Flight Theory and Aerodynamics. Joseph R. Badick

Flight Theory and Aerodynamics - Joseph R. Badick


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Pitching moments on a symmetrical airfoil (a) at zero AOA and (b) at positive AOA.

Schematic illustration of the pitching moments on a cambered airfoil: (a) zero lift, (b) developing lift. Schematic illustration of flaps extended pitching moments.

      Source: U.S. Department of Transportation Federal Aviation Administration (2016a).

      For cambered airfoils, the CP moves along the chord line when the AOA changes. As the AOA increases, the CP moves forward and vice versa. This movement makes calculations involving stability and stress analysis very difficult from an engineering perspective. There is a point on an airfoil where the pitching moment is a constant with changing AOA, if the velocity is constant. This point is called the aerodynamic center (AC).

      The AC, unlike the CP, does not move with changes in AOA. If we consider the lift and drag forces as acting at the AC, the calculations will be greatly simplified. The location of the AC varies slightly, depending on airfoil shape. Subsonically, it is between 23 and 27% of the chord back from the leading edge. Supersonically, the AC shifts to the 50% chord.

      In summary, the pitching moment at the AC does not change when the angle of attack changes (at constant velocity) and all changes in lift effectively occur at the AC. As an airfoil experiences greater velocity, its AC commonly moves toward the trailing edge, with the AC near 25% chord subsonically and at 50% supersonically. A more detailed discussion on the aerodynamic center of a wing, and its relation to longitudinal stability, is found in Chapter 12.

      On 8 January 2003, Air Midwest Flight 5481 experienced a loss of pitch control on takeoff in Charlotte, NC and crashed, killing 2 crew members and 19 passengers. Several factors that led to this accident were topics addressed within this chapter and deserve application to the principles of aerodynamics and safety of flight. Due to the length of the NTSB accident report (NTSB/AAR‐04/01), only the factors that directly relate to this chapter will be discussed, and it is recommended that the reader review the entire accident report.

Schematic illustration of beech 1900D pitch control system.

      Source: Courtesy: National Transportation Safety Board.

      As the aircraft departed the runway, the nose experienced a pitch upward. Due to the aforementioned maintenance error, the pilots only had 7° AND travel with the elevator, about one‐half of normal travel. This resulted in an increasing angle of attack and the flight crew was unable to recover. In this example, the flight crew was not at fault and could not have known about the maintenance error. Chapter 4 contains a more detailed discussion on the importance of understanding the principles of lift, and the consequences on safety of flight if these principles are not understood.

AC Aerodynamic center
AF Aerodynamic force (lb)
AOA Angle of attack (degrees)
CP Center of pressure
D Drag (lb)
L Lift (lb)
RW Relative wind
α (alpha) Angle of attack (degrees)

      Aerodynamic center

      Aerodynamic force

      Aileron

      Airfoil

      Angle of attack

      Antiservo tab

      Center of pressure

      Chord

      Chord line

      Differential aileron

      Elevator

      Flaps

      Flight path

      Lateral axis

      Longitudinal axis

      Magnus effect

      Pitch

      Relative wind

      Roll

      Rudder


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