Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Energy Optimal Traversal Between Hover Waypoints for Lift+Cruise Electric Powered Aircraft

Akshay Mathur, Ella Atkins

Abstract

Advanced Air Mobility aircraft require energy efficient flight plans to be economically viable. This paper defines minimum energy direct trajectories between waypoints for Lift+Cruise electric Vertical Take-Off and Landing (eVTOL) aircraft. Energy consumption is optimized over accelerated and cruise flight profiles with consideration of mode transitions. Because eVTOL operations start and end in hover for vertical take-off and landing, hover waypoints are utilized. Energy consumption is modeled as a function of airspeed for each flight mode, providing the basis to prove energy optimality for multi-mode traversal. Wind magnitude and direction dictate feasibility of straight-line traversal because Lift+Cruise aircraft point into the relative wind direction while hovering but also have a maximum heading rate constraint. Energy and power use for an experimentally validated QuadPlane small eVTOL aircraft are characterized with respect to airspeed and acceleration in all flight modes. Optimal QuadPlane traversals are presented. Constraints on acceleration and wind are derived for straight-line QuadPlane traversal. Results show an optimal QuadPlane $500m$ traversal between hover waypoints saves $71\%$ energy compared to pure vertical flight traversal for a representative case study with a direct $4m/s$ crosswind. Energy optimal eVTOL direct trajectory definition with transitions to and from hover is novel to this work. Future work should model three-dimensional flight and wind as well as optimize maneuver primitives when required.

Energy Optimal Traversal Between Hover Waypoints for Lift+Cruise Electric Powered Aircraft

Abstract

Advanced Air Mobility aircraft require energy efficient flight plans to be economically viable. This paper defines minimum energy direct trajectories between waypoints for Lift+Cruise electric Vertical Take-Off and Landing (eVTOL) aircraft. Energy consumption is optimized over accelerated and cruise flight profiles with consideration of mode transitions. Because eVTOL operations start and end in hover for vertical take-off and landing, hover waypoints are utilized. Energy consumption is modeled as a function of airspeed for each flight mode, providing the basis to prove energy optimality for multi-mode traversal. Wind magnitude and direction dictate feasibility of straight-line traversal because Lift+Cruise aircraft point into the relative wind direction while hovering but also have a maximum heading rate constraint. Energy and power use for an experimentally validated QuadPlane small eVTOL aircraft are characterized with respect to airspeed and acceleration in all flight modes. Optimal QuadPlane traversals are presented. Constraints on acceleration and wind are derived for straight-line QuadPlane traversal. Results show an optimal QuadPlane traversal between hover waypoints saves energy compared to pure vertical flight traversal for a representative case study with a direct crosswind. Energy optimal eVTOL direct trajectory definition with transitions to and from hover is novel to this work. Future work should model three-dimensional flight and wind as well as optimize maneuver primitives when required.

Paper Structure

This paper contains 20 sections, 2 theorems, 31 equations, 17 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Optimal Traversal between Hover Waypoint Pairs with No Wind
  4. General Traversal between Hover Waypoint Pairs with No Wind
  5. Energy Cost for General Traversal between Hover Waypoints with No Wind
  6. Energy Optimal Traversal in No Wind
  7. Traversal between Hover Waypoints in Steady Wind
  8. Straight-line Traversal in Steady Wind
  9. Energy Cost for Traversal in Steady Wind
  10. Energy Optimal Straight-line Traversal in Steady Wind
  11. Steady Wind Traversal with Cubic Spline Maneuver Primitives
  12. QuadPlane Traversal Case Study
  13. Modeling QuadPlane Power and Energy Consumption
  14. Power consumption in steady flight
  15. Power consumption in accelerated flight
  16. ...and 5 more sections

Key Result

Lemma III.1

Let $\Vec{w}_i$ and $\Vec{w}_{i+1}$ be sequential hover waypoints at the same altitude traversed by trajectory $\mathbb{T}_{i,i+1}$. If $S^{cr}=\emptyset$ and $l_{i,i+1} \leq l_{min}^{V_c^*}$, energy optimal traversal is given by $\mathbb{T}_{i,i+1}^*=\{\mathcal{T}_+^*$, $\mathcal{T}_-^*\}_{i,i+1}$

Figures (17)

  • Figure 1: Aircraft velocity in Body (left) and Earth (right) coordinates McClamroch. Relative wind is also shown (left).
  • Figure 2: General traversal trajectory $\mathbb{T}_{i,i+1}$ over a segment with hover waypoints.
  • Figure 3: Cubic-spline profile for an airspeed maneuver between hover and $V_c$ defined by $\mathcal{T}_+$ (left) and $\mathcal{T}_-$ (right).
  • Figure 4: Maneuver primitive traversal in steady wind.
  • Figure 5: QuadPlane Power consumption vs airspeed for steady level flight in $Quad$, $Hybrid$ and $Plane$ Modes.
  • ...and 12 more figures

Theorems & Definitions (4)

  • Lemma III.1
  • proof
  • Lemma IV.1
  • proof