Dr. Eberhardt's Talk

Understanding Flight:
Newton Reigns in
Aerodynamics!
Scott Eberhardt
March 26, 2007

General Aviation

Military Aviation

Commercial Aviation

What you will learn today
• Some of the things you learned might
be wrong
• The physical description of lift, using
Newton’s Laws
• The connection between lift and power
• Some ideas about why wings look the
way they do

Descriptions of Lift

Explaining Lift
• Mathematical description
–Taught to Aeronautical Engineers
• Popular description
–Taught by flight schools, FAA,
NASA, etc
• Physical description
–What you are learning today

The Myth of the Bumblebee – The Aerodynamicist’s Bane
The tabloids do
it to science
again?
Aerodynamicist Proves
Bumblebees Can’t Fly!
Seattle
Muckraker
$1..00
September 10
Elvis is Alive,
Living in
Argentina
News Flash….
Britney Spears
to run for governor
of New York
Guru remains
in trance
for 20 years
..without food or drink
A 380
Giant fly
devours
jumbo jet
…. Hundreds missing
Astrophysicists find dark matter
…its cosmic cow poop

The Actual Origin of the Bumblebee Myth
From A. Magnan, Le Vol Des Insects,
Paris: Herman and Cle, 1934 (p. 8):
“Tout d’abord, pouss’e par ce qui fait en
aviation, j’ai applique’ aux insectes les
lois de la resistance del’air, et je suis
arrive’ avec M. [Andre] SAINTE-LAGUE a
cette conclusion que leur vol est
impossible.”

Popular Description of Lift
(what you might have learned)
• Bernoulli relates pressure to
velocity
• Focuses on shape of wing to
determine velocity
• Perpetuates Myths

Physical Description of Lift
“Forget Bernoulli’s Theorem”
Stick and Rudder, published 1944

Lift is a Reaction Force

Physical Description
• Based on Newton’s laws
• Easy to understand without
equations
• Leads to an understanding of
power required for flight

Newton’s Third Law
To every Action there is an
equal and opposite Reaction

Newton’s First Law
A body at rest will remain at rest,
or a body in motion will continue
in straight line motion unless subjected
to an external applied force

So….
For a wing to go up
it must force air down
Lots of air!

Cessna Citation flying over fog
(Photo By Paul Bowen)

A Rotating Wing Pushes Air Down

Does this picture show an
airfoil generating lift?

No, the air must experience a
net change, as shown below
Upwash
Downwash

Downwash
Wing pulls air down -- Downwash
Downwash is related to angle of
attack and airspeed, which the
pilot can control

Why does the air follow the
top surface of the wing?

Nature Abhors a Vacuum
This cannot happen

Air could fill from below?

Air could fill from below?
Can’t happen (except in “superfluids”)

Air could fill from back

Air could fill from back

Stall on flat plate

Air could fill from top

Air could fill from top

Air
Picture a curved hose
Force

Air
Hose is like an airfoil
Force

Viscosity
Force on glass
Force on water

Newton’s Second Law
The thrust of a rocket is equal to the
velocity of the exhaust times the amount
of mass ejected per second

Newton’s 2nd law
applied to a wing
The lift on a wing is proportional
to the amount of
air diverted per second times
the vertical velocity of the air
Lift = mass/sec * vertical velocity

Lift
So, wing diverts air down for lift
Lift = mass/sec * vertical velocity
or
Lift = (m/t) * V downwash
(m/t) is mass flow rate of air
pumped down

Diverted Air
The amount of air diverted is
proportional to:
•The speed
•The air density

The wing as a scoop
The scoop can be calculated with
the “Biot-Savart Law.”

Vertical Velocity
The vertical velocity is proportional
to:
•The speed
•The angle of attack

Vertical Velocity
a:
b:
c:
Speed (x2)
Downwash
Pilot controls airspeed and
angle of attack
α
Speed
α
Downwash
Speed
α(x2)
Downwash
Vv
Vv(x2)
Vv(x2)

Angle of Attack

Lift is a Function of
Lift
1
Angle of Attack
Critical angle of attack
5 10 15 20
Effective angle of attack (degrees)
(at constant density and speed)

Vertical Velocity
Vertical velocity is related to
angle of attack and the airspeed
of the wing
Pilot controls airspeed
and angle of attack

How much air is pushed
down?
A Cessna 172
diverts approximately
5 times its own weight per second!

What’s going on in this photo?

Summary of Lift
• Lift is proportional to:
Amount of air diverted per second
Downwash velocity of that air
• Amount of air diverted per second is proportional
to: Speed of wing
Density of air
• Downwash velocity of air is proportional to:
Angle of attack
Speed of wing

T=0
Myth: 1
Particles reach trailing edge at same time.
T f

With Equal Transit times,
How Can...
• An airfoil fly upside down?
• A paper airplane fly?
• A wing fly in ground effect?
Equal transit times says it can’t happen
Equal transit times is wrong!

Reality
Air goes much quicker over the top

Lift is a Function of
Lift
1
Angle of Attack
Critical angle of attack
5 10 15 20
Effective angle of attack (degrees)

Myth #2
These two pictures are not
the same thing

Cessna Citation flying over
fog
(Photo By Paul Bowen)

Summary of Lift
• Lift is proportional to:
Amount of air diverted per second
Downwash velocity of that air
• Amount of air diverted per second is proportional
to: Speed of wing
Density of air
• Downwash velocity of air is proportional to:
Angle of attack
Speed of wing

Power

If Lift didn’t require Power
• Planes would have same range
empty or full
• Helicopters could hover at any
altitude and load
• Propulsion would not require
power either (same physics)

Power required for lift
• Power is Force times Velocity
• “Induced Power” is the lift times
the vertical velocity
Induced Power = Lift * Vertical Velocity

What is the Lift?
•Lift = Weight
(for straight and level flight)
•Weight isn’t changing
•Lift is constant
So

How does Vertical Velocity
Change?
As speed increases, more air passes
past wing so the amount of air diverted
per second increases.
Lift = (m/t) * vertical velocity
or
Vertical velocity = Lift/(m/t)

Therefore, as speed increases,
downwash decreases

So,
Induced Power= Lift * Vertical Velocity
Induced Power decreases with speed!
But, don’t forget power to overcome
skin and form drag

Induced Power
At half the speed:
Half the air is diverted
therefore, you need to double
the vertical velocity by increasing
the angle of attack
Induced power goes as 1/speed

Power
120
100
80
60
40
20
0
Induced Power
Cessna 172 “Skyhawk”
0 20 40 60 80 100 120 140 160
V - mph

Parasitic Power
The energy loss to collision with the air
is proportional to speed squared (1/2mv 2 )
Number of collisions is proportional
to speed
Parasitic power goes as speed cubed

Power
120.0000
100.0000
80.0000
60.0000
40.0000
20.0000
0.0000
Parasitic Power
Cessna 172 “Skyhawk”
0 20 40 60 80 100 120 140 160
V - mph

Power
120.0
100.0
80.0
60.0
40.0
20.0
0.0
Power Required
Ve
0 50 100 150
V - mph

Langley’s Law

Summary of Power
• Lift requires power
• Power due to lift: Induced Power

Wing Efficiency

Wing Efficiency
• Induced power is proportional to lift times vertical
velocity
• If you double the span of the wing you double the
amount of air diverted and therefore halve the
vertical velocity
Induced Power and Induced Drag
decrease as wingspan increases

Gliders have efficient wings

Classical Aerodynamics
• Lift does no work!
• But, classical aerodynamics
assumes a wing of infinite span
if span -> infinity
power induced -> 0!

Summary
• Lift is a REACTION FORCE
• Lift is described using Newton’s
Laws
• Lift requires Power
• High span increases wing
efficiency

References
• http://home.comcast.net/~clipper-108/Professional.html
– English
– French
– Spanish
– Italian
– Japanese

Research Trends
• From the University Perspective
– “Smart” Structures
– Active Flow Control
– Coordinated and Formation Flying of UAV’s
– Better Materials
• From the Boeing Perspective:

Composite Structure
Lower Maintenance
Costs
Innovative Systems
Flexible for
the Future
Large Cargo
Capacity
More Revenue
Potential
Innovations That Add Value
Breakthrough
Cabin
Passenger
Preference
Advanced Wing
Enhanced
Efficiency
Enhanced
Flight Deck
Operational
Reliability
Advanced
Engines
Fuel Efficiency
Lower Noise

Many Thanks!