Airspace Constrained Free-Flight Analysis: Implications for Uncrewed Air Traffic Management

Abstract

This paper provides a study of free-flight air traffic behaviour in increasingly constrained airspace environments. Traffic assumes three different free-flight operational constructs with airspace constraints considered as restricted (no-fly) regions. Simulations combine path planning and Monte Carlo techniques to qualitatively analyse emergent traffic behaviour and quantitatively assess spatial–temporal airspace conflict as the airspace constraints vary. Findings indicate that airspace constraints have a much stronger influence on aircraft behaviour than the free-flight operational construct, with any benefits of free flight rapidly diminishing as the airspace becomes more constrained. We conclude that structured traffic route (or network) designs and associated risk modelling approaches should be considered for safe and efficient traffic management of highly constrained and congested (or dense) airspace. This work therefore provides evidence to inform new airspace design and management initiatives, including low-altitude uncrewed traffic.

1. Introduction

The aviation industry faces significant challenges regarding air traffic congestion due to increasing volumes and diversity of aircraft operations needing access to finite airspace with limited capacity. It is crucial to design airspace and manage air traffic to ensure efficient and safe flight of both crewed and uncrewed operations. Air Traffic Management (ATM) systems, Uncrewed Traffic Management (UTM or U-Space), and more recently, Integrated Traffic Management (ITM) systems are expected to collectively accommodate the increasing diversity and complexity within our airspace and safely manage traffic flow. Regardless of the management system, different operational constructs (i.e., how aircraft are expected to operate) may be used to add a degree of structure to the air traffic flow.

Structured operations force aircraft to fly along strategically designed (and often indirect) flight routes. The routes are designed by authorities to aid (or simplify) conflict management whilst improving traffic flow and efficiency in busy (often terminal) airspace regions. Free-flight operations allow aircraft to choose their own (often direct) routes. The routes are designed by operators and chosen to aid operational efficiency in less busy (often transit/en route) airspace regions. Importantly, free flight would still need to consider airspace constraints that limit where aircraft may operate. These constraints may increase due to factors such as airspace class, temporary operational restrictions (due weather, military operations, government directives, etc.), societal concerns (noise, privacy, and environmental protection), and geopolitical issues (sensitive areas, conflicts, trade sanctions, etc.). With such constraints, the benefit and appropriateness of free flight become uncertain.

The contribution of this paper is the analysis of unmitigated (i.e., no collision avoidance or management) free-flight traffic behaviour in increasingly constrained environments. First, we use simulated flight paths to qualitatively evaluate emergent traffic behaviour as the airspace becomes more constrained, aiming to understand its impact on traffic pattern and flow. Second, we quantitatively analyse the impact airspace constraints have on usable airspace (proxy for capacity or efficiency) and introduce a simple metric to assess unmitigated collision risk (proxy for safety) as a function of the spatial–temporal overlap (proxy for separation). Third, results are combined to consolidate the impact of allowing free flight traffic in constrained environments. Importantly, this provides evidence instead of an opinion or hypothesis that can be used when debating the practical merits and requirements of free flight versus structured airspace design and management strategies (see Remark 1).

Remark 1. 

The paper preferences near-term large-scale uncrewed operations given they are positioned to adopt free-flight concepts for operations at low-level (i.e., restricted altitudes) consisting of highly variable airspace constraints and proposed management strategies. The airspace constraints ensure no overflights, and terrain is highly variable, so analysis is restricted to the more challenging two-dimensional case. The findings can, however, be translated accordingly for other airspace regions, traffic types, and management assumptions.

The paper is organised as follows: Section 2 reviews related works, Section 3 outlines the simulation methodology and metrics, Section 4 presents simulation results and analysis for different free-flight patterns, and Section 5 provides conclusions and future research.

2. Background and Related Works

The decision between free flight and structured flight remains a topic of debate in the aviation industry, with region-specific factors such as current regulations and management systems, traffic density, and airspace constraints playing a crucial role [1,2]. Given the bespoke (region-specific) nature of the problem and the inherent complexity arising from numerous interrelated factors that influence decision-making, simulation studies have played a pivotal role in examining future airspace scenarios, assessing UTM separation distances [1], optimising airspace configurations [3], and analysing conflicts in structured and free routeing operations [4].

Simulation studies comparing structured and free-flight operations have generally found lower collision risk in free flight versus structured routeing [4,5,6,7]. Others have shed light on factors influencing collision risk and efficiency, suggesting that free flight may be preferred due to advancements in communication and navigation technologies [8] but with potential increases in air traffic controller workload due to unpredictable traffic [9,10,11]. Past free flight versus structured comparison studies have generally focused on the volume of aircraft in an unconstrained (open or en-route flight) area with merely generalised assumptions about traffic behavior. These neglect to account for region-specific factors such as environmental constraints and the natural emergence of traffic patterns and structures for which the research is further advanced in vehicle-based transportation and generally [12,13,14]. Despite the advancement of technologies and automation, free-flight approaches will remain largely conceptual as the need for improved efficiency and safety in an increasingly complex and dynamic airspace environment warrants structured approaches.

Research is ongoing into improved structured airspace configurations that better balance performance, safety, and operational constraints [2,3,8,15]. A structured approach relies upon tailored airspace designs (altitude layers, zones, etc.) to ensure aircraft are separated in space and time, for which there are many past studies such as [9,10,16,17,18]. There is also ongoing research into airspace separation standards and collision risk modelling [19,20,21,22]. Recent studies have considered the impact of structure and flight rules on unwanted emergent behaviours but not the impact of environmental constraints [23].

Prior studies often focused on structured or free-flight designs with generalised assumptions about traffic behaviour, neglecting broader environmental constraints and the emergence of traffic patterns. Our aim is to emphasise the importance of considering environmental constraints and emergent traffic patterns when determining whether a specific region should adopt a structured or free-flight approach. Through simulation studies, we aim to capture the complex behaviours that can emerge in free-flight-constrained airspace to gain an assessment of the efficiency and risk factors associated with free-flight operations, enabling informed decision-making and effective future planning.

3. Air Traffic Simulations

This section describes the methodology used to simulate air traffic in constrained environments and the metrics used to uncover and assess emergent traffic behaviour.

3.1. Methodology

The study focuses on a fixed geographical area with varying airspace constraints in location, size, and number. A simulation-based approach was adopted, which involved generating two-dimensional free-flight traffic paths for aircraft such that constrained airspace is avoided. Simulation parameters are chosen to reflect the emerging case of large-scale uncrewed operations at low altitudes (see Remark 1). Simulations involve four main steps:

• Step 1: Airspace Constraints and Departure/Landing Zone Generation

Airspace constraints are represented by a set of circles with variable diameters in which aircraft are required to fly around such that flight over or through the constraints is prohibited (see Remark 2). Prohibiting constraint overflight is intentional such that the study can analyse the effect of increasing constraints on traffic patterns and assumes that collisions in enroute flight typically occur at the same altitudes (see conflict factors study by [6]). Constraint parameters are generated randomly and include circle centre location and diameter. This enables both isolated and overlapping constraints to be generated, resulting in convex and non-convex prohibited regions.

A defined number of departure/landing zones (DLZ) are generated as fixed locations within the constraint-free region for takeoff and landing. DLZ can be generated at randomly chosen or fixed locations. This means paths can be generated for different free-flight constructs aligned to operational preferences or business cases (see Step 2).

Remark 2. 

By representing constraints as circular areas, we have assumed they appropriately represent constraints due to weather, restricted zones (military, ATC), sensitive environments, noise restrictions, etc. These constraints can be generalised from the local (as per this analysis) to regional or continental scales. With increased constraints, non-circular shapes emerge to better model size and shape variability. The constraint model becomes less valid for (piece-wise) pseudo-linear constraints such as prohibited flights above roads and railway lines. Note, constraints could be adapted to specific operational requirements or environments if required.

• Step 2: Air Traffic Scenario Generation

Monte Carlo simulation techniques are used to generate scenarios that consider variability in the air traffic routes and airspace constraints. To generate a single air traffic scenario, airspace constraints and DLZ sets are generated at random. Then, the number of flights per hour (fph) to generate and the range of flight speeds for the traffic are defined.

Individual flight routes are generated considering realistic scenarios over an urban area where traffic motion assumes three types of free-flight operational constructs, including random takeoff and random landing (RR) locations to simulate ad-hoc irregular flights, fixed takeoff and random landing (FR) locations to simulate delivery flights from warehouse hubs to homes and businesses, and fixed takeoff and fixed landing (FF) to simulate routine logistics and transport services such as cargo or passenger movement.

Flight paths are generated as follows: the software generates low-fidelity routes efficiently using the route generation method described in Section 3.2. The routes are then transformed to high-fidelity flight paths using interpolation to efficiently produce a high volume of flight paths. Each flight path is augmented with a time vector of constant step size over the hour such that the average speed for the path is also satisfied. The simulation, therefore, records the location and time each flight path was at each location in the region for the given constraint set. The simulator is run until the requested number of fph with defined flight speed variation is satisfied. Multiple simulation sets are then run to compare and validate results. Key assumptions are included in Remarks 3–6.

• Step 3: Air Traffic Assessment

The simulation results are then assessed qualitatively and quantitatively. Regarding qualitative assessment, emergent structured-like patterns are highlighted through visualisation. Regarding quantitative assessment, constraint metrics capture how constrained the airspace is (defined in Section 3.3), and collision risk metrics calculate how dense or occupied the airspace is both spatially and temporally (defined in Section 3.4).

Remark 3. 

The simulation does not consider strategic nor tactical mitigation applied in relation to aircraft separation and collision avoidance between aircraft. This is intentional as we seek to uncover where aircraft may be forced to operate given airspace constraints.

Remark 4. 

The simulation only considers en route flights at a constant altitude, assuming that most collision risk is from flights at the same altitude (as indicated by [4]). It does not consider terminal operations risk.

Remark 5. 

We assume pseudo-optimal avoidance of constraints, such that aircraft fly around constraints in such a way that they head straight to the destination as soon as a clear line of sight path exists between the current location and the destination (assume pseudo-optimal transitions). i.e., the paths will not be optimally avoiding constraints because of our use of random waypoint selection/variation in the paths.

3.2. Flight Route Generation

To simulate a single flight route, a modified version of the stochastic path planning algorithm known as Rapidly-exploring Random Trees (RRT) was utilised to generate feasible random routes for the simulated aircraft (Algorithm A1 in Appendix A). The RRT algorithm is commonly used in robotics and path planning to find a feasible path around obstacles from a start location to a destination, and in this case, it was applied to the simulation of aircraft routes in a constrained environment.

The RRT algorithm was modified to control the tendency for aircraft to fly directly to the destination as soon as a direct, constraint-free path to the final destination was available. This was accomplished by introducing a random variable $u_{rand}\in [0,1]$ (Algorithm A1) that selects the destination as the candidate waypoint if it exceeds a goal selector threshold $u_{goal}\in [0,1]$, otherwise selects a random waypoint. The goal selector threshold $u_{goal}$ can be chosen to simulate paths that bias the search towards indirect routes ($u_{goal}=0$) or direct routes ($u_{goal}\to 1$) to the destination. We set $u_{goal}$ to favour direct routes to the destination such that each path will have reduced intermediate waypoints with less random behaviour towards the goal, but not always the optimal route. This inclusion contrasts standard RRT implementations used in real-time robot path planning, which might (for more complete search space exploration in complex constrained environments) first construct a complete random tree even if a direct route is available. Our modification helps introduce more realistic behaviour for both human and autopilot-calculated flight routes and planning behaviours (see Remark 5), whilst reducing the time needed to find a solution, which is important as we will simulate thousands of flight routes.

The remaining parameters for the algorithm include the start and destination locations for the route ($p_{start}$, $p_{goal}$), the maximum number of iterations K for guiding the search process, and a distance threshold $\mathrm{\Delta }p$ for checking if a destination or location has been reached and thus stopping the search. K is chosen large enough to give time for the search to find a solution, but not too large to reduce computation time.

The RRT algorithm was used to generate feasible and constraint-abiding routes for each simulated aircraft in the airspace. Route lengths are not globally optimised with respect to time or distance, which naturally allows for variability such as taking indirect routes, detours, or go-arounds, produced at random by the RRT algorithm. We believe this approach provides more realistic traffic patterns, accounting for locally optimal or satisfying path-keeping human or autopilot behaviours.

Remark 6. 

The route generation assumes perfect operating conditions, neglecting weather conditions, ATC rules, aircraft performance characteristics, and takeoff or landing procedures that could influence flight paths. We believe these assumptions are justified given that we use Monte Carlo simulation approaches that include random path variability and retain only feasible paths.

3.3. Constraint Metrics

A constraint density measure $P_c\in [0,1]$ is defined as the total area of all constraints $A_{c_i}$ normalised by the area of the region $A_R$ such that

$$P_c=\sum _{i=1}^{n_c}{\displaystyle \frac{A_{c_i}}{A_R}}.$$

(1)

This metric gives an indication of the amount of free-space area restricted by constraints such that $P_c=0$ would be a region with no constraints and $P_c=1$ is fully constrained (i.e., no available space for operations).

3.4. Risk Metrics

To determine traffic density, a $I\times J\times T$ sized grid is defined over the region R with square grid cells indexed by row i and column j and time by t. A minimum separation distance between aircraft of 100 m was chosen following the approach in [20], yielding square cells with 100 m side length. After defining a grid, the flight paths that transit each cell in space and time were recorded. Histogram binning was then applied to the track flight times within each cell to give the number of spatial–temporal overlaps $n_{ijt}$ in each time bin t at location $ij$. We chose a temporal resolution (histogram bin width) of $t=5$, giving 12 bins per hour $n^b$. The histogram bin width was chosen to be 5 min to account for uncertainty in temporal resolution, such that any two tracks within the same 100 m cell and 5 min time period were deemed to overlap in space and time.

To account for uncertainty in flight takeoff times, different flight start times were randomly sampled m times for each track to give a set of $n_{ijt}^m$. The average frequency ${\overline{f}}_{ijt}\in [0,\infty ]$ of spatial–temporal overlap in each 5 min time bin t was then calculated as

$${\overline{f}}_{ijt}=m^{-1}\sum _{k=1}^m{n}_{ijt}^k.$$

(2)

The average hourly spatial–temporal overlap frequency $f_{ij}$ was calculated by

$$f_{ij}={n^b}^{-1}\sum _{t=1}^{n^b}{\overline{f}}_{ijt}.$$

(3)

That is $f_{ij}=1.2$ means there were on average 1.2 overlaps in the hour at location $ij$ and so acts as a basic collision risk metric (see Remark 7). The empirical cumulative distribution function (eCDF) $F\left(f\right)$ of the average hourly spatial–temporal overlap frequencies for the whole region can then be calculated as

$$F\left(f\right)=P\left[f_{ij}\le f\right]$$

(4)

where P denotes a probability. The eCDF cumulatively sums the number of unconstrained locations in the region with average spatial–temporal overlap frequencies less than or equal to $f\in [0,\infty ]$. Only cells $ij$ within the unconstrained region (usable airspace) are considered to ensure the eCDF is correctly normalised. Importantly, the f and $F\left(f\right)$ metrics link collision risk to the impact of airspace constraints.

Remark 7. 

The frequency $f_{ij}$ can be considered an approximate measure of collision risk or separation infringement. If $f_{ij}=1$, there are always spatial–temporal overlaps such that $P(d_s<100)\to 1$, where $d_s$ is the separation distance. However, more refined collision risk models exist for structured air traffic flows [20,24,25].

4. Simulation Results and Analysis

To assess the impact of constraints on free flight, 2000 flights in a 100 × 100 km region over 1 h were simulated with an increasing number of constraints from $P_c$ = 0 to $P_c$ = 1. Flight start and end locations and speeds $\in [10.29,36.01]$ m/s were chosen at random (uniformly). Constraints were modelled as circles of radius $\in [100,3000]$ m, with each constraint size and location chosen according to a uniform distribution. Three free-flight traffic scenarios were simulated, including the following:

RR 

Random takeoff and random landing locations to model ad-hoc flights within the region;

FR 

Fixed takeoff and random landing locations to model “hub and spoke"-like flights (e.g., delivery) within the region;

FF 

Fixed takeoff and fixed landing locations to model “hub-to-hub"-like flights (e.g., logistics, passenger ferry) within the region.

To simulate free flight hub and spoke (FR) or hub-to-hub (FF) operations, the fixed takeoff or landing locations are selected at random for each flight. In all cases, aircraft have freedom of movement between the fixed takeoff and landing locations (no dedicated flight routes between takeoff and landing are defined). The motion is free flight as the resultant flight paths are only products of the feasible random route generation process (Section 3.2), not pre-planned or predefined routes.

4.1. Qualitative Analysis: Emergent Behaviours, Patterns, and Flow

Qualitative analysis is used to understand the emergence of structure in these scenarios. We define structure as when traffic tends to flow along the same path (either direction) as if on a defined network or flight route, so appearing as dense lines of traffic. In contrast, free flight is when traffic appears to travel in many different (random) directions (no apparent structure), so dense lines of traffic do not appear. We emphasise that we simulate potential future traffic volumes and constraints for a single hour over the region, so the exact emergent patterns would change with the region and as dynamic constraints change over time (regarding quantity, location, and size). This does not invalidate results; it just suggests that emergent structure may present in all cases but appear differently.

4.1.1. Random–Random (RR) Analysis

Figure 1 shows flight paths of simulated free-flight traffic for random departure and random arrival locations within the region with increasing constraints over an hour.

▶

With no constraints (Figure 1a), traffic density increases towards the middle of the region. This is due to the simulation randomly choosing start and end points within the constrained region (simulating within a larger, unconstrained region may show more uniformity in density). High traffic density emerges randomly at specific locations (seen as darker regions or spots), but the absence of emergent structure is clear.

▶

As the constraints increase (Figure 1b,c), the regions become noticeably denser, indicating the traffic density increases as constraints increase. Some structure is noticeable as soon as Figure 1b, where few darkened linear flight regions can be seen. Many regions still appear as random free flight, similar to the unconstrained case.

▶

With the highest number of constraints (Figure 1d–h), dominant structured-like patterns emerge in the traffic as the amount of available space reduces significantly. Constraints also impose segregation within the airspace as the constraints restrict airspace access, causing regions to be divided into sub-regions.

Figure 1. Random Takeoff and Random Landing: Free flight paths (−) with increasing constraints (∘) and random DLZ locations (not shown). Note the emergence of network-like patterns with increasing constraints despite random takeoff and landing locations. (a) 0 constraints; (b) 100 Constraints; (c) 250 Constraints; (d) 350 Constraints; (e) 500 Constraints; (f) 600 Constraints; (g) 750 Constraints; (h) 850 Constraints.

Figure 1. Random Takeoff and Random Landing: Free flight paths (−) with increasing constraints (∘) and random DLZ locations (not shown). Note the emergence of network-like patterns with increasing constraints despite random takeoff and landing locations. (a) 0 constraints; (b) 100 Constraints; (c) 250 Constraints; (d) 350 Constraints; (e) 500 Constraints; (f) 600 Constraints; (g) 750 Constraints; (h) 850 Constraints.

4.1.2. Fixed–Random (FR) Analysis

Figure 2 shows the flight paths of the simulated free-flight traffic for a fixed DLZ set for departure (randomly selected from the same set for each flight) and random landing locations within the region with increasing constraints over an hour.

▶

In the previous traffic scenario, where takeoff and landing locations were random, the focus was solely on constraints. With the introduction of dedicated landing zones, new constraints have emerged that guide traffic in specific directions, which create operational networks. Despite these changes, existing patterns still appear to be heavily influenced by the constraints in place as opposed to the DLZ set. However, the limited options for takeoff and landing via DLZ set has resulted in a tighter structure.

▶

As constraints increase, it becomes apparent that certain DLZs may become difficult to reach (long travel paths) or inaccessible. This limitation adds another layer of complexity because, as the available DLZs become more restricted, maintaining connectivity and traffic flow may require alternative routes or concentrated traffic between the remaining accessible DLZs (Figure 2h). Intuitively, the coupling between constraints and the distribution (and density) of DLZ locations shapes the overall traffic pattern but can lead to restricted movement and thus utility.

▶

As the number of DLZ increases, the traffic patterns will resemble those observed in random traffic scenarios. Conversely, when the quantity of DLZ decreases, traffic will concentrate around the remaining landing zone locations (i.e., emergent "hotspots").

Figure 2. Fixed Takeoff and Random Landing: Free flight paths (−) with increasing constraints (∘) and fixed DLZ locations (•). Note the emergence of network-like patterns with increasing constraints despite fixed takeoff and random landing locations (e.g., hub and spoke delivery). (a) 0 constraints; (b) 100 Constraints; (c) 250 Constraints; (d) 350 Constraints; (e) 500 Constraints; (f) 600 Constraints; (g) 750 Constraints; (h) 850 Constraints.

Figure 2. Fixed Takeoff and Random Landing: Free flight paths (−) with increasing constraints (∘) and fixed DLZ locations (•). Note the emergence of network-like patterns with increasing constraints despite fixed takeoff and random landing locations (e.g., hub and spoke delivery). (a) 0 constraints; (b) 100 Constraints; (c) 250 Constraints; (d) 350 Constraints; (e) 500 Constraints; (f) 600 Constraints; (g) 750 Constraints; (h) 850 Constraints.

4.1.3. Fixed–Fixed (FF) Analysis

Figure 3 shows the flight paths of the simulated free-flight traffic for a fixed DLZ set for departure and landing locations (randomly selected from the same set for each flight) within the region with increasing constraints over an hour.

▶

Clear directional patterns resembling operational networks have emerged as aircraft travel between dedicated takeoff and landing locations. This suggests that traffic patterns in free-flight regions conducting specific operations, like routine cargo transport, are intuitively similar to structured traffic patterns with designated operational networks. As the pathways are already restricted, there are limited advantages to free-flight traffic so structuring the airspace accordingly for such operations is more natural.

▶

The tendency for traffic to form structured networks and routes occurs with typically fewer airspace constraints (e.g., $P_c<0.2$) than the previous two cases. This provides insight on how collision risk should be modelled in such regions. Traditional risk models, such as the gas model, will not be appropriate in this context as the traffic is neither homogeneous nor random. Models that either recover or account for airspace structure are required.

4.2. Quantitative Analysis: Overlap Frequency

Figure 4 presents the average hourly overlap frequencies (3) at each location with increasing constraints for the RR (Figure 4a–d), FR (Figure 4e–h), and FF (Figure 4i–l) cases. Quantifying the overlap frequencies at each location provides additional safety and traffic management insights into the effect of increasing constraints and the different types of operations.

4.2.1. Random–Random (RR) Analysis

▶

For the unconstrained case (Figure 4a), scattered areas of overlap frequency from $f_{ij}$ = 0.01 to 0.2 are appearing and mostly appearing towards the centre of the region.

▶

As the constraints increase (Figure 4b–d), areas of high overlap ($f_{ij}>$ 0.5) become visible and concentrated into network-like structures.

▶

Generally, along with the emergence of structure, the increased density ($f_{ij}\to 1$) in these regions becomes more apparent as constraints increase. This reveals clear candidates for structuring these routes as constraints increase, in the interest of safety.

4.2.2. Fixed–Random (FR) and Fixed–Fixed (FF) Analysis

▶

For the unconstrained fixed cases (Figure 4e,i), the areas of overlap appear along the networked routes between DLZs or emerging from DLZs, as may be expected in an unconstrained region.

▶

As the constraints increase (Figure 4f–h,j–l), the areas of high overlap become more concentrated into network-like structures as before, but they are also influenced by the DLZ such that they depend on the accessibility of the DLZ locations. Constraints have imposed limited pathways between locations, causing dense approach/departure tracks, which suggests that structuring and sequencing are more critical along the approaches and departures of DLZ regions.

4.2.3. General Comparisons

Comparing each RR figure (e.g., Figure 4a–d) with its counterpart FR or FF, the emergent overlap patterns for both the RR and FR or FF cases appear quite similar, apart from some differences due to DLZ noted previously. This is particularly noticeable for the 850 constraints case (compare the dark regions of Figure 4d with those of Figure 4l). This illustrates that region constraints play the most significant role in determining the location of emerging structures. The type of operations (RR, FR, or FF) expected in the region has very limited influence on where emergent structure appears but has an influence on the amount of overlap at the locations with structures. For example, comparing the highest overlap areas $f_{ij}=1$ of Figure 4d with Figure 4h or Figure 4l reveals similar patterns; however, differences can be seen where the $f_{ij}=1$ locations appear.

Generally, the width (and hence area) of high overlap regions appear thinner for FF cases than for the RR or FR cases. This can be explained by aircraft flying more direct routes between DLZ, with overlaps being focused along the emergent network routes. This considers that certain operational types (which themselves can cause emergent structure in the airspace by repeatedly using fixed and dedicated DLZ) can magnify the emergence of structure and have some effect in reducing the size of the high overlap areas, but with a corresponding increase in overlap frequency along the routes. As noted, these differences are less noticeable as the number of constraints increases, but also implies any structure arising from dedicated DLZ cannot alone improve safety in highly constrained environments.

4.3. Quantitative Analysis: Cumulative Overlap Frequency

Empirical CDFs (eCDF) were calculated for the average hourly spatial–temporal overlap frequencies (4). The eCDFs for the maximum overlaps (i.e., take maximum values over t in ${\overline{f}}_{ijt}$) were also calculated for comparison. Figure 5 compares the eCDFs of average spatial–temporal overlap frequencies for the $P_c=\{0,0.2,0.4,0.6\}$ constraint cases (corresponding to 0, 250, 500, and 850 constraints). Note that $P(f_{ij}\le 0.9)$, for example, is equivalent to saying $90\%$ of the usable airspace (see Remark 8). The following refers to Figure 5:

▶

For the unconstrained case where $P_c=0$, 80% of the usable airspace has a mean overlap frequency of zero (sparse), and almost 100% of the usable airspace has a mean overlap frequency of less than one overlap per hour ($f<1$). Considering the maximum overlap frequencies, almost 100% of the usable airspace exceeds two overlaps per hour.

▶

For the constrained cases where $P_c>0$, less of the usable airspace has an overlap frequency of 0 (sparse) as the constraints increase. Considering the most constrained case, $P_c=0.6$, only 60% of the usable airspace has a mean overlap frequency near 0. As the constraints increase, more airspace has a higher overlap frequency, such that almost 100% of the usable airspace will have an average overlap frequency of less than two per hour ($f<2$). Considering the maximum overlap frequencies, almost 100% of the usable airspace exceeds five overlaps per hour (doubling the unconstrained case).

Remark 8. 

For convenience, corresponding figures of $P(f_{ij}>f)$ Figure A1 are included in Appendix A, showing the percentage of airspace that has an overlap frequency greater than f.

▶

Figure 5 may be used to support airspace management in predicting how much of the available airspace is likely to be overlapped. For example, if it is determined that free flight should be adopted when the overlap frequency is sparse ($f=0$) and the region is constraint-free, then Figure 5 suggests that approximately 80% of the airspace may be free flight and the remaining 20% a candidate for active management or structuring. Similarly, only 60% of the airspace may be free flight for the most constrained case.

Figure 5. eCDFs of spatial–temporal overlap frequencies with increasing constraints ($P_c$). The y axis represents the proportion of usable airspace with average hourly overlap frequency less than or equal to the corresponding x axis value (hourly overlap frequency f). Mean (thick) and maximum (thin) overlap frequencies are included and all curves $P\to 1$ as $f\to \infty$. (a) 0 constraints ($P_c=0$); (b) 250 constraints ($P_c=0.2$); (c) 500 constraints ($P_c=0.4$); (d) 850 constraints ($P_c=0.6$).

Figure 5. eCDFs of spatial–temporal overlap frequencies with increasing constraints ($P_c$). The y axis represents the proportion of usable airspace with average hourly overlap frequency less than or equal to the corresponding x axis value (hourly overlap frequency f). Mean (thick) and maximum (thin) overlap frequencies are included and all curves $P\to 1$ as $f\to \infty$. (a) 0 constraints ($P_c=0$); (b) 250 constraints ($P_c=0.2$); (c) 500 constraints ($P_c=0.4$); (d) 850 constraints ($P_c=0.6$).

4.4. Quantitative Analysis: Separation

In aviation risk analysis, it is customary to define a minimum separation distance or standard for identifying overlaps. We conducted a study to investigate the influence of a selected separation standard on the frequency of spatial–temporal overlap. We used the grid cell size as a proxy for separation breaches, such that varying the grid cell size mimics a different separation standard.

In this study, we varied the separation standard (grid cell size) between aircraft from 100 (previous study) to 500 m. We performed RR analysis (Figure 6), repeating it with increasing grid sizes. As expected, the amount of usable airspace with more overlaps increased as the grid size expanded, due to a greater number of aircraft within each cell. For example, if less than 200 m was deemed a sufficient separation standard, then 70% and 100% of the airspace would have under 2 and 10 overlaps per hour, respectively. If 400 m was deemed a sufficient separation standard, then 70% and 100% of the airspace would have under 10 and 40 overlaps per hour, respectively.

Although the trend is intuitive, the analysis numerically couples or links three key metrics: the overlap frequency, usable airspace, and separation standard. This shows how separation standard choice impacts the feasibility of constrained free flight with respect to assumed traffic management capabilities. Essentially, we have found a basic mechanism to see if the airspace design makes achieving separation more or less challenging.

Figure 6. Average overlap frequency with increasing grid cell sizes (separation distances) from 100 m to 1000 m. As separation distance increases traffic sparsity reduces (i.e., proportion of usable airspace with few overlaps decreases).

Figure 6. Average overlap frequency with increasing grid cell sizes (separation distances) from 100 m to 1000 m. As separation distance increases traffic sparsity reduces (i.e., proportion of usable airspace with few overlaps decreases).

4.5. Airspace Design and Management Implications

Regarding airspace design, results of the study indicate that when air traffic flows through a constrained region, regardless of the type of operations (ad-hoc, delivery, logistics, etc.), free-flight routes would eventually exhibit the emergence of dominant high-density directional network-like traffic flows (structure). This suggests that there is a threshold in terms of traffic volume and constraints beyond which the implementation of structured airspace becomes necessary to manage traffic safely (i.e., a network of designated routes within the region may be required). To determine this threshold, a desired overlap frequency (risk) could be used as a proxy threshold for determining when to structure the airspace. When exceeded, structured airspace is allocated; otherwise, the airspace could remain unstructured. For instance, given the presented simulations, if an average or maximum overlap frequency of 0.1 is deemed acceptable for free flight and self-separation in a highly constrained environment (with $P_c=0.6$), it can be observed from Figure 5 that less than 60% of the airspace is suitable for free flight. Consequently, around 40% of the airspace would require predefined routes and traffic management support to maintain safe separation.

These findings can also inform how to design airspace that can accommodate a desired number of flights per hour. For example, in a highly constrained environment (Figure 5), sustaining 2000 flights per hour while maintaining a maximum overlap frequency of less than 1 within an hour for 90% of the usable airspace may not be achievable. In such cases, reducing the allowable traffic density would be necessary to meet stricter overlap requirements. These conclusions are based on the assumption of 2000 flights per hour, but similar analyses can be conducted for other traffic rates through additional simulations. Note also that results indicate that there is a maximum limit on traffic density.

A practical consideration is that constraints introduced to address specific issues may unintentionally lead to the emergence of issues and connectivity concerns in other regions due to the effective changes and consequences of re-routing traffic (see Remark 9).

Remark 9. 

This has related implications for proposals on uncrewed traffic management. Assuming that uncrewed aircraft will receive reserved airspace volumes is analogous to placing many time-varying airspace constraints. If such constraints persist in large volumes, then the remaining airspace becomes limited and the other airspace users are forced to operate in the network-like environment. In essence, the act of segregation for one aircraft class will create challenges for remaining aircraft.

Regarding air risk, analysis typically involves examining the likelihood of aircraft collisions within a given airspace. The widely used “gas model" treats aircraft as point masses and calculates collision probabilities based on basic geometric relationships [26]. However, it is important to select an appropriate collision risk model that suits the characteristics of the airspace and traffic patterns. Underestimating risk can compromise safety, while overestimating risk can limit airspace capacity, particularly in low-altitude urban areas where available airspace is a valuable resource.

This analysis helps identify suitable collision modelling approaches when considering general airspace assessments related to free-flight assumptions. In unconstrained areas, the gas model remains reasonable. However, as constraints increase and high-density directional traffic flows emerge, alternative models like the Reich model or new risk models that reveal underlying airspace patterns and structures may be necessary (refer to Figure 1f–h for examples). Essentially, common assumptions linking free flight and simplistic risk modelling are not appropriate when airspace is restricted or constrained. Further research and analysis is required to validate these observations and develop appropriate risk models tailored to the unique characteristics of such traffic behaviours.

Remark 10. 

Our analysis can help support decisions concerning airspace design and establishment of rules, regulations, and procedures (e.g., equipage requirements, performance standards, traffic management practices, etc.) and collision risk estimation.

5. Conclusions

The simulation studies were designed to provide evidence of emergent traffic behaviour under different free-flight constructs. The behaviour is characterised in terms of spatial traffic patterns and flow (to provide airspace design insights) and unmitigated collision risk (to provide safety insights). Collectively, this helps identify implications for airspace and air traffic management strategies.

Key implications for airspace design include the following:

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The interplay between traffic flows and airspace constraints plays a crucial role in determining the presence and extent of both structured and free-flight traffic regions. Once an airspace region is constrained by 20%, structure emerges but flows are not tightly bounded (suggesting self-separation may be sufficient). Once an airspace region is constrained by greater than 50%, structures with tightly bounded flows result (suggesting separation services may be required).

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Emergent structure in constrained environments justifies departing from free-flight assumptions and necessitates structuring a portion of the airspace in terms of pre-defined routes/pathways. The threshold for such structuring may depend on risk tolerances and the capability of the aircraft and traffic management system (to manage overlaps/conflict). The actual pre-defined paths can be identified from simulations like those presented here.

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The constraints imposed on the airspace have a greater impact on operations than the specific free-flight construct (FF, RR, FR). Essentially, when operations scale up the specific locations where different types of operations occur (e.g., ad hoc flights, routine delivery, or logistics), it has limited impact compared with the imposed airspace constraints.

Key implications for risk analysis include the following:

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For largely unconstrained regions (less than 20%), simplistic risk analysis techniques, such as the gas model, would be applicable. The key is to model more random motion.

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For largely constrained regions (greater than 20%), more compared withplex risk analysis techniques, such as those used for crossing, parallel, etc. paths, would be applicable. The key is to model or capture structure and not random motion.

The natural progression of this research is to consider the mitigated case by incorporating active traffic management, including suitable strategic approaches (e.g., altitude and hemispherical restrictions or structuring), tactical mitigation techniques (e.g., sequencing and scheduling, collision avoidance), and dynamic airspace constraints. Note, adding dynamic constraints can mimic some mitigation approaches (e.g., 4D trajectories, dynamic airspace allocation, etc.), so constraint metrics may require re-definition or augmentation. To complement such developments, additional metrics that measure path deviation and complexity (noting coupling to air traffic management systems) could be explored.

By examining these factors, a more comprehensive understanding of the relationship between airspace constraints, traffic patterns, and management strategies (and requirements) can be achieved. This can help build resilient future traffic management systems.