A Unified Approach for Optimal Cruise Airspeed with Variable Cost Index for Fuel-powered and All-electric Aircraft

TL;DR

This work addresses DOC minimization for aircraft under a time-varying cost index ($CI$) commanded by ATC. It formulates a unified optimal-control framework that includes energy dynamics for both fuel-powered and all-electric propulsion and treats $CI$ as a first-order filtered input, $CI(t)=e^{-t/\tau}(CI_0- CI_{in})+CI_{in}$. The key contributions are (i) introducing time-varying $CI$ into DOC minimization, (ii) deriving a unified solution for both propulsion types with explicit expressions for the optimal cruise speed $v^{*}$ and flight time under $CI$ changes, and (iii) validating the approach via a simulated in-flight scenario that demonstrates real-time adjustments to $v^{*}$, $t_f$, and energy consumption in response to ATC updates. The results show the method can adapt cruise performance in real time, supporting potential future all-electric air mobility by delivering operationally feasible speeds and timelines that respect ATC-imposed constraints.

Abstract

This paper proposes for the first time a unified optimal approach to solve a direct operating cost (DOC) minimization problem where the cost index (CI) is time-varying. More specifically, the coefficient CI is modeled as a time-varying parameter commanded by Air Traffic Control (ATC). The proposed unified approach relies on the solution of an optimal control problem both for fuel-powered and all-electric aircraft. Furthermore, this paper demonstrates how a variable CI affects the solution of the optimization problem as it presents the equations that allow the computation of optimal constant cruise airspeed and flight time in response to step changes in the CI value. The proposed methodology is validated by a simulated flight scenario. In this scenario the inputs from the ATC are received during flight and the aircraft is required to adjust its optimal airspeed, flight time, and total energy consumption to comply with the operational restrictions imposed by the ATC. The optimal values of airspeed, flight time and energy consumption are computed for both a fuel-powered and an all-electric aircraft, thus enabling applications of the proposed approach to future air mobility all-electric vehicles.

Figures (9)

• Figure 1: Block diagram of minimum DOC with ATC input
• Figure 2: Optimal airspeed and flight time calculation flowchart
• Figure 3: Flight scenario
• Figure 4: Total Cost as a function of the fuel-powered aircraft’s airspeed
• Figure 5: Total Cost as a function of the all-electric aircraft’s airspeed