Capacity Estimation for Airspaces with Convective Weather Constraints

Transcription

1 AIAA Guidance, Navigation, and Control Conf., Hilton Head, SC, Aug., Capacity Estimation for Airspaces with Convective Weather Constraints Jimmy Krozel, Ph.D. * Metron Aviation, Inc., Herndon, VA, Joseph S. B. Mitchell, Ph.D. State University of New York, Stony Brook, NY, Valentin Polishchuk, Ph.D. Helsinki Institute for Information Technology, University of Helsinki, FI Joseph Prete, Ph.D. Metron Aviation, Inc., Herndon, VA, We estimate the capacity of a generic airspace region given convective weather constraints and various operational conditions. We model en route airspace for future operations where jetway routing is removed and aircraft paths may conform with the geometry of hazardous weather constraints. Within a constant flight level, decentralized and centralized control of traffic are considered. Decentralized, Free Flight operational conditions consider aircraft flying in any direction vs alternating altitude rules. Centralized operational conditions consider traffic that monotonically progresses in one primary direction and a unidirectional flow where all traffic must remain within pre-defined flows (e.g., from West to East). Under these conditions, we compute the theoretical maximum capacity and compare it to algorithmic solutions. Additionally, we compute the capacity when aircraft fly in platoons two or more aircraft flying in the same direction in close proximity in order to understand the effect of platooning on airspace capacity. Finally, we define a complexity metric, and compare the complexity of the resulting traffic flows under each experimental condition. Nomenclature AllAlt = All-Altitudes Rule Mono = Monotonic Rule AltAlt = Alternating Altitudes Rule NAS = National Airspace System ATM = Air Traffic Management NGATS = Next Generation Air Transportation System FBRP = Flow-Based Route Planning NWS = National Weather Service FCA = Flow Constrained Area RNP = Required Navigation Performance FEA = Flow Evaluation Area Uni = Unidirectional Rule FL = Flight Level WSI = Weather Severity Index I. Introduction stimating the capacity of an airspace is fundamental to Air Traffic Management (ATM). If demand for an E airspace exceeds the capacity, then a Traffic Flow Management (TFM) control strategy must be implemented. Demand for an airspace is determined by the number and type of aircraft that desire to fly through the airspace during a given time interval. This includes level of equipage, level of Required Navigation Performance (RNP), and any other feature of the aircraft that affects its routing. The capacity of an airspace is loosely defined as the maximum number of aircraft per unit time that can be safely accommodated by the airspace given controller and pilot workload constraints as well as airspace constraints, which include Special Use Airspace (SUA), Letters of Agreement (LOAs), convective weather constraints, turbulence constraints, icing constraints, etc. The primary * Senior Engineer, Research and Analysis Department, 131 Elden Street, Suite 200, AIAA Associate Fellow. Professor, Department of Applied Mathematics and Statistics, Stony Brook University. Postdoctoral Researcher, Helsinki Institute for Information Technology, University of Helsinki. Senior Analyst, Metron Aviation, Research and Analysis Department, 131 Elden Street, Suite

2 concern of this paper is the effect of convective weather constraints on airspace capacity, with capacity determined by the (geometric) constraints induced by hazardous weather (rather than by controller workload constraints). The weather has a huge influence on the performance of the NAS. The average weather-related delays in the National Airspace System (NAS) are double the average non-weather delays 1,2. The Aviation Capacity Enhancement Plan 3 lists weather as the leading cause (65% to 75%) of delays greater than 15 minutes, with terminal volume as the second leading cause (12% to 22% of delays). Thunderstorms account for approximately 50% of the weather-related delays, low visibility 35%, and heavy fog the remainder 4. Because weather is such a major factor limiting capacity, we focus on the relationship between capacity and weather severity under a wide variety of operational conditions spanning centralized to decentralized control. The operational conditions considered in this paper are motivated by the Next Generation Air Transportation System (NGATS) 5,6 with a timeframe of applicability of roughly 2020 to We consider the estimation of capacity in a future ATM system where aircraft are not required to follow jet routes. Rather, we consider operational rules for en route airspace as follows (Figure 1): All-Altitudes Rule (AllAlt) No restrictions are placed on the direction of travel at any Flight Level (FL). Alternating Altitudes Rule (AltAlt) At any given FL, the dominant direction of travel, for all aircraft, from sector boundary to sector boundary, must be either east or west. (The direction is given by the rule East is Odd; West is Even.) Monotonic Rule (Mono) All flights must enter the sector from one designated direction, and exit the sector in any other direction. Unidirectional Rule (Uni) All flights must enter the sector from one designated direction, and exit the sector to a different designated direction. Additionally, we experimentally compare and contrast two operational concepts that may govern the flow of aircraft. The first is the Free Flight concept; individual flights are responsible for determining their own courses without regard to any global plan or system. The second is a highly constrained Centralized Packing system, in which a given sector is tightly constrained and all flights must follow predetermined paths in order to use the sector. An additional operational condition modeled in our experiments is a rule for platooning (Figure 2). Because we are investigating en route airspace concepts, the separation standard is 5 nmi between aircraft. Conflict detection and resolution between aircraft is embedded into the solution approach, in addition to hazardous weather avoidance. The separation between aircraft and hazardous weather has been left as a user-specified parameter in our research. (a) All Altitudes Rule (b) Alt. Altitudes Rule (c) Monotonic Rule (d) Unidirectional Rule Figure 1. Increasing constraints on entry-exit sides. (a) Platoon Size of 1 (b) Platoon Size of 2 (c) Platoon Size of 3 Figure 2. Increasing levels of Platooning. 2

3 II. Modeling Capacity estimation includes several factors which are discussed next. A. Pilot Weather-Avoidance Behavior While icing, turbulence, and other non-convective weather constraints are important to aviation, weather constraints in the NAS arise primarily from convective weather. The National Weather Service (NWS) scale classifies convective weather according to severity (Table 1). Regions of airspace with NWS level above a certain threshold are considered to pose a safety hazard and therefore to be constraints. While the criteria for weather avoidance depends on pilot preferences and airline guidelines, research 7,8 shows that pilots generally avoid NWS level 3 and higher weather cells. While the altitude of cloud tops in severe storms is also an important factor 9,10 that pilots consider in determining which storm cells to avoid, it is not modeled in our problem statement. Note that ignoring storm echo tops in determining blockage of today s fixed jet routes could result in overestimating the number of routes blocked by a factor of two 10. Table 1. NWS Standard Reflectivity Levels and weather classifications. NWS Color Rainfall Rate Reflectivity Type Level (mm/hr) (dbz) 0 None <0.49 dbz<18 None 1 Light Green dbz<30 Light Mist 2 Dark Green dbz <41 Moderate 3 Yellow dbz <46 Heavy 4 Orange dbz <50 Very Heavy 5 Deep Orange dbz <57 Intense 6 Red > dbz Extreme For this paper, we define a Weather Severity Index (WSI) for en route airspace. The WSI for a given en route airspace (sector, center, Flow Evaluation Area (FEA), or Flow Constrained Area (FCA)) is defined as the percentage of the airspace that is occupied by convective weather with NWS level 3 or greater, as illustrated in Figure 3. We acknowledge that the structure of weather cells, not just their number, can have a significant impact on the throughput 11 ; we generate synthetic weather cells according to a common distribution, across all severity levels, so that the structure of cells can be expected to be similar even as severity is varied. a b c ZTL06 ZTL06 ZTL06 WSI = 0.23 Figure 3. En Route WSI is found by (a) taking all convective weather data of an airspace, (b) identifying only NWS Level 3-6 cells, then (c) calculating the ratio of hazardous weather area to total sector area. B. Modeling the En Route Airspace In order to avoid complications in interpreting the fundamental results of this research, we have chosen a very simple experimental model for an airspace. We do not model any particular sector or center boundary, rather we choose a simple experimental square (60 x 60 nmi) airspace region, representing a single en route flight level. We only allow traffic to pass into the airspace from the sides of the airspace (left, right, top, and bottom), and thus, no aircraft enter or exit the airspace region from within the interior. Depending on the ATM rules chosen for the experiment (AllAlt, AltAlt, Mono, Uni), aircraft may be constrained to enter and exit on a limited number of sides of the airspace (see Figure 1). We examine two operational concepts: Decentralized Free Flight and Centralized Packing. Free Flight, where all pilots have the freedom to choose an arbitrary route, is modeled by randomization. A representative subset of the airspace entry and exit points is randomly paired to give rise to a set of routes for each timestamp. The set of routes selected is different for each timestamp. By contrast, Packed scenarios assume that the air traffic is managed to produce maximum throughput in a given airspace, according to some reasonable centralized packing scheme. The 3

4 packing scheme is different for each ruleset. In the AllAlt and AltAlt rulesets, open (not currently covered by convective weather) entry/exit points on the boundaries are paired off across corners; in this way as many flights as possible are routed between west and north, west and south, north and east, and south and east boundaries. Any remaining free space on the boundaries is used for routes directly across the sector. In the Mono rule, as many entry waypoints as possible on the west boundary are paired off with evenly-spaced waypoints on the other three boundaries, such that the straight-line paths of all routes do not cross each other. In the Uni rule, as many entry waypoints as possible on the west boundary are paired off with exit waypoints on the east boundary, evenly spaced on each boundary and such that the straight-line paths of all routes do not cross each other. See Figure 4 for an illustration of the packing schemes. Small arrowheads mark the endpoint of each potential route. (a) All Altitudes Rule (b) Alt. Altitudes Rule (c) Monotonic Rule (d) Unidirectional Rule Figure 4. The packing methods for each rule are chosen for high potential throughput. In this paper, all experiments are done with synthetic weather data. Theoretical maximum capacity experiments are run with cases that span no weather present (WSI=0) through extreme weather cases (WSI=1). However, empirical (algorithmic) maximum capacity experiments are run with WSI=0 through WSI=0.7, as illustrated in Figure 5. For empirical results, we do not analyze cases above WSI=0.7, since there is no significant flow in such severe weather conditions. The weather synthesis is done as follows. Within a larger square containing the airspace region, circular hazard disks are generated uniformly at random, with random radii. Disks are added or subtracted at random, until the desired WSI coverage percentage is obtained (within certain small tolerance). WSI is determined by the area of the union of all disks, calculated using a simple Monte Carlo estimation. WSI = 0.1 WSI =0.2 WSI = 0.3 WSI = 0.4 WSI=0.5 WSI = 0.6 WSI = 0.7 Figure 5. Synthetic weather data based on randomly generated weather constraints ranging from no weather (WSI=0 not shown) to severe weather cases (up to WSI=0.7). C. Modeling of Capacity Route-planning techniques are used to model capacity. In general, we estimate the capacity by counting the number of aircraft within the experimental airspace region. Specifically, throughput is defined as the number of aircraft that are able to make use of the airspace in the time span of one hour. The airspace is a 60 x 60 nmi-square region, and we set up our experiments so that an aircraft does not trivially clip a corner, that is, it enters and leaves the airspace a minimum of 15 nmi from any corner. This metric does not limit the capacity due to pilot or controller workload constraints, for reasons explained next. D. Modeling of Airspace Complexity We also consider airspace complexity in our comparison of methods of estimating capacity. Airspace complexity is often measured in terms of dynamic density. As stated by the RTCA 12 : Dynamic density is described as the essential factor affecting conflict rate in both the en route and terminal airspace. These factors are traffic density, complexity of flow, and separation standards. In several investigations on dynamic density, the relative importance of factors affecting dynamic density were determined These investigations typically determine dynamic density as a linear combination of multiple factors. However, reviews of the literature 16,17 do not report any single agreed upon model for dynamic density. 4

5 Most studies consider only a few of the top ranking factors in a dynamic density measurement for airspace complexity: 1. Density ρ = N / Aref of aircraft, which is the number N of aircraft per reference area A ref. The reference area is typically defined to be a sector, center, or a circular region. 2. Average proximity of neighboring aircraft δ NN (the average nearest neighbor distance): N 1 δ NN = min{ d ij}, where d ij is the distance between aircraft i and aircraft j at time t. N i j i= 1 N 3. Average Points of Closest Approach (PCA) distribution: 1 δ PCA = PCAi, where PCA i is the N i= 1 closest approach distance between aircraft i and j, over a look ahead window of time. Studies often use one of these factors or some linear combination of these factors, with the relative weighting determined by various issues relevant to the study. In our study, algorithms are designed to maximize throughput, so we expect the density of aircraft to approach a maximum as the methods are pushed to their limits. Thus, metrics from the literature that focus on density or proximity to neighboring traffic will not add discriminative value to our research. Density is designed to be maximized in our work, and proximity is forced to be at the separation limit as aircraft pass around the bottlenecks within the weather constraints. The complexity metric we use for our experiments is defined for points of a regular square grid laid in the airspace. The complexity of a grid point p defined in terms of a weighted average of the variance of the velocity vectors of aircraft in the neighborhood of p, scaled according to distance from p. More specifically, for some radius R, for each aircraft a i, a scaling factor: max( R d( ai, p),0) si ( p) = (1) R is introduced, where d(a i,p) is the distance from a i to p,. This scaling implies that the contribution of an aircraft to the complexity of the airspace at p falls off linearly, from 1 to 0, with distance from p, up to the radius R. Technically, any function monotonically decreasing to zero (such as a Gaussian function) would achieve a similar result, although not all would work equally well (e.g. a metric that gives equal weights to all flights within a particular radius will tend to produce complex discontinuities in the complexity). Flights for which d(a i,p)>r are not considered in the calculation of the complexity for point p. The average contribution of all aircraft is computed, with aircraft a i s contribution scaled according to s i (p). For an instant in time t, define the average local velocity and variance of velocity as follows. Let V avg (p,t) be the local average velocity vector in the neighborhood of grid point p, at time t, scaled according to the factors s i (p): si ( p) vi ( t) Vavg ( p, t) =, (2) s ( p) where v i (t) is the velocity (vector) of aircraft a i at time t. The (scalar) quantity vi ( t) Vavg ( p, t) gives the squared deviation of the velocity of aircraft a i from the local average velocity vector in the neighborhood of grid point p ( u is the Euclidean length of vector u). Intuitively, the larger this quantity, the more variation there is in the velocity vectors, as contributed by aircraft a i, in the neighborhood of point p. Summing over all aircraft, and scaling by s i (p) to account for the distance from point p, we obtain the expression for the scaled-contribution velocity variance at point p, at time t: 2 Var( p, t) = s ( p) v ( t) V ( p, t). (3) i i Our complexity metric is based on a linear combination of this variance term and a density term, N(p,t), where N(p,t) is the number of aircraft at time t within distance R of grid point p. The overall composite complexity metric takes into account velocity variation and density: 2 C p, t) = λ s ( p) v ( t) V ( p, t) + λ N( p, ). (4) ( 1 i i avg 2 t In our experiments, we use λ 1 =0.36, λ 2 =2, and R=35 nmi. The overall complexity at time t in a given region of airspace is obtained by summing C(p,t), over all grid points within the region. The time is discretized into 1-minute intervals to get a better time-averaged view of complexity. We sum the complexity values over 15-minute intervals to get the complexity values reported below. i avg 2 5

6 Finally, we do not limit the complexity of the airspace, for instance, to model pilot or controller workload limits. Given our complexity results, a threshold may be applied to limit the complexity and thus, limit the throughput (capacity), however, this threshold is dependent on a definition of the specific roles and responsibilities of the pilot and controller in NGATS, and the level of automation that assists them. For instance, in NGATS, some researchers are considering separation management to be fully automated, while others are considering pilots to manage conflicts through self-separation, while others are proposing that controllers separate aircraft with the assistance of decision support tools. In order to provide an upper limit for capacity and a complexity metric that can be useful for all these cases, we do not threshold or limit our complexity results (nor capacity results) due to any particular controller or pilot workload limit. We do, however, recognize that such a limit would reduce the theoretical capacity as reported in this paper. III. Theoretical Maximum Capacity of an Airspace In this section, we outline how to find the theoretical maximum capacity of an airspace given deterministic weather constraints. Some of the key results have been published in related literature 11, and are summarized here as they apply to the present work. The problem is posed in 2D with static weather constraints. The theoretical solution works for weather hazards that may take on arbitrary shape and size grid cells, pixels, overlapping disks, or general polygonal regions. For ease of computation, we work with an airspace, which is a rectangular region, and we model the hazardous weather constraints with a set of (possibly overlapping) disks (covering hazardous weather). A weather avoidance safety margin around each disk-hazard is included. A. Continuous Fluid Model The capacity of an airspace (experimental square region, sector, center, FEA, FCA or other region) may be estimated based on extensions of the Maxflow/Mincut Theory. 18,19 Below we give relevant definitions, facts, and notation from the theory. A capacitated network N = (V,E) is a graph on a set of nodes V and a set of edges E, such that each edge e E has associated with it a positive capacity c e. A flow from a source s to a sink t, where s and t are nodes within the network, is an assignment of numbers, f e, to every edge e of the network such that for every edge f e c e, and for every node, except s and t, the flow in equals the flow out. The value of the flow is the total flow out of s (or into t). An s-t cut in N is the partition of V into disjoint sets S and T, V = S T, S T =, such that s S, t T. An edge e E connecting the vertices i and j of V is said to cross the cut if i S, j T or i T, j S. The capacity of the cut is the sum of the capacities of all edges that cross it. The minimum cut, or mincut through the network is a cut of minimum capacity. The Mincut/Maxflow Theorem states that the value of the maximum s-t flow equals the capacity of the mincut through the network. The mincut and the maxflow can be computed efficiently. 18 In our work 19 and the work of others 20,21, the network Mincut/Maxflow Theorem has been extended to a continuous version of the maximum flow problem. In this version, instead of a discrete network, a polygon P (possibly, with holes, or obstacles) is given. Two edges of P are marked as a source s and a sink t (Figure 6). The portion of the s-t mincut boundary of P clockwise (resp. counterclockwise) between s and t is Figure 6. The theoretical capacity of a continuous flow field is called the bottom (resp. top). A flow in determined by the s-t mincut. P is a divergence-free vector field σ with support in P. The value of σ is given by integrating along edge s the dot product of vector field σ with the inward normal vector for edge s (or by computing an analogous integral along edge t). An s-t cut of P is the partition of P into two sets S and T, P=S T, S T =, such that s S, t T. The capacity of the cut is the length of the boundary between S and T, measured according to the 0/1 metric 22, which assigns cost 1 for traveling through P and cost 0 for traveling through the holes. The minimum cut, or mincut through P is a cut of minimum capacity. In previous work, Mitchell 19 proved that the value of the maximum flow equals the capacity of the mincut and provided algorithms for finding the mincut and maxflow. Specifically, it was shown that the mincut equals to the length of the shortest path from the bottom to the top in the critical graph of the domain 19,22 that has a node for every obstacle i, for the bottom and for the top, and in which the length l(i,j) of an 6

7 edge (i,j) is the distance between obstacles i and j. For further details of the mincut computation, see the paper by Mitchell et al 11. B. Discrete Air Lanes Model In our estimation of the maximum airspace capacity, we consider a model in which the routes travel through the airspace with constant-width air lanes, representing a fixed RNP requirement for passing through the gaps in the weather constraints (Figure 7). A modification of the Mincut/Maxflow Theorem for continuous flows allows us to estimate capacity in the discrete air lanes model 11,23. The modification consists of thresholding the lengths of the edges of the critical graph based on a minimum width requirement: the length of every edge is divided by the width of air lane, and is rounded down to the nearest integer. Then, as for the continuous flow model, the shortest path from the bottom to the top is found; the (integral) length of this shortest path (mincut) gives the maximum number of air lanes that can be packed in the domain while avoiding the obstacles. Another version of our problem results in the case of mixed RNP. With mixed RNP, aircraft may have different RNP requirements (due to a variety of equipment limitations and user preferences), for instance, some aircraft having RNP-1, RNP-2, and RNP-10 capabilities. The capacity of the airspace with mixed RNP would seek a sufficient number of air lanes with different widths such that the RNP requirements of the aircraft approaching the airspace can be accommodated. The solution to this problem is left to future research. Figure 7. Weather model, theoretical mincut, and non-intersecting air lanes designed to pass through the Mincut bottleneck and follow the direction of the flow. C. Maximum Theoretical Capacity for Different Operational Rules In our theoretical modeling of maximum airspace capacity, we are able to model three fundamentally different maximum capacities associated with operational rules specified in the Introduction. AllAlt and AltAlt Rulesets. As defined above, under the AllAlt rule, flights may enter the airspace on any side, and exit through any side; the only restriction is that the entry and exit sides are different (the flights are also not allowed to clip a corner of the airspace, see Figure 8, where the corners are labeled A, B, C, and D). In the AltAlt rule, east-to-west traffic is altitude separated from west-to-east traffic. For the maximum capacity calculation, we first calculate the mincut between the corners AB, BC, CD, and DA, giving us the mincut lengths of x AB, x BC, x CD, and x DA. Since the flights are not allowed to enter and exit through the same side, each flight must cross two of the mincuts. Thus, an upper bound on the capacity is given by ½(x AB + x BC + x CD + x DA ). Figure 8. Theoretical bottleneck for All-Altitudes and Alternating Altitude Rulesets. 7

8 Monotonic Rule. Flights enter the airspace on the west side, but exit anywhere on the other three sides; this means that the flights are monotonically progressing eastward (Figure 9). The theoretical maximum capacity is determined by a mincut that progresses from A to D, with length x DA. Monotonic flows may be established in any direction, North, East, South, or West, depending on user input. Unidirectional Rule. Flights enter the airspace on the west side and exit on the east side (Figure 10). No flight is allowed to enter or exit the top or bottom boundary. The theoretical maximum capacity is determined by the mincut that progresses from the bottom segment from CD to the top segment from AB. From AllAlt, AltAlt, Monotonic, to Unidirectional, the ATM control laws become more and more restrictive. Theoretically, any path, feasible for the Unidirectional rule is also feasible for the Monotonic rule and AllAlt/AltAlt rulesets; any flight path, feasible for the Monotonic rule is also feasible for the AllAlt/AltAlt rulesets. Thus, the capacity for Unidirectional rule is always less than or equal to the capacity for Monotonic rule, which, in turn, is less than or equal to the capacity for the AllAlt/AltAlt rulesets. This can also be seen experimentally when applying the appropriate mincut (Figure 11) for a wide range of weather severities spanning 0 to 1. Capacity (number of air lanes crossing the mincut) General Trend: Free Flight offers the greatest degree of freedom for flow through the airspace, facilitating the greatest capacity, but as will be shown later, this is at the expense of greater airspace complexity. Monotonic Rule Unidirectional Rule Free Flight Figure 9. Theoretical bottleneck for the Monotonic Rule. Figure 10. Theoretical bottleneck for the Unidirectional Rule (West to East). Results based on random generated weather constraints ranging from no weather (WSI=0) to severe weather cases (WSI = 1.0); 25 samples per WSI value in 0.05 increments, 0 safety margin with respect to aircraft position relative to hazards. Weather Severity Index (WSI) Figure 11. Theoretical maximum capacity given synthetic weather data prepared using randomly generated weather constraints (as illustrated in Figure 5). IV. Algorithmic Solutions In this section, we consider algorithmic solutions that search for the maximum capacity of an airspace by planning the maximum number of routes across the airspace. Because of modeling assumptions, approximations, and algorithmic limitations, we expect that these solutions will not achieve the theoretical maximum capacity, but may be close to it. 8

9 (a) Platoon Size of 1 (b) Platoon Size of 2 (c) Platoon Size of 3 Figure 12. Increasing levels of Platooning modeled in the FBRP algorihtm. Routes were designed with the Flow-Based Route Planning (FBRP) algorithm The FBRP algorithm allowed us to plan the route of a single aircraft, a platoon, or a continuous flow of aircraft through space-time such that each aircraft avoid conflicts with one another, as well as conflicts with hazardous weather constraints. See Figure 12. All aircraft within a platoon use the same set of waypoints to define their weather avoidance routing, and each flow (platoon) avoids all the other flows (platoons). For a platoon size to one, we plan a route for a single aircraft and deconflict it with all other aircraft flying through space-time. If we set the platoon size to be 2, 3, 4, etc., we plan a route to be used by a platoon of 2, 3, 4, etc. aircraft, all flying the same route, deconflicted with all other aircraft flying through space-time. With a very large platoon size (e.g., 50), our results approach continuous flows. A. Overall Findings Next, we present the overall findings of the experiments. The capacity results are displayed in Figure The complexity results as shown in Figure The capacity results can be compared to the trends in real world capacity data as shown in Figure 21. There are quite a bit of trends that are revealed in all these data, and they are described in the next several paragraphs, as well as through annotations on Figures First, the general nature of planning aircraft with any of our ATM rulesets is that the throughput decreases with increasing weather severity, as would be intuitively expected, and is demonstrated by the theoretical maximum capacity mincut results (Figure 11) and real-world data (Figure 21). For a given level of weather severity, throughput is greatest with Free Flight, which does not restrict the flow of aircraft to arrive from any particular direction. However, the monotonic and unidirectional control rulesets, because they restrict the flow of aircraft to start from one side of the airspace (the west side), they have lower capacity. The capacity is at a trade off with the complexity of the airspace, which is higher for Free Flight than with the monotonic and unidirectional rulesets. In order to achieve a capacity that is close to the theoretical upper limit, some form of systematic packing is needed. In all cases where random initial conditions are used, the throughput is lower in comparison to when a systematic packing scheme is employed. As for platoon size, the trend is that a larger platoon size leads to greater throughput. The trend is significantly stronger with systematic packing, but it is present in Free Flight scenarios as well. Large gains can typically be found with a small platoon size; the gain in routing individual aircraft (1-platoons) to sets of two aircraft at a time (2-platoons) or three aircraft at a time (3-platoons) is considerable, while the gain in further increases in platoon size to 10-platoons or 50-platoons is not universally significant. The greatest gain in very large platoon sizes is found when the two most flexible ATM rules (AllAlt and AltAlt) are combined with systematic packing. In terms of complexity, an increase in variability and flexibility of the ATM rule going from Packed scenarios to Free Flight scenarios, and going from AllAlt to AltAlt to Mono to Uni rulesets, produces an increase in complexity; an increase in platoon size tends to produce a decrease in complexity; and an increase in weather severity (WSI) produces a decrease in complexity. While complexity peaks at a WSI of approximately 30-40%, below that value, there is little enough weather that a platoon will generally take a fairly straight path to its destination, with few turns, which lowers the complexity. Above that value, reduced throughput dominates, and complexity falls simply because fewer aircraft are actually present in the airspace. As a general rule, complexity increased substantially when the directions of flights were permitted a larger degree of freedom. When flights can cross in any direction, the resultant situation is theoretically more complex than when only east-to-west flights are permitted, or when flights are even more constrained to only enter from the west and exit at the east. Complexity generally decreased with larger platoon sizes because larger platoons enforce more order on the aircraft paths and result in more organized sets of routes (flows). The complexity values of 1- platoon and 3-platoon scenarios are generally comparable. 9 Lines between aircraft denote aircraft in the same platoon and on the same flight path.

10 Increasing platoon size General Trend: If aircraft arrive at random, or if systematic packing is used, the affect of platooning is to increase the throughput. Increasing platoon size Figure 13. Throughput vs WSI and Platoon size for All Altitudes Rule. The greatest gain in very large platoon sizes is found when the two most flexible ATM rules (AllAlt and AltAlt) are combined with systematic packing. There is still room for improvement for a better packing scheme (compared to the one we executed), which can potentially produce results closer to the theoretical upper bound. Figure 14. Throughput vs WSI and Platoon Size for AltAlt Rule. 10

11 Figure 15. Throughput vs WSI and Platoon size for Monotonic Rule. Off all the methods tested, systematic packing and unidirectional flow control produced results closest to the theoretical maximum capacity. Figure 16. Throughput vs WSI and Platoon size for Unidirectional Rule. 11

12 A Tradeoff: Free Flight produces the highest capacity, but at the expense of high complexity; while monotonic and unidirectional rulesets produce lower capacity, they also have lower complexity. Complexity falls with high WSI values simply because fewer aircraft are actually present in the airspace. Figure 17. Complexity as a function of WSI and Platoon Size for All Altitude Rule. Complexity actually increased with platoon size in Packed scenarios using the All-Alt and Alt- Alt rulesets. The large amounts of throughput achieved in these scenarios using Complexity large platoon sizes actually results in increased higher with complexity platoon simply size in from Packed the higher scenarios density of using aircraft the in the airspace and the larger number of potential conflicts. Figure 18. Complexity as a function of WSI and Platoon Size for Alternating Altitude Rule. 12

13 Figure 19. Complexity as a function of WSI and Platoon size for Monotonic Rule. Low complexity results from unidirectional flow constraints systematic packing eliminates conflicts from crossing traffic. Figure 20. Complexity as a function of WSI and Platoon size for Unidirectional Rule. 13

14 Maximum Sector Occupancy (fraction of published MAP) Data represents 19 en route sectors in the NAS Linear model of Maximum Throughput in the NAS WSI Figure 21. Historical 15-minute Maximum Sector Occupancy vs weather severity. The general shape of the maximum capacity curves in our experiments basically agrees with the nature of data as we observe it in the NAS today (Figure 21) throughput (sector count) as a function of weather severity goes to zero approximately at 50% WSI. In our experiments, throughput is negligible at roughly 70% to 75% WSI, depending on the ruleset and platoon size. The theoretical results of Figure 11 show capacity going to zero at about 90% to 100%, however, these results were based on aircraft flying at their limits, with no safety margin around hazardous weather constraints, and aircraft packed against the separation standard (laterally and longitudinally). B. Use of Results in NGATS Research The results of our experiments help to define possible airspace capacity limits for en route airspace. This is useful for NGATS simulation experiments, for instance, where one must limit the number of aircraft flying through an airspace based on some criteria applicable to a future NGATS concept. In related research 26, using NASA s Airspace Concept Evaluation System (ACES) 27, we have just begun to study the modeling of Free Flight and FBRP techniques in certain regions of airspace in the NAS for future NGATS experiments. We have used curves such as Figure 21 for current airspace limits, and curves such as Figure 13 through Figure 16, to compare airspace capacity limits for today s NAS to future NGATS operational concepts for a variety of weather days. A better understanding of how airspace capacity limits the performance of the NAS in NGATS is thus left for future research. V. Conclusion This paper presented approaches to estimating the capacity of en route airspaces under a variety of operational conditions. The results indicate that the throughput within a constant flight level reduces with increasing weather severity, and is negligible at a weather severity of 70% to 75% (percentage of hazardous weather present within the airspace). We demonstrated how platooning provides increased capacity for an airspace; the greatest increase is gained by platoons of 2-aircraft compared to 1-aircraft (no platooning), with smaller amounts of capacity benefit for 3-aircraft or larger platoon sizes. Airspace complexity is reduced as platoon sizes increase, and as the flow control constrains the number of directions of travel from all directions to alternating altitude rules to unidirectional flows. There is a clear tradeoff between Free Flight capacity gains and an increase in complexity of the airspace versus lower capacities from the increased structure in unidirectional flows that provide lower complexity. VI. Acknowledgment This research was funded by NASA Ames Research Center under Virtual Airspace Modeling and Simulation (VAMS) Project contract NAS and Next Generation Air Transportation System (NGATS) Project contract NNA07BA84C. We appreciate the comments of our NASA VAMS Technical Monitor, Rob Fong, for his guidance, which helped focus the effort. Additionally, we appreciate the discussions with our NGATS contract monitor, Doug Isaacson. Finally, we appreciate the financial support of the sponsor of the research, NASA Ames Research Center, the VAMS Project Manager and NGATS Airspace Project Manager, Mr. Harry Swenson. VII. References 1 Krozel, J., Hoffman, B., Penny, S., and Butler, T., Aggregate Statistics of the National Airspace System, AIAA Guidance, Navigation, and Control Conf., Austin, TX, Aug.,

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