## Physics: Principles with Applications (7th Edition)

Airplanes bank when they turn so that the lift force generated by the wings has a horizontal component, which the plane requires to move in a horizontal circle. The required angle can be calculated by $\theta = tan^{-1}(\frac{gr}{v^{2}})$.
The way to calculate the banking angle is as follows. See the diagram. The lift force’s vertical component balances the plane’s weight. $$F_{L}sin \theta = mg$$ The horizontal component provides the necessary centripetal force. $$F_{L}cos \theta = m \frac{v^{2}}{r}$$ By dividing the two equations and solving, we can find the required bank angle. $$\theta = tan^{-1}(\frac{gr}{v^{2}})$$