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Stability and Controllability

Objective​

To understand the effects of design choices on the stability of an aircraft along its three axes.

Motivation​

Helps a student develop an intuitive understanding of stability and controllability that they can use to make sense of the control inputs as they fly in different conditions.

Timing​

45 minutes

Format​

Elements​

Stability​

  • Airplane axes:
    • Longitudinal
    • Lateral
    • Vertical
  • Airplane always rotates around its CG
  • Static stability (positive, negative, neutral)
    • Will the system course-correct back to a neutral position when disturbed
    • Example: [Ball in a halfpipe, flat surface, on a hill]
  • Dynamic stability (positive, negative, neutral)
    • After the system course-corrects, does it overshoot and continue to oscillate
    • Or, do the osculations dampen naturally
  • Longitudinal, pitch stability:
    • CG, CL, Tail
    • [Elevator downforce in slow, level, and high speeds]
    • Positive stability: Wing is providing downforce onto tail
      • If aircraft is pitched up, it slows, meaning less downwash on the tail
        • Less down wash mean less down force, and nose pitches back down
      • If the aircraft is pitched down, it speeds up, meaning more downwash on the tail
        • More down wash means more down force, and the nose pitches up
    • Dynamic stability: the affect of the downforce dampens over time
    • Decrease in thrust has similar effect: less force over tail, nose wants to drop and pickup airspeed
    • Thrust line vs CG: Above CG, below CG, at CG
  • Lateral, roll stability
    • What is roll stability? Negative, neutral, positive
      • Aerobatic planes: neutrally stable
    • If a wind gust lowers a wing, the lift vector tilts
      • This isn't a nice coordinated turn, no rudder input
      • A sideslip occurs
    • Dihedral wing
      • Slightly larger AoA on down wing: Raises the lowered wing
    • Deeper explanation [Commercial]
      • Dihedral effect: [2D drawing `from front of plane, wind coming up from lowered wing]
        • Wing bends around the fuselage
        • Lower wing has lower angle of attack
        • High wing has higher angle of attack
      • Dihedral angle
        • [2D low-wing with dihedral]
        • Gust of wind raises a wing, airplane sideslips slightly into the wind
        • Because of the dihedral, low wing makes large AoA than up wing
        • Larger AoA means more lift = raise the lowered wing
      • High wing airplanes and dihedral
        • [2D high-wing without dihedral]
        • Wind has to "bend" over the top of the fuselage
      • What if we have too much roll stability?
        • Anhedral
      • Wing sweep
        • Airplane yaws into the wind
        • Lowered wing make`s more perpendicular angle with the wind = more lift
  • Vertical, yaw stability:
    • Wind striking fuselage aft of CG
    • Rudder has it's own angle of attack
  • Lateral stability vs vertical stability [Commercial]
    • Strong directional (yaw) stability and weak lateral (roll) stability
      • Wing drops due to wing and a yaw is introduced
      • The airplane weathervanes into the wind, making the outboard wing fly faster
      • This is all before the lateral stability (dihedral effect) can raise the wing
      • This exhibits the overbanking tendency, causing the airplane to roll further into the turn
      • This gradually becomes a steep spiral dive
      • We call this spiral instability
    • Strong lateral (roll) stability and weak directional stability
      • Gust of air lowers a wing, sideslip into the wind
      • Dihedral effect raises the wing, but due to weak directional stability yaws too far in the other direction
      • This can cause an bank/yaw oscillation which is uncomfortable and dangerous if undamped
      • We call this Dutch roll
    • Generally, spiral instability is preferred over Dutch roll, since spiral tendencies are easier for a pilot to fix with control inputs

Maneuverability​

  • Controllability is dependent Cp vs Cg
    • CG close to CL: Elevator needs to produce very small forces, sensitive
    • CG far from CL: Elevator need to produce larger forces
  • Maneuverability: How fast an aircraft can change its direction of flight or attitude
    • Maneuverability vs stability

References​