Flight Dynamics II - Lecture Notes

Course Overview

• Focus on the motion of flying objects in air
• Study equilibrium conditions and perturbed motion caused by disturbances (e.g., wind gusts)
• Emphasis on atmospheric flight dynamics, particularly aircraft

Key Concepts

Steady Equilibrium Motion

• Aircraft flying in steady equilibrium: Lift = Weight, Thrust = Drag
• Disturbances from equilibrium lead to small and large motions
  • Small motions: Caused by minor disturbances
  • Large motions: Require control effort

Types of Flying Objects

• Living Examples: Birds, insects
• Man-Made Examples: Gliders, spacecraft, missiles, aircraft

Aircraft Aerodynamics

• Aircraft uses its aerodynamic shape to generate forces/moments for sustained motion
• Cruise Condition: Lift balances weight, thrust overcomes drag
• Various factors affecting motion include:
  • Density of air depending on altitude
  • Aircraft component geometries (fuselage, wings, control surfaces)

Atmospheric Conditions

• Density at sea level: 1.225 kg/m³
• Density reduction at increasing altitudes:
  • 20 km: 0.088 kg/m³
  • 47 km: 0.00147 kg/m³
  • 61 km: 0.00025 kg/m³
  • 80-90 km: ~10^-5 kg/m³

Aircraft Components Influencing Motion

• Control Surfaces: Ailerons, elevators, rudders
  • Ailerons: Change lift & moments, mounted on wings
  • Elevator: Small flap on horizontal tail
  • Rudder: Mounted on vertical tail
• Fuselage: Affects aerodynamics based on design and mission requirements

Motion Parameters

Axis System

• Fixed Axis System: Center of gravity as origin (XB-YB-ZB)
• Rigid aircraft has 6 degrees of freedom:
  • Translational Motion: u (forward), v (sideways), w (vertical)
  • Rotational Motion: Roll (p), Pitch (q), Yaw (r)

Forces and Moments

• Axial Force (X): Sum of forces along X-axis:
  • X = Q * S * Cx
• Side Force (Y): Sum of forces along Y-axis:
  • Y = Q * S * Cy
• Vertical Force (Z): Sum of forces along Z-axis:
  • Z = Q * S * Cz
• Moments:
  • Rolling Moment (L): L = Q * S * Cl * b
  • Pitching Moment (M): M = Q * S * Cm * c'
  • Yawing Moment (N): N = Q * S * Cn * b
• Q: Dynamic pressure, Q = 0.5 * rho * V^2

Angle Definitions

• Angle of Attack (alpha): Between velocity vector projection on XZ plane and X-axis.
• Sideslip Angle (beta): Between the permitted plane and XZ plane.

Additional References

• Books recommended for further reading:
  • Flight Stability and Automatic Control by Robert C Nelson
  • Dynamics of Atmospheric Flight by Bernard Etkin
  • Mechanics of Flight by Warren F. Phillips
  • Airplane Performance Stability and Control by C D Perkins and R E Hage
  • Performance Stability Dynamics and Control of Airplanes by Bandu N Pamadi

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