Airplanes

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Airplanes

• Physics of Modern Devices
• January 28, 2009

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What makes an airplane fly?

• Almost everyone has flown in a plane these days,
  but how does it work?

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Observations about Airplanes

• Airplanes support themselves in the air
• Airplanes seem to follow their tilt, up or down
• Airplanes need airspeed to fly
• Airplanes can rise only so quickly
• Airplane wings often change shape in flight
• Airplanes have various propulsion systems

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Aerodynamic Forces

• First lets review the aerodynamic forces
• Drag
• Lift
• Sometimes I will use a baseball as an example.

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Aerodynamic Forces Drag

• Air resistance is also known as drag
• When an object (e.g. a ball) moves through air,
  drag forces arise
• The air pushes the ball downstream
• and the ball pushes the air upstream
• Drag forces transfer momentum
• air transfers downstream momentum to ball
• ball transfers upstream momentum to air

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Reynolds number

• The Reynolds number is used to indicated whether
  the drag on an object is mainly the result of
  viscous or form (depends on shape of object)
  resistance.
• Dimensionless quantity
• Viscous drag predominates when Rlt1
• Small objects moving slowly through viscous
  fluids
• As R becomes larger
• Form resistance becomes increasingly more
  significant
• Baseballs, tennis balls, etc have R 104-105

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Drag, cont

• Drag coefficient
• Depends on nature of object
• Size, shape, irregularity, roughness
• Characteristics of the flow
• The more streamlined the object, the lower the
  drag coefficient
• Determined by direct measurement
• Usually given as a function of the Reynolds number

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CD vs. R

• For a smooth sphere
• CD large at low R
• Viscous resistance dominates
• Decreases rapidly as R increases
• For R 103-105 , CD constant at 0.5
• Rgt105 CD dips sharply and then levels off
• Transition due to fluid flow in boundary layer
  changing from smooth motion to turbulent motion

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Perfect Flow Around a Ball

• Air bends away from balls front
• high pressure, slow flow
• Air bends toward balls sides
• low pressure, fast flow
• Air bends away from balls back
• high pressure, slow flow
• Pressures balance perfectly, so only viscous drag

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The Onset of Turbulence

• Air flowing into the rising pressure behind ball
• accelerates backward (decelerates)
• and it loses speed and kinetic energy
• Air flowing near the balls surface
• experiences viscous drag,
• accelerates backward even more,
• and rapidly loses speed and kinetic energy
• If this surface flow stops, turbulence ensues

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Example of Turbulent Flow

• Smoke rising from a cigarette
• Shows a transition from steady flow to non-steady
  or turbulent flow.
• The speed of the smoke particles increases as
  they rise and, at a certain critical speed, the
  flow changes character from steady to non-steady.

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Imperfect Flow a Slow Ball

• Pressure rises in front
• Pressure drops on side
• Flow detaches just beyond sides
• Big wake (air trail free of turbulence) forms
  behind ball
• Large Turbulent Wake
• Wake pressure is nearly ambient
• Ball experiences imbalancedpressure big
  pressure drag

R 2000-100,000
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Imperfect Flow a Fast Ball

• Pressure rises in front
• Pressure drops on side
• Flow detaches near back of ball
• Small wake forms behind ball
• Small Turbulent Wake
• Wake pressure is nearly ambient
• Ball experiences imbalancedpressure small
  pressure drag

R gt 100,000
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Aerodynamic Forces Lift

• When a ball deflects passing air, lift forces
  arise
• the air pushes the ball to one side
• and the ball pushes the air to the other side
• Lift forces transfer momentum
• air transfers sideways momentum to ball
• ball transfers sideways momentum to air
• This is dynamic lift and not to be confused with
  buoyant or static lift, in accordance with
  Archimedes principle.
• Dynamic lift act only when the object and the
  fluid stream are in relative motion.

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Bernoulli and the Lift Force
The more air diverted under the wing and the
faster the velocity of the air, the greater the
lift force!
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7 Questions about Airplanes

• How does an airplane support itself in the air?
• How does the airplane lift off the runway?
• Why does plane tilt up to rise, down to descend?
• Why are there different wing shapes?
• How does a plane turn?
• How does a plane propel itself through the air?
• How can one measure the speed of the plane
  relative to the air?

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Question 1

• How does an airplane support itself in the air?
• What pushes up on airplane to balance its weight?
• What does it do with the momentum gravity gives
  it?

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Using a Wing to Obtain Lift (part 1)

• As air flows under a wing,
• air bends away from the wing
• airs pressure rises, speed drops
• As air flows over the wing,
• air bends toward the wing
• airs pressure drops, speed rises

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Using a Wing to Obtain Lift (part 2)

• The wing experiences
• a strong upward lift force
• a small downstream drag force
• Wing pushes air down, air pushes wing up!
• Downward momentum is transferred from
• the earth to the airplane by gravity
• the airplane to the air by lift forces
• from the air to the earth by pressure on the
  ground

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Problem

• A small plane has a wing area of 9.3 m2 (100
  ft2). At a certain air speed, air flows over the
  upper wing surface at 49 m/s (160 ft/s) and over
  the lower wing surface at 40 m/s (130 ft/s).
  What is the weight of the plane?

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Answer
One wing
FL
W/2
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Question 2

• How does the airplane lift off the runway?
• How does the pilot initiate the rise?
• How is landing different from takeoff?

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At Take-Off

• As a wing starts moving in air
• the airflow is symmetric
• and the wing experiences no lift
• However, this airflow is
• unstable at trailing edge bend
• and the wing sheds a vortex
• After the vortex leaves, the wing has lift

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Producing Lift
Example smoke trails in a wind tunnel
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Question 3

• Why does plane tilt up to rise, down to descend?
• Does a plane always go in the direction its
  pointed?
• How can plane land if its nose is higher than its
  tail?

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Angle of Attack

• A wings lift depends on
• the shape of its airfoil
• and on its angle of attackits tilt relative to
  the wind
• Tilting an airplanes wings
• changes the net force on the airplane
• and can make the airplane accelerate up or down
• but usually requires tilting the airplanes
  fuselage
• Planes tilt controls lift, not direction of
  travel

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Lift vs. angle of attack

• Typically, the lift begins to decrease at a
  "critical angle" of attack of about 15 degrees.
• The forces necessary to bend the air to such a
  steep angle are greater than the viscosity of the
  air will support, and the air begins to separate
  from the wing, or stall.

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Limits to Lift Stalling

• At too great an angle of attack,
• Upper boundary layer stalls
• Airstream detaches from wing
• Lift nearly vanishes
• Pressure drag appear
• Wing cant support plane
• Plane plummets abruptly

Example smoke trails in a wind tunnel
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Question 4

• Why are there different wing shapes?

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Wing Shape

• Asymmetric airfoils produce large lifts
• well suited to low-speed flight
• Symmetric airfoils produce small lifts
• well suited to high-speed flight
• can fly inverted easily
• High-speed planes often change wing shape in
  flight

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Question 5

• How does a plane turn?

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Turning and Orientation

• Airplanes also use lift to accelerate to the side
• Three orientation controls
• Angle of attack controlled by elevators
• Left-right tilt controlled by ailerons
• Left-right rotation controlled by rudder
• Steering involves ailerons and rudder
• Elevation involves elevators and engine

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Question 6

• How does a plane propel itself through the air?
• How does a plane maintain its forward momentum?

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Propellers

• Propellers are spinning wings
• They deflect air backward
• Do work on air (add energy)
• Pump air toward rear of plane
• Action-Reaction
• They push the air backward
• Air pushes them forward

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Jet Engines (Part 1)

• Jet engines pump air toward rear of plane
• Engine consists of an oval ball with a
  complicated duct or passageway through it
• Air inside the duct exchanges pressure andspeed
  repeatedly
• Engine addsenergy to airinside the duct

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Jet Engines (Part 2)

• Air entering diffuser slows and its pressure
  rises
• Compressor does work on air
• Fuel is added to air and that mixture is burned
• Expanding exhaust gas does work on turbine
• As exhaust leavesnozzle it speeds upand
  pressure drops

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Jet Engines (Part 3)

• Turbojet obtains forward momentum by
• moving relatively little air
• giving that air too much energy
• Turbofan obtains forward momentum by
• moving much more air
• giving that air less energy

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Question 7

• How can one measure the speed of the plane
  relative to the air?

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Air-speed indicator Pitot tube

• Air flows past opening at point b
• Velocity of air reduced to zero at point a
• Applying Bernoullis equation
• Device can be calibrated to read v directly and
  is then known as an air-speed indicator.

Cross-sectional diagram of a Pitot tube
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Problem

• A Pitot tube is mounted on an airplane wing to
  determine the speed of the plane relative to the
  air, which is at 0oC. The tube contains alcohol
  and indicates a level difference of 26 cm. What
  is the planes speed relative to air? (?alcohol
  0.81x103kg/m3)

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Summary about Airplanes

• Airplanes use lift to support themselves
• Propulsion overcomes induced drag
• Speed and angle of attack affect altitude
• Extreme angle of attack causes stalling
• Propellers do work on passing airstream
• Jet engines do work on slowed airstream
• HW1 due on Monday Feb 2.