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

Steven Li, Luis Rodrigues

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.

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

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.
Paper Structure (9 sections, 1 theorem, 59 equations, 3 figures, 3 tables)

This paper contains 9 sections, 1 theorem, 59 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. System Model
  3. Flight Dynamics Model
  4. Electricity Consumption Model
  5. Minimum Total Energy
  6. Simulation Results
  7. Influence of Cruising Altitude and Aircraft Weight on Optimal Cruise Airspeed
  8. Influence of Aircraft Weight and Initial Charge on the Minimum Feasible Electrical System Efficiency
  9. Conclusions

Key Result

Theorem 1

Given $a$, $b$, $x_0$, $x_f$, $Q_0$, $Q_{min}$, and $Q_{max}$, the optimal airspeed is with optimal final cruise time if $v_{stall} < v^* < v_{max}$ and if $Q_0 < Q_{max}$, $Q(t_f) > Q_{min}$, where with

Figures (3)

  • Figure 1: Example of a battery discharge cycle obtained from the Oxford Battery Degradation Dataset 1 howey2017oxford.
  • Figure 2: Optimal cruise airspeed $v^*$ as a function of cruising altitude for different values of the aircraft weight $W$.
  • Figure 3: Minimum electrical system efficiency $\eta$ required to satisfy $Q(t_f) > Q_{min}$ as a function of the aircraft weight $W$ for various values of $Q_0$.

Theorems & Definitions (5)

  • Remark 1
  • Remark 2
  • Theorem 1
  • proof
  • Remark 3