Dr. Eberhardt's Talk

physics.ohio.state.edu

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!

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