Aerodynamics

1
Lecture 4

• Aerodynamics
• Chapter 3, Jeppesen Sanderson
• Chapters 3 and 4, Kroes and Rardon

2
Overview of the Lecture

• Four forces in flight
• LIFT, WEIGHT, THRUST, DRAG
• Basic physics involved with these forces
• Important features and concepts involved with
  LIFT
• Three factors in LIFT
• How pilot can control LIFT
• WEIGHT, THRUST
• DRAG
• Ground Effect

3

• Four forces involved in flight
• LIFT WEIGHT THRUST DRAG

4
The four forces involved in flight

• Four forces are involved for an airplane to fly
• WEIGHT the gravitational force that pulls the
  plane down towards the center of the earth.
• LIFT the upward force that lift up the plane
  against its weight.
• THRUST the force that propels the plane
  forward. This forward movement also results in
  the lift with the help of the wings.
• DRAG the backward force opposing the forward
  movement of the plane. It comes from the
  resistance of the air to the movement.

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Equilibrium State

• When the LIFT equals the WEIGHT the plane stays
  at a constant height
• When the DRAG equals the THRUST the plane flies
  at a constant speed
• When these four forces balance each other they
  are said to be in equilibrium, and the plane
  stays at a constant height and travels at a
  constant speed.
• Fig on next page

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Equilibrium State
7
Some physical definitions

• A force is a physical entity which has a tendency
  to move objects.
• When a force is acting on a surface, the force
  acting on a unit area of the surface is called
  the pressure.
• Velocity of a moving object is its change of
  position in unit time.
• Acceleration of an object is its change of
  velocity in unit time. If it is unaccelerated
  (acceleration 0), that means its velocity
  remains constant.

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Components of a force (1)

• A force has a magnitude (strength) and a
  direction. Thus it can be represented by an
  arrow (called a vector). The length of the arrow
  represents the strength of the force and the
  direction of the arrow represents the force
  direction.

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Components of a force (2)

• A force can be broken up into two components
  using two arrows joined head-to-tail, the head of
  the first component overlaps with the head of the
  original vector, while the tail of the second
  component overlaps with the tail of the original
  vector.
• The effect of the two components acting together
  on an object will be exactly the same as the
  single original force acting on the object.

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Components of a force (3)

• Often, the two components are chosen so that they
  are perpendicular to each other.
• In such case, the two components are said to be
  independent of each other because each of them
  cannot be broken down again to include a
  sub-component that is parallel to the other
  component.

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Newtons 3 Laws of Motion

• Air flight (and all motion of objects) is
  governed by Newtons three laws of motion
• 1st Law (Inertia) An object at rest remains at
  rest and an object moving remains moving at the
  same speed and the same direction (unless acted
  upon by a force).
• 2nd Law (Fma) When an object is acted upon by
  a force, its acceleration is directly
  proportional to the strength of the force and
  inversely proportional to its own mass.
• 3rd Law (ActionReaction) For every (force)
  action there is an equal and opposite reaction.

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Bernoullis Principle

• From Newtons laws, a Swiss mathematician, Daniel
  Bernoulli, deduced a theorem that can apply to
  fluids, including air
• Bernoullis Principle As the velocity of a
  fluid (air) increases, its pressure decreases
• An experiment shown in Fig 3-3 illustrates
  Bernoullis principle.
• This principle is one of the major reason why
  well-designed wings can help lift the airplane.

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Illustrating Bernoullis Principle (Fig 3-3)
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Bernoullis Equation

• The above is the Bernoullis equation governing
  the relationship between velocity and pressure of
  an incompressible gas,
• v velocity of the gas
• g gravitational constant
• h the height where the gas is
• P pressure of the gas
• ? density of the gas
• You are NOT responsible for this equation

15
The Wing in Air Flow - LIFT (1)

• The wing of an airplane is called an airfoil .
  An airfoil is any surface that provides
  aerodynamic force when it interacts with moving
  air.
• Fig 3-4 shows the detailed design of a wing of
  an airplane and the surrounding air while the
  plane is flying.
• Notice that the curvature of the upper surface of
  the wing is more curved than the lower surface.
• The longer distance air has to travel along the
  upper surface than along the lower surface
  implies a higher air velocity over the upper
  surface relative to the velocity over the lower
  surface.

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Airflow around wing in flight (3-4)
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The Wing in Air Flow - LIFT (2)

• From Bernoullis principle, this means that the
  air pressure on the upper surface of the wing is
  lower than the pressure on the lower surface of
  the wing.
• As a result of this pressure difference, a LIFT
  force is applied to the wing by the moving air.
• This lifting force is one of the main forces
  lifting the airplane in the air.

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The Wing in Air Flow - LIFT (3)

• Notice also in Fig 3-4 that there is a downward
  movement of the air stream at the trailing edge
  of the wing.
• This downward air stream is called the downwash.
• By Newtons 3rd law, action reaction, this air
  downwash also produce an upward lifting force to
  the wing.
• This is a second source for the LIFT.

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The Wing in Air Flow - LIFT (4)

• As shown in Fig 3-4 the front of the wing is
  called its leading edge.
• The imaginary line joining the leading edge and
  the trailing edge is called the chord line of the
  wing. (Fig 3-5)
• Fig 3-5 also shows that a relative wind stream is
  formed in a direction approximately parallel and
  opposite to the flight path.

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Chord Line and Angle of Attack (from 3-5)
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The Wing in Air Flow - LIFT (5)

• The angle between the chord line and the
  direction of the relative wind is called the
  angle of attack. (see also Fig 3-5)
• When the angle of attack is positive (the wing
  tilting slightly upwards), the air stream of the
  relative wind strikes at the lower surface of the
  wing, resulting in a force on the wing that has
  an upward component.
• This provides the third LIFT to the wing.
• When the angle of attack increases the lift also
  increases.

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The Wing in Air Flow - LIFT (6)

• Thus there are three factors contributing to the
  LIFT force on a plane
• 1. The pressure difference between the upper and
  lower surfaces of the wing due to Bernoullis
  principle.
• 2. The reaction to the downwash at the trailing
  edge of the wing.
• 3. The air stream of the relative wind striking
  the lower surface of the wing when there is a
  positive angle of attack.

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LIFT Angle of Attack (1)

• The amount of LIFT increases as the angle of
  attack increases, to a certain maximum.
• If the angle of attack continues to increase
  beyond this critical angle of attack the lifting
  force, instead of keep increasing, decreases
  rapidly instead. (Fig. 3-7)
• Each plane has its own critical angle, usually
  around 15o.

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LIFT vs. Angle of Attack (3-7)
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Lift Equation

• The above is the Lift equation relating the Lift
  L, the coefficient of lift CL, the density of
  air?, the airspeed V, and the surface area of the
  airfoil A.
• CL is a function of the angle of attack as shown
  in Fig 3-7 in the previous slide.
• You are NOT responsible for this equation

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LIFT Angle of Attack (2)

• When the angle of attack goes considerably beyond
  the critical angle of attack the plane will
  stall, that is, the plane will start to lose its
  lift.
• In a stall the plane will start to go down.
  However because of the design of the center of
  gravity, the head will go down more, result in a
  decrease in the angle of attack.
• The onset of a stall is gradual. When you feel a
  stall is coming (or warned by a stall warning
  device) you must immediately decrease the angle
  of attack to restore smooth airflow.

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Pilot Control of Lift

• How can the pilot control the lift?
• Change the angle of attack with the elevator.
• Change the airspeed with the throttle. Lift is
  proportional to the square of the airplanes
  speed when other factors remain unchanged.
• Change the shape of the wing (the chord line)
  using the flap. For some type of flaps the wing
  area might also be changed.

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High Lift Devices the Flaps

• The flaps can increase the lift efficiency of the
  wing even at low speed.
• As shown in Fig 3-13, as the flap goes down, the
  chord line changes in a direction which increase
  the angle of attack.
• In another type of flaps called the Fowler flap
  which no only flips down but also extends out
  (Fig. 3-17), extension of the flap also enlarge
  the total surface area of the wing, resulting
  also an increase in lift.

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Flipping the flap down enlarge angle of attack
(3-13)
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Fowler Flap flips down and extends out (3-17)
31
Weight

• A second force acting on the plane is its weight.
• It is due to gravity acting on the center of the
  plane pulling the plane towards the center of the
  earth.
• The weight of a plane depends on the plane model,
  the equipments installed, passengers, cargo, and
  the fuel load.
• During the course of a flight the weight
  decreases as fuel is consumed. The lift to
  counterbalance the weigh has to be reduced
  accordingly.

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Thrust (1)

• The third force acting on the plane is the
  thrust, which is produced by the propeller or the
  air jet from the engine and moves the plane
  forward.
• At take off, the thrust is larger than the drag,
  resulting in a net forward force that accelerates
  the plane (increase its speed), due to Newtons
  2nd law.

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Thrust (2)

• During cruising (unaccelerated flight) thrust
  exactly counterbalance the drag, and the plane
  moves with a constant speed due to Newtons 1st
  law.
• If you increase the throttle the plane
  accelerates again because the thrust is larger
  than the drag again.
• However, as speed increases the drag also
  increases. Eventually thrust and drag become
  equal again and the plane travels at constant
  speed again (but faster than before).

34
Drag

• The 4th (and last) force acting on the plane is
  the drag.
• Drag is due to resistance of the air. This
  resistance acts in a direction opposite to the
  movement of the plane and limits its movement.
• There are two kinds of drag parasite drag and
  induced drag.

35
Parasite Drag

• Parasite drag is due to any objects sticking out
  the smooth surface of the plane and interfere
  with the smooth airflow around the pane.
• It is proportional to the square of the airspeed
  around the plane.

36
Induced Drag

• Induced drag is generated by the airflow
  circulation around the wing as it creates lift.
• Because the downwash air stream at the back of
  the wing mentioned earlier moves downwards and
  backwards, the average air stream actually points
  a little bit down instead of straightly opposite
  to the direction of flight.
• Thus the lift has a small backward component in
  addition to the large upward component.
• This backward component is the induced drag.
• The change of geometry at the wing tip also
  causes air current to add to this drag.

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Total Drag

• Different from parasite drag the induced drag
  decreases with increasing airspeed.
• Fig 3-24 plots the parasite drag, the induced
  drag, and their sum (total drag) against
  airspeed.
• At the point where total drag is a minimum, the
  ratio lift/drag is at a maximum. This point is
  called L/Dmax and is a favorable point for the
  airplanes performance.

38
Parasite, Induced, Total Drag Forces (3-24)
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Drag Equation

• The above is the Drag equation
• D is the drag force
• ?is the density of air
• V is the airspeed
• A is the surface area of the airfoil
• CD the coefficient of drag and depends on the
  geometry and material of the wing
• You are NOT responsible for this equation

40
Ground Effect (1)

• When the wing is close to the ground, at about
  its own length from ground or less, the earths
  surface changes the 3-dimensional airflow
  pattern.
• This changes the downwash and the wingtip effect,
  resulting in a reduction of the induced drag.
• When the wing is about half its length from the
  ground, induced drag reduces by about 25.

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Ground Effect (2)

• Because of this reduction in drag, the plane can
  take off with a thrust smaller than it would have
  been.
• However, when the plane leaves ground and the
  wing is away from the ground by a distance more
  than its length, the drag suddenly increases. If
  you do not have enough thrust the plane might
  sink back onto the ground.

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Ground Effect (3)

• Ground effect is noticeable in landing too. When
  the plane gets close to the ground, the drag
  suddenly reduces and you might feel that your
  plane is floating on a cushion of air beneath it.
• You will have to reduce the power further to help
  the airplane land.