Assessment of Approach and Departure Paths for Vertical Takeoff and Landing Aircraft

Open AccessTechnical NotesAssessment of Approach and Departure Paths for Vertical Takeoff and Landing AircraftSuyoung Shin and Keumjin LeeSuyoung ShinKorea Aerospace University, Goyang 412-791, Republic of Korea*Graduate Student, Department of Air Transportation; currently Junior Engineer, Hanwha Systems; .Search for more papers by this author and Keumjin Lee https://orcid.org/0000-0002-3938-449XKorea Aerospace University, Goyang 412-791, Republic of Korea†Professor, Department of Air Transportation; . Member AIAA (Corresponding Author).Search for more papers by this authorPublished Online:8 Nov 2023https://doi.org/10.2514/1.I011278SectionsRead Now ToolsAdd to favoritesDownload citationTrack citations ShareShare onFacebookTwitterLinked InRedditEmail AboutNomenclatureAset of available approach and departure directionsFATObackback distance of obstacle-free volume on final approach and takeoff areaFATOfrontfront distance of obstacle-free volume on final approach and takeoff areaFATOwidthwidth of obstacle-free volume on final approach and takeoff areah1low hover height of obstacle-free volumeh2high hover height of obstacle-free volumeIobsset of indies of the voxels that Pobs occupiesIOFV(ψ)set of indies of the voxels that POFV(ψ) occupiesKnumber of buildingsLnumber of pointslix-axis index of the voxel where pi occupiesMnumber of IOFVmiy-axis index of the voxel where pi occupiesNnumber of IobsNxsize of voxelated space in x directionNysize of voxelated space in y directionNzsize of voxelated space in z directionniz-axis index of the voxel where pi occupiesPobsset of points that represent obstacle dataPOFV(ψ)set of points that represent obstacle-free volume in a specific orientation angle ψpiith point in Psxvoxel size in x directionsyvoxel size in y directionszvoxel size in z directionTObackback distance of obstacle-free volume at h2TOfrontfront distance obstacle-free volume at h2TOwidthwidth of obstacle-free volume at h2Vset of voxels for the region of interestvlmnvoxel located at l, m, and n in the x, y, and z directions, respectivelyxix-axis coordinate of pixox-axis coordinate of reference point of voxelated spaceyiy-axis coordinate of piyoy-axis coordinate of reference point of voxelated spaceziz-axis coordinate of pizoz-axis coordinate of reference point of voxelated spaceα(Θ)directional availability under Θδappdivergence of approach surfaceδdepdivergence of departure surfaceΘset of the specification parameters of obstacle-free volumeθappslope of approach surfaceθdepslope of departure surfaceΨset of orientation angles of obstacle-free volumeψorientation angle between the true north and the centerline of approach/departure surfaceI. IntroductionUrban air mobility (UAM) is a new form of transportation to take passengers and cargo over urban areas, in turn promoting reduced traffic congestion and CO2 emissions [1,2]. Yet, the safety of low-altitude flights in congested areas must be addressed before UAM is used commercially. Especially, identifying available approach and departure paths for UAM aircraft at vertiports in obstacle-rich environments is crucial for ensuring safety.The approach/departure path is defined as the flight track that the vertical takeoff and landing (VTOL) aircraft follow when landing at or taking off from a vertiport [3]. The approach/departure path should align with the predominant wind direction to minimize the aircraft’s downwind and crosswind operations. However, the range of possible approach/departure directions is often constrained by tall buildings or natural features such as mountains. Therefore, identifying airspace obstructions and available approach/departure directions is a vital step when designing a vertiport. This process is usually done by using various geographic information system (GIS) tools but could be time-consuming and error-prone due to the inherent complexity of spatial analysis [4,5].There have been several research efforts to identify available airspace for uncrewed aircraft systems in urban areas. In one study, the concept of a containment boundary was proposed to assess the use of low-altitude airspace near airports and to evaluate the potential impact of UAM operations on conventional air traffic [6]. Another study proposed a topological analysis framework to identify usable airspace in urban areas that utilizes keep-out and keep-in geofences [7]. Still another research effort presented a data-driven approach to identify available airspace separated from conventional air traffic using historical aircraft track and meteorological data [8]. One study proposed a method of spatial modeling for airspace obstruction analysis using the octree technique, but its applicability is limited to assessing the restrictive height of an individual obstacle for a given location [9]. Despite those efforts, a practical method to analyze the range of possible directions for approach/departure paths using real obstacle data is still lacking.This paper introduces a novel framework to analyze available approach and departure directions for VTOL-capable UAM aircraft using the voxelization technique and obstacle-free volume (OFV). The main contributions of this research are twofold. First, in the proposed framework, obstacle, terrain, and OFV data are converted into voxels, making 3-D spatial analysis more efficient. The conventional approach for airspace obstruction analysis is based on modeling an individual obstacle as a spike and assessing whether it obstructs the obstacle limit surface (OLS) along a specified approach/departure path [4,10–12]. Since the modeling techniques differ for obstacles, terrain, and OLS, the conventional approach exhibits a limitation in efficiently searching for possible approach/departure directions in an environment with many obstacles. In contrast, the proposed method provides a means to uniformly model the entire obstacle and OLS environment in voxelated space, enabling the rapid exploration of possible approach and departure directions, as illustrated in Fig. 1. The second contribution of the research is to validate the effectiveness of OFV with real geographical data. The OFV is a newly emerging OLS concept aimed at promoting UAM operations in densely built-up areas. However, no previous study has conclusively demonstrated the actual effectiveness of OFV in a real urban setting.This paper is organized as follows: Sec. II outlines the proposed analysis framework; Sec. III demonstrates the feasibility of the proposed framework with real obstacle data from the Yongsan area in Seoul, Republic of Korea; and Sec. IV provides a discussion and conclusion of the study.Fig. 1 Airspace obstruction analysis: conventional approach (top) and proposed approach (bottom) (TIN: triangulated irregular network).II. MethodologyA. Obstacle-Free Volume, Approach, and Departure SurfaceThe OFV is an imaginary funnel-shaped volume reserved for vertical parts of the landing and takeoff trajectories of UAM aircraft [13]. The basic concept of the OFV is to provide separation between aircraft and obstacles in an upward direction, ensuring that obstacles do not penetrate the surface and, thus, that aircraft fly above it, maintaining an acceptable level of collision probability. As depicted in Fig. 2, the approach/departure surface is attached to the top of the OFV, enabling UAM aircraft to transition to or from forward flight along the surface, following or preceding its vertical part of takeoff or landing trajectories. Although VTOL aircraft might have the capability to depart or land entirely vertically, it is not recommended from energy efficiency and safety standpoints [1,14]. Note that although the aircraft configurations in the approach and departure phases are distinct, approach and departure surfaces are typically defined as identical to the same design specification [13]. Therefore, in this paper, only one approach/departure surface is attached to the top of the OFV when available approach and departure directions at a vertiport are identified.There are two types of OFVs, depending on their cross-sectional shape: bidirectional (square cross section) and omnidirectional (circular cross section). One of the main differences between these types is their operational flexibility. The bidirectional OFV restricts the possible approach or departure directions to only each side of the square cross section. On the other hand, the omnidirectional OFV provides increased flexibility, as it allows for approach or departure in any direction, depending on various operational conditions, such as wind patterns. However, it should be noted that, for a given size of UAM aircraft, the omnidirectional OFV requires a larger airspace volume than the bidirectional OFV. This can lead to a reduction in its availability in certain urban or densely populated regions. Choosing between bidirectional and omnidirectional OFVs involves careful consideration of the specific operational needs and constraints. While the omnidirectional OFV offers greater operational flexibility, the bidirectional OFV could be more suitable for urban areas with restricted space and numerous obstacles.Fig. 2 Obstacle-free volume with approach/departure surface.As illustrated in Fig. 2, the bidirectional and omnidirectional OFVs are defined by several parameters: width, front, and back of the lowest part of the OFV (FATOwidth, FATOfront, and FATOback, respectively), the highest part of the OFV (TOwidth, TOfront, and TOback, respectively), the low hover height (h1), the high hover height (h2), and the slopes and divergence of approach and departure surfaces (θapp, θdep, δapp, and δdep, respectively). For an omnidirectional OFV, radii are used instead of the width, front, and back dimensions for final approach and takeoff (FATO) and takeoff (TO) areas, as illustrated in Fig. 2c.B. Proposed Framework for Approach and Departure Path AssessmentThe proposed framework consists of three steps summarized in Fig. 3. In the first step, 3-D geographic information of obstacles and OFV is modeled as a set of uniformly spaced points, denoted as Pobs and POFV, respectively. By taking this step, voxelization in the second step can be easily conducted using a simple process of division followed by rounding down [15].For example, the building data given in the vector format (i.e., an ordered set of vertex coordinates constituting the cross section of a building) is transformed into a stack of 2-D points created at regular intervals along the boundary of the cross section at a specific altitude, as illustrated in Fig. 4a. For the OFV, the coordinates of the edge vertices of each surface are first computed based on the specification parameters for an orientation angle ψ, which is the angle between the true north and the centerline of approach/departure surface. Then, the same process is applied to create the points along the boundary of the cross section at a specific altitude, as illustrated in Fig. 4b.Fig. 3 Overview of the proposed framework.In the second step, the geographical data of the obstacles and OFV, represented as sets of points (Pobs and POFV) are translated into the voxelated space. Let V={vlmn:1≤l≤Nx,1≤m≤Ny,1≤n≤Nz} be the 3-D Cartesian grid for the region of interest with a unit voxel of size sx×sy×sz. For each point pi=(xi,yi,zi)∈Pobs, the index (li,mi,ni) of the voxel containing the point can be found using li=⌊(xi−x0)/sx⌋, mi=⌊(yi−y0)/sy⌋, ni=⌊(zi−z0)/sz⌋ where ⌊⋅⌋ represents the quotient function, and (x0,y0,z0) is the coordinate of the reference point of the grid. The set of indices of all points in Pobs forms the obstacle data Iobs in the voxelated space V. The same process can be applied to the OFV point data POFV(ψ) in a given orientation ψ, resulting in IOFV(ψ).Fig. 4 Point modeling of a) a building and b) the bidirectional OFV.In the final step, possible directions for approach or departure are determined by checking the voxels occupied by both obstacles and the OFV for a range of the orientation angles ψ. Using Iobs and IOFV(ψ), a set of available approach and departure directions, A, can be identified as follows: A={ψj|Iobs∩IOFV(ψj)=Ø,ψj∈Ψ}(1)where Ψ={ψ1=0°,…,ψM=360°−Δψ} represents a finite set of all ψ ranging from 0 to 360° with the bin size Δψ for discretization. For accurate detection of intersections between obstacles and the OFV, the interval between points in the first step should be set as small enough compared to the size of the unit voxel. If the interval is too large, disconnected voxels may occur, as shown in Fig. 5b, resulting in missed intersections between obstacles and the OFV.Fig. 5 Bidirectional OFV modeled with the unit voxel size of 5 m×5 m×5 m.III. Case StudyThe proposed framework is demonstrated for the Yongsan International Business District (YIBD), a potential vertiport location in Seoul, Republic of Korea, with superior ground transportation connections. As shown in Fig. 6a, the YIBD is surrounded by buildings, with the Han River in the south, along which the UAM corridor is expected to be established [16].The circular region with a radius of 1.3 km and an altitude below 180 m (mean sea level, MSL) centered at YIBD is modeled in voxels with a unit size of 2 m×2 m×2 m, resulting in a 3-D Cartesian grid with over 2 million voxels. The buildings in this voxelated space are shown in Fig. 6b; given computational limitations in the rendering process, obstacles in this figure are depicted with a voxel size 10 times larger than their actual size. The FATO area in the vertiport is located at the center of YIBD, with an elevation of 3 m above ground level (AGL).Fig. 6 a) Aerial image of YIBD, and b) obstacles in voxelated space.Available approach and departure directions for the vertiport location in Fig. 6 are identified by the proposed method, using bidirectional and omnidirectional OFVs with different orientation angles 0°≤ψ<360° in 1° increments. The specification parameter values for bidirectional and omnidirectional OFVs are given in Table 1. Most specification parameters are referenced to the diameter of the minimum enclosing circle of the UAM aircraft (as “D” in this paper) in landing and takeoff configurations, which is set to be the same value for both OFVs for a fair comparison. Note that, as illustrated in Fig. 7, the radii of the omnidirectional OFVs are set to be 1.415D and 2.5D at FATO and TO, respectively, so that their circular cross section circumscribes the square cross section of the bidirectional OFV, allowing for flexible choice for approach or departure direction during operations. Additionally, other specification parameters such as hovering heights (h1, h2), slopes (θapp/dep), and divergence (δapp/dep) are set to be the same values as the reference volume outlined in the vertiport standard provided by the European Union Aviation Safety Agency (EASA) [13].As shown in Fig. 8, a larger directional availability is achieved by the bidirectional OFV, while the available approach or departure direction based on the omnidirectional OFV is more constrained due to its larger cross section. In the figure, the shaded blue area represents the possible approach or departure directions for UAM aircraft to the vertiport. Directional availability is defined as α(Θ)≔(|A|/|Ψ|), where |⋅| represents the cardinality of a set and Θ represents the specification parameters of the OFV.Fig. 7 Cross section of omnidirectional and bidirectional OFV: a) FATO and b) TO.The sensitivity of directional availability was examined with respect to D and the high hover height h2 of the OFV. Figure 9 shows directional availabilities for different parameter combinations. For comparison, the directional availability of conventional OLS for heliport design is also depicted in the figure with a red dashed line. For both omnidirectional and bidirectional OFVs, directional availabilities increase as D decreases and h2 increases. The omnidirectional OFV is more sensitive to changes in D than the bidirectional OFV, but its effect becomes less restrictive when h2 is sufficiently high, or approximately when 35 m≤h2 for both types of OFVs. This analysis provides insight into the tradeoff between the maximum size of the UAM aircraft and the required height of the vertical section for landing or takeoff trajectories. Although a longer vertical landing and takeoff section can increase directional availability, the aircraft’s handling quality and ground clearance after failure conditions must also be considered [13].Fig. 8 Directional availability for approach or departure: a) bidirectional and b) omnidirectional.The time complexities of the proposed method for each step are presented in Table 2. The execution times of the first and second steps, namely point modeling and voxelization, linearly increase with their input sizes. However, the time complexity of the final step of overlap detection is log-linear due to the use of a binary search process while comparing the indexes in Iobs and IOFV. In the example provided in this paper, the actual computation times were approximately 48 s for bidirectional OFV and 64 s for omnidirectional OFV. These computations were conducted on a desktop personal computer with an Intel Core i7 processor. The distribution of computation times for each step is depicted in Fig. 10. Note that the computation time of the proposed method can be significantly reduced by increasing the unit voxel size. Thus, the choice of unit voxel size can be tailored according to the purpose of the specific analysis.Fig. 9 Directional availability for the a) bidirectional and b) omnidirectional OFV.Fig. 10 Distribution of calculation time for analyzing available approach/departure directions.IV. ConclusionsWe proposed a practical method using OFV to identify available directions for UAM approach/departure paths at a vertiport that are safely separated from obstacles. This study has two main contributions in terms of methodological and operational aspects. Methodologically, we suggested a computationally efficient method for geographic analysis. In this study, we use point modeling and voxelization methods that allow us to model obstacle data and OFVs in a unified form and use simple formulas to straightforwardly detect overlaps between OFVs and obstacles. Voxelization detects any overlap between OFV and obstacles, making it easier to identify directional availability.On the operational side, we validated the effectiveness of OFV. We compared the directional availability of different OFVs and found that the omnidirectional OFV has less availability. The result indicates that the OFV should be carefully chosen, considering that high freedom of flight entails high restrictions on obstacles. In the sensitivity analysis, we showed that not only the height of vertical operation but also the size of aircraft have a significant effect on directional availability. From the comparison with conventional OLS, we found that sufficiently high-altitude vertical takeoff and landing maneuvers are essential to materialize the benefits of OFV.Future work should focus on optimizing OFV specification parameters based on UAM aircraft performances as well as improving directional availability by using curved-formed approach and departure surfaces. The proposed method contributes to the efficient integration of UAM in urban airspace, with the potential to be applied in practical applications.P. WeiAssociate EditorAcknowledgmentsThis work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIT) (NRF-2021R1F1A1061752) and by the Korea Agency for Infrastructure Technology Advancement (KAIA) Grant funded by the Ministry of Land, Infrastructure and Transport (RS2022-00156364). References [1] Bauranov A. and Rakas J., “Designing Airspace for Urban Air Mobility: A Review of Concepts and Approaches,” Progress in Aerospace Sciences, Vol. 125, Aug. 2021, Paper 100726. https://doi.org/10.1016/j.paerosci.2021.100726 CrossrefGoogle Scholar[2] Holden J. and Goel N., Uber Elevate: Fast-Forwarding to a Future of On-Demand Urban Air Transportation, Uber Technologies, Inc., San Francisco, 2016, pp. 1–4. Google Scholar[3] “Engineering Brief No. 105, Vertiport Design,” Federal Aviation Administration, 2022. Google Scholar[4] Chang S. W., “A GIS Model for Analyzing Airspace Obstructions and Safety near Airports,” Journal of Civil Engineering and Architecture, Vol. 10, May 2016, pp. 553–562. https://doi.org/10.17265/1934-7359/2016.05.004 Google Scholar[5] Horonjeff R., Planning and Design of Airports, 5th ed., McGraw–Hill, New York, 2010, pp. 213–228. Google Scholar[6] Vascik P. D. and Hansman R. J., “Assessing Integration Between Emerging and Conventional Operations in Urban Airspace,” AIAA Aviation 2019 Forum, AIAA Paper 2019-3125, 2019. https://doi.org/10.2514/6.2019-3125 LinkGoogle Scholar[7] Cho J. and Yoon Y., “How to Assess the Capacity of Urban Airspace: A Topological Approach Using Keep-In and Keep-Out Geofence,” Transportation Research Part C: Emerging Technologies, Vol. 92, July 2018, pp. 137–149. https://doi.org/10.1016/j.trc.2018.05.001 CrossrefGoogle Scholar[8] Murça M. C. R., “Identification and Prediction of Urban Airspace Availability for Emerging Air Mobility Operations,” Transportation Research Part C: Emerging Technologies, Vol. 131, Oct. 2021, Paper 103274. https://doi.org/10.1016/j.trc.2021.103274 CrossrefGoogle Scholar[9] Panayotov A., Georgiev I. and Georgiev I., “A Practical Approach for Airport Spatial Modeling,” Proceedings of the 13th International Conference on Computer Systems and Technologies, Assoc. for Computing Machinery, New York, June 2012, pp. 321–328. https://doi.org/10.1145/2383276.2383323 Google Scholar[10] Falavigna G. P., Iescheck A. L. and Souza S. F., “3D Modeling to Identify and Quantify Obstacles in Aerodrome Protection Zone,” Boletim de Ciências Geodésicas, Vol. 26, No. 2, 2020, Paper e2020009. https://doi.org/10.1590/s1982-21702020000200009 Google Scholar[11] Contreras-Alonso M. R., Ezquerra-Canalejo A., Pérez-Martín E., Herrero-Tejedor T. R. and López-Cuervo Medina S., “Environmental Assessment of Obstacle Limitation Surfaces (OLS) in Airports Using Geographic Information Technologies,” PLoS ONE, Vol. 15, No. 2, 2020, Paper e0229378. https://doi.org/10.1371/journal.pone.0229378 CrossrefGoogle Scholar[12] Ayeni A. O., Musah A. and Udofia S. K., “Assessment of Potential Aerodrome Obstacles on Flight Safety Operations Using GIS: A Case of Murtala Mohammed International Airport, Lagos-Nigeria,” Journal of Geographic Information System, Vol. 10, Jan. 2018, pp. 1–24. https://doi.org/10.4236/jgis.2018.101001 CrossrefGoogle Scholar[13] “Vertiports—Prototype Technical Specifications for the Design of VFR Vertiports for Operation with Manned VTOL-capable Aircraft Certified in the Enhanced Category (PTS-VPT-DSN), 2022,” European Union Aviation Safety Agency, 2022, https://www.easa.europa.eu/downloads/136259/en [retrieved 2 March 2023]. Google Scholar[14] “Helicopter Flying Handbook (FAA-H-8083-21B),” Federal Aviation Administration, 2019. Google Scholar[15] Nourian P., Gonçalves R., Zlatanova S., Ohori K. A. and Vo A. V., “Voxelization Algorithms for Geospatial Applications Computational Methods for Voxelating Spatial Datasets of 3D City Models Containing 3D Surface, Curve and Point Data Models,” MethodsX, Vol. 3, Jan. 2016, pp. 69–86. https://doi.org/10.1016/j.mex.2016.01.001 CrossrefGoogle Scholar[16] “K-UAM Concept of Operations 1.0,” UAM Team Korea, 2021. Google ScholarTablesTable 1 Specification parameters for the OFVs SpecificationsOFVCross sectionOthersBidirectionalFATOback=1DD=20 m FATOfront=1Dh1=3 m FATOwidth=2Dh2=30 m TOback=2Dθapp=12.5% TOfront=2Dθdep=12.5% TOwidth=3Dδapp=15%OmnidirectionalRadius on FATO=1.415Dδdep=15% Radius at h2=2.5D Table 2 Time complexity of each stepStepPoint modelingVoxelizationOverlap detectionInput parameterNumber of buildings (K)Number of points (L)Number of IOFV (M)Number of Iobs (N)Time complexity (O)O(K)O(L)O(NlogM) Next article FiguresReferencesRelatedDetails What's Popular Articles in Advance Metrics CrossmarkInformationCopyright © 2023 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. All requests for copying and permission to reprint should be submitted to CCC at www.copyright.com; employ the eISSN 2327-3097 to initiate your request. See also AIAA Rights and Permissions www.aiaa.org/randp. TopicsAeronauticsAir MobilityAircraft OperationsAircraft Operations and TechnologyAviationTakeoff and LandingVertical Takeoff and Landing KeywordsVertical Take off and LandingUrban Air MobilityObstacle Free VolumeObstacle Limit SurfaceAirspace Obstruction AnalysisVoxelizationAvailable Approach and Departure DirectionsAirspace AssessmentAcknowledgmentsThis work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIT) (NRF-2021R1F1A1061752) and by the Korea Agency for Infrastructure Technology Advancement (KAIA) Grant funded by the Ministry of Land, Infrastructure and Transport (RS2022-00156364).PDF Received3 April 2023Accepted13 October 2023Published online8 November 2023