# Dr. Eberhardt's Talk

Dr. Eberhardt's Talk

Dr. Eberhardt's Talk

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Understanding Flight:<br />

Newton Reigns in<br />

Aerodynamics!<br />

Scott Eberhardt<br />

March 26, 2007

General Aviation

Military Aviation

Commercial Aviation

What you will learn today<br />

• Some of the things you learned might<br />

be wrong<br />

• The physical description of lift, using<br />

Newton’s Laws<br />

• The connection between lift and power<br />

• Some ideas about why wings look the<br />

way they do

Descriptions of Lift

Explaining Lift<br />

• Mathematical description<br />

–Taught to Aeronautical Engineers<br />

• Popular description<br />

–Taught by flight schools, FAA,<br />

NASA, etc<br />

• Physical description<br />

–What you are learning today

The Myth of the Bumblebee – The Aerodynamicist’s Bane<br />

The tabloids do<br />

it to science<br />

again?<br />

Aerodynamicist Proves<br />

Bumblebees Can’t Fly!<br />

Seattle<br />

Muckraker<br />

$1..00<br />

September 10<br />

Elvis is Alive,<br />

Living in<br />

Argentina<br />

News Flash….<br />

Britney Spears<br />

to run for governor<br />

of New York<br />

Guru remains<br />

in trance<br />

for 20 years<br />

..without food or drink<br />

A 380<br />

Giant fly<br />

devours<br />

jumbo jet<br />

…. Hundreds missing<br />

Astrophysicists find dark matter<br />

…its cosmic cow poop

The Actual Origin of the Bumblebee Myth<br />

From A. Magnan, Le Vol Des Insects,<br />

Paris: Herman and Cle, 1934 (p. 8):<br />

“Tout d’abord, pouss’e par ce qui fait en<br />

aviation, j’ai applique’ aux insectes les<br />

lois de la resistance del’air, et je suis<br />

arrive’ avec M. [Andre] SAINTE-LAGUE a<br />

cette conclusion que leur vol est<br />

impossible.”

Popular Description of Lift<br />

(what you might have learned)<br />

• Bernoulli relates pressure to<br />

velocity<br />

• Focuses on shape of wing to<br />

determine velocity<br />

• Perpetuates Myths

Physical Description of Lift<br />

“Forget Bernoulli’s Theorem”<br />

Stick and Rudder, published 1944

Lift is a Reaction Force

Physical Description<br />

• Based on Newton’s laws<br />

• Easy to understand without<br />

equations<br />

• Leads to an understanding of<br />

power required for flight

Newton’s Third Law<br />

To every Action there is an<br />

equal and opposite Reaction

Newton’s First Law<br />

A body at rest will remain at rest,<br />

or a body in motion will continue<br />

in straight line motion unless subjected<br />

to an external applied force

So….<br />

For a wing to go up<br />

it must force air down<br />

Lots of air!

Cessna Citation flying over fog<br />

(Photo By Paul Bowen)

A Rotating Wing Pushes Air Down

Does this picture show an<br />

airfoil generating lift?

No, the air must experience a<br />

net change, as shown below<br />

Upwash<br />

Downwash

Downwash<br />

Wing pulls air down -- Downwash<br />

Downwash is related to angle of<br />

attack and airspeed, which the<br />

pilot can control

Why does the air follow the<br />

top surface of the wing?

Nature Abhors a Vacuum<br />

This cannot happen

Air could fill from below?

Air could fill from below?<br />

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<br />

Picture a curved hose<br />

Force

Air<br />

Hose is like an airfoil<br />

Force

Viscosity<br />

Force on glass<br />

Force on water

Newton’s Second Law<br />

The thrust of a rocket is equal to the<br />

velocity of the exhaust times the amount<br />

of mass ejected per second

Newton’s 2nd law<br />

applied to a wing<br />

The lift on a wing is proportional<br />

to the amount of<br />

air diverted per second times<br />

the vertical velocity of the air<br />

Lift = mass/sec * vertical velocity

Lift<br />

So, wing diverts air down for lift<br />

Lift = mass/sec * vertical velocity<br />

or<br />

Lift = (m/t) * V downwash<br />

(m/t) is mass flow rate of air<br />

pumped down

Diverted Air<br />

The amount of air diverted is<br />

proportional to:<br />

•The speed<br />

•The air density

The wing as a scoop<br />

The scoop can be calculated with<br />

the “Biot-Savart Law.”

Vertical Velocity<br />

The vertical velocity is proportional<br />

to:<br />

•The speed<br />

•The angle of attack

Vertical Velocity<br />

a:<br />

b:<br />

c:<br />

Speed (x2)<br />

Downwash<br />

Pilot controls airspeed and<br />

angle of attack<br />

α<br />

Speed<br />

α<br />

Downwash<br />

Speed<br />

α(x2)<br />

Downwash<br />

Vv<br />

Vv(x2)<br />

Vv(x2)

Angle of Attack

Lift is a Function of<br />

Lift<br />

1<br />

Angle of Attack<br />

Critical angle of attack<br />

5 10 15 20<br />

Effective angle of attack (degrees)<br />

(at constant density and speed)

Vertical Velocity<br />

Vertical velocity is related to<br />

angle of attack and the airspeed<br />

of the wing<br />

Pilot controls airspeed<br />

and angle of attack

How much air is pushed<br />

down?<br />

A Cessna 172<br />

diverts approximately<br />

5 times its own weight per second!

What’s going on in this photo?

Summary of Lift<br />

• Lift is proportional to:<br />

Amount of air diverted per second<br />

Downwash velocity of that air<br />

• Amount of air diverted per second is proportional<br />

to: Speed of wing<br />

Density of air<br />

• Downwash velocity of air is proportional to:<br />

Angle of attack<br />

Speed of wing

T=0<br />

Myth: 1<br />

Particles reach trailing edge at same time.<br />

T f

With Equal Transit times,<br />

How Can...<br />

• An airfoil fly upside down?<br />

• A paper airplane fly?<br />

• A wing fly in ground effect?<br />

Equal transit times says it can’t happen<br />

Equal transit times is wrong!

Reality<br />

Air goes much quicker over the top

Lift is a Function of<br />

Lift<br />

1<br />

Angle of Attack<br />

Critical angle of attack<br />

5 10 15 20<br />

Effective angle of attack (degrees)

Myth #2<br />

These two pictures are not<br />

the same thing

Cessna Citation flying over<br />

fog<br />

(Photo By Paul Bowen)

Summary of Lift<br />

• Lift is proportional to:<br />

Amount of air diverted per second<br />

Downwash velocity of that air<br />

• Amount of air diverted per second is proportional<br />

to: Speed of wing<br />

Density of air<br />

• Downwash velocity of air is proportional to:<br />

Angle of attack<br />

Speed of wing

Power

If Lift didn’t require Power<br />

• Planes would have same range<br />

empty or full<br />

• Helicopters could hover at any<br />

altitude and load<br />

• Propulsion would not require<br />

power either (same physics)

Power required for lift<br />

• Power is Force times Velocity<br />

• “Induced Power” is the lift times<br />

the vertical velocity<br />

Induced Power = Lift * Vertical Velocity

What is the Lift?<br />

•Lift = Weight<br />

(for straight and level flight)<br />

•Weight isn’t changing<br />

•Lift is constant<br />

So

How does Vertical Velocity<br />

Change?<br />

As speed increases, more air passes<br />

past wing so the amount of air diverted<br />

per second increases.<br />

Lift = (m/t) * vertical velocity<br />

or<br />

Vertical velocity = Lift/(m/t)

Therefore, as speed increases,<br />

downwash decreases

So,<br />

Induced Power= Lift * Vertical Velocity<br />

Induced Power decreases with speed!<br />

But, don’t forget power to overcome<br />

skin and form drag

Induced Power<br />

At half the speed:<br />

Half the air is diverted<br />

therefore, you need to double<br />

the vertical velocity by increasing<br />

the angle of attack<br />

Induced power goes as 1/speed

Power<br />

120<br />

100<br />

80<br />

60<br />

40<br />

20<br />

0<br />

Induced Power<br />

Cessna 172 “Skyhawk”<br />

0 20 40 60 80 100 120 140 160<br />

V - mph

Parasitic Power<br />

The energy loss to collision with the air<br />

is proportional to speed squared (1/2mv 2 )<br />

Number of collisions is proportional<br />

to speed<br />

Parasitic power goes as speed cubed

Power<br />

120.0000<br />

100.0000<br />

80.0000<br />

60.0000<br />

40.0000<br />

20.0000<br />

0.0000<br />

Parasitic Power<br />

Cessna 172 “Skyhawk”<br />

0 20 40 60 80 100 120 140 160<br />

V - mph

Power<br />

120.0<br />

100.0<br />

80.0<br />

60.0<br />

40.0<br />

20.0<br />

0.0<br />

Power Required<br />

Ve<br />

0 50 100 150<br />

V - mph

Langley’s Law

Summary of Power<br />

• Lift requires power<br />

• Power due to lift: Induced Power

Wing Efficiency

Wing Efficiency<br />

• Induced power is proportional to lift times vertical<br />

velocity<br />

• If you double the span of the wing you double the<br />

amount of air diverted and therefore halve the<br />

vertical velocity<br />

Induced Power and Induced <strong>Dr</strong>ag<br />

decrease as wingspan increases

Gliders have efficient wings

Classical Aerodynamics<br />

• Lift does no work!<br />

• But, classical aerodynamics<br />

assumes a wing of infinite span<br />

if span -> infinity<br />

power induced -> 0!

Summary<br />

• Lift is a REACTION FORCE<br />

• Lift is described using Newton’s<br />

Laws<br />

• Lift requires Power<br />

• High span increases wing<br />

efficiency

References<br />

• http://home.comcast.net/~clipper-108/Professional.html<br />

– English<br />

– French<br />

– Spanish<br />

– Italian<br />

– Japanese

Research Trends<br />

• From the University Perspective<br />

– “Smart” Structures<br />

– Active Flow Control<br />

– Coordinated and Formation Flying of UAV’s<br />

– Better Materials<br />

• From the Boeing Perspective:

Composite Structure<br />

Lower Maintenance<br />

Costs<br />

Innovative Systems<br />

Flexible for<br />

the Future<br />

Large Cargo<br />

Capacity<br />

More Revenue<br />

Potential<br />

Innovations That Add Value<br />

Breakthrough<br />

Cabin<br />

Passenger<br />

Preference<br />

Advanced Wing<br />

Enhanced<br />

Efficiency<br />

Enhanced<br />

Flight Deck<br />

Operational<br />

Reliability<br />

Advanced<br />

Engines<br />

Fuel Efficiency<br />

Lower Noise

Many Thanks!