This paper presents a flight envelope protection method for aircraft. Specifically, a bank angle protection strategy is proposed and analyzed using potential functions and gradient descent algorithm. In the proposed method, the flight envelope limit is treated as an obstacle in the state-space, and a repulsive potential function is defined in the proximity to this obstacle, generating a repellent control command to prevent the state from violating the limit. One advantage of this method is that no prediction of limit violation is required, and only limited information about the system dynamics is needed to tune the algorithm. The designer can balance protection performance and pilot authority by changing the triggering point of the algorithm. Exponential stability is proved for the closed-loop system and simulation example of bank angle protection of a linearized aircraft (NASA's Transport Class) model is provided to verify the effectiveness of the algorithm.