How do you calculate the bank angle required for a turn?

The calculation of the bank angle required for a turn in aviation is based on the relationship between the aircraft's speed, the turning radius, and the force of gravity. The formula used to determine the bank angle involves the relationship of centripetal force required for the turn to the gravitational force acting on the aircraft.

The correct formula—Bank Angle = arcsin(V^2 / (g * radius))—derives from the principles of circular motion. In a turn, the horizontal component of lift must equal the required centripetal force to maintain the turn. This leads to the necessity of determining the bank angle that yields the appropriate lift component to balance this force.

When an aircraft is in a coordinated turn, the lift vector tilts along with the bank angle. The vertical component of the lift must equal the weight of the aircraft, while the horizontal component supplies the necessary centripetal force. The equation rearranges these relations into using the sine function relating velocity, gravity, and radius of the turn, ultimately yielding this specific expression for calculating the bank angle.

The other formulas provided do not correctly represent the relationships required to find the bank angle in a turn. They either misuse trigonometric relationships or misplace the variables concerning gravity, velocity, and