What is the formula for calculating the angle of bank for a rate one turn given true airspeed?

The formula for calculating the angle of bank necessary for a rate one turn (which is defined as a turn that completes a full 360-degree rotation in two minutes) is derived from the relationship between the aircraft's speed and the turn radius. For a rate one turn, a common useful approximation involves using the true airspeed of the aircraft.

When calculating the bank angle, the established formula is that the true airspeed is divided by 10, and then a constant (in this case, 7) is added to that result. This structure comes from the need to maintain a specific load factor required for level flight during the turn. The formula effectively correlates the speed of the aircraft with the angle of bank in such a way that it allows for a consistent and safe turn radius while ensuring that the aircraft does not exceed its performance limits.

The reason the chosen formula is applicable relates to the physics of flight and centripetal force. As the speed increases, a greater angle of bank is required in order to maintain the same turn rate. The derivation and application of this formula illustrate both the importance of velocity in flight dynamics and the necessity for pilots to understand the relationship between speed and bank angle in order to execute turns safely and efficiently.