Minimum fuel consumption of fuel-cell-powered airplanes driven by fixed-pitch propellers

Electric airplanes powered by fuel cells are a promising alternative for green aviation. However, many technological obstacles still have to be overcome for this type of aircraft to be commercially viable. For example, the relatively low output power capacity of fuel cells still constrains the application of these devices to power heavier aircraft. These limitations make performance optimization an even more important subject. This article presents a novel formulation for the analysis of electric current, fuel and oxidizer consumption of fuel-cell-powered airplanes driven by fixed-pitch propellers. Due to its simplicity, lighter weight and lower cost, the fixed-pitch propeller is widely used on aircraft with small flight speed variation. Also, since the efficiency of this type of propeller is known to vary with airspeed, a dedicated method is necessary. A parametric description of the relevant aircraft systems is developed, and expressions for instantaneous and total consumption are formulated. Optimal conditions for these performance metrics are investigated, and analytical solutions are derived and presented in closed form. The formulation employs a parametric model for the fixed-pitch propeller and eliminates the need to determine the motor and propeller rotation speed. A numerical approach for method validation is used, and simulations are provided to give the reader a quantitative insight into the problem. The results show that the optimal speeds for minimum fuel consumption of fuel-cell-powered aircraft driven by fixed-pitch propellers can be higher than what is predicted by traditional methods. Mathematical proofs are provided to show that this can happen.