Banked Turn - Banked Turn in Aeronautics

Banked Turn in Aeronautics

When a fixed-wing aircraft is making a turn (changing its direction) the aircraft must roll to a banked position so that its wings are angled towards the desired direction of the turn. When the turn has been completed the aircraft must roll back to the wings-level position in order to resume straight flight.

When any moving vehicle is making a turn, it is necessary for the forces acting on the vehicle to add up to a net inward force, to cause centripetal acceleration. In the case of an aircraft making a turn, the force causing centripetal acceleration is the horizontal component of the lift acting on the aircraft.

In straight, level flight, the lift acting on the aircraft acts vertically upwards to counteract the weight of the aircraft which acts downwards. During a balanced turn where the angle of bank is θ the lift acts at an angle θ away from the vertical. It is useful to resolve the lift into a vertical component and a horizontal component. If the aircraft is to continue in level flight (i.e. at constant altitude), the vertical component must continue to equal the weight of the aircraft. The horizontal component is unbalanced, and is thus the net force causing the aircraft to accelerate inward and execute the turn.

During a banked turn in level flight the lift on the aircraft must support the weight of the aircraft, as well as provide the necessary component of horizontal force to cause centripetal acceleration. Consequently, the lift required in a banked turn is greater than that one required in straight, level flight and can be achieved either by increasing the angle of attack of the wing (typically by pulling on the elevator control) or by deploying flaps. The maneuver is usually complemented by an increase in power, in order to maintain airspeed.

Because centripetal acceleration is:

Newton's second law in the horizontal direction can be expressed mathematically as:

where:

L is the lift acting on the aircraft

θ is the angle of bank of the aircraft

m is the mass of the aircraft

v is the true airspeed of the aircraft

r is the radius of the turn

In straight flight, lift is approximately equal to the aircraft weight. In turning flight the lift exceeds the aircraft weight, and is equal to the weight of the aircraft (mg) divided by the cosine of the angle of bank:

where g is the gravitational field strength.

The radius of the turn can now be calculated:

This formula shows that the radius of turn is proportional to the square of the aircraft’s true airspeed. With a higher airspeed the radius of turn is larger, and with a lower airspeed the radius is smaller.

This formula also shows that the radius of turn is inversely proportional to the angle of bank. With a higher angle of bank the radius of turn is smaller (as in pylon turn), and with a lower angle of bank the radius is greater.

The angle of bank is the sole determinant of the aircraft’s load factor during the turn.