Minimum Energy Cruise of All-Electric Aircraft with Applications to Advanced Air Mobility

TL;DR

This paper formulates and solves an optimal control problem to minimize energy consumption for all-electric aircraft in steady cruise, providing analytical solutions and feasibility conditions relevant for sustainable Advanced Air Mobility.

Contribution

It introduces a novel optimal control framework with closed-form solutions for energy-efficient cruise and feasibility conditions for all-electric aircraft.

Findings

Optimal cruise airspeed and time are derived analytically.

Feasibility depends on available electric charge and aircraft parameters.

Numerical simulations demonstrate the impact of various factors on energy efficiency.

Abstract

Electrified propulsion is expected to play an important role in the sustainable development of Advanced Air Mobility (AAM). However, the limited energy density of batteries motivates the need to minimize energy consumption during flight. This paper studies the minimum total energy problem for an all-electric aircraft in steady cruise flight. The problem is formulated as an optimal control problem in which the cruise airspeed and final cruise time are optimization variables. The battery supply voltage is modeled as an affine function of the battery charge. Pontryagin's Minimum Principle is used to derive the necessary and sufficient conditions for optimality, from which closed-form expressions for the optimal cruise airspeed and optimal final cruise time are obtained. Additional analytical conditions are derived that determine when all-electric operation is feasible, one of which is that sufficient electric charge must be available. Numerical simulations based on the BETA Technologies CX300 all-electric aircraft and a representative AAM scenario illustrate how the aircraft weight, cruising altitude, electrical system efficiency, and initial battery charge influence the optimal airspeed and the feasibility of all-electric cruise.