, Department of Mechanical, MaterialsProfessor, Department of Mechanical, Materials

and Aerospace Engineeringand Aerospace Engineering

Illinois Institute of TechnologyIllinois Institute of Technology

Physics and Skydiving?You must be kidding!

GravityGravity

Laws of motionLaws of motion

AerodynamicsAerodynamics

Air density, pressure, temperatureAir density, pressure, temperature

Design of Equipment and InstrumentsDesign of Equipment and Instruments

Materials for equipment.Materials for equipment.

Deflecting air forwards causes the Deflecting air forwards causes the skydiver to move rearwards skydiver to move rearwards (Newton’s 3rd law)(Newton’s 3rd law)..

Forward motion is achieved Forward motion is achieved by deflecting air backwardsby deflecting air backwards

Twisting the body deflects air to the side Twisting the body deflects air to the side and allows the skydiver to turn and steer.and allows the skydiver to turn and steer.

A modern parachute has two surfaces and A modern parachute has two surfaces and is inflated by air entering the front. When is inflated by air entering the front. When inflated it has the shape of a wing. It flies inflated it has the shape of a wing. It flies forward three feet for every foot it forward three feet for every foot it descends.descends.

The parachute flies forward at The parachute flies forward at around 30mph, and descends at around 30mph, and descends at 10mph. It is fully steerable, 10mph. It is fully steerable, like a glider.like a glider.

Control lines attached to Control lines attached to the canopy pull down the the canopy pull down the rear to (a) deflect air rear to (a) deflect air downwards and (b) downwards and (b) increase drag. This slows increase drag. This slows the jumper down for the jumper down for landing.landing.

FREEFALL!

HOW FAST DO YOU GO?

What is “Terminal Velocity”?

Drag = 0.5 A Cd

v2

Gravity = mg

Fall rate is controlled by the balance Fall rate is controlled by the balance between gravity and air resistancebetween gravity and air resistance

DragDrag = 0.5 = 0.5 A CA Cd d vv22

is the density of the air (1.23kg/mis the density of the air (1.23kg/m3 3 at sea level)at sea level)

A is the frontal area of the objectA is the frontal area of the object

CCdd is the “drag coefficient” which measures how is the “drag coefficient” which measures how

streamlined and slippery the object isstreamlined and slippery the object is

v is the velocityv is the velocity

Forces acting on skydiver

0

500

1000

1500

2000

2500

0 10 20 30 40 50 60 70 80 90 100

Speed (m/s)

Ne

wto

ns

gravity

drag

Forces Acting on 70Kg Skydiver

Terminal VelocityTerminal Velocity

Drag = 0.5 A Cd

v2

Gravity = mg

Fall rate is controlled by the balance Fall rate is controlled by the balance between gravity and air resistancebetween gravity and air resistance

Velocity vs Time after Jumping from 4,300m

Speed (m/s)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18

Time (s)

Sp

ee

d (

m/s

)

Speed (m/s)

Distance vs Time after Jumping from 4,300mdistance

0

100

200

300

400

500

600

700

800

900

0 2 4 6 8 10 12 14 16 18

time (seconds)

dis

tan

ce

(m

)

distance

How to Change Fall RateHow to Change Fall Rate

1.1. Change Cd (body position, jumpsuit)Change Cd (body position, jumpsuit)

2.2. Change mass (weight vest, tandem)Change mass (weight vest, tandem)

3.3. Change area presented to the windChange area presented to the wind

4. 4. Change air density (altitude) Change air density (altitude)

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 > 300mph

AIR DENSITY vs ALTITUDE

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Altitude (1000 ft)

Fra

ctio

n o

f se

a le

ve

l va

lue

Series3

Air density varies with altitude

(h)(0) e- 0.0000306h

Terminal Velocity

0

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Altitude (ft)

MP

H Belly to Earth

Head down

Terminal velocity increases as air density decreasesTerminal velocity increases as air density decreases

So you go slower the farther you fall!So you go slower the farther you fall!

Hollywood SkydivingHollywood SkydivingClips from “Point Break” Clips from “Point Break”

IIT DOES NOT CONDONE IIT DOES NOT CONDONE THE USE OF BAD THE USE OF BAD

LANGUAGE IN THE LANGUAGE IN THE MOVIE CLIPS!MOVIE CLIPS!

SPOT THE PHYSICS ERRORSSPOT THE PHYSICS ERRORS

At 125 mph it takes approximately 5 seconds to fallAt 125 mph it takes approximately 5 seconds to fall1000ft. It takes about 10 seconds to reach 1000ft. It takes about 10 seconds to reach terminal velocity, which also covers 1000ft.terminal velocity, which also covers 1000ft.

SO - a jumper leaving a plane at 12,000 feet willSO - a jumper leaving a plane at 12,000 feet will

take 65 seconds to reach the ground.take 65 seconds to reach the ground.

ORORA freefall lasting 4 minutes must exit the plane A freefall lasting 4 minutes must exit the plane atatan altitude of 47,000 ft even if we ignore the an altitude of 47,000 ft even if we ignore the increase in terminal velocity due to the extremeincrease in terminal velocity due to the extremealtitude (in fact, it’s 59,000 ft if you account for altitude (in fact, it’s 59,000 ft if you account for this). this).

Ever feel left behind?Ever feel left behind?

In a 125mph freefall, a skydiver who leaves In a 125mph freefall, a skydiver who leaves 1 second late will be left 180 ft behind his or 1 second late will be left 180 ft behind his or her partner(s)her partner(s)

A jumper who waits 8 seconds will be 1,440 A jumper who waits 8 seconds will be 1,440 feet behind (about the height of Sears feet behind (about the height of Sears Tower).Tower).

HOW ABOUT THOSE DRAMATIC RESCUES?HOW ABOUT THOSE DRAMATIC RESCUES?

Two skydivers holding on to each other willTwo skydivers holding on to each other will

fall at about 1.4 times the speed of a solo jumperfall at about 1.4 times the speed of a solo jumper

(175mph or 260 ft/sec).(175mph or 260 ft/sec).

The parachute takes about 2 seconds to slow you The parachute takes about 2 seconds to slow you

down, so the deceleration is 260/2 = 130 ft/secdown, so the deceleration is 260/2 = 130 ft/sec22

which is 4g. If the person weighs 140lb theywhich is 4g. If the person weighs 140lb they

will have to be able to hold on with a force ofwill have to be able to hold on with a force of

700 pounds! Not very likely!700 pounds! Not very likely!

Projectile Motion !

vvvvyy

vvxx

DD

Dx

DDyy

mgmg

D = - k vD = - k v2 2 = -k (v= -k (vxx22+ v+ vyy

2 2 ))

DDx x = - k (v = - k (vxx22+ v+ vyy

2 2) v) vxx / / (v (vxx22+ v+ vyy

2 2 ))

m dvm dvxx/dt = - k v/dt = - k vxx (v (vxx22+ v+ vyy

2 2 ))

SimilarlySimilarly

m dvm dvyy/dt = - k v/dt = - k vyy (v (vxx22+ v+ vyy

2 2 ) -mg) -mg

Avoiding Mid-Air Collisions

2-d Model2-d Model

Thank you for your Thank you for your attention.attention.

Physics Rules!Physics Rules!