Flight Dynamics

AAE 6710

Lesson 01-1

Aircraft Components & Nomenclature

Earth Atmosphere

Aircraft Components

Flight Controls

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A330 IL-96-300

F-22 Raptor SU-30 MKM

Elevators

Ailerons

Rudder

Angle of Attack

Angle of Attack, 𝛼, positive nose up, and generally in radians, is the angle between a convenient body-fixed reference line and the tangent to the flight path at the airplane center of gravity. It is the difference between where the aircraft is pointed and where it is going.

Flight Path Angle & Pitch Angle Flight path angle, 𝛾, positive upward from the horizontal, the angle of

the path traced by the airplane center of gravity. It is where the aircraft is going.

Pitch angle, 𝜃, positive nose up, is the angle between the reference line and the horizontal. It is where the airplane is pointed.

Sideslip Angle

Angle of Attack & Side Slip Angle

Aircraft Symmetry

Lift

𝑳 = 𝑪𝑳𝑸𝑺

𝑄 = 𝑑𝑦𝑛𝑎𝑚𝑖𝑐 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 =1

2𝜌𝑉2

Symbol Quantity English Units

SI Units

𝐿 Lift 𝑙𝑏𝑓 𝑁

𝑄 Dynamic Pressure 𝑙𝑏/𝑓𝑡2 𝑁/𝑚2

𝜌 Air Density 𝑠𝑙𝑢𝑔/𝑓𝑡3 𝑘𝑔/𝑚3

𝑉 Free stream Velocity 𝑓𝑡/𝑠 𝑚/𝑠

𝑆 Wing Area 𝑓𝑡2 𝑚2

Typical Lift Forces

F16C ( F100 PW engine)

• Weight empty = 8 433 kg

• Takeoff Weight = 12 138 kg

Airbus A380-800

• Empty : 277,000 kg

• Max Takeoff : 560,000 kg

• Fuel Capacity : 260,900 kg

• Max Payload : 84,000 kg

Axis System

Axis System

• For flight dynamics and control the axis system or reference frame is fixed to the flight vehicle

• The convention for flight dynamics is to place the origin at the centre of mass of the aircraft with

– The positive x axis points towards the nose

– The positive y axis points towards the right wing

– The positive z axis points downwards

• NB : Aerodynamics, propulsion & structures use different conventions

Axis System

Aircraft Motion

Forces and Moments

𝑺 = Wing planform area 𝒃 = Wing span for the rolling and yawing moments 𝒄 = Mean chord for the pitching moment

𝑿 = 𝑪𝒙𝑸𝑺 axial force 𝒀 = 𝑪𝒚𝑸𝑺 side force

𝒁 = 𝑪𝒛𝑸𝑺 normal force

𝑳 = 𝑪𝒍𝑸𝑺𝒃 rolling moment 𝑴 = 𝑪𝒎𝑸𝑺𝒄 pitching moment 𝑵 = 𝑪𝒏𝑸𝑺𝒃 yawing moment

Nomenclature & Symbols

• 𝛼 : angle of attack (AOA) • 𝛽 : sideslip angle • 𝛿𝑎 : aileron deflection • 𝛿𝑒 : elevator deflection • 𝛿𝑟

: rudder deflection • 𝜌 : air density • 𝜙, 𝜃,Ψ : roll, pitch and yaw angles • 𝐿,𝑀,𝑁 : roll, pitch & yaw moments • 𝑝, 𝑞, 𝑟 : roll, pitch and yaw angular rates • 𝑢, 𝑣, 𝑤 : velocity X,Y & Z components

Types of Motion

• Longitudinal motions are described by the velocities 𝑢 and 𝑤 and rotations about the y-axis, described by 𝑞

• Lateral/directional motions are described by the velocity 𝑣 and rotations about the x and/or z axes, described by 𝑝 and/or 𝑟

END