13  Aircraft performance

Aircraft performance models are used to study how aircraft fly. They are based on the laws of physics and can be used to predict the aircraft’s speed, altitude, thrust, drag, and fuel consumption. There are different categories of performance models, with varying levels of detail. The most detailed, non-linear six-degree-of-freedom models are commonly used in aircraft control studies. Air traffic management research often assumes a stable aircraft and neglects fast rotational dynamics. This assumption means that a point-mass aircraft performance model is sufficient in most use cases. Such a point-mass model is used in most of the aviation research.

Two prominent aircraft performance models are widely used in the aviation community. BADA [1], developed by Eurocontrol, is a well-established model that includes both kinematic and dynamic models. The BADA aircraft performance operation file (OPF) models the dynamic properties of the aircraft, while the airline procedures file (APF) models the kinematic aspects of flights. Unlike BADA, which relies on strict user license agreements, OpenAP [2], a recent open aircraft model, also provides both kinematic and dynamic models for common aircraft types with full open access.

13.1 Point-Mass Models

There are two different types of point-mass models: kinematic and dynamic. The primary difference is that while a dynamic model focuses on forces and energy, a kinematic model deals only with aircraft motions.

Table 13.1: Comparison of kinematic and dynamic point-mass models

Aspect	Kinematic Model	Dynamic Model
Focus	Observable motion parameters (speed, altitude, acceleration)	Forces (thrust, drag, weight) and energy
Equations	Simple differential equations for position and velocity	Force balance and energy conservation equations
Data Requirements	Surveillance data (ADS-B, Mode-S), statistical distributions	Aircraft mass, thrust coefficients, drag polar, fuel flow parameters
Computational Complexity	Low - fast computation, suitable for real-time	Moderate to high - iterative calculations required
Use Cases	Flight phase identification, trajectory prediction, pattern recognition	Fuel estimation, emissions, trajectory optimization, what-if analysis
Model Development	Data-driven from surveillance data	Physics-based with parameter calibration
Physical Constraints	May not respect all aircraft limits	Respects aircraft performance envelope

13.2 Kinematic Model

The kinematic model is a simplified way of describing aircraft motion without considering the forces involved. It is commonly used to analyze the motion of an aircraft during various flight phases, including takeoff, initial climb, climb, cruise, descent, final approach, and landing.

13.2.1 Flight Phases and Data-Driven Approaches

The kinematics of aircraft motion varies across different flight phases. Through surveillance data, we can directly observe essential parameters such as velocity, altitude, and range. For example. with the openly accessible ADS-B data, we can construct accurate kinematic models, as demonstrated in the OpenAP’s kinematic model component [3].

The kinematic models allow us to describe the behavior and performance of aircraft during different flight phase. Furthermore, the adoption of large-scale open data in constructing kinematic models is a powerful approach for analyzing and improving flight operations. In the following part, we will explain two different kinematic models, which are part of the OpenAP and BADA aircraft performance models.

13.2.2 Examples of Kinematic Models

13.2.2.1 OpenAP Kinematic Model

The OpenAP’s kinematic model divides flight into seven distinct flight phases, each characterized by a set of specific kinematic parameters. The model is data-driven, based on openly accessible ADS-B surveillance data, and uses probability density functions (normal, gamma, or beta distributions) to represent the statistical variation of each parameter.

Table 13.2: OpenAP kinematic parameters by flight phase

Flight Phase	Key Parameters	Description
Takeoff	$V_{lof}$ [m/s] $d_{tof}$ [km] ${\overline{a}}_{tof}$ [m/s²]	Liftoff speed Takeoff distance Mean takeoff acceleration
Initial Climb	$V_{cas,ic}$ [m/s] $V_{S,ic}$ [m/s]	Calibrated airspeed Vertical rate
Climb	$R_{top,cl}$ [km] $V_{cas,cl}$ [m/s] $V_{S,cas,cl}$ [m/s] $M_{cl}$ [-] $V_{S,mach,cl}$ [m/s]	Range to top of climb Constant CAS climb speed Vertical rate during CAS climb Constant Mach number Vertical rate at Mach climb
Cruise	$R_{cr}$ [km] $h_{cr}$ [km] $M_{cr}$ [-]	Cruise range Cruise altitude Cruise Mach number
Descent	$R_{top,de}$ [km] $M_{de}$ [-] $V_{S,mach,de}$ [m/s] $V_{cas,de}$ [m/s] $V_{S,cas,de}$ [m/s]	Range from top of descent Constant Mach number Vertical rate at Mach descent Constant CAS descent speed Vertical rate during CAS descent
Final Approach	$V_{cas,fa}$ [m/s] $V_{S,fa}$ [m/s] ${\gamma }_{fa}$ [deg]	Calibrated airspeed Vertical rate Flight path angle
Landing	$V_{tcd}$ [m/s] $d_{lnd}$ [km] ${\overline{a}}_{lnd}$ [m/s²]	Touchdown speed Braking distance Mean braking deceleration

In OpenAP’s kinematic module, each parameter is provided with a default value, minimum and maximum bounds, and a statistical distribution model, allowing for both deterministic and stochastic generation of trajectory parameters.

13.2.2.2 BADA APF - Airline Procedures File

The BADA Airline Procedures File contains speed procedure parameters for different aircraft types and mass categories. Unlike OpenAP’s parametric approach, BADA APF provides procedural speed schedules that are “typically” followed in flight operations.

Note

There are only three procedure profiles available depending on the weight of the flight. The profile should only be used as references, as in reality, the flight profiles can differ a lot.

Speed schedules by flight phase:

• Climb speeds: Low altitude CAS ($CA{S}_{lo}$), high altitude CAS ($CA{S}_{hi}$), and climb Mach number
• Cruise speeds: Low altitude CAS, high altitude CAS, and cruise Mach number
• Descent speeds: Descent Mach number, high altitude CAS, and low altitude CAS

Mass categories:

Each aircraft type in BADA has speed schedules for three mass ranges:

• LO (Low): Lighter aircraft configurations, typically faster climb rates
• AV (Average): Nominal operating mass, most common configuration
• HI (High): Heavier configurations, reduced climb performance

This categorization allows the model to reflect performance variations with aircraft weight, particularly important for climb and descent phases where mass significantly affects vertical performance.

Note

Quick summary: key characteristics of kinematic models:

• Focus on observable motion parameters (speed, altitude, acceleration)
• Do not require detailed force calculations
• Can be constructed from surveillance data (e.g., ADS-B)
• Useful for flight phase identification and trajectory prediction
• Lower computational complexity compared to dynamic models

13.3 Dynamic Model

When aircraft forces are taken into account, a more complex model is required to accurately describe the aircraft’s performance compared to what a kinematic model can provide.

In air traffic management-related studies, the total energy model is commonly used to describe the aircraft’s behavior. This model takes into account the conservation of total energy generated by the aircraft’s engines to counteract drag and the change of kinetic and potential energy. This model is especially useful for trajectory-based studies, like optimization and fuel estimations.

The main components of the dynamic model are thrust, drag, and mass of the aircraft. Thrust represents the force generated by the aircraft’s engines, while drag represents the force that opposes the motion of the aircraft through the air. Mass refers to the total weight of the aircraft, including fuel and passengers.

13.3.1 Total Energy Model

In air traffic management, the point-mass dynamic model is commonly formulated using the total energy approach. This model describes the aircraft’s motion through a set of differential equations that account for both translational motion and energy changes.

13.3.1.1 Four-Degrees-of-Freedom Equations

Under ISA conditions and zero wind, the aircraft motion is described by:

$$\begin{array}{}\text{(13.1)}& \frac{dx}{dt}=V\cos (\psi )\cos (\gamma )\end{array}$$

$$\begin{array}{}\text{(13.2)}& \frac{dy}{dt}=V\sin (\psi )\cos (\gamma )\end{array}$$

$$\begin{array}{}\text{(13.3)}& \frac{dh}{dt}=V\sin (\gamma )\end{array}$$

$$\begin{array}{}\text{(13.4)}& \frac{dV}{dt}=\frac{T-D}{m}-g\sin (\gamma )\end{array}$$

$$\begin{array}{}\text{(13.5)}& \frac{d\psi }{dt}=\frac{g\tan (\varphi )}{V\cos (\gamma )}\end{array}$$

$$\begin{array}{}\text{(13.6)}& \frac{dm}{dt}=-f_{fuel}(T,h)\end{array}$$

Where:

• $V$: True airspeed [m/s]
• $\psi$: Heading angle [rad]
• $\gamma$: Flight path angle [rad]
• $\varphi$: Bank angle [rad]
• $T$: Thrust [N]
• $D$: Drag [N]
• $m$: Aircraft mass [kg]
• $g$: Gravitational acceleration [m/s²]
• $h$: Altitude [m]
• $f_{fuel}$: Fuel flow function [kg/s]

13.3.1.2 Total Energy Equation

The total energy model relates the net force (thrust minus drag) to changes in kinetic and potential energy:

$$\begin{array}{}\text{(13.7)}& T-D=mg\sin (\gamma )+m\frac{dV}{dt}\end{array}$$

This equation expresses the conservation of energy: the net force produced by the aircraft’s engines (after overcoming drag) is used to climb against gravity and to accelerate. This formulation is particularly useful for trajectory-based studies such as optimization and fuel estimation, as it directly links the aircraft’s energy state to its performance capabilities.

Note

Note: The total energy model assumes that changes in aircraft attitude are much slower than changes in velocity and altitude, which is valid for most air traffic management applications. For more detailed aircraft control studies, higher-order models that include rotational dynamics would be required.

13.3.2 Model Examples

13.3.3 Thrust

Thrust is produced by the engines of the aircraft, and modeling aircraft engine performance can be complicated. A thrust model often provide the maximum available thrust of the engines at specific flight conditions, like altitude and speed.

In air traffic management studies, the maximum thrust models are also often simplified. For example, in BADA v3, thrust is modeled as a polynomial model related to the aircraft altitude. In OpenAP, the thrust model is based on an empirical model for two-shaft turbofan engines proposed by Bartel and Young [4]. The model is constructed and evaluated based on engine performance data, where the maximum thrust is modeled as functions of both altitude and speed, as well as the vertical rate.

Note

For many applications in aviation, such as, studying fuel, emission, and noise, the net thrust is often used. The net thrust is not calculated with the these thrust models. It is usually derived based on the drag model and equilibrium of forces (see below).

13.3.4 Drag

Aircraft drag is typically modeled using drag polar equations, which relate the drag coefficient to the lift coefficient. The total drag consists of two main components: parasitic drag (zero-lift drag) and induced drag (drag due to lift generation).

The drag polar is commonly expressed as: $$C_D=C_{D_0}+k{C}_L^2$$

Where:

• $C_D$: Total drag coefficient
• $C_{D_0}$: Zero-lift drag coefficient
• $k$: Lift-induced drag coefficient, where $k=\frac{1}{\pi \cdot AR\cdot e}$
• $C_L$: Lift coefficient
• $AR$: Aspect ratio (wingspan² / wing area)
• $e$: Oswald efficiency factor (typically 0.7–0.85 for transport aircraft)

This equation is sometimes written in the expanded form:

$$C_D=C_{D_0}+\frac{C_L^2}{\pi \cdot AR\cdot e}$$

13.3.4.1 Estimating Drag Parameters

Drag polar parameters can be estimated through various methods:

1. Wind-tunnel testing: Traditional method using scaled models
2. Computational Fluid Dynamics (CFD): Numerical simulations of airflow
3. Flight test data: Direct measurements from instrumented aircraft
4. Data-driven approaches: Using flight data to infer drag characteristics

The values of drag coefficients can change depending on the aerodynamic configurations of the aircraft. These configuration-specific coefficients reflect how flaps, slats, and landing gear affect aircraft drag.

Clean configuration (e.g. during later stage of climb, cruise, and earlier stage of descent) has the lowest drag, while landing configuration with full flaps and gear down produces the highest drag. The following figure shows some indicative values of the zero-lift drag coefficient and lift-induced drag coefficient.

Table 13.3: Typical drag coefficients for modern commercial jets

Configuration	Typical $C_{D0}$	Typical $k$	Description
Clean (Cruise)	0.020 - 0.025	0.045 - 0.055	Minimal drag, optimal for cruise
Initial Climb	0.025 - 0.030	0.050 - 0.060	Partial flaps extended
Takeoff	0.025 - 0.030	0.050 - 0.060	Takeoff flap setting
Approach	0.045 - 0.055	0.055 - 0.065	More flaps, moderate drag
Landing	0.080 - 0.100	0.055 - 0.065	Full flaps + gear down, maximum drag

Note

Example: For an Airbus A320 or Boeing 737-800, the clean configuration drag polar coefficients are approximately $C_{D0}\approx 0.023$ and $k\approx 0.050$. In landing configuration, $C_{D0}$ increases to approximately 0.090, representing a nearly 4-fold increase in parasitic drag due to flaps and landing gear.

It is worth noting that with the same aerodynamic configuration, the drag coefficient can also be affected by the speed aircraft, especially when the aircraft operates near the maximum Mach number. And a wave drag coefficient should be introduced to count for increase of drag.

13.3.5 Mass

Aircraft mass is one of the most challenging parameters to determine accurately in air traffic management studies. The actual mass varies significantly throughout a flight due to fuel consumption and differs between flights based on payload (passengers, cargo) and fuel loading decisions.

Estimating aircraft mass presents several challenges. Privacy concerns arise because airlines treat payload and fuel data as commercially sensitive information, limiting access to actual mass figures. Additionally, aircraft mass varies continuously throughout a flight due to fuel consumption, making it difficult to determine an accurate value at any given time. Data availability is another issue, as real-time mass information is rarely provided by surveillance systems, further complicating mass estimation efforts in operational contexts.

13.3.5.1 Mass Estimation Methods

Several approaches exist to estimate aircraft mass:

1. Fixed mass assumptions: Using typical operating weights (conservative but inaccurate)
2. Statistical models: Based on flight distance, aircraft type, and historical data
3. Performance-based estimation: Inferring mass from observed climb/descent performance
4. Machine learning approaches: Using multiple factors including origin/destination airports, time of day, airline fuel policies, and 4D trajectory characteristics

13.3.5.2 Typical Mass Ranges

Aircraft mass is typically characterized by several reference values:

• OEW (Operating Empty Weight): Aircraft structure, systems, and crew (but no payload or fuel)
• MTOW (Maximum Takeoff Weight): Maximum certified takeoff weight for safety and structural integrity
• MLW (Maximum Landing Weight): Maximum weight allowed for landing (usually less than MTOW)

Following table provides typical mass ranges for some common commercial aircraft:

Table 13.4: Typical mass ranges for common commercial aircraft

Aircraft Type	OEW [kg]	MTOW [kg]	Typical Operating [kg]	Range [NM]
A320	~42,000	~78,000	60,000 - 70,000	~2,700
A20N	~42,400	~79,000	62,000 - 72,000	~3,500
B738	~41,000	~79,000	60,000 - 70,000	~2,000
A321	~48,500	~90,000	70,000 - 80,000	~2,400
B77W	~168,000	~350,000	280,000 - 320,000	~7,400

13.3.5.3 Impact of Mass on Performance

Aircraft mass significantly affects several performance aspects:

• Climb performance: Rate of climb decreases with increasing mass (heavier aircraft climb more slowly)
• Fuel consumption: Fuel flow increases with mass (more thrust required for heavier aircraft)
• Maximum altitude: Cruise ceiling decreases with increasing mass (requires higher air density for higher lift)
• Stall speeds: All stall speeds increase with mass (proportional to $\sqrt{m}$)

13.4 Model Comparison and Use Cases

The choice between kinematic and dynamic models depends on the specific research objectives and available data:

13.4.1 When to Use Kinematic Models

• Flight phase identification and classification
• Trajectory prediction without force calculations
• Real-time applications requiring low computational cost
• Studies where surveillance data is the primary input
• Pattern recognition in flight operations

13.4.2 When to Use Dynamic Models

• Fuel consumption estimation
• Trajectory optimization problems
• What-if scenario analysis with different aircraft configurations
• Performance envelope studies
• Emission calculations
• Studies requiring physical consistency with aircraft limitations

13.4.3 Trade-offs

Selecting the appropriate model requires careful consideration of several factors:

Table 13.5: Detailed comparison of kinematic and dynamic models

Factor	Kinematic Model	Dynamic Model
Data Requirements	Surveillance data (ADS-B, Mode-S) Statistical distributions Flight phase definitions	All kinematic data plus: Aircraft mass Thrust coefficients Drag polar parameters Fuel flow models Engine specifications
Computational Cost	Fast - simple differential equations Suitable for real-time operations Can handle thousands of aircraft	Moderate - more complex equations Iterative thrust/drag calculations Still feasible for large-scale studies
Accuracy	Excellent for trajectory shape/timing Cannot predict fuel consumption May not respect all physical constraints Statistical uncertainty from distributions	Physically consistent trajectories Fuel predictions within ±5-10% Respects aircraft performance limits Better for off-nominal scenarios
Model Calibration	Data-driven - minimal calibration needed Automatically learned from surveillance data	Requires detailed parameter estimation Calibration against flight test data May need proprietary information
Flexibility	Quick trajectory generation Easy to adapt to new aircraft types Good for pattern analysis	Supports what-if scenarios Can model different configurations Enables optimization studies
Applications	Flight phase identification Trajectory prediction Conflict detection Pattern recognition Fast-time simulation	Fuel/emission estimation Trajectory optimization Economic analysis Environmental impact Performance studies

The choice often depends on the research question: if the goal is to understand where and when aircraft will be (trajectory prediction, conflict detection), kinematic models are sufficient and computationally efficient. If the goal is to understand fuel burn, emissions, or to optimize flight paths subject to physical constraints, dynamic models are necessary despite their higher complexity and data requirements.

13.5 Other Performance Models

Beyond OpenAP and BADA, several other aircraft performance models are used in specialized applications:

ECAC Doc 29: A model primarily designed for aircraft noise and emission calculations around airports. It provides a less detailed performance data for noise certification and environmental impact assessments, focusing on standard flight procedures and reference trajectories.

In-house models: Many research institutions and airlines develop proprietary performance models tailored to their specific needs [5], [6]. These models often combine publicly available data with organization-specific calibrations and enhancements.

13.6 Advanced Aircraft Mass Estimation

Accurately estimating aircraft mass is a fundamental challenge in air traffic management research and operations. Aircraft mass is typically considered proprietary information by airlines, preventing ground-based decision support tools from accessing this critical parameter directly. This necessitates the development of sophisticated ground-based inverse estimation techniques capable of inferring mass from observable kinematic data such as ADS-B or Mode-S surveillance data.

The need for accurate mass estimation extends beyond trajectory prediction to encompass fuel consumption modeling, emission calculations, and safety management. The challenge is compounded by the fact that mass varies continuously throughout a flight due to fuel consumption and differs significantly between flights based on payload and fuel loading decisions.

13.6.1 Foundational Physics: The Point-Mass Framework

Ground-based mass estimation fundamentally relies on inverse modeling, where observable kinematic variables are used to infer non-observable operational parameters within the framework of the aircraft performance model. The most reliable approach for inferring mass from observed data involves fitting the dynamics to the aircraft’s total energy rate.

The energy of an aircraft is composed of kinetic and potential energy:

$$E=\frac{1}{2}m{V}_a^2+mgh$$

The observed power input is related to the energy rate equation:

$$\text{Power}=(\text{Thr}-D)V_a$$

By comparing the derived energy rate from observed trajectory data (altitude and speed changes) to the power equation, the unknown mass ($m$) can be estimated. Many modern ATM tools utilize the industry-standard Base of Aircraft Data (BADA) equations for drag polar and thrust modeling; consequently, mass estimation is often framed as inferring the mass parameter that minimizes the deviation between the observed dynamics and the BADA equations.

13.6.2 Methodological Approaches

Ground-based mass estimation methods can be classified into five major categories, each with distinct advantages and limitations.

13.6.2.1 1. Inverse Physics Methods

Early ground-based approaches employed classical inverse physics techniques, comparing adaptive methods against least squares methods to estimate mass from trajectory data. These methods fit the observed dynamics to the point-mass equations, typically assuming maximum climb thrust during the analyzed segment. The challenge lies in solving differential algebraic equations to find the mass value that minimizes deviation between predicted and observed trajectories.

These methods are computationally efficient but highly sensitive to uncertainties in coupled parameters such as thrust setting, drag coefficients, and wind velocity. Their accuracy depends entirely on how well the simplified point-mass model reflects the actual forces acting on the aircraft.

13.6.2.2 2. Recursive Bayesian Filtering

A significant advancement came from recursive Bayesian methods, particularly the particle filter approach applied to mass and thrust estimation. This methodology treats mass estimation as a stochastic state estimation problem, enabling real-time tracking with rigorous uncertainty quantification.

The particle filter method utilizes open surveillance data (ADS-B, Mode-S) and explicitly models observation noise using the Navigation Accuracy Category (NAC) parameters native to ADS-B transmissions. This approach achieves mass convergence typically within 30 seconds of takeoff during the initial climb phase, with validation studies reporting Mean Absolute Errors (MAE) of approximately 4.3-4.6% relative to true aircraft mass.

The primary advantages of recursive Bayesian filtering are real-time capability, uncertainty quantification, and the ability to simultaneously estimate coupled parameters (mass and thrust setting). However, the computational demand is high, often requiring millions of particles to balance accuracy and processing speed.

13.6.2.3 3. Large-Scale Machine Learning

Data-driven machine learning approaches leverage massive datasets from sources like the OpenSky Network to learn operational factors that minimize trajectory prediction errors. Neural networks and gradient-boosting machines are trained on millions of flight segments to predict mass and speed profiles during climb.

Rather than optimizing for mass accuracy directly, these methods focus on operational utility—minimizing the Root Mean Square Error (RMSE) in predicted altitude and speed trajectories. Studies report RMSE reductions of 29-58% in altitude prediction compared to baseline methods using reference mass assumptions. When using only information available before takeoff, ML approaches can still achieve 25% average RMSE reduction.

The strength of ML methods lies in their scalability and ability to capture complex, non-linear relationships without strict reliance on proprietary performance coefficients. However, purely data-driven models risk producing non-physical results in flight regimes not adequately represented in training data.

13.6.2.4 4. High-Fidelity Data Methods

When proprietary Quick Access Recorder (QAR) or Flight Data Recorder (FDR) data is available, specialized techniques achieve higher accuracy. Gaussian Process Regression applied to takeoff ground roll data has demonstrated MAE as low as 3.6%. Multilayer perceptron neural networks combined with QAR data also show strong performance for initial climb mass estimation.

These methods represent an accuracy benchmark but are limited by data accessibility, making them less applicable for ground-based ATM systems that must rely on surveillance data.

13.6.2.5 5. Hybrid Physics-Guided Models

An emerging trend addresses the limitations of purely data-driven approaches by incorporating physical constraints directly into neural network architectures. Physics-guided deep neural networks embed aircraft equations (fuel flow dynamics, force balance) into the loss function, penalizing results that violate known physics.

This hybridization ensures physical consistency and robustness, yielding improved generalization in unseen flight regimes while maintaining the learning advantages of neural networks. This approach represents a promising convergence between model-based and data-driven methodologies.

13.6.3 Key Challenges and Sensitivities

Several persistent challenges affect all ground-based estimation methods:

• Coupled parameter uncertainty: Mass estimation requires simultaneous knowledge or estimation of thrust setting and pilot speed intent. Inaccurate assumptions about maximum thrust introduce systematic bias.
• Wind uncertainty: The total energy model is highly sensitive to true airspeed, which requires accurate wind vector calculation. Errors in numerical weather predictions directly propagate to mass estimation errors.
• Flight phase selection: The initial climb phase is strongly preferred for mass estimation due to high engine performance and significant energy changes, maximizing the signal-to-noise ratio. The cruise phase is generally less suitable for mass inference.
• Observation noise: Altitude is typically derived from barometric pressure, introducing uncertainties that propagate through energy rate calculations.

13.6.4 Comparative Analysis

The following tables synthesize the leading scientific approaches and provide a qualitative assessment of their strengths and limitations.

Table 13.6: Summary of key aircraft mass estimation methodologies and performance benchmarks

Methodology Class	Specific Approach (Key Authors)	Primary Flight Phase	Input Data Source	Reported Accuracy (Error Type)
Stochastic Bayesian	Particle Filter [7]	Initial Climb	ADS-B, Mode S (Open Data, NAC Noise)	MAE 4.6%
Bayesian Inference	Total Energy Model Integration [8]	Initial Mass (Post-Process)	Trajectory Data	MAE 4.3%
Data-Driven ML	Neural Networks/GBM [9]	Climb	OpenSky ADS-B (Large Scale)	RMSE Reduction ≥ 29% (Altitude TP)
Statistical Regression	Gaussian Process Regression [10]	Takeoff Ground Roll	FDR/QAR (Proprietary)	MAE 3.6%
Inverse Physics	Adaptive/Least Squares [11]	Climb	ADS-B Track Data	Trajectory Error Reduction

Table 13.7: Qualitative assessment of mass estimation methodology classes

Methodology Class	Primary Advantage	Primary Limitation	Data Accessibility	Computational Demand
Recursive Bayesian Filtering (Sun)	Real-time state tracking, Uncertainty quantification	Sensitivity to observation noise model, High PF execution cost	Open (ADS-B, Mode S)	High (Run-Time)
Data-Driven ML (Alligier)	Highly scalable, Maximizes trajectory prediction accuracy	Requires massive training data, Risk of non-physical results in extreme regimes	Open (OpenSky Network)	High (Training)
High-Fidelity Data ML (QAR/FDR)	Highest potential accuracy (MAE ≈ 3.6%), Robust inputs	Requires proprietary data, Limited applicability across diverse fleets	Proprietary/Internal	Medium
Inverse Physics/Adaptive	Simple physical interpretation, Low computational overhead	Highly sensitive to unknown parameters (Thrust, Drag, Wind)	Open (Track Data)	Low

13.6.5 Performance Insights

The comparative analysis reveals several important insights:

1. State Fidelity vs. Operational Utility: Recursive Bayesian methods prioritize minimizing the MAE of the estimated mass parameter itself, establishing high state fidelity (MAE 4.3–4.6%). In contrast, ML methods prioritize operational utility for ATM, focusing on large reductions in RMSE of the resulting trajectory output (29–58% reduction).

2. Data Quality Compensation: The accuracy gap between high-fidelity proprietary data methods (MAE ~3.6%) and open surveillance data methods (MAE ~4.3-4.6%) is remarkably small. This demonstrates that sophisticated mathematical techniques—particularly those that explicitly model measurement noise—can effectively compensate for data quality limitations.

3. Trade-offs: The choice of methodology involves balancing computational complexity, data requirements, and optimization objectives. Both state fidelity (critical for performance analysis) and trajectory prediction accuracy (essential for ATM decision support tools) are valuable metrics.

13.6.5.1 The EUROCONTROL Data Challenge

A comprehensive data challenge organized by EUROCONTROL Performance Review Commission analyzed around 530,000 flights from 2022 across 30 distinct aircraft types to advance mass estimation methodologies [12]. The dataset provided new insights into the factors affecting aircraft takeoff weight, with the top 10 aircraft types accounting for approximately 80% of all flights in the dataset.

Dataset Composition

The dataset represents a collection of flight information, combining:

• Flight information: Origin/destination airports, take-off/landing times, and aircraft type identifiers
• ADS-B trajectory data: Complete 4D trajectories from OpenSky Network, covering 5 minutes before actual off-block time to 30 minutes after arrival
• Actual take-off weight data: Airline-reported weights from EUROCONTROL’s Network Manager, with airline information anonymized through agreements for open data sharing
• Meteorological data: Enhanced with Copernicus ERA5 atmospheric data via the fastmeteo library

The dataset spans 527,162 flights throughout Europe in 2022, representing 6.1% of all flights in EUROCONTROL airspace. All data is openly available at 4TU.ResearchData data repository. The dataset is more than 300 GB.

Table 13.8: Top 10 aircraft types in the EUROCONTROL data challenge dataset

ICAO Code	Aircraft Name	Flights	% of Flights	Range [NM]	Max Pax
A320	Airbus A320	113,971	21.6%	2,700	180
A20N	Airbus A320neo	54,245	10.3%	3,500	194
B738	Boeing 737-800	53,813	10.2%	2,000	189
A321	Airbus A321	41,819	7.9%	2,350	220
E195	Embraer 195	35,370	6.7%	2,300	124
A21N	Airbus A321neo	33,158	6.3%	4,000	244
CRJ9	Bombardier CRJ900	32,846	6.2%	1,550	90
A319	Airbus A319	25,074	4.8%	1,800	142
A333	Airbus A330-300	24,316	4.6%	5,650	335
B38M	Boeing 737 Max 8	17,396	3.3%	3,550	210

Dataset Features and Structure

Each flight record in the dataset includes:

• Flight identification: Callsign, aircraft registration (ICAO 24-bit address), aircraft type (ICAO code)
• Temporal information: Date, actual off-block time, takeoff time, landing time, arrival time
• Spatial information: Origin and destination airports (ICAO codes)
• Mass information: Actual take-off weight (TOW) in kilograms, anonymized airline identifier
• Trajectory data: Time-series ADS-B state vectors including latitude, longitude, altitude, ground speed, track angle, vertical rate
• Meteorological context: Temperature, pressure, wind components at flight level from ERA5 reanalysis

The dataset is organized daily, with one Parquet file per day throughout 2022 (366 files total), plus summary CSV files for training and testing subsets used in the original data challenge. This structure enables efficient access to specific time periods while maintaining the complete temporal coverage necessary for understanding seasonal and operational patterns in aircraft mass.

13.7 Conclusion

Aircraft performance modeling is fundamental to air traffic management research and operations. This chapter has explored the two primary approaches to point-mass performance modeling: kinematic and dynamic models, each serving distinct but complementary purposes in aviation studies.

Choosing the Appropriate Model

The selection between kinematic and dynamic models depends primarily on the research objectives and available resources. Kinematic models excel at describing observable aircraft motion and are ideal for applications requiring computational efficiency and real-time performance, such as trajectory prediction and conflict detection. Dynamic models, while more complex, are essential when physical forces, fuel consumption, or emissions must be accurately represented, making them indispensable for trajectory optimization and environmental impact studies.

Model Fidelity and Practical Applicability

A key insight from comparing BADA and OpenAP approaches is the trade-off between model fidelity and practical applicability. BADA offers comprehensive, rigorously validated performance data but requires user agreements that limit accessibility. OpenAP demonstrates that data-driven approaches using openly available surveillance data can achieve comparable accuracy while promoting reproducibility and broader adoption in the research community. This balance between model sophistication and accessibility is crucial for advancing the field.

The Trend Toward Open and Data-Driven Approaches

The aviation research community is increasingly embracing open-source models and data-driven methodologies. The success of OpenAP in deriving performance parameters from ADS-B data illustrates how modern surveillance systems can support model development without relying solely on proprietary manufacturer data. This trend democratizes access to performance modeling capabilities and enables researchers worldwide to contribute to and benefit from shared knowledge.

Aircraft performance modeling continues to evolve, driven by advances in surveillance technology, computational capabilities, and the increasing availability of operational data. The models and methodologies presented in this chapter provide a foundation for understanding aircraft behavior, but the field remains dynamic, with ongoing research addressing current limitations and expanding capabilities to meet emerging aviation challenges.

[1]

A. Nuic, “User manual for the base of aircraft data (BADA) revision 3.10,” Eurocontrol Experimental Centre, Bretigny-sur-Orge, France, 2010.

[2]

J. Sun, J. M. Hoekstra, and J. Ellerbroek, “OpenAP: An open-source aircraft performance model for air transportation studies and simulations,” Aerospace, vol. 7, no. 8, p. 104, 2020.

[3]

J. Sun, J. Ellerbroek, and J. M. Hoekstra, “WRAP: An open-source kinematic aircraft performance model,” Transportation Research Part C: Emerging Technologies, vol. 98, pp. 118–138, 2019.

[4]

M. Bartel and T. M. Young, “Simplified thrust and fuel consumption models for modern two-shaft turbofan engines,” Journal of Aircraft, vol. 45, no. 4, pp. 1450–1456, 2008.

[5]

D. I. A. Poll and U. Schumann, “An estimation method for the fuel burn and other performance characteristics of civil transport aircraft in the cruise. Part 1 fundamental quantities and governing relations for a general atmosphere,” The Aeronautical Journal, vol. 125, no. 1284, pp. 257–295, 2021.

[6]

D. I. A. Poll and U. Schumann, “An estimation method for the fuel burn and other performance characteristics of civil transport aircraft during cruise: Part 2, determining the aircraft’s characteristic parameters,” The Aeronautical Journal, vol. 125, no. 1288, pp. 1004–1051, 2021.

[7]

J. Sun, H. A. Blom, J. Ellerbroek, and J. M. Hoekstra, “Particle filter for aircraft mass estimation and uncertainty modeling,” Transportation Research Part C: Emerging Technologies, vol. 105, pp. 145–162, 2019.

[8]

J. Sun, J. Ellerbroek, and J. M. Hoekstra, “Aircraft initial mass estimation using bayesian inference method,” Transportation Research Part C: Emerging Technologies, vol. 90, pp. 59–73, 2018.

[9]

R. Alligier, D. Gianazza, and N. Durand, “Machine learning and mass estimation methods for ground-based aircraft climb prediction,” IEEE Transactions on Intelligent Transportation Systems, vol. 16, no. 6, pp. 3138–3149, 2015.

[10]

Y. S. Chati and H. Balakrishnan, “Modeling of aircraft takeoff weight using gaussian processes,” Journal of Air Transportation, vol. 26, no. 4, pp. 153–162, 2018.

[11]

R. Alligier, D. Gianazza, and N. Durand, “Ground-based estimation of the aircraft mass, adaptive vs. Least squares method,” 2013.

[12]

E. Spinielli et al., “Aircraft take-off weight estimation: The EUROCONTROL PRC 2024 data challenge,” Journal of Open Aviation Science, vol. 3, no. 1, 2025.