A comparative study of algebraic and 3DoF models for predicting performance of all electric aircraft

Due to the rapid advancement of battery and electric motor technologies, all electric aircraft (AEA) are quickly becoming a promising pathway for reducing the CO2 emissions and air pollutants of small aircraft. New design tools are needed for predicting the performance of AEA. In this study, a three-degrees of freedom (3DoF) model is developed for predicting the performance of AEA under different mission profiles and electric propulsion system efficiencies. Based on a temporal integration of the equations of motion, the 3DoF model also incorporates the AEA weight, energy storage, aerodynamics, efficiency of electric propulsion system, and atmospheric conditions in its performance predictions. Additionally, two simpler and computationally cheaper algebraic models (AM) are proposed to enable rapid performance predictions at the AEA design stage. The baseline AM is based on the flight range equation under steady conditions, which is modified in the improved AM by incorporating atmospheric effects. For a 300 nautical miles range, the improved AM predicts the maximum motor power and energy consumption with relative errors less than 4% and 5% of the 3DoF model, respectively compared with 85% and 17% from the baseline AM. The design tools are used to conduct an AEA trajectory analysis under different climb profiles and motor efficiencies. The analysis reveals that if constant motor efficiency is assumed, optimization of the AEA climb profile has little effect on the total energy consumption, with the total energy consumption differing by less than 0.5%. However, when the motor efficiency is more realistically modeled as a function of motor shaft power, differences in the total energy consumed by the AEA increase, with a maximum difference of 2.8%. Since the battery energy storage is closely related to the AEA weight and cost, this finding suggests that trajectory optimization can reduce the cost, improve the performance, and accelerate the design of AEA systems.