CR

2.02 - 4 Forces

The Four Forces of Flight

  • In flight, an airplane is acted on by four forces: Lift (L), Weight (W), Thrust (T), and Drag (D).
    • Lift: upward force generated by the wings as air flows around them; it keeps the airplane in the air.
    • Weight: downward force toward the center of the earth, opposite lift, due to gravity.
    • Thrust: forward force typically produced by propellers or turbine engines; pushes or pulls the aircraft through the air.
    • Drag: force opposite to thrust; it limits the airplane’s performance.
  • Straight and level flight (unaccelerated) vs accelerated flight:
    • In straight and level flight, the aircraft maintains constant altitude and airspeed.
    • In accelerated flight, Lift equals Weight and Thrust equals Drag (L = W and T = D).

Airfoils and Lift Generation

  • An airfoil is a surface that generates aerodynamic force as air flows around it. In this course, wings, flight control surfaces, and the propeller are treated as airfoils. The fuselage can act as an airfoil, but is not very lift-efficient.
  • Key terms:
    • Leading edge: forward-most portion of the wing.
    • Trailing edge: rearmost edge of the wing.
    • Chord line: imaginary line connecting the leading and trailing edges.
    • Flight path: path that the airplane travels through the air.
    • Relative wind: the air flow that is parallel to, but opposite to, the aircraft’s flight path.
    • Angle of attack (α): the angle between the chord line and the relative wind.
  • The angle of attack is a major factor in lift production.

How a Wing Creates Lift

  • Two major theories explain lift generation when used together:
    • Newton’s laws of motion (particularly the third law): for every action there is an equal and opposite reaction. Deflecting air downward creates an upward lift on the wing (action-reaction).
    • Example: if you stick your hand out of a moving car window and tilt it, you deflect air downward, and the air pushes your hand upward.
    • Bernoulli’s principle: faster airflow over a surface leads to lower pressure on that surface.
    • Visual: air flowing through a venturi increases velocity in the narrow section, causing a drop in pressure.
  • Wing analogy to a venturi:
    • A wing’s top is more rounded and the bottom is flatter, causing faster flow over the top and a pressure difference that creates lift.
    • The resulting pressure gradient (high pressure under the wing, lower pressure over the wing) produces lift as air moves from high to low pressure.
  • Lift is influenced by several factors, summarized in the lift equation (standard form):
    • L = frac{1}{2} \rho v^{2} S C_{L}
    • where: ρ is air density, v is velocity, S is wing area, C_L is the coefficient of lift (depends on AoA, camber, Reynolds number, etc.).
  • The wing’s lift depends on airfoil shape, angle of attack, and other factors captured in the lift coefficient (C_L).

Wing Terms and Airflow Concepts

  • Shape and orientation terms:
    • Camber: curvature of the airfoil; cambered airfoils generally produce more lift and have a higher maximum C_L than symmetric ones.
    • Symmetrical airfoil: zero camber (zero net curvature about the chord line).
  • Airfoil geometry concepts:
    • Aspect ratio (AR): the relationship between wingspan and wing area; AR = b^2 / S (where b is wingspan and S is wing area).
    • Higher aspect ratio generally yields more efficient lift generation (e.g., gliders have high AR).
  • Other lift-influencing aspects:
    • Angle of attack (α) affects lift; increasing α increases lift up to a critical point beyond which stall occurs.
    • Wing area (S) contributes to lift via the lift equation; other shape factors are merged into C_L in the lift coefficient term.

High Lift Devices (Flaps)

  • High lift devices increase lift and drag at low airspeeds, aiding approaches and landings.
  • Four common flap types:
    • Plain flap: hinged at the front edge of the flap; when deflected downward, it changes the chord line and increases camber, increasing lift.
    • Split flap: hinged on the bottom of the wing; the top edge remains aligned while the flap deflects downward, increasing drag more than lift.
    • Slotted flap: extends with a gap (slot) between the flap and the wing; the slot allows high-pressure air from below to energize the air above the flap, delaying separation and increasing lift.
    • Fowler flap: slides backward along a track while extending, increasing both wing area and lift surface area, enhancing lift rapidly.

Weight, Thrust, and Drag in Detail

  • Weight (W):
    • The force of gravity acting downward toward the Earth.
    • Acts vertically downward from the center of gravity (CG).
    • Weight is not constant; it varies with installed equipment, passengers, cargo, and fuel (fuel burn reduces weight during flight).
  • Thrust (T):
    • Forward force opposing drag, propelling the airplane through the air.
    • In small general aviation airplanes, thrust is typically generated by a propeller; larger jets use turbine engines.
    • Like lift, thrust is generated on the principle of accelerating air and reacting via Newton’s third law to move the aircraft forward.
  • Drag (D):
    • The force opposing thrust, limiting forward speed.
    • Two main types:
    • Parasite drag: caused by air resistance to the airplane as it moves through the air.
      • Three subtypes:
      • Form drag: due to turbulence around the aircraft’s body (larger cross-sections create more drag).
        • Components include landing gear and antennas.
      • Interference drag: occurs where surfaces meet (e.g., wing-to-fuselage junction).
        • Proximity of objects can increase drag by up to about 200% compared to when they are separate; designers mitigate with small angled pieces at junctions.
      • Skin friction drag: caused by surface roughness (rivets, seams) disrupting smooth airflow.
        • Reducing with clean/waxed surfaces and flush-mounted fasteners.
      • Parasite drag varies with speed and increases as speed increases. Specifically, parasite drag is proportional to the square of airspeed:
      • D_{p} \propto v^{2}
    • Induced drag (lift-induced drag): occurs behind the wing due to downwash and wingtip vortices.
      • As the wing generates lift, downwash and wingtip vortices tilt the lift vector rearward, adding a backward component to lift (i.e., drag).
      • Induced drag is higher at slower airspeeds and decreases as speed increases.
      • It is worsened at high angle of attack (slow speeds).
      • Ground effect can reduce induced drag by altering downwash when flying within a wingspan of the ground, shifting the lift vector forward.
      • Used in short-field takeoff to lift off at lower speeds.
  • Drag and speed relationship in flight:
    • Drag curve vs speed: slower speeds yield higher drag due to parasitic drag not yet being offset by lift, illustrating the concept of the backside of the power curve.
    • The glide scenario (engine-out) is characterized by the best glide speed, the speed at which the aircraft will descend the slowest for a given configuration.
    • The phrase "backside of the power curve" describes the range where increasing power is required to maintain speed; in this region, drag dominates and thrust must be increased substantially to accelerate.
  • Flight controls at slow airspeeds:
    • With less air flowing over control surfaces, control inputs are less responsive; controls may feel mushy and require larger inputs for a noticeable response.

Practical and Conceptual Implications

  • The lift vector is produced by pressure differences; the wing “pulls” air downward (downwash) and, via Newton’s third law, the air pushes the wing upward.
  • The interplay between lift and weight, and thrust and drag, governs flight regimes (level flight, climb, descent, stall).
  • Stall considerations:
    • A stall occurs when the airflow over the wing separates from the upper surface, creating turbulence and loss of lift.
    • A stall is defined by the critical angle of attack; for a given airplane, stall occurs at a constant α_c regardless of weight, airspeed, or attitude.
  • Design trade-offs:
    • Camber increases lift capability and lowers stall speed, but can affect drag characteristics.
    • Higher aspect ratio wings are more efficient for lift generation and are favored in gliders; lower AR designs may be more maneuverable but less lift-efficient.
  • Ground effect and propulsion integration:
    • Ground effect can reduce induced drag and improve takeoff performance in close-to-ground operations.
    • Short-field (noted as "saw field" in the transcript) takeoffs exploit ground effect to achieve an earlier lift-off.
  • Summary of key dynamic relationships:
    • Lift: L = \tfrac{1}{2} \rho v^{2} S C_{L}
    • Parasite drag: D_{p} \propto v^{2}
    • Induced drag: D{i} = q S C{D{i}}, \quad C{D{i}} = \dfrac{C{L}^{2}}{\pi e AR}
    • AR: AR = \dfrac{b^{2}}{S}
  • In practice, pilots manage lift, weight, thrust, and drag through speed control, AoA management, and deployment of high-lift devices to ensure safe takeoffs and landings, while considering airspeed, altitude, configuration, and environmental factors.