Turning Flight Dynamics

Coordinated Turn

• Aircraft turns in a circular path at constant airspeed in the horizontal plane.

• Turn occurs solely due to banking.

• Angle of sideslip is kept at zero using aileron and rudder coordination.

Level Turn Definition

• A change in flight path direction.

• Curved flight path lies in a horizontal plane, parallel to the ground.

• Altitude remains constant during level turns.

• Flight path resembles circular motion.

Parameters of Motion

• Turn radius (r): Distance between flight path and instantaneous center of curvature.

• Velocity: Tangential to the flight path.

• Centripetal force: Perpendicular to flight path, directed towards the center of curvature.

Centripetal Force Equation

• $F_c = ma$ where $a = \frac{v^2}{r}$

  • $F_c$ is the centripetal force.

  • $m$ is the mass.

  • $a$ is the centripetal acceleration.

  • $v$ is the velocity.

  • $r$ is the radius of curvature.

Newton's First Law of Motion (Law of Inertia)

• An object remains at rest or in motion in a straight line unless acted upon by an external force.

• Aircraft requires a sideward force to turn, provided by banking.

Lift Components During a Turn

• Lift is generated perpendicular to the mean aerodynamic chord.

• In banking conditions, lift acts inward and upward.

  • Vertical Component of Lift: Acts vertically, opposing weight.

  • Horizontal Component of Lift (Centripetal Force): Acts horizontally towards the center of the turn.

    • Pulls the aircraft from a straight path to initiate the turn.

Centrifugal Force

• Equal and opposite reaction to the change in direction.

• Acts equal and opposite to the horizontal component of lift.

• Turning force is not supplied by the rudder in a correctly executed turn.

Role of the Rudder

• Corrects deviations between the nose and tail track relative to the wind.

• A good turn: Nose and tail track along the same path.

• Without rudder: Nose yaws to the outside of the turn.

• Rudder use: To align the nose with the relative wind during turn entry.

• Minimal rudder needed once established in the turn.

Free Body Diagram

• Vertical plane shows the forces acting on the aircraft.

Force Balance in Horizontal/Radial Directions

• Transverse slope/bank angle creates centripetal force ($F_c$) perpendicular to the flight direction.

• $F_c = ma = m\frac{v^2}{r}$

  • $F_c$ is the centripetal force.

  • $m$ is the mass.

  • $v$ is the velocity.

  • $r$ is the radius of curvature.

Vertical Force Balance

• Lift exceeds weight because the vertical component of lift sustains the weight.

• $L \cos(\phi) = W$ , where $L = \frac{W}{\cos(\phi)}$

  • $L$ is Lift.

  • $\phi$ is Bank angle.

  • $W$ is Weight.

• At a 60-degree bank angle ($\cos(60) = 0.5$), lift must be twice the weight.

Implications of Increased Lift

• Aircraft must increase its angle of attack (AOA) to generate higher lift.

• Increased AOA also raises the drag coefficient.

• Throttle adjustments needed. Throttle should be added to maintain speed and counteract increased drag.

Force Balance in the Direction of Flight (X-axis)

• Thrust equals drag.

Centripetal Force and Bank Angle

• Centripetal force ($F_c$) is equal to the horizontal component of lift ($L \sin(\phi)$).

• $L \sin(\phi) = F_c = m\frac{v^2}{r}$

  • $L$ is Lift.

  • $\phi$ is Bank angle.

  • $m$ is the mass.

  • $v$ is the velocity.

  • $r$ is the radius of curvature.

Circular Motion Parameters

• Aircraft travels from initial position to point P.

• Angular distance: Distance = Radius of curvature * Angular displacement

  • $s = r\theta$

    • $s$ is arc length.

    • $r$ is radius.

    • $\theta$ is the angular displacement.

• Speed at point P: Tangential speed = Angular velocity * Radius of curvature

  • $v = \omega r$

    • $v$ is the tangential velocity.

    • $\omega$ is the angular Velocity.

    • $r$ is the radius.

• Radial acceleration: Radial acceleration = Angular acceleration * Radius of curvature

  • $a_r = \alpha r$

    • $a_r$ is the radial acceleration.

    • $\alpha$ is the angular acceleration.

    • $r$ is the radius.

• Tangential acceleration: Tangential acceleration = (Angular velocity)^2 * Radius of curvature

  • $a_t = \omega^2 r$

    • $a_t$ is the tangential acceleration.

    • $\omega$ is the angular velocity.

    • $r$ is the radius.