Cross-country Flight Research Articles

Optimization of the geometry of the glider wing taking into account statistical data

The article presents a synthesis of an optimization algorithm for an aerodynamic characteristics of a sailplane in preliminary design phase aimed at increasing average cross-country speed. The flight data of SZD-48-3 standard class FAI glider was collected and analyzed from weglide.org portal as a flight track files, saved in igc format. The general structure of an atmosphere was analyzed during cross-country flight basing on collected statistics. New integral criterion for the target function has been presented for usage in optimization routine loop. The criterion permits a reduction of multicriterial optimization problem to united parameter.
 Genetic Optimization algorithm has been selected as a main optimization tool due to its ability to find global optimum of an unsmooth multidimensional target function and robustness in general. The parametrization scheme with minimal number of parameters has been presented for a wing with a complex planform. The Lifting-Line Theory and XFOIL solver implemented as a mathematical model of an aerodynamic characteristics of the wing. As a result, prospective ways for consecutive development have been revealed. In particular, application of synthesized optimization algorithm towards any other classes of aerial vehicle and introduction of airfoil to wing parameterization.

Use of flight tracking data to inform safety deficiencies for general aviation cross-country operations in challenging flying environments

Background: Air carriers, but not general aviation, have long employed in-flight data to identify risks/implement corrective measures for improved safety. Herein, using in-flight data, aircraft (in non-instrument-rated private pilots (PPLs) ownership) operations in two potentially hazardous environments (mountains, degraded visibility) were researched for safety practice deficiencies. Four questions were posed, the first two related to mountainous terrain operations: were aircraft (a) flown with hazardous ridge-level winds, (b) within gliding distance of level terrain? Regarding degraded visibility, did aviators (c) depart with low cloud ceilings (≤3,000 ft.), (d) fly at night away from urban lighting? Methods: The study cohort comprised: (a) single engine aircraft in sole PPL proprietorship (b) registered in Automatic Dependent Surveillance-Broadcast (ADS-B-Out) equipage-required locations prone to low cloud ceilings in three mountainous states. ADS-B-Out data for cross-country flights (>200 nm) were collected. Results: 250 flights (50 airplanes) were tracked (spring/summer 2021). For aircraft transiting areas subject to mountain winds influences, 65% completed one/multiple flights with potentially hazardous ridge-level winds. Two thirds of airplanes traversing mountainous topography would have, for at least one flight, been unable to glide to level terrain with a powerplant failure. Encouragingly, flight departures for 82% of the aircraft were with >3,000 ft. cloud ceilings. Likewise, flights for >86% of the study cohort were undertaken during daylight. Employing a risk scale, operations for 68% of the study cohort did not exceed low-risk (i.e., ≤1 unsafe practice) and high-risk flight(s) (three concurrent unsafe practices) were rare (4% of airplanes). In log-linear analysis, no interactions were evident between the four unsafe practices (p = 0.602). Discussion: Hazardous winds and inadequate engine failure planning were identified as safety deficiencies for general aviation mountain operations. Practical Application: This study advocates for the expanded use of ADS-B-Out in-flight data to inform safety deficiencies/implement corrective measures toward improving general aviation safety.

In-flight measurement of free-stream turbulence in the convective boundary layer

Natural laminar flow airfoils have achieved such a level of refinement that further optimisation and subsequent wind tunnel testing need to regard the specific free-stream turbulence to be expected during operation. This requires the characterisation of this turbulence in terms of those properties which are relevant for boundary layer receptivity and subsequent transition. These parameters of turbulence change with environmental conditions and, in case of aircraft, along the flight profile. This study investigates the free-stream turbulence relevant for the case of sailplane airfoils. In-flight measurements with a constant temperature anemometer x-wire probe were conducted during cross-country flights in Central Europe and provided 22 h of flight data, covering thermalling phases as well as straight flight legs. Longitudinal and transversal velocity fluctuations were recorded well into the dissipation range. The special challenges of operating a constant temperature anemometer probe continuously for several hours are addressed. The permanent unsteadiness of the inflow poses challenges for the evaluation, but also provides a broad database of measured turbulence levels. The quality of the measurements is shown by verifying some of the predictions of Kolmogorov's inertial range theories. Free-stream turbulence in thermalling phases is sufficiently homogeneous to be described accurately, as the dissipation range fluctuates only in a limited range and follows a log-normal distribution. On the straight flight legs, the turbulence depends on the convective activity along the flight path. In general, within the convective part of the atmosphere, turbulence levels are found to be significantly larger than in low-turbulence wind tunnels.Graphical abstract

Assessment of the Potential of Electric Propulsion for General Aviation Using Model-Based System Engineering (MBSE) Methodology

Climate change currently taking place around the world requires humanity to take decisive action. One way, as envisaged in the European Green Deal, is to reduce the emissions of harmful chemical compounds of the transport sector by 90% by 2050. This reduction also applies to aviation. The most commonly suggested means of achieving this goal is the electrification of aviation. In this paper, the possibilities of using small general aviation aircraft (for up to two people) with electric propulsion used for sport flying, particularly for pilot training and glider towing, have been analysed. For this purpose, simulation models have been developed in MATLAB/Simulink environment for three different tasks: cross-country flight, performing a certain number of touch-and-go procedures during one flight, and towing a glider. Three aircraft representing different classes were selected for analysis: Diamond DA20 Katana, WT-9 Dynamic, and PZL-101 Gawron. Based on data collected from pilots and publicly available flight records, minimum performance requirements for particular tasks were determined. The number of batteries that power the electric propulsion system of the analysed aircraft was selected in such a way that no geometrical changes in the aircraft structure are necessary and the MTOW (Maximum Take Off Weight) is not exceeded. Obtained results indicate the possibility of using small electric aircrafts derived from UL (ultralight) class in flights taking place near airports, performing touch-and-go procedures and towing gliders.

A Two-Stage Model of Diversion Knowledge and Skills Highlights Where Pilot Factors Impact Safety-Related Outcomes

ABSTRACT Objective: To assist stakeholders apply targeted safety strategies, we developed and tested a two-stage model of diversion knowledge and skills. Background: Understanding pilot factors in weather-related diversions is integral to reducing the phenomenon of visual flight rules flight into meteorological conditions. Method: Thirty-six general aviation pilots flew a cross-country flight in a Cessna 172 simulator where they encountered an ATC-directed diversion due to deteriorating weather. Path analyses quantified effects in a two-stage model based on criteria specified by aviation regulations. Results: In stage 1, low cognitive flexibility and fewer recent pilot-in-command hours were associated with greater likelihood of ignoring the diversion instruction. Low cognitive flexibility was also associated with errors in locating the alternate aerodrome and incorrect procedures at the alternate. At stage 2, there were significant positive paths from a diversion efficiency variable to all aspects of pilotage. Pilotage positively predicted awareness of ownship and traffic, and was associated with fewer altitude violations. Conclusion: We provide empirical evidence for the association between the cognitive factors related to continuation bias and high-risk responses to diversion instructions. Using a two-stage model to conceptualize pilot performance illuminates the impact of cognitive factors in weather-related diversions. Highlighting the pivotal human factors at two clear junctions of an unexpected diversion can more fully prepare pilots to safely manage these risk-laden events.

Rancangan VFR Corridor Majalengka Control Zone di Perum LPPNPI Unit Pelayanan Kertajati

This study aims to design VFR Corridor connecting Cakrabhuwana Airport in Cirebon with Tunggul Wulung Cilacap Airport and Cijulang Nusawairu Airport.The research method used is level one research and development with a qualitative approach and descriptive exposure. Data collection techniques in the form of interviews, literature studies, and documentation studies. Meanwhile, data processing techniques use data reduction, data presentation, and verification. Based on the data collected, it is known that the flights from Cirebon to Cilacap and Nusawiru or vice versa do not have a clear VFR Corridor to connect the three airports, while the number of traffic overflying that makes Cross Country flights to Tunggul Wulung Cilacap and Cijulang Nusawiru airports is quite large.

Pneumocephalus and Facial Droop on an Airplane: A Case Report.

IntroductionPneumocephalus (PNC) is most commonly associated with trauma or intracranial surgery, less commonly secondary to an infectious source, and is rarely caused by barotrauma.Case reportA 32-year-old woman presented to the emergency department with complaint of resolved left-sided facial droop and a lingering paresthesia of her left upper extremity after a cross-country flight. Computed tomography demonstrated several foci of air in the subdural space consistent with PNC.ConclusionFor PNC to occur there must be a persistent negative intracranial pressure gradient, with or without an extracranial pressure change. In this case the pressure change occurred due to cabin pressure.

Oh, the Places You'll Go

One day, years ago, I was on a cross-country flight with my mother. A distinguished-looking gentleman across the aisle from us was fiddling with his digital watch. After watching him struggle for a few minutes, my mom asked if she could help. “Well, if you've got teeny tiny fingers, sure,” he said, handing over the watch. “I want to move it forward an hour for the new time zone.” My mother took it, then reached into her seat pocket and pulled out the motion sickness bag. She ripped off the part you fold down when the bag is full and stripped away everything but the thin wire inside. In a matter of seconds, she handed back the watch, the time now fixed. Both the stranger and I were amazed. It's not every day that someone MacGyvers your electronics with, of all things, an airplane barf bag. But then, my mom doesn't have an everyday mind.

Aviation Human Factors Related Industry News

Aviation Human Factors Related Industry News

The Effect of Electronic Flight Bags in Flight Training on Preflight Skill Development and Aeronautical Decision-Making

This study was designed to evaluate the effects of utilizing Electronic Flight Bags (EFBs) in flight training with emphasis on preflight skill development and Aeronautical Decision Making. The study participants were student pilots or private pilots who used EFBs in flight training and had not logged more than 100 total flight hours. The study utilized a simulation of the preflight process of a Visual Flight Rules cross country flight in which the participants answered questions related to the flight preparation. Fifty percent of the study’s population completed this survey with the information provided through an EFB and the other 50% population had to answer the questions without an EFB using traditional unabridged raw data. A comparative analysis of the data collected from both groups was performed. The largest degradation of performance was noted in Notices to Airmen (NOTAM) interpretation and the least degradation in performance was noted in weather-related decision-making.

Physicians’ Perceptions of Radiation Dose Quantity Depend on the Language in Which It Is Expressed

PurposeRadiation dose information is increasingly requested by nonradiology providers, but there are no standard methods for communicating dose. The aim of this study was to compare physicians’ perceptions of the amount of radiation associated with similar dose quantities expressed using different dose terms to evaluate the impact of word choice on physicians’ understanding of radiation dose. MethodsInternal medicine and pediatric residents were surveyed online for 42 days. After obtaining demographics and training levels, respondents were asked to rank five different radiation dose quantities, each corresponding to one of the five ACR relative radiation levels (RRLs) expressed using different dose terms. Respondents ranked the choices from least to greatest (ie, from 1 to 5) or indicated if all five were equal. For the final question, the same dose quantity was expressed five different ways. ResultsFifty-one medicine and 45 pediatric residents responded (a 44% response rate). Mean differences in rankings were as follows: for chest x-rays, 0.109 (95% confidence interval [CI], −0.018 to 0.236); for cross-country flights, 0.462 (95% CI, 0.338 to 0.585); for natural background radiation, −0.672 (95% CI, −0.793 to −0.551); for cancer risk, −0.294 (95% CI, −0.409 to −0.178); and for ACR RRL, 0.239 (95% CI, 0.148 to 0.329). Statistically significant differences were found in the distributions of rankings (P < .001) and percentage of correct rankings across each radiation dose term (P < .001), with the ACR RRL having the highest percentage of correct rankings (61.2%). ConclusionsAdult and pediatric physicians consistently over- or underestimated radiation dose quantities using different terms to express radiation dose. These results suggest that radiation dose information should be communicated using standard terminology such as the ACR RRL scale to foster consistency and improve the accuracy of physicians’ radiation risk perceptions.

VFR Into IMC: Using Simulation to Improve Weather-Related Decision-Making

Safety-related training policies restrict pilots from encountering challenging weather during flight training. This potentially inhibits the development of critical decision-making skills. To identify gaps in weather-related flight training, high-fidelity weather-simulation was developed to re-create historical weather events. Sixteen visual-only pilots and 16 instrument-rated pilots flew a simulated cross-country flight under visual flight rules in marginally visual weather that encountered instrument conditions. Procedural performance and experience-related demographic factors were analyzed to identify key flight skills and experience that contributed to safe weather-related decisions. Previous experience with actual instrument weather was found to be the only statistically significant demographic predictor of safe performance. Pilots who performed more safely were more likely to use in-cockpit weather information during the flight to detect and avoid instrument weather. Implications of this study and opportunities for future research are discussed.

Sense and Avoid

This study explored the ability of operators to provide separation between three unmanned aircraft using basic cockpit traffic displays. Four groups of three general aviation, instrument-rated pilots flew cross-country flights controlling simulated twin-engine unmanned aircraft systems (UAS). They were required to maintain 2 nautical miles (nmi) horizontal and 500 ft vertical separation from all other aircraft. To examine the effect of two important safety factors, the flights were conducted with and without communication among the operators and with and without variable accuracy in the displayed traffic location due to degraded sensor quality. Twenty four different three-dimensional traffic conflict trajectories with three UASs, were repeated randomly for each of the four experimental conditions for each group. Of the 1152 aircraft encounters 12.8% were in violation of separation minimums. Eighteen of these were closer than 400 ft vertically or 1.6 nmi horizontally. The minimum separation of all aircraft pairs was 293 ft and 0.13 nmi. No difference in minimum separations was found due to the presence of communications, the variable accuracy of traffic position, or the participant group. The type and time of evasive maneuvers showed no effect when displayed horizontal position accuracy was variable. When operators were able to communicate and coordinate their maneuvers, the time to resolve the conflict was reduced. Participant groups varied significantly in: time of conflict resolution, frequency and type of maneuvers, control activity, reported amount of threat, confidence, satisfaction, and appraisal of the efficacy of their communications. The findings of this study serve as a benchmark for the development of sense and avoid procedures and minimum equipage standards for operating UASs in the airspace over the United States.

Solar-powered plane begins cross-country flight

Solar-powered plane begins cross-country flight

Exposure to flame retardant chemicals on commercial airplanes

BackgroundFlame retardant chemicals are used in materials on airplanes to slow the propagation of fire. These chemicals migrate from their source products and can be found in the dust of airplanes, creating the potential for exposure.MethodsTo characterize exposure to flame retardant chemicals in airplane dust, we collected dust samples from locations inside 19 commercial airplanes parked overnight at airport gates. In addition, hand-wipe samples were also collected from 9 flight attendants and 1 passenger who had just taken a cross-country (USA) flight. The samples were analyzed for a suite of flame retardant chemicals. To identify the possible sources for the brominated flame retardants, we used a portable XRF analyzer to quantify bromine concentrations in materials inside the airplanes.ResultsA wide range of flame retardant compounds were detected in 100% of the dust samples collected from airplanes, including BDEs 47, 99, 153, 183 and 209, tris(1,3-dichloro-isopropyl)phosphate (TDCPP), hexabromocyclododecane (HBCD) and bis-(2-ethylhexyl)-tetrabromo-phthalate (TBPH). Airplane dust contained elevated concentrations of BDE 209 (GM: 500 ug/g; range: 2,600 ug/g) relative to other indoor environments, such as residential and commercial buildings, and the hands of participants after a cross-country flight contained elevated BDE 209 concentrations relative to the general population. TDCPP, a known carcinogen that was removed from use in children’s pajamas in the 1970’s although still used today in other consumer products, was detected on 100% of airplanes in concentrations similar to those found in residential and commercial locations.ConclusionThis study adds to the limited body of knowledge regarding exposure to flame retardants on commercial aircraft, an environment long hypothesized to be at risk for maximum exposures due to strict flame retardant standards for aircraft materials. Our findings indicate that flame retardants are widely used in many airplane components and all airplane types, as expected. Most flame retardants, including TDCPP, were detected in 100% of dust samples collected from the airplanes. The concentrations of BDE 209 were elevated by orders of magnitude relative to residential and office environments.

Whispers and Roars

Whispers and Roars Patrick James Dunagan (bio) Of Indigo and Saffron: New and Selected Poems. Michael McClure; Leslie Scalapino, ed. University of California Press. http://www.ucpress.edu. 344 pages; cloth, $55.00, paper, $24.95, eBook, $24.95. A friend of mine recently awoke from a nap while aboard a cross-country flight to the quite surreal shock of seeing poet Michael McClure up on the in-flight film screen. McClure's visage was soon exchanged for a clip of Jim Morrison crooning out a rock ballad, the film being a recent documentary of the late 1960s psychedelic band The Doors. A habitué of the Haight-Ashbury scene, McClure was familiar with many rock 'n roll stars of the era, even assisting Janis Joplin with writing the lyrics for her hit "Mercedes Benz." In recent years, he has been collaborating with Doors keyboardist Ray Manzarek, releasing albums together and frequently playing tour dates in major cities. Short to say, McClure gets around. He's nothing less than a living icon. Throughout his life, McClure has remained a dedicatee of the arts, friend to artists such as Bruce Conner, Jay DeFeo, Stan Brakhage, Jess, Wallace Berman, George Herms, and many others, all the while dedicating himself to his work as a poet. As McClure says in his brief preface, he wishes his poems "be soft and vigorous as the breath of a sparrow on the redwood deck rail and as tumultuous as a lion purring in the rain by the roadside in Kenya." He's not kidding, either. McClure is bombastically driven to using rather hyperbolic images, yet his work also exhibits a lucid, Zen-inspired embrace of beauty and calm. In contrast to the at times overbearing enthusiasm with which he hurls images onto the page, McClure also offers up subtle rhythmic play of alliteration and rhyme as he delights in all forms of life. Whether it is as a young father watching his daughter in "Two Weeks Baby Sunbathing": This old brown velvet by daylight is not eternal velvetbut the baby on it, bright in the morning sun, is more beautiful than human. Her glory fills the room. Her back and buttocks are mounds of color. Her toes and fingers are fat stars. Or celebrating what he assumes to be the playfulness of wild creatures, as below in "Gray Fox at Solstice." The fox coughs, "Hahh!" Kicks his feet— stretches. Beautiful claw toesin purple brodiaea lilies. He dance-runs through the Indian paintbrush. Galaxies in spirals. Galaxies in balls. Whether just imagined or eye witnessed, McClure's vivid imagery engages the imagination as strongly as any documentary. McClure's conception of his own poetics follows the lead set by Charles Olson's essay "Projective Verse" (1950), which bases the measure of the free verse line on the breath of the poet writing, yet for McClure, this focus yields a cosmic, ecological sense of identification within a greater whole from out of which he derives both purpose and value centered in the self as physical body. Our breath IS TO SERVE THE ULTIMATE beautyof ourselves. Possessed with a near manic desire to share a Message with his art, he verges on, and for many readers no doubt crosses over, a too-thin display of an easily come by sense of there being a higher meaning to the order of things. In this regard, he's prone to a quasi-New Age Spiritualism that encourages an erstwhile yearning in his work to give space to representing the perspective and assumed interests of the non-human. In "Hummingbird Ode," McClure addresses a dying hummingbird "smashed on the plate / glass window." He pushes himself to ask: "WHAT'S / ON YOUR SIDE OF THE VEIL? / DO YOU DIP YOUR BEAK / in the vast black lily / of space? Does the sweetness / of the pain go on forever?" He can't help but continue: "WHERE ARE THE LOVES THAT MAKE THE BLOSSOM / of your body? Do they still spin / in the air? Your wives / and loves? Are you now / more than this meat? Finally / A STAR??" Meanwhile in "The Air," McClure goes so far as to adopt the mask of a lion...

Effects of Pilot Experience on Recall of Information From Graphical Weather Displays

Good weather-related decision making is critical for the safe conduct of general aviation flights. A number of tools have been developed in recent years to help pilots visualize the actual and forecast weather for their planned flight. In this study we compare the effectiveness of a graphic weather visualization tool designed for preflight decision making with conventional coded reports and plain English translations. Qualified pilots from several aero clubs were asked to view 4 hypothetical cross-country flights. Departure and destination weather reports (METARs) were provided for each flight in 1 of 4 formats—code, plain English, graphic, or both graphic and plain English. Following a short interference task, the pilots were asked to recall as much of the weather information as possible. Results showed that pilots correctly recalled most information from the dual graphic and plain English display but this was largely attributable to the additional time required to process the 2 displays. Although the formats were rated as equally interpretable, experienced pilots were able to recall much more from the traditional coded METARs than less experienced pilots. Implications for the design and acceptance of novel display formats of meteorological information for pilots are discussed.

Pilot Error During Visual Flight Into Instrument Weather: An Experiment Using Advanced Simulation and Analysis Methods

This study details competing literature findings surrounding visual flight rules (VFR) flight into instrument meteorological conditions (IMC), and it utilizes advanced simulation to fulfill training inadequacies and bring clarity to the research. An experiment involving 16 visual-only pilots was conducted to simulate cross-country flight in marginal weather. Participants' abilities to aviate, navigate, communicate, and process weather information were measured and correlated with demographics and the pilots' abilities to adhere to visual flight regulations. 11 out of the 16 pilots committed violations, and the pilots' previous exposure to instrument weather made them better at collecting in-flight weather reports and obeying VFR regulations. Pilots that penetrated simulated IMC were found to be more reliant on cockpit automation such as autopilot and navigation equipment. Misuse of automation often lead pilots to become overwhelmed by IMC, and in severe cases, pilots displayed flight profiles characteristic of spatial disorientation and lost control of the aircraft or they wandered at dangerously low altitudes in zero visibility, putting them at risk for controlled flight into terrain. This study represents a validation of the advancement of weather simulation to improve flight training, practical examination, and investigation. Language: en

Elite Exoticism: Sea-rail Cruise Tourism to South Africa, 1926–1939

South Africa's railway and harbours operator (SAR&H) was the arch promoter of overseas tourism to South Africa for thirty years after Union in 1910. To its package tours for independent inbound tourists, the SAR&H added exclusive port-to-port rail trips across South Africa by partnering with overseas cruise ship operators. Whereas the European market was a mainstay, the more distant North American market only became accessible in relation to lengthy round-the-world cruises. Between 1926 and 1939 approximately fifty long-distance luxury trains met thirty-one cruise liners to transport some 5,000 wealthy tourists through various inland scenic, cultural and wildlife attractions in southern Africa. Port calls by visiting cruise liners created their own spectacle and stir. Eventually more cruise passengers elected to stay on board ship at the end of long ocean voyages, elite visitors took cross-country flights to increase the novelty of travel, and this first period of South African sea-rail tourism came to a close.

Feedback Control of the National Airspace System

DOI: 10.2514/1.51203 This paper proposes a general modeling framework adapted to the feedback control of traffic flows in Eulerian modelsof the NationalAirspace System. It is shown thatthe problems of scheduling androuting aircraft flowsin the NationalAirspaceSystemcanbeposedasthecontrolofanetworkofqueueswithload-dependentservicerates.Focus can then shift to developing techniques to ensure that the aircraft queues in each airspace sector, which are an indicator of the air traffic controller workloads, are kept small. This paper uses the proposed framework to develop control laws that help prepare the National Airspace System for fast recovery from a weather event, given a probabilistic forecast of capacities. In particular, the model includes the management of airport arrivals and departures subject to runway capacity constraints, which are highly sensitive to weather disruptions. I. Introduction T HE frequent occurrence of air traffic delays in the National Airspace System (NAS), along with the projected increase in demand, motivate the scheduling of flight operations to better use available system resources. The process of planning operations to balancetheavailablecapacityandthedemandforresourcesisknown asTrafficFlowManagement(TFM).Thistaskiscurrentlyconducted manually by air traffic controllers (ATC), and contributes significantlytotheirworkload.Tomeettheincreasingtrafficdemand,there is a desire to introduce a greater level of automation and decision support for air traffic management. Research on the TFM problem has traditionally focused on developing open-loop policies for scheduling aircraft operations. Because of the typical travel times of cross-country flights, openloop traffic flow management policies need to be determined 5– 6 hours ahead of the time of operations. Such policies prescribe the positionofeachaircraftinthesystemateachinstant,andareobtained by solving large-scale integer programs [1,2]. This approach is difficult to scale to the scheduling of approximately 40,000 flights a day, and typically does not address the many sources of uncertainty present in the system. Weather, in particular, is a major source of disruption that requires constant adjustment of the schedules. For instance, 66% of all NAS delays in 2009 were attributed toweather. ‡ Moreover, open-loop traffic flow management algorithms require precise weather forecasts several hours ahead of time, which are arguably beyond the limits of even state-of-the-art weather forecasting tools [3]. The disturbance attenuation properties of feedback control make closed-loop control policies for the NAS very attractive. Attempts have been made to introduce some feedback in the decision algorithmswhilestilltryingtooptimizeeachaircrafttrajectory[4,5]. More recently, researchers have started developing new models that are more tractable for the purpose of control, which only record aircraft counts in specific control volumes of airspace rather than follow individual aircraft. These aggregate flow models, called