# OpenAP: An Open-Source Aircraft Performance Model for Air Transportation Studies and Simulations

^{*}

## Abstract

**:**

## 1. Introduction

## 2. OpenAP Building Blocks

## 3. Aircraft and Engine Properties

## 4. Kinematic Performance

## 5. Dynamic Performance

#### 5.1. Aircraft Dynamic Model

#### 5.2. Thrust

#### 5.2.1. Takeoff Thrust

#### 5.2.2. Climb and Cruise Thrust

- (i)
- For the en-route segment from 30 k ft to 40 k ft, the thrust ratio is modeled as follows:$$\frac{T}{{T}_{\mathrm{cr}}}={c}_{1}\mathrm{ln}\left(\right)open="("\; close=")">\frac{p}{{p}_{\mathrm{cr}}}$$$$\begin{array}{cc}\hfill {c}_{1}& =-0.4204\left(\right)open="("\; close=")">\frac{M}{{M}_{\mathrm{cr}}}+1.0824\hfill \end{array}$$
- (ii)
- For the segment from 10 k ft to 30 k ft, the thrust is derived similarly, with the exception that the reference calibrated airspeed is used instead of Mach number. The thrust can be approximated as:$$\frac{T}{{T}_{\mathrm{cr}}}={c}_{3}{\left(\right)}^{\frac{p}{{p}_{\mathrm{cr}}}}{c}_{4}$$$$\begin{array}{cc}\hfill {c}_{3}& ={\left(\right)}^{\frac{{V}_{cas}}{{V}_{cas,cr}}}-0.1\hfill \end{array}$$In order to find the value of ${c}_{5}$, a look-up table is used in [22]. To simplify the computation, a linear approximation for ${c}_{5}$ is adopted in OpenAP as follows:$${c}_{5}=2.667\times {10}^{-5}\phantom{\rule{3.33333pt}{0ex}}{V}_{S}+0.8633$$
- (iii)
- For the climbing segment from takeoff up to 10 k ft, a linear model is used to approximate the thrust ratio, with respect to the thrust ratio at 30 k ft. The relationship is as follows:$$\frac{T}{{T}_{\mathrm{cr}}}={c}_{6}\left(\right)open="("\; close=")">\frac{p}{{p}_{\mathrm{cr}}}$$$$\begin{array}{cc}\hfill {c}_{6}=& -1.2043\times {10}^{-1}\left(\right)open="("\; close=")">\frac{{V}_{\mathrm{cas}}}{{V}_{\mathrm{cas},\mathrm{cr}}}-8.8889\times {10}^{-9}\phantom{\rule{3.33333pt}{0ex}}{{V}_{S}}^{2}\hfill \end{array}$$

#### 5.2.3. Reference Cruise Thrust

#### 5.3. Drag

#### 5.4. Flaps

#### 5.5. Compressibility

#### 5.6. Landing Gear

#### 5.7. Final Drag Polar Model

#### 5.8. Fuel Flow

## 6. Other Databases and Utility Libraries

#### 6.1. Flight Phase

#### 6.2. Aeronautical Calculations

#### 6.3. Navigation Database

## 7. Analysis of OpenAP

#### 7.1. Trajectory Generation

#### 7.2. Comparison with BADA

#### 7.2.1. Thrust Model

#### 7.2.2. Drag Polar

#### 7.2.3. Fuel Flow Model

#### 7.3. Analysis Based on Flight FMS Data

## 8. Discussions

#### 8.1. Limitations

#### 8.2. Future Development

- OpenAP Emission: Research is being conducted to incorporate an open emission model for emission and climate-related air transport studies.
- OpenAP Optimization: Based on the dynamic model, a trajectory optimization model shall be developed. This will further enhance the trajectory generation capability of OpenAP, extending from kinematic models to dynamic models.
- WRAP model: As more ADS-B data is collected, we plan to update the WRAP kinematic model every few years to include new aircraft types, as well as to improve models for less common aircraft types.

#### 8.3. Sharing and Community Contributions

## 9. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

x | downrange position (m) |

y | cross-range position (m) |

h | altitude (m) |

${h}_{\mathrm{cr}}$ | reference cruise altitude (ft) |

a | acceleration (m/s${}^{2}$) |

g | gravitational acceleration (m/s${}^{2}$) |

V | aircraft speed (m/s) |

${V}_{S}$ | vertical speed (m/s) |

$\psi $ | heading angle (deg) |

$\gamma $ | flight path angle (deg) |

$\varphi $ | bank angle (deg) |

${\delta}_{T}$ | thrust setting (-) |

T | net thrust (N) |

${T}_{0}$ | maximum static thrust, sea level (N) |

${T}_{10}$ | thrust at altitude of 10,000 feet (N) |

${T}_{\mathrm{cr}}$ | thrust at the top of climb (N) |

D | total drag (N) |

L | total lift (N) |

m | aircraft mass (kg) |

q | dynamic pressure (Pa) |

${q}_{c}$ | impact pressure (Pa) |

${p}_{0}$ | pressure at sea level (Pa) |

${p}_{10}$ | pressure at altitude of 10,000 feet (Pa) |

p | pressure (Pa) |

${p}_{\mathrm{cr}}$ | pressure at reference cruise altitude (Pa) |

$\rho $ | air density (kg/m${}^{3}$) |

${\rho}_{0}$ | air density at sea level (kg/m${}^{3}$) |

$\tau $ | air temperature (K) |

${\tau}_{0}$ | air temperature at sea level (K) |

M | Mach number (-) |

${M}_{cirt}$ | critical Mach number (-) |

${M}_{\mathrm{cr}}$ | reference cruise Mach number (-) |

${C}_{D}$ | drag coefficient (-) |

${C}_{L}$ | lift coefficient (-) |

${C}_{D0}$ | zero-lift drag coefficient (-) |

${C}_{D,w}$ | wave drag coefficient (-) |

${C}_{\mathrm{ff}}$ | fuel flow coefficient (-) |

k | lift-induced drag coefficient (-) |

e | Oswald factor (-) |

S | wing area (m${}^{2}$) |

$\lambda $ | bypass ratio (-) |

## Appendix A. Available Aircraft Types

Type | Aircraft Model | Engine Options |
---|---|---|

A319 | Airbus A319 | CFM56-5B5, CFM56-5B6, CFM56-5A4, CFM56-5A5, CFM56-5B7, V2522-A5, V2524-A5, V2527M-A5 |

A320 | Airbus A320 | CFM56-5-A1, CFM56-5-A1, CFM56-5A3, CFM56-5B4, CFM56-5B5, CFM56-5B6, V2500-A1, V2527-A5, V2527E-A5 |

A321 | Airbus A321 | CFM56-5B1, CFM56-5B2, V2530-A5, CFM56-5B3, CFM56-5B1, CFM56-5B2, V2533-A5, V2530-A5 |

A332 | Airbus A330-200 | CF6-80E1A2, CF6-80E1A4, CF6-80E1A3, PW4168A, PW4170, Trent 772 |

A333 | Airbus A330-300 | CF6-80E1A2, CF6-80E1A4, CF6-80E1A3, PW4164, PW4168, PW4168A, Trent 768, Trent 772, Trent 772 |

A343 | Airbus A340-300 | CFM56-5C2, CFM56-5C3, CFM56-5C4 |

A359 | Airbus A350-900 | Trent XWB-84 |

A388 | Airbus A380-800 | Trent 970-84, Trent 972-84, GP7270 |

B734 | Boeing 737-400 | CFM56-3B-2, CFM56-3C-1 |

B737 | Boeing 737-700 | CFM56-7B20, CFM56-7B22, CFM56-7B24, CFM56-7B26, CFM56-7B27 |

B738 | Boeing 737-800 | CFM56-7B24, CFM56-7B26, CFM56-7B27 |

B739 | Boeing 737-900 | CFM56-7B24, CFM56-7B26, CFM56-7B27 |

B744 | Boeing 747-400 | PW4062, CF6-80C2B1F, RB211-524G |

B748 | Boeing 747-8 | GEnx-2B67 |

B752 | Boeing 757-200 | PW2037, RB211-535E4 |

B763 | Boeing 767-300 | JT9D-7R4D, PW4056, CF6-80C2B2 |

B772 | Boeing 777-200ER | GE90-94B, PW4077, Trent 895 |

B773 | Boeing 777-300 | GE90-110B1, PW4090, Trent 892 |

B77W | Boeing 777-300ER | GE90-115B |

B788 | Boeing 787-8 | GEnx-1B70, GEnx-1B67, GEnx-1B64, Trent 1000-E2, Trent 1000-C2, Trent 1000-A1 |

B789 | Boeing 787-9 | GEnx-1B75, GEnx-1B74, Trent 1000-K2, Trent 1000-J2, Trent 1000-A2 |

C550 | Cessna Citation II | JT15D-4 |

E145 | Embraer ERJ145 (LR) | AE3007A1 |

E170 | Embraer E170 | CF34-8E5, CF34-8E6 |

E190 | Embraer E190 (LR) | CF34-10E5 |

E195 | Embraer E195 (LR) | CF34-10E5 |

E75L | Embraer E175 (LR) | CF34-8E5, CF34-8E6 |

## Appendix B. OpenAP Sample Data

#### Appendix B.1. Aircraft Property Data Structure

#### Appendix B.2. Drag Polar Data Structure

## Appendix C. OpenAP Python Library Programming Interface Examples

#### Appendix C.1. Access OpenAP Aircraft and Engines

#### Appendix C.2. Access WRAP Parameters

#### Appendix C.3. Calculate Aircraft Thrust

#### Appendix C.4. Calculate Aircraft Drag

#### Appendix C.5. Calculate Aircraft Fuel Flow

#### Appendix C.6. Inferring Flight Phase

#### Appendix C.7. Use of Navigation Library

#### Appendix C.8. Generation of Flight Trajectories

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**Figure 3.**Drag polar estimated for common Airbus and Boeing aircraft under clean configurations at low Mach number.

**Figure 11.**Absolute difference of drag polar between BADA (3.12) and the model derived in this paper under clean configuration.

Parameter | Notation | Remarks |
---|---|---|

name | - | engine common identifier |

manufacture | - | - |

bpr | $\lambda $ | bypass ratio |

pr | - | pressure ratio |

max_thrust | ${T}_{0}$ | maximum static thrust, sea level (unit: N) |

fuel_c3 | ${C}_{\mathrm{ff}3}$ | fuel flow coefficient, 3rd order term (unit: kg/s) |

fuel_c2 | ${C}_{\mathrm{ff}2}$ | fuel flow coefficient, 2nd order term (unit: kg/s) |

fuel_c1 | ${C}_{\mathrm{ff}1}$ | fuel flow coefficient, 1st order term (unit: kg/s) |

cruise_thrust | ${T}_{\mathrm{cr}}$ | thrust at the top of climb (unit: N) |

cruise_mach | ${M}_{\mathrm{cr}}$ | cruise Mach number for the thrust condition |

cruise_alt | ${h}_{\mathrm{cr}}$ | cruise Mach altitude for the thrust condition (unit: ft) |

Takeoff | ${\mathit{V}}_{\mathbf{lof}}$ ${d}_{\mathrm{tof}}$ ${\overline{a}}_{\mathrm{tof}}$ | liftoff speed takeoff distance mean takeoff acceleration | m/s km m/s${}^{2}$ |

Initial climb | ${V}_{\mathrm{cas},\mathrm{ic}}$ ${{V}_{S}}_{\mathrm{ic}}$ | calibrated airspeed vertical rate | m/s m/s |

Climb | ${R}_{\mathrm{top},\mathrm{cl}}$ ${h}_{\mathrm{cas},\mathrm{cl}}$ ${V}_{\mathrm{cas},\mathrm{cl}}$ ${{V}_{S}}_{\mathrm{cas},\mathrm{cl}}$ ${h}_{\mathrm{mach},\mathrm{cl}}$ ${M}_{\mathrm{cl}}$ ${{V}_{S}}_{\mathrm{mach},\mathrm{cl}}$ ${{V}_{S}}_{\mathrm{precas},\mathrm{cl}}$ | range to the top of climb constant CAS crossover altitude constant CAS vertical rate during constant CAS climb constant Mach climb crossover altitude constant Mach number vertical rate at constant Mach climb vertical rate before constant CAS climb | km km m/s m/s km - m/s m/s |

Cruise | ${R}_{\mathrm{cr}}$ ${h}_{\mathrm{init},\mathrm{cr}}$ ${h}_{\mathrm{cr}}$ ${M}_{\mathrm{cr}}$ | cruise range initial cruise altitude cruise altitude cruise Mach number | km km km - |

Descent | ${R}_{\mathrm{top},\mathrm{de}}$ ${M}_{\mathrm{de}}$ ${h}_{\mathrm{mach},\mathrm{de}}$ ${{V}_{S}}_{\mathrm{mach},\mathrm{de}}$ ${V}_{\mathrm{cas},\mathrm{de}}$ ${h}_{\mathrm{cas},\mathrm{de}}$ ${{V}_{S}}_{\mathrm{cas},\mathrm{de}}$ ${{V}_{S}}_{\mathrm{postcas},\mathrm{de}}$ | range from the top of descent constant Mach number constant Mach descent crossover altitude vertical rate at constant Mach descent constant CAS constant CAS crossover altitude vertical rate at constant CAS descent vertical rate after constant CAS descent | km - km m/s m/s km m/s m/s |

Final approach | ${V}_{\mathrm{cas},\mathrm{fa}}$ ${{V}_{S}}_{\mathrm{fa}}$ ${\angle}_{\mathrm{fa}}$ | calibrated airspeed vertical rate path angle | m/s m/s deg |

Landing | ${V}_{tcd}$ ${d}_{lnd}$ ${\overline{a}}_{lnd}$ | touchdown speed braking distance mean braking deceleration | m/s km m/s${}^{2}$ |

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## Share and Cite

**MDPI and ACS Style**

Sun, J.; Hoekstra, J.M.; Ellerbroek, J.
OpenAP: An Open-Source Aircraft Performance Model for Air Transportation Studies and Simulations. *Aerospace* **2020**, *7*, 104.
https://doi.org/10.3390/aerospace7080104

**AMA Style**

Sun J, Hoekstra JM, Ellerbroek J.
OpenAP: An Open-Source Aircraft Performance Model for Air Transportation Studies and Simulations. *Aerospace*. 2020; 7(8):104.
https://doi.org/10.3390/aerospace7080104

**Chicago/Turabian Style**

Sun, Junzi, Jacco M. Hoekstra, and Joost Ellerbroek.
2020. "OpenAP: An Open-Source Aircraft Performance Model for Air Transportation Studies and Simulations" *Aerospace* 7, no. 8: 104.
https://doi.org/10.3390/aerospace7080104