Abstract: The present disclosure relates to a battery management system for an electric air vehicle such as an eVTOL aircraft for observing a battery system state and a battery health state of an energy storage system of the air vehicle. Based on an observation result, a state prediction, in particular, a prediction of the remaining accessible energy, is carried out during a flight. In particular, the observation and prediction is performed by two independent and dissimilar lanes of the battery management system. A first lane predicts the battery state according to a pre-defined flight profile representing a worst case scenario. A second lane predicts the battery state according to a planned flight profile so as to determine a range of the flight. Hence, it can be confirmed during the flight that the intended destination can be safely reached with the remaining accessible energy.