# OpenAP.top: Open Flight Trajectory Optimization for Air Transport and Sustainability Research

## Abstract

**:**

## 1. Introduction

#### 1.1. Short Overview of Flight Trajectory Optimizations

#### 1.2. Aircraft Performance Models and Optimization Scopes

#### 1.3. Contributions of This Paper

## 2. Aircraft Fuel and Emission Models

_{2}O , CO

_{2}, SO

_{X}, and soot are considered to be proportional [25] to the fuel flow regardless of the atmosphere conditions:

_{X}, CO, and HC, are first estimated based on the sea-level atmospheric conditions based on data from the ICAO engine emission databank. To simplify the model, piecewise linear interpolation models are designed to approximate emissions under different thrust conditions. After that, the Fuel Flow Method 2 developed by Boeing [26] is used to correct the emission values based on the flight altitude.

## 3. Non-Linear Optimal Control for Trajectory Optimization Problems

#### 3.1. System Equations

#### 3.2. Non-Linear Optimal Control

#### 3.3. Numerical Approximations

#### 3.4. Solver

## 4. Flight Trajectory Optimization Constraints

#### 4.1. Complete Flight Trajectory

#### 4.1.1. Endpoint Constrains

#### 4.1.2. Path Constrains for States

#### 4.1.3. Path Constraints for Aircraft Performance

#### 4.1.4. Path Constrains for Smooth Control Variable Changes

#### 4.2. Cruise-Only Flight Trajectory

#### 4.2.1. Additional (Optional) Constrains for Cruise Flight

#### 4.3. Climb-Only Flight Trajectory

#### 4.4. Descent-Only Flight Trajectory

#### 4.5. Multiphase Complete Trajectory

## 5. Objective Functions

#### 5.1. Optimizing for Fuel Consumption

#### 5.2. Optimizing for Flight Time

#### 5.3. Optimizing for Cost Index

#### 5.4. Minizing Global Warming and Temperature Potential

_{2}at different time horizons (20, 50, and 100 years), while GTP models the temperature change at the end of these different periods.

## 6. Experiments

#### 6.1. Single Trajectory and Flight Phases Optimizations

#### 6.1.1. Optimization of the Entire Trajectory

#### 6.1.2. Optimization of Different Flight Phases

#### 6.2. Objective Metric

_{2}compared to other emissions. Since CO

_{2}has a linear correlation to fuel consumption, these objectives are essentially the same as minimizing fuel consumption.

_{X}and SO

_{X}have a very large negative effect when contributing to the temperature potential at 20-year horizon. When minimizing GTP20, the optimizer yields trajectories that produce as much NO

_{X}and SO

_{X}as possible, which translates to greater fuel consumption.

#### 6.3. Uncertainties

#### 6.3.1. The Influences of Takeoff Mass

#### 6.3.2. Effects of Engine Configurations

#### 6.3.3. Simple Analysis of Cost Index

#### 6.3.4. Comprehensive Analysis of Initial Mass and Cost Index Optimality

#### 6.3.5. Effects of Varying Wind Conditions

## 7. Discussion

#### 7.1. Insights into the Optimal Control Flight Optimization

_{X}and SO

_{X}as possible.

_{X}and SO

_{X}to climate cost would lead to a similar situation as the GTP20 objective for en-route flights. However, the air quality cost from these studies would provide a different insight into the optimal trajectories for the climb and descent flights.

#### 7.2. Limitations

#### 7.3. Future Recommendations

## 8. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Using the openap.top Python Library

- Produce a complete fuel optimal flight trajectory:
`import``openap.top as otop``optimizer = otop.CompleteFlight("A320", "EHAM", "LGAV", m0=0.85)``flight = optimizer.trajectory(objective="fuel")` - Produce a GWP50 optimal flight trajectory with an alternative engine type:
`import``openap.top as otop``optimizer = otop.CompleteFlight("A320", "EHAM", "LGAV", m0=0.85)``op.change_engine("V2527E-A5")``flight = optimizer.trajectory(objective="GWP50")` - Consider wind for a cost index optimized cruise flight:
`import``openap.top as otop``windfield = otop.wind.read_grib("era5_wind_file.grib")``optimizer = otop.Cruise("A320", "EHAM", "LGAV", m0=0.85)``op.enable_wind(windfield)``flight = optimizer.trajectory(objective="CI:50")`

`flight`variable is a

`DataFrame`object that can be further processed by the

`pandas`library.

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**Figure 4.**Optimization of complete flight trajectory including climb, cruise, and descent phases. The example flight leaves EHAM, arrives at LGAV, and considers the real 3D wind conditions. Only the wind field at a specific altitude is shown for illustration purposes. (

**a**) Complete 4D trajectory and (

**b**) Multiphase 4D trajectory, both optimized for fuel consumption.

**Figure 5.**Optimization of different flight phases for minimizing fuel consumption. The example flight leaves EHAM, arrives at LGAV, and considers the real 3D wind conditions. Only the wind field at a specific altitude is shown for illustration purposes. (

**a**) Optimal cruise trajectory, (

**b**) Optimal climb trajectory, and (

**c**) Optimal descent trajectory.

**Figure 6.**Optimality metric using different objectives. A higher value indicates two objectives are more similar, and lower value indicates larger differences.

**Figure 7.**Fuel optimal trajectories under different takeoff weight (A320, optimized for fuel consumption).

**Figure 8.**Optimal trajectory with different engine types (A320, optimized for fuel consumption, with 90% of takeoff mass).

**Figure 12.**Optimal trajectories of the same origin and destination under different wind conditions over the course of a day.

**Figure 13.**Optimal ground track of the same origin and destination under different wind conditions over the course of a day. The wind fields at cruise altitudes are shown for illustration purposes.

${\mathit{C}}_{{\mathrm{CO}}_{2}}\phantom{\rule{3.33333pt}{0ex}}$ | ${\mathit{C}}_{{\mathrm{H}}_{2}\mathrm{O}}\phantom{\rule{3.33333pt}{0ex}}$ | ${\mathit{C}}_{{\mathrm{NO}}_{\mathrm{X}}}\phantom{\rule{3.33333pt}{0ex}}$ | ${\mathit{C}}_{{\mathrm{SO}}_{\mathrm{X}}}\phantom{\rule{3.33333pt}{0ex}}$ | ${\mathit{C}}_{\mathsf{soot}}$ | |
---|---|---|---|---|---|

GWP_{20} | 1 | 0.22 | 619 | −832 | 4288 |

GWP_{50} | 1 | 0.1 | 205 | −392 | 2018 |

GWP_{100} | 1 | 0.06 | 114 | −226 | 1166 |

${\mathit{C}}_{{\mathrm{CO}}_{2}}\phantom{\rule{3.33333pt}{0ex}}$ | ${\mathit{C}}_{{\mathrm{H}}_{2}\mathrm{O}}\phantom{\rule{3.33333pt}{0ex}}$ | ${\mathit{C}}_{{\mathrm{NO}}_{\mathrm{X}}}\phantom{\rule{3.33333pt}{0ex}}$ | ${\mathit{C}}_{{\mathrm{SO}}_{\mathrm{X}}}\phantom{\rule{3.33333pt}{0ex}}$ | ${\mathit{C}}_{\mathsf{soot}}$ | |
---|---|---|---|---|---|

GTP_{20} | 1 | 0.07 | −222 | −241 | 1245 |

GTP_{50} | 1 | 0.01 | −69 | −38 | 195 |

GTP_{100} | 1 | 0.008 | 13 | −31 | 161 |

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**MDPI and ACS Style**

Sun, J.
OpenAP.top: Open Flight Trajectory Optimization for Air Transport and Sustainability Research. *Aerospace* **2022**, *9*, 383.
https://doi.org/10.3390/aerospace9070383

**AMA Style**

Sun J.
OpenAP.top: Open Flight Trajectory Optimization for Air Transport and Sustainability Research. *Aerospace*. 2022; 9(7):383.
https://doi.org/10.3390/aerospace9070383

**Chicago/Turabian Style**

Sun, Junzi.
2022. "OpenAP.top: Open Flight Trajectory Optimization for Air Transport and Sustainability Research" *Aerospace* 9, no. 7: 383.
https://doi.org/10.3390/aerospace9070383