VTOL site location considering obstacle clearance during approach and departure

doi:10.1016/j.commtr.2024.100118

Communications in Transportation Research
交通研究通讯

Volume 4, December 2024, 100118
第 4 卷，2024 年 12 月，100118

https://doi.org/10.1016/j.commtr.2024.100118 Get rights and content 获取权利和内容

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Abstract 摘要

Urban air mobility (UAM) extends urban transportation to low-altitude airspace using electric vertical take-off and landing (eVTOL) vehicle to reduce traffic congestion. The vertical take-off and landing (VTOL) site connecting ground and air transport is the critical infrastructure of the UAM. Determining its locations is essential for the design and operation of the air route. This study focuses on the problem of the location of the VTOL site, using Shenzhen as the study area, and establishes an integer programming model with the objective of maximizing travel cost savings to identify the optimal locations of the VTOL sites. This study is different from existing ones in that it explicitly considers the three-dimensional spatial availability of VTOL sites. Geographic information system (GIS) tools are used to identify locations that satisfy two-dimensional (2D) planar availability, and an obstacle assessment model of the approach/departure and transitional surfaces of the VTOL site is built to further screen the locations. The selected potential sites are used as input to the integer programming model, ensuring that the locations identified to establish the VTOL site are optimal. The impact of the number of VTOL sites, the user's transfer time at the VTOL sites, and the eVTOL pricing on the model solution is also discussed. Although this study uses Shenzhen as a research object, the proposed methodology is generalized and applicable to any other city or region, providing recommendations and references for initial planning and related operations of the UAM in selected areas.
城市空中交通（UAM）利用电动垂直起降（eVTOL）飞行器将城市交通扩展到低空空域，以减少交通拥堵。连接地面和空中运输的垂直起降（VTOL）场地是城市空中交通的关键基础设施。确定其位置对于空中航线的设计和运营至关重要。本研究以深圳为研究区域，重点关注垂直起降点的选址问题，并建立了一个整数编程模型，以最大限度地节约旅行成本为目标，确定垂直起降点的最佳位置。与现有研究不同的是，本研究明确考虑了 VTOL 场址的三维空间可用性。使用地理信息系统（GIS）工具来确定满足二维（2D）平面可用性的地点，并建立 VTOL 场址的进场/离场和过渡表面的障碍物评估模型，以进一步筛选地点。选定的潜在地点将作为整数编程模型的输入，确保确定的 VTOL 场址是最佳地点。此外，还讨论了 VTOL 站点数量、用户在 VTOL 站点的换乘时间以及 eVTOL 定价对模型解决方案的影响。虽然本研究以深圳为研究对象，但所提出的方法具有普适性，适用于其他任何城市或地区，为选定地区的无人机空中作业区的初步规划和相关运营提供建议和参考。

Keywords 关键词

Urban air mobility (UAM)

Vertical take-off and landing (VTOL) site location

Advanced air mobility (AAM)

Hub location problem

Urban transportation

城市空中机动性（UAM）垂直起降（VTOL）场址定位先进空中机动性（AAM）枢纽定位问题城市交通

1. Introduction 1.导言

Traffic congestion presents a significant challenge in the majority metropolitan areas around the world, causing substantial economic loss and considerable impact on society. Among the 10 most congested cities in the world, the average commuter wastes more than 150 h of additional time on the roads each year (Friedman, 2020), and when this figure exceeds 35 h, it signifies a negative impact on the economy (Badger, 2013). In addition to impeding economic development, traffic congestion leads to additional travel time, resulting in reduced efficiency and loss of productivity. Motor vehicles moving on congested roads spend longer periods at low speeds, leading to inadequate fuel combustion due to reduced speed and higher levels of harmful substances such as nitrogen oxides in the exhaust. Furthermore, extended travel time contribute to increased pollutants emissions, leading to air pollution and climate change. This, in turn, affects physical well-being and poses significant challenges to public health (Nadrian et al., 2019, 2020).
交通拥堵是全球大多数大都市地区面临的重大挑战，造成了巨大的经济损失和社会影响。在全球最拥堵的 10 个城市中，通勤者平均每年在路上浪费的时间超过 150 小时（Friedman，2020 年），当这一数字超过 35 小时时，就意味着对经济产生了负面影响（Badger，2013 年）。除了阻碍经济发展外，交通拥堵还会导致额外的出行时间，从而降低效率和损失生产力。机动车在拥堵的道路上低速行驶的时间更长，速度降低导致燃料燃烧不充分，尾气中的氮氧化物等有害物质含量更高。此外，行车时间延长也会导致污染物排放量增加，从而造成空气污染和气候变化。这反过来又会影响身体健康，对公众健康构成重大挑战（Nadrian 等人，2019 年，2020 年）。

To address the problem of traffic congestion, researchers are exploring various new technologies and methods (Jan et al., 2019; Sills, 2018; Wang et al., 2020). With the emergence of unmanned aerial vehicles (UAVs), efforts are being made to extend urban transportation from the ground to the air (Qu et al., 2022). The concept of Advanced Air Mobility (AAM) has been jointly proposed by the Federal Aviation Administration (FAA) and the National Aeronautics and Space Administration (NASA) in USA, with the aim of developing an aviation transportation system that uses electric aircraft to transport passengers and cargo (Federal Aviation Administration (FAA), 2020). Urban Air Mobility (UAM) is a subset of AAM that includes a set of rules, procedures, and technologies that enable the operation of airborne passenger and cargo traffic in urban environments. Extensive research efforts have already focused on various aspects of UAM, leading to significant advances in airspace planning (Bauranov and Rakas, 2021), market demand assessment (Long et al., 2023), and aircraft design (Piccinini et al., 2020).
为解决交通拥堵问题，研究人员正在探索各种新技术和新方法（Jan 等人，2019 年；Sills，2018 年；Wang 等人，2020 年）。随着无人驾驶飞行器（UAV）的出现，人们正在努力将城市交通从地面延伸到空中（Qu 等人，2022 年）。美国联邦航空管理局（FAA）和美国国家航空航天局（NASA）联合提出了先进空中交通（AAM）的概念，旨在开发一种使用电动飞机运送乘客和货物的航空运输系统（联邦航空管理局（FAA），2020 年）。城市航空交通系统（UAM）是航空交通系统的一个子集，包括一整套规则、程序和技术，使空中客货运输能够在城市环境中运行。大量的研究工作已经集中在城市空中交通的各个方面，从而在空域规划（Bauranov 和 Rakas，2021 年）、市场需求评估（Long 等人，2023 年）和飞机设计（Piccinini 等人，2020 年）方面取得了重大进展。

In 2016, Uber released a white paper that provides a comprehensive outline of the use of vertical electric take-off and landing aircraft (eVTOL) to transport passengers within urban environment (Holden and Goel, 2016). The document explicitly outlined the main challenges facing the implementation of eVTOL operations, one of them being the establishment of vertical take-off and landing (VTOL) infrastructure. In 2023, the FAA issued the “Advanced Air Mobility Implementation Plan”, aiming to achieve the required infrastructure elements and procedural measures, including the VTOL infrastructure setup, necessary for scaled AAM operations by 2028 (FAA, 2023a). A recent study has compared the UAM systems in the metropolitan areas in USA and China (Wang et al., 2023). VTOL infrastructure serves as the ground-based foundation for eVTOL operations, encompassing activities such as takeoffs, landings, passenger embarkation, and charging. Given the constraints posed by intensive land use in urban areas, community acceptance, and construction costs, establishing densely distributed VTOL facilities to facilitate door-to-door eVTOL operations is not feasible. Consequently, a single journey UAM comprises three distinct segments, as shown in Fig. 1. Sequentially, these segments consist of ground transportation from the position of departure to the VTOL take-off site (commonly referred to as the “first mile”), airborne transportation from the VTOL take-off site to the VTOL landing site, and finally, ground transportation from the VTOL landing site to the destination (commonly referred to as the “last mile”). As such, strategic placement of the VTOL infrastructure profoundly impacts the safe, efficient, and orderly operation of eVTOLs within the urban environment. The location of the VTOL infrastructure is also fundamental for research on eVTOL flight routes. Therefore, a well-distributed network of VTOL infrastructure is of great significance for the continued advancement of UAM.
2016 年，Uber 发布了一份白皮书，全面概述了使用垂直电动起降飞机（eVTOL）在城市环境中运送乘客的情况（Holden 和 Goel，2016 年）。该文件明确概述了实施 eVTOL 运营所面临的主要挑战，其中之一就是建立垂直起降（VTOL）基础设施。2023 年，美国联邦航空局发布了 "先进空中机动性实施计划"，旨在到 2028 年实现所需的基础设施要素和程序措施，包括垂直起降（VTOL）基础设施的设置，这对于大规模的 AAM 运营是必不可少的（美国联邦航空局，2023a）。最近的一项研究比较了美国和中国大都市地区的无人机空中交通系统（Wang 等人，2023 年）。VTOL 基础设施是 eVTOL 运营的地面基础，包括起飞、着陆、乘客登机和充电等活动。鉴于城市地区密集的土地使用、社区接受度和建设成本所带来的限制，建立密集分布的 VTOL 设施以促进门到门的 eVTOL 运营并不可行。因此，如图 1 所示，单程 UAM 由三个不同的部分组成。这些航段依次包括从起飞地点到 VTOL 起飞地点的地面运输（通常称为 "第一英里"）、从 VTOL 起飞地点到 VTOL 降落地点的空中运输，以及最后从 VTOL 降落地点到目的地的地面运输（通常称为 "最后一英里"）。因此，VTOL 基础设施的战略布局对 eVTOL 在城市环境中的安全、高效和有序运行影响深远。VTOL 基础设施的位置也是研究 eVTOL 飞行路线的基础。因此，一个分布合理的 VTOL 基础设施网络对继续推进无人机空中作业具有重要意义。

According to Amap's “China Major City Traffic Analysis Report Q2 2022”, Shenzhen ranks first in suboptimal urban traffic health (AutoNavi, 2022). The “Ratio of Mileage in Frequently Congested Road Sections” index is relatively high in Shenzhen. On the Xiangmi Lake Road (south to north) during workdays, the accumulated severe congestion time reached 144 h, equivalent to an average daily severe congestion of 2.3 h. Follow closely along Henan Road (east to west) with a cumulative severe congestion time of 127 h. In 2023, Shenzhen, for the first time in its government work report, introduced the concept of developing the “low-altitude economy”, with the aim of establishing a center for the low-altitude economy and creating a civil UAV test zone. Multiple UAV companies are collaborating to facilitate the high-quality development of Shenzhen's low-altitude economy. For example, Shanghai Peak Fly Aviation Technology Co., Ltd. plans to inaugurate the world's first eVTOL route in Shenzhen in October 2023 (Shenzhen China, 2023). Although there have been numerous studies on the selection of VTOL sites, few have considered whether designated locations meet the required clearances for safe eVTOL takeoffs and landings. Although eVTOLs can take off and land vertically. For safety reasons, normal departure and arrival procedures for passenger-carrying eVTOLs or large eVTOLs require transitional surfaces. A NASA report on various aspects of vertiports has highlighted that the initial step in physical considerations should be identifying the obstacle clearance of existing structures for takeoff and landing (Mendonca et al., 2022). Here, we propose a novel method to determine optimal locations within the city of Shenzhen to establish VTOL sites. Specifically, our research incorporates considerations of three-dimensional airspace availability when choosing VTOL site locations. Within a two-dimensional (2D) space, we leverage GIS tools to initially exclude drone-restricted areas within Shenzhen, ensuring that eVTOL operations comply with regulatory regulations. Subsequently, we exclude occupied areas, such as buildings and zones unsuitable for VTOL site construction, such as parks, and identify remaining areas suitable for VTOL site construction. Uber has also highlighted the possibility of establishing VTOL sites on building rooftops; thus, we identify locations with sufficiently large rooftop surfaces. Subsequently, we established an obstacle assessment model for the VTOL site approach, departure, and transitional surfaces. Using location sites that satisfy 2D planar availability, we further refine our selection. The model outputs VTOL site locations that meet requirements for obstacle clearance during approach and departure, along with corresponding angles for approach and departure trajectories. Finally, we establish an integer programming model, incorporating the identified alternate locations and our processed UAM candidate routes. The model ultimately determines the optimal locations of the VTOL sites, the number of UAM trips, and the mode of transport for the access of passengers to and from the VTOL sites.
根据高德软件（Amap）发布的《2022 年第二季度中国主要城市交通分析报告》，深圳在城市交通健康度方面排名第一（高德软件，2022 年）。深圳的 "常堵路段里程比 "指数相对较高。工作日香蜜湖路（南往北）累计严重拥堵时间达 144 小时，相当于日均严重拥堵 2.3 小时。紧随其后的河南路（由东向西），累计严重拥堵时间为 127 h。2023年，深圳在政府工作报告中首次提出发展 "低空经济 "的概念，旨在建立低空经济中心，打造民用无人机试验区。多家无人机企业合作，推动深圳低空经济高质量发展。例如，上海峰飞航空科技有限公司计划于 2023 年 10 月在深圳开通全球首条 eVTOL 航线（中国深圳，2023 年）。尽管对 VTOL 场址的选择进行了大量研究，但很少有人考虑过指定地点是否满足 eVTOL 安全起降所需的净空要求。虽然 eVTOL 可以垂直起降。出于安全考虑，载客 eVTOL 或大型 eVTOL 的正常起飞和到达程序需要过渡表面。美国国家航空航天局（NASA）一份关于垂直起降港各个方面的报告强调，物理考虑的第一步应该是确定现有结构在起飞和降落时的障碍物间隙（Mendonca 等人，2022 年）。在此，我们提出了一种新方法来确定深圳市内建立 VTOL 场址的最佳位置。具体来说，我们的研究在选择 VTOL 场址时考虑了三维空域的可用性。在二维（2D）空间内，我们利用地理信息系统（GIS）工具，首先排除深圳市内的无人机禁飞区，确保电子无人机的运营符合监管规定。随后，我们将建筑物等占用区域和公园等不适合建造 VTOL 场址的区域排除在外，并确定其余适合建造 VTOL 场址的区域。Uber 还强调了在建筑物屋顶建立 VTOL 站点的可能性；因此，我们确定了具有足够大屋顶面积的地点。随后，我们为 VTOL 场址的进场、离场和过渡表面建立了障碍物评估模型。利用满足二维平面可用性的地点，我们进一步完善了我们的选择。该模型可输出符合进场和离场期间障碍物清除要求的 VTOL 场址位置，以及进场和离场轨迹的相应角度。最后，我们建立了一个整数编程模型，将已确定的备用地点和已处理的 UAM 候选路线纳入其中。该模型最终确定了 VTOL 场址的最佳位置、UAM 行程数量以及乘客往返 VTOL 场址的交通方式。

The remainder of this paper is organized as follows. Section 2 reviews the relevant studies on the VTOL site location problem; Section 3 describes the assumptions, parameters, and modeling process of the study; Section 4 shows the results of our model and the sensitivity analysis of the relevant parameters; Section 5 explores the effects of three key factors on the modeling results: the number of VTOL sites, the transfer time, and the cost of eVTOL; and Section 6 concludes the study and discusses the direction of future research.
本文的其余部分安排如下。第 2 节回顾了关于 VTOL 场址定位问题的相关研究；第 3 节介绍了研究的假设、参数和建模过程；第 4 节展示了我们的模型结果和相关参数的敏感性分析；第 5 节探讨了三个关键因素对模型结果的影响：VTOL 场址数量、转移时间和 eVTOL 成本；第 6 节总结了本研究并讨论了未来的研究方向。

2. Literature review 2.文献综述

There is increasing interest in the study of the location of VTOL sites. In Lim and Hwang (2019), the authors focused on the three most congested commuter routes in the Seoul metropolitan area. A k-means clustering algorithm was developed based on commuting data represented by latitude and longitude coordinates, and the centroids of the resulting clusters are as VTOL site locations. A UAM traffic demand analysis for commuters across the bay in the San Francisco Bay Area is presented in Bulusu et al. (2021). Rational constraints for the cost of constructing additional VTOL sites and capacity limits were developed to determine the upper and lower limits for the number of VTOL sites. Iteratively, a k-means cluster was applied to identify the distribution of the VTOL site that maximizes passenger volume while adhering to time-saving thresholds. The work in Rath and Chow (2022) addressed the selection of landing points for aerial taxis bound for the three major airports of New York City. A Revenue Distance Ratio (RDR) model was formulated that aimed to maximize the flow of passengers from aircraft taxis and an REV (revenue) model aimed at maximizing the income of aircraft taxis. Three pricing scenarios were established, and the optimal locations of the VTOL sites were computed on the basis of these models and objectives. The results indicated that the locations of the VTOL sites exhibit high sensitivity to different pricing scenarios. The REV model provided a more fair distribution of the demand for and income allocation of the VTOL sites. Each of the aforementioned studies aimed to determine rational locations of the VTOL sites to meet specific needs or within localized regions. They also considered various associated parameters in their analyses.
人们对 VTOL 站点选址的研究兴趣与日俱增。在 Lim 和 Hwang（2019）一文中，作者重点研究了首尔大都市区三条最拥堵的通勤路线。他们根据以经纬度坐标表示的通勤数据开发了一种 k-means 聚类算法，并将聚类结果的中心点作为 VTOL 站点的位置。Bulusu 等人（2021 年）对旧金山湾区跨海湾通勤者的 UAM 交通需求进行了分析。对增建 VTOL 站点的成本和容量限制进行了合理约束，以确定 VTOL 站点数量的上限和下限。通过迭代法，应用 k-means 聚类来确定 VTOL 站点的分布，从而在遵守节省时间阈值的同时使乘客量最大化。Rath 和 Chow（2022 年）的研究解决了前往纽约市三大机场的空中出租车着陆点的选择问题。他们建立了一个收入距离比（RDR）模型和一个 REV（收入）模型，前者旨在最大化飞机出租车的乘客流量，后者旨在最大化飞机出租车的收入。根据这些模型和目标，确定了三种定价方案，并计算了 VTOL 站点的最佳位置。结果表明，VTOL 站点的位置对不同的定价方案非常敏感。REV 模型为 VTOL 场址的需求和收入分配提供了更公平的分配。上述每项研究都旨在确定合理的 VTOL 用地位置，以满足特定需求或在局部区域内使用。他们在分析中还考虑了各种相关参数。

In another line of research, researchers have investigated the locations of VTOL sites from other perspectives. For example, it is assumed that the UAM demand is distributed across an entire metropolitan area. The entire region is then modeled as a grid and VTOL sites can be established in each cell of the grid (Chen et al., 2022). A subset of p VTOL sites from these cells has been selected as hubs to minimize overall transportation costs. The Weighted Linear Combination (WLC) method is used to select suitable areas for UAM ground infrastructure in combination with Geographic Information Systems information (Fadhil, 2018). The weights for WLC were determined through expert interviews and the analytical hierarchy process-Delphi method. In Daskilewicz et al. (2018), the demand for UAM is estimated using the American Community Survey and household employment statistics, and an integer programming model is formulated to set the locations of the VTOL sites that maximize time savings compared to car travel. A hub location model is developed that considers the risk of air collisions when determining optimal VTOL site locations and demand distribution for an aerial taxi transport network (Sinha and Rajendran, 2023). The model aimed to minimize the total cost composed of travel, facility, and collision risk costs. Based on previous studies on aerial taxi demand, the study in Sinha and Rajendran (2022) used the Clustering LARge Applications (CLARA) algorithm to identify 14 VTOL locations. These VTOL locations were gradually opened in multiple stages that are optimized by an integer programming model considering parameters such as rental costs and road facility convenience. In Wang et al. (2022), UAM demand is generated by scaling taxi demand to study the vertiport planning problem. An adaptive discretization approach was developed to find the optimal solution of the model.
在另一项研究中，研究人员从其他角度调查了 VTOL 场址的位置。例如，假设 UAM 需求分布在整个大都市地区。然后将整个区域建模为一个网格，并在网格的每个单元建立 VTOL 站点（Chen 等人，2022 年）。从这些单元中选择 p 个 VTOL 站点的子集作为枢纽，以最大限度地降低总体运输成本。加权线性组合（WLC）方法用于结合地理信息系统信息为 UAM 地面基础设施选择合适的区域（Fadhil，2018 年）。WLC 的权重是通过专家访谈和层次分析法-德尔菲法确定的。在 Daskilewicz 等人（2018 年）的研究中，利用美国社区调查和家庭就业统计数据估算了对 UAM 的需求，并制定了一个整数编程模型，以设定与汽车旅行相比可最大限度节省时间的 VTOL 场址位置。在确定空中出租车运输网络的最佳 VTOL 站点位置和需求分布时，考虑了空中碰撞的风险，开发了一个枢纽位置模型（Sinha 和 Rajendran，2023 年）。该模型旨在最大限度地降低由旅行成本、设施成本和碰撞风险成本组成的总成本。基于之前对空中出租车需求的研究，Sinha 和 Rajendran（2022 年）的研究使用聚类 LARge 应用（CLARA）算法确定了 14 个 VTOL 位置。考虑到租金成本和道路设施的便利性等参数，这些 VTOL 位置分多个阶段逐步开放，并通过整数编程模型进行优化。在 Wang 等人（2022 年）的研究中，UAM 需求是通过缩放出租车需求生成的，用于研究 vertiport 规划问题。他们开发了一种自适应离散化方法来寻找模型的最优解。

VTOL site selection can be modeled as an enhanced single-allocation p-hub median location problem (Willey and Salmon, 2021). Subgraph isomorphism can be used to identify optimal VTOL site locations considering vehicle constraints and operational strategies, especially for trips involving more than two aerial ports. In Ploetner et al. (2020), the Munich metropolitan area agent-based microsimulation model (MITO) is used to estimate the 2030 traffic demand. A total of three possible demand scenarios are proposed that represent high, medium, and low density demand. The three associated VTOL site networks consisting of 130, 74, and 24 VTOL sites were developed, respectively (Willey and Salmon, 2021). In Rajendran and Zack (2019), a two-stage approach is proposed to solve the problem of the location of the aerial taxi infrastructure. The authors first filtered conventional taxi customers as potential aerial taxi users and used an iterative k-means clustering algorithm to identify the locations of the VTOL site. To improve the quality of initial seed solutions in k-means, the fitness of candidate sites is first calculated based on the percentage of satisfied customer demands, and the top ten candidate locations are used as input for the k-means algorithm. Compared to traditional k-means, this algorithm runs efficiently by generating a significantly fewer number of clusters, thus limiting the number of VTOL site locations. A later work extended the work in Rajendran and Zack (2019) from a single-objective decision to include five socioeconomic factors (Sinha and Rajendran, 2022). A group of potential sites were ranked using a weighted average, and the top five sites with the highest total scores were used as initial inputs for the k-means algorithm. The results showed better performance with smaller Davies–Bouldin index (DBI) values, indicating better clustering with smaller intra-cluster distances and larger inter-cluster distances. An interesting study can be found in Peng et al. (2022), in which a k-medoids clustering algorithm is developed to divide potential UAM user origin-destination pairs into completely connected main zones. The number of main zones is the maximum of zones that meet all UAM aggregated time constraints. The number of VTOL sites in each main zone was increased until capacity limits were met. Then an integer programming model was formulated, combining a constrained clustering of k-medoids to allocate demand to VTOL sites and determine their locations. This method yielded a network consisting of 6 main zones and 116 VTOL sites in the San Francisco Bay Area. Of the 16,308 UAM trips selected, 78% saved travel time, with an average time savings of 27 min compared to driving.
VTOL 场址选择可建模为增强型单分配 p 枢纽中值位置问题（Willey 和 Salmon，2021 年）。考虑到车辆限制和运营策略，尤其是涉及两个以上航空港的行程，子图同构可用于确定最佳 VTOL 场址位置。Ploetner 等人（2020 年）使用慕尼黑大都市区代理微观模拟模型 (MITO) 估算 2030 年的交通需求。共提出了三种可能的需求情景，分别代表高、中、低密度需求。三个相关的 VTOL 站点网络分别由 130、74 和 24 个 VTOL 站点组成（Willey 和 Salmon，2021 年）。Rajendran 和 Zack（2019 年）提出了一种两阶段方法来解决空中出租车基础设施的选址问题。作者首先将传统出租车客户筛选为潜在的空中出租车用户，并使用迭代 k-means 聚类算法来确定 VTOL 站点的位置。为了提高 k-means 中初始种子解的质量，首先根据满足客户需求的百分比计算候选地点的合适度，然后将前十个候选地点作为 k-means 算法的输入。与传统的 k-means 算法相比，该算法生成的聚类数量大大减少，从而限制了 VTOL 场址的数量，从而提高了运行效率。后来的一项工作将 Rajendran 和 Zack（2019 年）的工作从单一目标决策扩展到包括五个社会经济因素（Sinha 和 Rajendran，2022 年）。采用加权平均法对一组潜在地点进行排序，将总分最高的前五个地点作为 k-means 算法的初始输入。结果表明，戴维斯-博尔丁指数（DBI）值越小，性能越好，表明簇内距离越小，簇间距离越大，聚类效果越好。Peng 等人（2022 年）进行了一项有趣的研究，开发了一种 k-medoids 聚类算法，将潜在的 UAM 用户出发地-目的地对划分为完全相连的主要区域。主区域的数量是满足所有 UAM 聚合时间限制的区域的最大值。每个主区的 VTOL 站点数量不断增加，直到满足容量限制。然后制定一个整数编程模型，结合 k-medoids 的约束聚类，将需求分配给 VTOL 站点并确定其位置。这种方法得出了一个由旧金山湾区 6 个主要区域和 116 个 VTOL 站点组成的网络。在选定的 16,308 次 UAM 旅行中，78% 节省了旅行时间，与驾车相比平均节省 27 分钟。

These studies extended single-demand scenarios to include various demands, resulting in VTOL site networks that can adapt to a wide range of travel needs. However, it is important to note that the locations of the VTOL sites derived from these studies are results of mathematical models. Despite considering the geographical restrictions of the real world in 2D space, the suitability of potential vertiports for take-off and landing has not been evaluated.
这些研究将单一需求情景扩展到各种需求，从而形成了能够适应各种旅行需求的 VTOL 站点网络。不过，需要注意的是，这些研究得出的 VTOL 场址位置都是数学模型的结果。尽管考虑到现实世界在二维空间中的地理限制，但尚未对潜在垂直起降点的适宜性进行评估。

There are studies that have considered the availability of space when selecting VTOL site locations. In Jeong et al. (2021), the authors used the iteration of k-means to determine the positions of the VTOL sites and used satellite imagery to assess the results of each grouping. If a chosen location is in a restricted area such as a green zone, the clustering process is repeated until all positions suitable for VTOL site construction are found. In Brühl et al. (2023), the authors calculated the total area required to establish a VTOL site based on the quantity and area of facilities, equipment, and road surfaces. Whether the location has sufficient area has to be determined. Then a hub-and-spoke network of VTOL sites will be devised based on eVTOL operational characteristics. In Wu and Zhang (2021), the authors used laser radar data and land usage information as input for the network design model and found the basis for identifying available ground areas for the recognition of the VTOL site. These studies considered ground availability when determining the location of the VTOL site, enabling research results to be more aligned with practical operations.
有些研究在选择 VTOL 站点位置时考虑了空间的可用性。在 Jeong 等人（2021 年）的研究中，作者使用 k-means 的迭代来确定 VTOL 场址的位置，并使用卫星图像来评估每次分组的结果。如果所选位置位于绿化带等限制区域，则重复聚类过程，直到找到适合建造 VTOL 场址的所有位置。在 Brühl 等人（2023 年）的研究中，作者根据设施、设备和路面的数量和面积计算了建立 VTOL 场址所需的总面积。必须确定该地点是否有足够的面积。然后，根据 eVTOL 的运行特点，设计一个由 VTOL 场址组成的辐辏网络。在 Wu 和 Zhang（2021 年）的研究中，作者使用激光雷达数据和土地使用信息作为网络设计模型的输入，为识别 VTOL 场址找到了确定可用地面面积的依据。这些研究在确定 VTOL 场址位置时考虑了地面可用性，使研究结果与实际操作更加一致。

However, VTOL sites serve as the link between road-side passengers and aerial eVTOL operations. In addition to satisfying the availability in the 2D space, the airspace at the chosen location must also provide eVTOL approach and departure routes that meet obstacle clearance requirements, ensuring safe takeoff and landing. Therefore, determining the locations of the VTOL sites that fulfill three-dimensional spatial availability deserves further research efforts.
然而，VTOL 场址是连接路边乘客和空中 eVTOL 运营的纽带。除了满足二维空间的可用性外，所选地点的空域还必须提供符合障碍物净空要求的 eVTOL 进场和离场路线，以确保安全起飞和着陆。因此，确定满足三维空间可用性的 VTOL 场址位置值得进一步研究。

Since taxis are greatly affected by ground traffic congestion, we focused on taxi users as the primary candidates for transitioning to UAM services. Therefore, the travel demand for UAM is derived from the operational data of the taxi. The data set obtained covers all time periods within a day and spans the entire geographic range of Shenzhen, covering various travel purposes such as commuting, leisure, and medical needs. We utilized GIS tools to identify potential 2D locations for the VTOL site, and establish an obstacle assessment model for the VTOL site approach and departure paths. This model aided in further refinement of the selection of potential site locations. We incorporate the potential locations into the input of an integer programming model to determine the final locations for the establishment of the VTOL sites. The established network not only captures diverse travel demands, but also meets three-dimensional spatial availability at each VTOL site location. We conducted sensitivity analyzes on the number of VTOL sites, transfer time, and eVTOL pricing, discussing the impacts on the location and design of the VTOL site. The approach presented in the document improves the feasibility of urban air traffic and provides a reference for the preliminary planning of UAM in a designated area.
由于出租车受地面交通拥堵的影响很大，我们将出租车用户作为过渡到 UAM 服务的主要候选者。因此，UAM 的出行需求来自出租车的运营数据。所获得的数据集涵盖了一天内的所有时间段，跨越了深圳的整个地理范围，涵盖了通勤、休闲和医疗需求等各种出行目的。我们利用地理信息系统工具确定了 VTOL 站点的潜在 2D 位置，并建立了 VTOL 站点进场和离场路径的障碍物评估模型。该模型有助于进一步完善潜在地点的选择。我们将潜在地点纳入整数编程模型的输入，以确定建立 VTOL 场址的最终地点。所建立的网络不仅能满足不同的旅行需求，还能满足每个 VTOL 站点位置的三维空间可用性。我们对 VTOL 站点数量、换乘时间和 eVTOL 定价进行了敏感性分析，讨论了对 VTOL 站点位置和设计的影响。文件中提出的方法提高了城市空中交通的可行性，为指定区域内无人机空中交通的初步规划提供了参考。

3. Methodology 3.方法论

3.1. Assumptions 3.1.假设

The following assumptions are made.
假设如下

(1)
Only taxi passengers are considered as potential customers who may shift to UAM services. This is because UAM trips are chosen to reduce the negative impacts of traffic congestion. Among the various modes of public transportation, buses have dedicated lanes, shared electric vehicles, shared bicycles, and subways are almost unaffected by traffic congestion, only taxis are most affected by road conditions.
只有出租车乘客才会被视为可能转用统一行车路线服务的潜在客户。这是因为选择 UAM 行程是为了减少交通拥堵的负面影响。在各种公共交通工具中，公交车有专用车道，共享电动车、共享自行车和地铁几乎不受交通拥堵的影响，只有出租车受路况的影响最大。
(2)
This study assumes that each UAM trip involves only two VTOL sites used, respectively, for take-off and landing, and does not consider inserting an additional VTOL site between them for transfer. Passengers choose UAM because it is time-saving, while additional transfer will increase the time of UAM trips. Additionally, in the early stages of establishing a new mode of transportation, an overly complex infrastructure network is not recommended.
本研究假設每次無障礙運輸只涉及兩個分別用作起飛和降落的虛擬機場，而沒有考慮在兩者之間加設一個虛擬機場作轉機之用。乘客选择 UAM 的原因是它节省时间，而额外的换乘会增加 UAM 旅程的时间。此外，在建立一种新的运输方式的初期阶段，不建议建立过于复杂的基础设施网络。
(3)
Four transport modes are considered for each ground segment of a UAM trip: taxi, shared electric bike, shared bicycle, and walking. The speed of each mode is assumed to be constant and is not affected by traffic condition.
UAM 行程的每个地面段都考虑了四种交通模式：出租车、共享电动自行车、共享自行车和步行。假定每种交通方式的速度恒定，不受交通状况的影响。
(4)
In this study, the range and endurance limitations of eVTOL are not considered. Since the geographic scope of this study is within the city of Shenzhen, the flight distance between any two VTOL sites is relatively short. Thus, the endurance of eVTOL is sufficient to perform any single flight mission. The range and flight-time limitations should be considered in a larger area, such as the cross-city operation of eVTOL.
本研究未考虑 eVTOL 的航程和续航能力限制。由于本研究的地理范围在深圳市内，任何两个 VTOL 站点之间的飞行距离都相对较短。因此，eVTOL 的续航时间足以执行任何单次飞行任务。在更大的范围内，如 eVTOL 的跨城市运行，应考虑航程和飞行时间的限制。
(5)
This study does not consider the capacity constraints of the VTOL site and the limitations of the eVTOL fleet size.
这项研究没有考虑 VTOL 场址的容量限制和 eVTOL 机队规模的限制。

3.2. Determination of potential UAM trips
3.2.确定潜在的不结盟运动行程

According to Assumption (1), this study only considers passengers traveling by taxi as potential customers who can use UAM services. The taxi data used in this study is from a study by Wang et al. (2019), which provides all the Global Positioning System GPS(GPS) data of taxis in Shenzhen on a certain day. Each piece of data includes information such as taxi ID, time, latitude, longitude, and passenger-carrying status. The raw data are processed as a passenger-carrying trip, which is presented in the format of vehicle identification, origin latitude and longitude, destination latitude and longitude, and travel time. Although the airborne flight segment of UAV services is characterized by high speed and free from traffic congestion, the total time involved in UAM services includes both the ground transport of approaching and departing from VTOL sites, as well as the transfer time. As a result, passengers who experience longer taxi travel times are more likely to consider switching to UAM services. Here, we set a threshold of 30 min. Taxi trips with a duration shorter than the threshold are considered unlikely to opt for eVTOL travel. Ultimately, a total of 46,537 taxi trips were retained as potential UAM journeys.
根据假设（1），本研究仅将乘坐出租车的乘客视为可以使用 UAM 服务的潜在客户。本研究使用的出租车数据来自 Wang 等人（2019）的一项研究，该研究提供了某一天深圳所有出租车的全球定位系统 GPS（GPS）数据。每条数据都包括出租车 ID、时间、经纬度和载客状态等信息。原始数据经过处理后作为载客行程，以车辆标识、起点经纬度、终点经纬度和行驶时间的格式呈现。虽然无人机服务的空中飞行段具有高速和无交通拥堵的特点，但无人机服务涉及的总时间包括接近和离开 VTOL 站点的地面交通以及换乘时间。因此，乘坐出租车时间较长的乘客更有可能考虑改乘 UAM 服务。在此，我们将阈值设定为 30 分钟。短于该临界值的出租车行程被认为不太可能选择 eVTOL 旅行。最终，共有 46,537 次出租车行程被保留为潜在的 UAM 行程。

In fact, the Assumption (1) is a very strong one on the potential UAM passengers. There are other methods to generate UAM demands, such as the grid-based method (Chen et al., 2022). To relax this assumption, we used a similar approach in Wang et al. (2022). To capture the demand for UAM, we must supplement existing data. Since origin-destination (OD) data are not uniformly distributed in terms of space and time, the data we generate should match the distribution of the real data. Here, we employ the Copulas statistical method, which allows us to generate new samples that match the actual data patterns. First, Copulas collects and analyzes real OD data to determine the marginal distribution and the correlation structure between them. Then, the marginal distributions and correlation structures are modeled. The Copulas model considers the dependencies between the variables, which allows the generated data to retain the correlation patterns of the original data. Once the copulas model is built, we can use this model to generate synthetic OD data. The generated data will retain marginal distributions and correlation structures similar to those of the real data, thus statistically matching the real data. We use this method to expand the original volume of taxi data by various multiples (that is, twice, three times, four times, and five times the current taxi data) to simulate the demand for all modes of transportation.
事实上，假设（1）对潜在的 UAM 乘客来说是一个非常强有力的假设。还有其他方法可以生成 UAM 需求，如基于网格的方法（Chen 等人，2022 年）。为了放宽这一假设，我们采用了 Wang 等人（2022 年）的类似方法。为了捕捉 UAM 需求，我们必须补充现有数据。由于出发地-目的地（OD）数据在空间和时间上并非均匀分布，因此我们生成的数据应与真实数据的分布相匹配。在此，我们采用了 Copulas 统计方法，该方法可以生成与实际数据模式相匹配的新样本。首先，Copulas 收集并分析真实的 OD 数据，以确定边际分布和它们之间的相关结构。然后，对边际分布和相关结构进行建模。Copulas 模型会考虑变量之间的依赖关系，从而使生成的数据保留原始数据的相关模式。一旦建立了 Copulas 模型，我们就可以使用该模型生成合成 OD 数据。生成的数据将保留与真实数据类似的边际分布和相关结构，从而在统计上与真实数据相匹配。我们用这种方法将原有的出租车数据量扩大不同倍数（即现有出租车数据的两倍、三倍、四倍和五倍），以模拟所有交通方式的需求。

3.3. Determination of potential locations for VTOL sites
3.3.确定 VTOL 场址的可能位置

3.3.1. Location availability in 2D space
3.3.1.二维空间中的位置可用性

A VTOL site consists of a collection of buildings and facilities, designated for eVTOL takeoff and landing, passenger embarkation and disembarkation, as well as all related operations within a specific area. The feasibility of establishing a VTOL site in a given area depends primarily on the availability of suitable space. To filter potential VTOL areas, we collected shapefiles containing spatial data for Shenzhen's administrative boundaries, buildings, road networks, water bodies, parks, scenic areas, no-fly zones for drones, etc. To establish ground-based VTOL pads, GIS tools were used to exclude areas already occupied, such as buildings, and locations not suitable for VTOL site establishment, such as no-fly zones for drones within Shenzhen. According to FAA guidelines, a regular hexagon with a short diagonal of 500 feet can provide sufficient space available for a VTOL site (Wu and Zhang, 2021). Thus, the remaining areas were densely covered with hexagons, and the centroids of these hexagons were chosen as candidate VTOL site locations. We also explored the potential of constructing VTOL sites on rooftops, inspired by Uber's concept.
VTOL 场址由一系列建筑物和设施组成，指定用于电子 VTOL 起飞和着陆、乘客登机和下机，以及特定区域内的所有相关操作。在特定区域建立 VTOL 场址的可行性主要取决于是否有合适的空间。为了筛选潜在的 VTOL 区域，我们收集了包含深圳行政边界、建筑物、道路网络、水体、公园、风景区、无人机禁飞区等空间数据的形状文件。为了建立地面 VTOL 停机坪，利用 GIS 工具排除了已被占用的区域（如建筑物）和不适合建立 VTOL 停机坪的地点（如深圳境内的无人机禁飞区）。根据美国联邦航空局的指导方针，一个对角线短 500 英尺的规则六边形可以为 VTOL 场地提供足够的可用空间（Wu 和 Zhang，2021 年）。因此，我们在其余区域密集布设了六边形，并选择这些六边形的中心点作为 VTOL 场址的候选地点。受 Uber 概念的启发，我们还探索了在屋顶建造 VTOL 站点的可能性。

3.3.2. Location filtering for three-dimensional (3D) spatial availability
3.3.2.三维（3D）空间可用性的位置过滤

VTOL sites serve as the location for the take-off and landing of eVTOL aircraft. Therefore, establishing suitable VTOL site locations requires not only available planar space, but also three-dimensional conditions that satisfy the obstacle avoidance requirements for eVTOL take-off and landing operations. In particular, according to the China Skyscraper City Ranking as of April 2023, Shenzhen ranks first nationwide in terms of the number of buildings taller than 200 and 300 m. Therefore, it is essential to consider the aerial conditions for the establishment of the VTOL sites in Shenzhen. A recent publication by the FAA outlines the design standards for VTOL sites, encompassing the geometry and dimensions of the surface and area used for eVTOL takeoff and landing, as well as approach and departure paths, along with requirements for markings, lighting, and navigational aids (FAA, 2023b). In particular, the dimensions of the Touchdown and Liftoff Area (TLOF), the Final Approach and Takeoff Area (FATO) and the Safety Area are based on the control dimension D (diameter of a circle that encompasses the entire aircraft) of the reference eVTOL. They are squares whose geometric centers coincide and measured with dimensions of 1D, 2D, and 3D, respectively. The design requirements for the approach/departure and transitional surface are illustrated in three views in Fig. 2, with the main view, left view, legend and top view in clockwise from the top left. Each FATO should have at least two obstacles-free approach/departure paths, maintaining a minimum separation of 135° between them.
VTOL 场址是 eVTOL 飞机起飞和着陆的地点。因此，建立合适的 VTOL 场址不仅需要可用的平面空间，还需要满足 eVTOL 起飞和着陆操作的避障要求的三维条件。特别是，根据截至 2023 年 4 月的 "中国摩天城市排行榜"，深圳 200 米和 300 米以上高层建筑数量均居全国首位。因此，在深圳建立 VTOL 场址必须考虑空中条件。美国联邦航空局（FAA）最近发布的一份出版物概述了 VTOL 场址的设计标准，包括用于 eVTOL 起飞和着陆的表面和区域的几何形状和尺寸，以及进场和离场路径，以及对标识、照明和导航辅助设备的要求（FAA，2023b）。特别是，着陆和升空区域 (TLOF)、最终进场和起飞区域 (FATO) 以及安全区域的尺寸是基于参考 eVTOL 的控制尺寸 D（包含整个飞机的圆的直径）。它们是几何中心重合的正方形，测量尺寸分别为一维、二维和三维。进场/离场面和过渡面的设计要求在图 2 中以三视图说明，从左上方顺时针依次为主视图、左视图、图例和俯视图。每个 FATO 至少应有两条无障碍进场/离场通道，两通道之间的最小间隔为 135°。

Following FAA regulations, we developed a VTOL site approach and departure path obstacle assessment model. The geometric center of the FATO, obtained from the locations identified in Section 3.3.1, was used as input for the model. Combining it with shapefile data containing elevation information for all buildings in Shenzhen, we evaluated whether the FATO associated with each location had unobstructed approach and departure paths as well as transition areas. The model output consisted of locations that satisfied eVTOL take-off and landing obstacle clearance requirements, along with the orientations of the approach and departure trajectories that met obstacle clearance criteria. The reference eVTOL chosen for this analysis was the unmanned EH216-S aircraft. Based on the “Special Conditions for the EHang EH216-S Unmanned Aircraft System” issued by the Civil Aviation Administration of China (CAAC), the control dimension D of the EH216-S aircraft is 5.63 m (Civil Aviation Administration of China (CAAC), 2022). This information was used to ensure that the designed FATO could accommodate the reference aircraft without violating safety regulations.
根据美国联邦航空局的规定，我们开发了一个 VTOL 场地进场和离场路径障碍物评估模型。从第 3.3.1 节中确定的地点获得的 FATO 几何中心被用作模型的输入。结合包含深圳所有建筑物高程信息的 shapefile 数据，我们评估了与每个地点相关的 FATO 是否具有畅通无阻的进场和离场路径以及过渡区域。模型输出包括满足 eVTOL 起飞和着陆障碍物清除要求的地点，以及符合障碍物清除标准的进场和离场轨迹方向。本次分析选择的参考 eVTOL 是无人驾驶的 EH216-S 飞机。根据中国民用航空局（CAAC）发布的《易航 EH216-S 无人驾驶航空器系统专用条件》，EH216-S 飞机的控制尺寸 D 为 5.63 米（中国民用航空局（CAAC），2022 年）。这一信息用于确保所设计的 FATO 能够在不违反安全规定的情况下容纳参考飞机。

As shown below, Algorithm 1 is a pseudo code for the proposed obstacle assessment model. Fig. 3(a) illustrates the assessment process for a specific location: the black dashed lines represent the initial approach/departure and transitional surfaces. The buildings being evaluated (in deep orange) are shown below the surfaces. By continuously rotating the three-dimensional model clockwise, the remaining buildings to be checked (in light yellow) are evaluated until the criteria for completing the assessment of that location are met. In Fig. 3(b), the top left part illustrates an example of approach and departure paths and transition areas with obstructions (highlighted in red). This is further magnified from another angle in Fig. 3(c). It is evident that eVTOL cannot approach or depart in that direction due to the penetrated obstacles. Since there are no obstacles blocking the path and the angle between the left bottom and right top faces in Fig. 3(b) is greater than 135°. Thus, this point satisfies the three-dimensional spatial availability and can be considered as a potential candidate location to establish a vertical landing and takeoff site.
如下图所示，算法 1 是建议的障碍物评估模型的伪代码。图 3(a) 展示了一个特定地点的评估过程：黑色虚线代表初始接近/离去和过渡表面。被评估的建筑物（深橙色）显示在曲面下方。通过不断顺时针旋转三维模型，其余待检查的建筑物（浅黄色）也将得到评估，直至满足完成该地点评估的标准。在图 3（b）中，左上角部分展示了进场和离场路径以及有障碍物的过渡区域（红色突出显示）。图 3(c) 从另一个角度对其进行了进一步放大。很明显，由于穿透了障碍物，eVTOL 无法从该方向进场或离场。由于没有障碍物阻挡路径，且图 3(b) 中左下方和右上方面之间的夹角大于 135°。因此，该点满足三维空间可用性要求，可作为建立垂直起降点的潜在候选地点。

Algorithm 1 算法 1

Location filtering for 3D spatial availability

三维空间可用性位置筛选

By integrating the starting and ending points of the UAM candidate trips from Section 3.2, we noticed that some of the locations identified by the model are situated in areas with extremely low or no travel demand, such as Nei Lingding Island and the southern part of Dapeng New District. Given that UAM services are demand driven, we opted to eliminate these locations. Additionally, we closely merged points within a small region among the remaining locations to avoid an excessive number of candidate positions, which could lead to unnecessary computations in subsequent research. As a result, we ultimately selected 37 potential VTOL site locations that satisfy three-dimensional spatial availability.
通过整合第 3.2 节中 UAM 候选行程的起点和终点，我们注意到模型确定的一些地点位于出行需求极低或没有出行需求的区域，如内伶仃岛和大鹏新区南部。考虑到 UAM 服务是由需求驱动的，我们选择剔除这些地点。此外，我们还将剩余地点中一个小区域内的点进行了紧密合并，以避免候选位置数量过多，从而导致后续研究中不必要的计算。因此，我们最终选择了 37 个满足三维空间可用性的潜在 VTOL 站点位置。

3.4. VTOL site locations determining model
3.4.确定模型的 VTOL 场址位置

The Hub Location Problem (HLP) is an extension of facility location problems and has found extensive applications in the field of aviation research (Farahani et al., 2013). Hubs are facilities that are used for transshipment between the origin and destination points in transportation. The HLP is typically framed under the condition that direct connections between transportation nodes are not allowed. It aims to determine optimal hub locations and their corresponding allocations to non-hub nodes, often using a discount factor α to reduce transportation costs between hubs (Alumur and Kara, 2008). Here, we consider the origin and destination points of trips as transportation nodes. Locations that satisfy three-dimensional spatial availability are considered candidate hub nodes. Our model is an adaptation of the traditional HLP, which aims to determine the optimal locations of the VTOL site. In this model, passengers choose transportation modes based on travel costs.
枢纽位置问题（HLP）是设施位置问题的延伸，已在航空研究领域得到广泛应用（Farahani 等人，2013 年）。枢纽是用于运输起点和终点之间转运的设施。HLP 通常是在不允许运输节点之间直接连接的条件下制定的。其目的是确定最佳枢纽位置及其对非枢纽节点的相应分配，通常使用折扣系数 α 来降低枢纽之间的运输成本（Alumur 和 Kara，2008 年）。在此，我们将出行的起点和终点视为交通节点。满足三维空间可用性的地点被视为候选枢纽节点。我们的模型是对传统 HLP 的改进，旨在确定 VTOL 站点的最佳位置。在该模型中，乘客根据出行成本选择交通方式。

3.4.1. Parameter setting 3.4.1.参数设置

The travel cost considered in this study comprises two main components: the monetary cost and the time cost. The monetary cost refers to the money paid based on the pricing of transportation modes. The Pricing Schemes for Taxis, Shared Electric Bikes, and Shared Bicycles are derived from actual operational data in Shenzhen. In addition to the monetary cost, travel time is another potential cost incurred by passengers. Prolonged travel time due to traffic congestion can negatively affect passengers, so we introduce the concept of time cost and monetize travel time. According to the Shenzhen Statistical Yearbook (Statistics Bureau of Shenzhen Municipality, 2023), we obtained the average annual wage of urban employees, which is 155,563 yuan. Dividing this by the general annual working time of 2,080 h, we derive a unit time cost of 78.7 yuan per hour for each traveler.
本研究考虑的旅行成本包括两个主要部分：货币成本和时间成本。货币成本是指根据交通方式的定价所支付的费用。出租车、共享电动自行车和共享单车的定价方案均来自深圳的实际运营数据。除货币成本外，出行时间也是乘客可能产生的另一项成本。交通拥堵导致的出行时间延长会给乘客带来负面影响，因此我们引入了时间成本的概念，将出行时间货币化。根据《深圳统计年鉴》（深圳市统计局，2023 年），我们得出城镇职工年平均工资为 155563 元。将其除以一般年工作时间 2 080 h，得出每位出行者的单位时间成本为 78.7 元/小时。

The speed settings for various transportation modes are reasonable values with common sense. The 36.7 km/h car speed is calculated from the Shenzhen Road Traffic Operation Index System by continuously sampling the average speed of the road at 1-h intervals from 06:00 to 24:00 over a week (Transport Bureau of Shenzhen Municipality, 2023). The cruise speed of eVTOL is from the “Special Conditions for the EH216-S Unmanned Aerial Vehicle System” (CAAC, 2022). The travel cost and speed parameters for each transportation mode are summarized in Table 1.
各种交通方式的车速设置都是符合常识的合理值。36.7 km/h 的车速是根据《深圳市道路交通运行指标体系》，对一周内 06:00 至 24:00 每隔 1 小时的道路平均车速进行连续采样计算得出的（深圳市交通运输局，2023）。eVTOL 的巡航速度来自《EH216-S 无人机系统专用条件》（中国民用航空局，2022 年）。各种交通方式的出行成本和速度参数见表 1。

Table 1. Pricing and speed of each mode of transportation.
表 1.各种交通方式的价格和速度。

Transportation mode 运输方式	Pricing 定价	Speed 速度
eVTOL	Starting pricing 40 yuan with mileage fee 起价 40 元，含里程费 3 yuan/km 3 元/公里	130 km·h⁻¹ 130 公里-小时 {{0}
Taxi 出租车	10 yuan within 2 km, 2.7 yuan/km beyond 2 公里以内 10 元，以外 2.7 元/公里 2 km 2 公里	36.7 km·h⁻¹ 36.7 公里-小时 ⁻¹
Shared electric bicycle 共享电动自行车	2 yuan within 10 min with 1 yuan/min beyond 10 分钟内 2 元，超出部分 1 元/分钟	15 km·h⁻¹ 15 公里-小时 {{0}
Shared bicycle 共享单车	1.5 yuan within 15 min with 1 yuan/min beyond 15 分钟内 1.5 元，超出部分 1 元/分钟	10 km·h⁻¹ 10 公里-小时 {{0}
Walk 步行	— -	5 km·h⁻¹ 5 公里-小时 {{0}

3.4.2. Decision variables
3.4.2.决策变量

Let P be the set of origins and destinations for potential UAM trips. R is the set of potential UAM trips, and each trip r in R contains a pair of origin and destination (o, d), ∀o, d ∈ P. S is the set of 37 potential locations of VTOL sites and M is the set of transport modes that can be used to access the VTOL sites. The decision variables are binary variables v_i, g^r, $u_{i j}^{r}$ , $a_{m i}^{r}$ , $e_{n j}^{r}$ . The meanings of each variable are given below.(1) $v_{i} = {\begin{cases} 1, establish a VTOL site at location i \\ 0, no VTOL site established at location i \end{cases}$ (2) $g^{r} = {\begin{cases} 1, trip r is completed by ground transportation \\ 0, trip r is completed by UAM \end{cases}$ (3) $u_{i j}^{r} = {\begin{cases} 1, r is a UAM trip with the takeoff VTOL site i and landing VTOL site j \\ 0, otherwise \end{cases}$ (4) $a_{m i}^{r} = {\begin{cases} 1, trip r arrives takeoff VTOL site i via ground transportation mode m \\ 0, otherwise \end{cases}$ (5) $e_{n j}^{r} = {\begin{cases} 1, trip r departs landing VTOL site j via ground transportation mode n \\ 0, otherwise \end{cases}$
假设 P 是潜在 UAM 旅行的出发地和目的地集合。R 是潜在 UAM 行程的集合，R 中的每个行程 r 包含一对出发地和目的地（o，d），∀o，d∈P。S 是 37 个 VTOL 潜在地点的集合，M 是可用于到达 VTOL 地点的交通方式的集合。决策变量为二进制变量 v、g ^r , $u_{i j}^{r}$ , $a_{m i}^{r}$ , $e_{n j}^{r}$ .各变量的含义如下。 (1) $v_{i} = {\begin{cases} 1, establish a VTOL site at location i \\ 0, no VTOL site established at location i \end{cases}$ (2) $g^{r} = {\begin{cases} 1, trip r is completed by ground transportation \\ 0, trip r is completed by UAM \end{cases}$ (3) $u_{i j}^{r} = {\begin{cases} 1, r is a UAM trip with the takeoff VTOL site i and landing VTOL site j \\ 0, otherwise \end{cases}$ (4) $a_{m i}^{r} = {\begin{cases} 1, trip r arrives takeoff VTOL site i via ground transportation mode m \\ 0, otherwise \end{cases}$ (5) $e_{n j}^{r} = {\begin{cases} 1, trip r departs landing VTOL site j via ground transportation mode n \\ 0, otherwise \end{cases}$

3.4.3. Constraints 3.4.3.制约因素

Since there are costs associated with the construction of VTOL sites, any UAM planning scheme must have a reasonable value for the number of VTOL sites to be built. In this study, the number of VTOL sites is set to N_VTOL, and the constraint 6 represents the limitation on the number of VTOL sites.(6) $\begin{array}{c} \sum_{i \in S} v_{i} = N_{VTOL}, \forall i \in S \end{array}$
由于建造 VTOL 站点需要成本，因此任何 UAM 规划方案都必须为将要建造的 VTOL 站点数量设定一个合理的值。在本研究中，VTOL 场址的数量设定为 N _VTOL ，约束条件 6 表示对 VTOL 场址数量的限制。约束条件 6 表示对 VTOL 场址数量的限制。 (6) $\begin{array}{c} \sum_{i \in S} v_{i} = N_{VTOL}, \forall i \in S \end{array}$

Passengers must choose one of the two modes, either ground or UAM, to complete their trip, therefore:(7) $\begin{array}{c} g^{r} + \sum_{i} \sum_{j \neq i} u_{i j}^{r} = 1, \forall r \in R \end{array}$
因此，乘客必须从地面或 UAM 两种方式中选择一种完成旅行： (7) $\begin{array}{c} g^{r} + \sum_{i} \sum_{j \neq i} u_{i j}^{r} = 1, \forall r \in R \end{array}$

If a UAM trip involves potential location i, a VTOL site must be constructed at i:(8) $\begin{array}{c} \sum_{i \in S, j \neq i} u_{i j}^{r} + \sum_{j \in S, i \neq j} u_{j i}^{r} \leq v_{i}, \forall i \in S, \forall r \in R \end{array}$
如果 UAM 行程涉及潜在地点 i，则必须在 i 处建造一个 VTOL 站点： (8) $\begin{array}{c} \sum_{i \in S, j \neq i} u_{i j}^{r} + \sum_{j \in S, i \neq j} u_{j i}^{r} \leq v_{i}, \forall i \in S, \forall r \in R \end{array}$

Regarding the choice of transportation mode for passengers entering and exiting the VTOL sites, it is assumed that each segment for entering and leaving the VTOL site is exclusively associated with one mode of transportation. Equation (9) indicates that if a trip involves UAM travel, a specific mode of transportation must be chosen to enter the VTOL site i:(9) $\begin{array}{c} \sum_{i} \sum_{j \neq i} u_{i j}^{r} = \sum_{m} \sum_{i} a_{m i}^{r}, \forall r \in R \end{array}$ Similarly, the UAM trip r must select a transportation mode to leave the landing VTOL site j:(10) $\begin{array}{c} \sum_{i} \sum_{j \neq i} u_{i j}^{r} = \sum_{n} \sum_{j} e_{n j}^{r}, \forall r \in R \end{array}$
关于乘客进出 VTOL 站点的交通方式选择，假定进出 VTOL 站点的每个航段只与一种交通方式相关。公式（9）表明，如果行程涉及 UAM 旅行，则必须选择特定的交通方式才能进入 VTOL 站点 i： (9) $\begin{array}{c} \sum_{i} \sum_{j \neq i} u_{i j}^{r} = \sum_{m} \sum_{i} a_{m i}^{r}, \forall r \in R \end{array}$ 同样，UAM 旅行 r 必须选择一种交通方式离开着陆 VTOL 站点 j： (10) $\begin{array}{c} \sum_{i} \sum_{j \neq i} u_{i j}^{r} = \sum_{n} \sum_{j} e_{n j}^{r}, \forall r \in R \end{array}$ 。

Equations (9) and (10) only ensure that a mode of transport has been chosen to enter the take-off VTOL site i and a mode of transportation has been chosen to leave the landing VTOL site j. However, they do not ensure that they correspond to the trip r: o→i→j→d. Therefore, Eq. (11) is added to ensure that the chosen modes of entering and exiting the VTOL sites accurately correspond to this UAM trip r:(11) $\begin{array}{c} 2 u_{i j}^{r} \leq \sum_{m} a_{m i}^{r} + \sum_{n} e_{n j}^{r}, \forall i, j \neq i, \forall r \in R \end{array}$
等式（9）和（10）只能确保选择了一种运输方式进入起飞的 VTOL 场点 i，以及选择了一种运输方式离开着陆的 VTOL 场点 j，但不能确保它们与行程 r：o→i→j→d 相对应。因此，增加了公式（11），以确保所选的进入和离开 VTOL 场址的模式与该 UAM 行程 r： (11) $\begin{array}{c} 2 u_{i j}^{r} \leq \sum_{m} a_{m i}^{r} + \sum_{n} e_{n j}^{r}, \forall i, j \neq i, \forall r \in R \end{array}$ 准确对应。

Passengers choose the mode of travel that minimizes their travel cost. The travel cost consists of monetary cost and the time cost. Let $f_{a i r}^{r}$ , $t_{a i r}^{r}$ , $f_{ground}^{r}$ , and $g_{ground}^{r}$ represent the UAM monetary cost, UAM travel time, ground transportation monetary cost, and ground transportation time for trip r, respectively. p is the unit time value (78.7 yuan/h). $f_{i j}^{r}$ and $t_{i j}^{r}$ denote the monetary cost and time to travel by eVTOL from the takeoff VTOL site i to the landing VTOL site j, where $t_{i j}^{r}$ is composed of the cruise time and the take-off/landing time. It is assumed that the time for a take-off and a landing operation is totally 10 min. Let $f_{m i}^{r}$ and $t_{m i}^{r}$ represent the monetary cost and time for passengers to travel to the takeoff VTOL site i for the trip r using the transportation mode m, $f_{n j}^{r}$ and $t_{n j}^{r}$ represent the monetary cost and time for passengers to travel from the landing VTOL site j for the trip r using the transportation mode n. $t_{transfer}^{r}$ represents the transfer time for the trip r when using UAM travel, including the time from leaving ground transportation to boarding the eVTOL at the take-off VTOL site $t_{g t}^{r}$ , and the time from the landing VTOL site to transferring to ground transportation $t_{l g}^{r}$ . In our study, tr transfer is set to 20 min. Travel cost is represented by f^r + t^r∙p. Passengers will choose the mode with the lowest travel cost. Therefore, passengers who satisfy the inequality 12 will move from ground transportation to UAM travel:(12) $\begin{array}{c} f_{air}^{r} + t_{air}^{r} ∙ p < f_{ground}^{r} + t_{ground}^{r} ∙ p \end{array}$ among which,(13) $\begin{array}{c} f_{air}^{r} = f_{m i}^{r} + f_{i j}^{r} + f_{n j}^{r} \end{array}$ (14) $\begin{array}{c} t_{air}^{r} = t_{m i}^{r} + t_{i j}^{r} + t_{n j}^{r} + t_{transfer}^{r} \end{array}$
乘客选择旅行成本最小的旅行方式。旅行成本包括货币成本和时间成本。假设 $f_{a i r}^{r}$ , $t_{a i r}^{r}$ , $f_{ground}^{r}$ p 为单位时间值（78.7 元/小时）。 $f_{i j}^{r}$ 和 $t_{i j}^{r}$ 表示乘坐 eVTOL 从起飞 VTOL 站点 i 到着陆 VTOL 站点 j 的货币成本和时间，其中 $t_{i j}^{r}$ 由巡航时间和起飞/着陆时间组成。假设起飞和着陆时间均为 10 分钟。让 $f_{m i}^{r}$ 和 $t_{m i}^{r}$ 代表乘客使用交通方式m前往起飞VTOL站点i的货币成本和时间， $f_{n j}^{r}$ 和 $t_{n j}^{r}$ 代表乘客使用交通方式n从着陆VTOL站点j前往r的货币成本和时间。 $t_{transfer}^{r}$ 代表使用UAM出行时r的换乘时间，包括从离开地面交通到在起飞VTOL站点登上eVTOL的时间 $t_{g t}^{r}$ ，以及从着陆VTOL站点到起飞VTOL站点的时间 $t_{l g}^{r}$ 。以及从 VTOL 降落地点到转乘地面交通工具的时间 $t_{l g}^{r}$ 。.在我们的研究中，换乘时间设定为 20 分钟。旅行成本表示为 f ^r + t ^r ∙p.乘客会选择出行成本最低的交通方式。因此，满足不等式 12 的乘客将从地面交通转向 UAM 旅行： (12) $\begin{array}{c} f_{air}^{r} + t_{air}^{r} ∙ p < f_{ground}^{r} + t_{ground}^{r} ∙ p \end{array}$ 其中 (13) $\begin{array}{c} f_{air}^{r} = f_{m i}^{r} + f_{i j}^{r} + f_{n j}^{r} \end{array}$ (14) $\begin{array}{c} t_{air}^{r} = t_{m i}^{r} + t_{i j}^{r} + t_{n j}^{r} + t_{transfer}^{r} \end{array}$

We use the Haversine formula to calculate the flight distance of the eVTOL. The Haversine formula is used to calculate the distance between two locations in a great circle, and given the coordinates of the takeoff VTOL site (lat 1, lon 1), the coordinates of the landing VTOL site (lat 2, lon 2), and the radius of the Earth R_E = 6378.137 km, the distance D_air between them is(15) $\begin{array}{c} D_{air} = 2 \arcsin \sqrt{\sin^{2} \frac{(l a t 1 - l a t 2)}{2} + \cos (l a t 1) ∙ \cos (l a t 2) ∙ \sin^{2} \frac{(l o n 1 - l o n 2)}{2}} ∙ R_{E} \end{array}$
我们使用哈弗辛公式计算 eVTOL 的飞行距离。哈弗辛公式用于计算一个大圆中两个地点之间的距离，给定 VTOL 起飞地点的坐标（纬度 1，经度 1）、VTOL 着陆地点的坐标（纬度 2，经度 2）和地球半径 R _E = 6378.137 千米，则它们之间的距离 D _air 为 (15) $\begin{array}{c} D_{air} = 2 \arcsin \sqrt{\sin^{2} \frac{(l a t 1 - l a t 2)}{2} + \cos (l a t 1) ∙ \cos (l a t 2) ∙ \sin^{2} \frac{(l o n 1 - l o n 2)}{2}} ∙ R_{E} \end{array}$ } 。= 6378.137 千米，它们之间的距离 D _air 为 (15) $\begin{array}{c} D_{air} = 2 \arcsin \sqrt{\sin^{2} \frac{(l a t 1 - l a t 2)}{2} + \cos (l a t 1) ∙ \cos (l a t 2) ∙ \sin^{2} \frac{(l o n 1 - l o n 2)}{2}} ∙ R_{E} \end{array}$

For the ground segments of entering and leaving the VTOL sites, we use the Manhattan distance as the driving distance for taxis. We consider 1.25 times the Euclidean distance as the riding distance for shared electric bikes and shared bicycles, and 1.2 times the walking distance. Since the ground segments to and from the VTOL sites are usually short, the error introduced by using the above methods instead of actual distances can be negligible. The airborne time for eVTOL flights and the time for entering and leaving VTOL sites using various modes are calculated based on Eq. (15) and the speed parameters in Section 3.4.1. For pure ground trips, the pure ground transportation time for each trip r is provided by the data in Section 3.2, and the distance for each trip is calculated using Networkx based on the Shenzhen road network data obtained from OpenStreetMap (Boeing, 2017), an open source map and geodatabase that can be freely used and edited according to the protocol. Osmnx and Networkx are Python extension packages that are used to obtain road network data and calculate the distance between two points in a complex network, respectively.
对于进出 VTOL 站点的地面段，我们使用曼哈顿距离作为出租车的行驶距离。共享电动自行车和共享单车的骑行距离为欧氏距离的 1.25 倍，步行距离为欧氏距离的 1.2 倍。由于往返 VTOL 站点的地面段通常很短，因此使用上述方法而不是实际距离带来的误差可以忽略不计。根据公式 (15) 和第 3.4.1 节中的速度参数计算 eVTOL 飞行的空中飞行时间以及使用各种模式进出 VTOL 场址的时间。对于纯地面行程，每次行程 r 的纯地面交通时间由第 3.2 节中的数据提供，每次行程的距离则根据从 OpenStreetMap（波音公司，2017 年）获得的深圳路网数据使用 Networkx 计算，OpenStreetMap 是一个开源地图和地理数据库，可根据协议自由使用和编辑。Osmnx 和 Networkx 是 Python 扩展包，分别用于获取路网数据和计算复杂路网中两点之间的距离。

Due to the NP-hard nature of large-scale hub location problems, there are no known polynomial-time methods to solve them. Only smaller-scale instances can yield exact solutions. To address this challenge, we propose two additional constraints based on the analysis of the characteristics of the UAM. These constraints significantly reduce the problem's size and the number of variables, allowing the model to be solved in a short time.
由于大规模集线器定位问题的 NP 难度，目前还没有已知的多项式时间方法来解决这些问题。只有较小规模的实例才能产生精确的解决方案。为了应对这一挑战，我们在分析 UAM 特性的基础上提出了两个额外的约束条件。这些约束条件极大地减少了问题的规模和变量的数量，使模型可以在短时间内求解。

First, based on the passenger mode choice criteria, we can identify those trips that, regardless of how the VTOL site combinations for take-off and landing are configured, cannot lower their travel costs. These trips will inevitably choose pure ground transportation over UAM. Thus, using inequality 16, we exclude these trips from the total set of trips, focusing on the remaining trips that have the potential to change direction towards UAM.(16) $\begin{array}{c} f_{m i}^{r} + f_{i j}^{r} + f_{n j}^{r} + (t_{m i}^{r} + t_{i j}^{r} + t_{n j}^{r} + t_{transfer}^{r}) ∙ p > f_{ground}^{r} + t_{ground}^{r} ∙ p, \forall r \in R, \forall i, j \in S \end{array}$
首先，根据乘客模式选择标准，我们可以识别出那些无论如何配置 VTOL 起飞和着陆场地组合，都无法降低其旅行成本的行程。这些乘客将不可避免地选择纯地面交通而非 UAM。因此，利用不等式 16，我们将这些航次从全部航次中剔除，重点关注其余有可能转向 UAM 的航次。 (16) $\begin{array}{c} f_{m i}^{r} + f_{i j}^{r} + f_{n j}^{r} + (t_{m i}^{r} + t_{i j}^{r} + t_{n j}^{r} + t_{transfer}^{r}) ∙ p > f_{ground}^{r} + t_{ground}^{r} ∙ p, \forall r \in R, \forall i, j \in S \end{array}$

Furthermore, when distributing two VTOL sites i and j in a single trip, if a passenger chooses to use i and j for eVTOL travel, they will invariably select the site closer to the departure point as the take-off VTOL site and the one closer to the destination point as the landing VTOL site. Assuming that VTOL site i is closer to the starting point of the trip o and VTOL site j is closer to the destination point of the trip d, a passenger's UAM journey will always follow the sequence o→i→j→d, rather than o→j→i→d. Therefore, using the inequality 17, we can eliminate the variables associated with the sequence o→j→i→d from consideration.(17) $\begin{array}{c} d_{m i}^{r} + d_{n j}^{r} \leq d_{m j}^{r} + d_{n i}^{r}, \forall r \in R, \forall i, j \in S \end{array}$
此外，在一次旅行中分配 i 和 j 两个 VTOL 场址时，如果乘客选择使用 i 和 j 进行 eVTOL 旅行，他们必然会选择离出发点较近的场址作为起飞 VTOL 场址，离目的地较近的场址作为着陆 VTOL 场址。假定 VTOL 场址 i 离行程起点 o 较近，VTOL 场址 j 离行程终点 d 较近，那么乘客的 UAM 旅程将始终遵循 o→i→j→d 的序列，而不是 o→j→i→d。因此，利用不等式 17，我们可以剔除与序列 o→j→i→d 相关的变量。 (17) $\begin{array}{c} d_{m i}^{r} + d_{n j}^{r} \leq d_{m j}^{r} + d_{n i}^{r}, \forall r \in R, \forall i, j \in S \end{array}$

Eventually, the set G of study objects is reduced to(18) $\begin{array}{c} G = {(r, i, j, m, n) | f_{air}^{r} + t_{air}^{r} ∙ p < f_{ground}^{r} + t_{ground}^{r} ∙ p, d_{m i}^{r} + d_{n j}^{r} \leq d_{m j}^{r} + d_{n i}^{r}} \end{array}$
最终，研究对象集合 G 被简化为 (18) $\begin{array}{c} G = {(r, i, j, m, n) | f_{air}^{r} + t_{air}^{r} ∙ p < f_{ground}^{r} + t_{ground}^{r} ∙ p, d_{m i}^{r} + d_{n j}^{r} \leq d_{m j}^{r} + d_{n i}^{r}} \end{array}$

3.4.4. Objective function
3.4.4.目标函数

The objective of the model is to maximize travel cost savings for all trips that may shift to UAM: $\max \sum_{r \in R} {\sum_{i} \sum_{j \neq i} [f_{ground}^{r} + t_{ground}^{r} ∙ p - (f_{i j}^{r} + t_{i j}^{r} ∙ p)] ∙ u_{i j}^{r}$ (19) $\begin{array}{c} - \sum_{m} \sum_{i} [f_{m i}^{r} + (t_{m i}^{r} + t_{gt}^{r}) ∙ p] ∙ a_{m i}^{r} - \sum_{n} \sum_{j} [f_{n j}^{r} + (t_{n j}^{r} + t_{\lg}^{r}) ∙ p] ∙ e_{n j}^{r}} \end{array}$ where v_i, g^r, $v_{i j}^{r}$ , $a_{m i}^{r}$ , $e_{n j}^{r}$ ∈{0,1}, (r, i, j, m, n) ∈ G.
该模型的目标是为所有可能转向 UAM 的出行最大限度地节约旅行成本： $\max \sum_{r \in R} {\sum_{i} \sum_{j \neq i} [f_{ground}^{r} + t_{ground}^{r} ∙ p - (f_{i j}^{r} + t_{i j}^{r} ∙ p)] ∙ u_{i j}^{r}$ (19) $\begin{array}{c} - \sum_{m} \sum_{i} [f_{m i}^{r} + (t_{m i}^{r} + t_{gt}^{r}) ∙ p] ∙ a_{m i}^{r} - \sum_{n} \sum_{j} [f_{n j}^{r} + (t_{n j}^{r} + t_{\lg}^{r}) ∙ p] ∙ e_{n j}^{r}} \end{array}$ 其中 v, g ^r , $v_{i j}^{r}$ , $a_{m i}^{r}$ , $e_{n j}^{r}$ ∈{0,1}，（r，i，j，m，n）∈G。

4. Results 4.成果

4.1. Data and settings 4.1.数据和设置

Our model has two main inputs, namely, the potential UAM trips that are given in Section 3.2, and the potential locations of the VTOL site in Section 3.3. The importance of the VTOL sites is illustrated in Fig. 4, with the size of each site indicating its significance. This will be discussed in more detail in Section 4.3. The speed and pricing parameters of various modes of transportation are shown in Table 1. The calculation of the distance and time of transportation is given in Section 3.4.1. Based on these data and settings, the model we built was solved using Python and the Gurobi solver, to determine the locations of the VTOL sites in Shenzhen, along with the number of UAM trips and the mode of transportation of each trip that arrived and left the VTOL sites.
我们的模型有两个主要输入，即第 3.2 节中给出的潜在 UAM 行程和第 3.3 节中给出的 VTOL 站点的潜在位置。VTOL 场址的重要性如图 4 所示，每个场址的大小表示其重要性。第 4.3 节将对此进行详细讨论。各种运输方式的速度和价格参数见表 1。运输距离和时间的计算见第 3.4.1 节。根据这些数据和设置，我们使用 Python 和 Gurobi 求解器对建立的模型进行求解，以确定深圳的 VTOL 站点位置，以及到达和离开 VTOL 站点的 UAM 次数和每次出行的交通方式。

4.2. VTOL sites and UAM benefits under current UAM demands
4.2.在当前普遍无人机需求下的 VTOL 场址和普遍无人机的效益

We aim to save as much travel cost and capture as much demand as possible under the premise that the number of VTOL sites is reasonable. To determine the number of VTOL sites to be established, we solved the UAM trips and travel cost savings corresponding to the number of VTOL sites from 2 to 37, and the result is shown in Fig. 5(a). When the number of VTOL sites exceeds 21, the incremental number of UAM trips resulting from building an additional VTOL site is less than 10 and the incremental travel cost savings is less than 800 yuan. This suggests that when the number of VTOL sites reaches 21, the ability of the infrastructure network to save travel costs and capture demand is approaching saturation, and the effect of saving more travel costs and attracting more riders to UAM by building more VTOL sites becomes less pronounced. Therefore, we have determined that the number of VTOL sites to be established is 21.
我们的目标是在 VTOL 站点数量合理的前提下，节省尽可能多的旅行成本，获取尽可能多的需求。为了确定 VTOL 站点的数量，我们求解了 2 至 37 个 VTOL 站点对应的 UAM 人次和节省的旅行成本，结果如图 5（a）所示。当 VTOL 场址数量超过 21 个时，增设一个 VTOL 场址带来的 UAM 出行增量小于 10 次，节省的旅行成本增量小于 800 元。这表明，当 VTOL 站点数量达到 21 个时，基础设施网络节约出行成本和捕捉需求的能力接近饱和，通过建设更多 VTOL 站点来节约更多出行成本和吸引更多乘客参与 UAM 的效果变得不那么明显。因此，我们确定拟建的 VTOL 站点数量为 21 个。

Regarding the ground transportation modes for passengers entering the VTOL sites, 1,331 trips choose shared electric bikes, 620 trips opt for taxis, and 3 trips involve walking. These percentages are 68.12%, 31.73%, and 0.15%, respectively, of the total of 1,954 UAM trips. For departing VTOL sites, 1,385 trips are on shared electric bikes, 562 trips in taxis, and 7 trips on foot. These percentages are 70.88%, 28.76%, and 0.36%, respectively. It is apparent that shared electric bikes are the predominant mode of transportation for ground segments between VTOL sites. The distribution of UAM trip time allocation among the VTOL site segments that enter, the eVTOL flight segments, and the VTOL site segments that exit are shown in Fig. 6(a). Segments entering and exiting the VTOL sites account for around 40% of the total UAM trip time, indicating room for further time reduction in the ground segments. This can be achieved by planning and designing the infrastructure network more rationally to improve the accessibility of the VTOL site. Fig. 6(b) illustrates the time savings by choosing the UAM option over the original taxi option. From Fig. 6(b), it is evident that opting for UAM travel leads to significant time savings. The most substantial time savings fall within 30–50 min intervals, with 10-min intervals. The time saved by choosing UAM travel is up to 3 h in some cases.
关于进入 VTOL 站点的乘客的地面交通方式，1331 人次选择了共享电动自行车，620 人次选择了出租车，3 人次选择了步行。这三个比例分别占 UAM 1954 人次总数的 68.12%、31.73% 和 0.15%。在离开 VTOL 站点时，1385 人次使用共享电动自行车，562 人次乘坐出租车，7 人次步行。这三个比例分别为 70.88%、28.76% 和 0.36%。显然，共享电动自行车是 VTOL 站点之间地面段的主要交通方式。图 6（a）显示了进入 VTOL 场址段、eVTOL 飞行段和离开 VTOL 场址段的 UAM 行程时间分配情况。进入和离开 VTOL 场址的航段约占 UAM 总行程时间的 40%，这表明地面航段的时间还有进一步减少的余地。这可以通过更合理地规划和设计基础设施网络来实现，以改善 VTOL 场址的可达性。图 6(b)说明了选择 UAM 方案比原来的出租车方案节省的时间。从图 6(b)中可以看出，选择 UAM 旅行可以节省大量时间。30-50 分钟的时间间隔内节省的时间最多，间隔为 10 分钟。在某些情况下，选择 UAM 方式出行节省的时间可达 3 小时。

4.3. VTOL sites and UAM benefits under scaled UAM demands
4.3.按比例计算的 UAM 需求下的 VTOL 场址和 UAM 效益

To further explore the location of VTOL sites and the potential advantages of UAM, we employ a similar approach to that of Wang et al. (2022) to generate UAM requests based on existing taxi requests. Future UAM demand is set to be 2, 3, 4, 5 times of current demand. The economic advantages of UAM become more pronounced as demand increases (Fig. 7(a)). In particular, the cost savings between different levels of UAM demand are more pronounced when the number of VTOL sites is greater than 10. The total number of UAM trips provided by each VTOL site is determined based on the UAM demand and the number of VTOLs (N_VTOL). The number of trips is then normalized using the MinMaxScaler algorithm from Scikit learn. We plot the normalized trips at each site in Fig. 7. VTOL sites can be divided into three categories: Group I (#trips ≥0.4), Group II (0.2 ≤ #trips < 0.4), and Group III (#trips < 0.2). The size of the markers in Fig. 4 also indicates three groups of VTOL sites. The most important ones, i.e., Group I sites, are located in the center of the city, where the demand for UAM is higher than other areas. If the resources for constructing VTOL sites are limited, these sites should be given priority.
为了进一步探索 VTOL 站点的位置和 UAM 的潜在优势，我们采用了与 Wang 等人（2022 年）类似的方法，根据现有的出租车请求生成 UAM 请求。未来的 UAM 需求被设定为当前需求的 2、3、4、5 倍。随着需求的增加，UAM 的经济优势更加明显（图 7(a)）。特别是当 VTOL 站点数量超过 10 个时，不同 UAM 需求水平之间的成本节约更为明显。根据 UAM 需求和 VTOL 数量（N _VTOL ）确定每个 VTOL 站点提供的 UAM 出行总次数。然后使用 Scikit learn 中的 MinMaxScaler 算法对出行次数进行归一化处理。我们在图 7 中绘制了各站点的归一化出行次数。VTOL 站点可分为三类：第一组（#trips ≥0.4）、第二组（0.2 ≤ #trips <0.4）和第三组（#trips <0.2）。图 4 中标记的大小也表明 VTOL 站点分为三组。最重要的站点，即第一组站点，位于城市中心，对 UAM 的需求高于其他区域。如果用于建造 VTOL 站点的资源有限，则应优先考虑这些站点。

5. Discussions 5.讨论情况

The establishment of VTOL sites is a key factor in the successful implementation of UAM to improve the efficiency of urban transportation. Three elements can have an effect on the results of our model: the number of VTOL sites, the transfer time, and the cost of eVTOL. In this section, we will explore the potential influence of these factors on the determination and development of VTOL sites.
建立 VTOL 站点是成功实施 UAM 以提高城市运输效率的关键因素。有三个因素会对我们模型的结果产生影响：VTOL 场址的数量、转移时间和 eVTOL 的成本。在本节中，我们将探讨这些因素对确定和发展 VTOL 站点的潜在影响。

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Impact of the number of the VTOL Sites: As shown in Fig. 5(b), with an increase in the number of VTOL sites, the proportion of time spent on the ground segments entering/exiting the VTOL pads and the eVTOL flight segments stabilizes around 13 min, while the overall time remains approximately 40 min. This suggests that the total travel time becomes relatively stable with a larger number of VTOL sites.
VTOL 场址数量的影响：如图 5(b)所示，随着 VTOL 场址数量的增加，进入/离开 VTOL 停机坪的地面段和 eVTOL 飞行段所花费的时间比例稳定在 13 分钟左右，而总体时间仍保持在 40 分钟左右。这表明，随着 VTOL 场址数量的增加，总飞行时间变得相对稳定。
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Effect of transfer time: We observed the impact of transfer time at the VTOL sites on total cost and UAM trip counts. Transfer time represents the convenience of transitioning from ground transportation to boarding an eVTOL, reflecting the operational efficiency of VTOL sites. Passengers choose UAM for its time savings, and when the transfer time increases from 5 to 30 min, as shown in Fig. 5(c), UAM trips decrease from 3,504 to 1,410, with 59.76% of UAM passengers switching to pure ground transportation. This indicates that as the transfer time increases, the advantage of time savings with UAM is offset, leading to a significant reduction in UAM users and diminishing the efficiency and competitiveness of UAM in the transportation market.
换乘时间的影响：我们观察了 VTOL 场址的换乘时间对总成本和 UAM 旅行次数的影响。换乘时间代表了从地面交通到登上 eVTOL 的便利性，反映了 VTOL 站点的运营效率。如图 5（c）所示，当换乘时间从 5 分钟增加到 30 分钟时，UAM 乘客从 3504 人次减少到 1410 人次，59.76%的 UAM 乘客转乘纯地面交通。这表明，随着换乘时间的增加，UAM 节省时间的优势被抵消，导致 UAM 用户大幅减少，降低了 UAM 在运输市场中的效率和竞争力。
• -
Influence of eVTOL price: Sensitivity analysis of the price of eVTOL demonstrates a certain impact on UAM trip counts and travel cost savings. By adjusting model parameters based on different eVTOL prices, we can observe changes in UAM trip counts and travel cost savings. The result of the analysis revealed that the demand for UAM is highly sensitive to the pricing structure of eVTOL. In Fig. 5(d), when the initial fare is set at 30 yuan and the per kilometer fare is 1 yuan, the UAM trips exceed 6,000, but with an initial fare of 50 yuan and a per kilometer fare of 5 yuan, the UAM trips decrease to around 1,000. When the initial fare is lower, the demand for UAM is more sensitive to changes in the per kilometer fare. For instance, when the initial fare is 30 yuan, an increase in the per kilometer fare from 1 to 5 yuan results in a decrease in UAM trips from 6,200 to 1,600. However, with an initial fare of 50 yuan, the same change in the per-km fare leads to a reduction in UAM trips from 3,200 to 1,000. The trend in travel cost savings follows a similar pattern. UAM operators should consider the relationship between eVTOL pricing and UAM demand more thoroughly, taking into account factors such as market dynamics, the size of the eVTOL fleet, and additional operational and management costs, while setting UAM prices.
eVTOL 价格的影响：对 eVTOL 价格的敏感性分析表明，eVTOL 价格对 UAM 行程数和节省的旅行成本有一定的影响。通过根据不同的 eVTOL 价格调整模型参数，我们可以观察到 UAM 行程次数和节省的旅行成本的变化。分析结果表明，UAM 需求对 eVTOL 的价格结构高度敏感。在图 5（d）中，当初始票价为 30 元，每公里票价为 1 元时，UAM 出行次数超过 6000 次，但当初始票价为 50 元，每公里票价为 5 元时，UAM 出行次数减少到 1000 次左右。当初始票价较低时，对 UAM 的需求对每公里票价的变化更为敏感。例如，当初始票价为 30 元时，每公里票价从 1 元增加到 5 元，则 UAM 的出行量从 6 200 人次减少到 1 600 人次。然而，当初始票价为 50 元时，每公里票价的同样变化会导致 UAM 人次从 3 200 降至 1 000。节约交通成本的趋势与此类似。UAM 运营商在制定 UAM 价格时应更全面地考虑 eVTOL 定价与 UAM 需求之间的关系，同时考虑市场动态、eVTOL 机队规模以及额外的运营和管理成本等因素。

These analyzes help us better understand the influence of different parameters on the model results, facilitating the optimization of UAM network design and planning strategies.
这些分析有助于我们更好地理解不同参数对模型结果的影响，从而促进 UAM 网络设计和规划策略的优化。

6. Conclusions 6.结论

This study presents a comprehensive process and methodology for determining the locations of VTOL sites in Shenzhen. Due to the significant impact of traffic congestion on taxi rides among various public transportation modes, this study considers taxi passengers as potential users to transfer to UAM. We use GIS tools to identify locations that satisfy 2D plane availability and establish an obstacle assessment model to further filter locations that satisfy 3D spatial availability. By adapting the traditional HLP based on UAM characteristics, an integer programming model is developed to locate the VTOL sites. The model takes potential UAM trips derived from processed taxi trip data, potential locations of the VTOL site determined using GIS and obstacle assessment, and relevant parameter settings as input. Maximize travel cost savings and solve for the locations of the VTOL sites, the number of UAM trips and the choice of transportation modes for each trip that enters and leaves the ground segments of the VTOL sites. Considering 3D spatial availability of locations ensures that each VTOL site's location not only represents the mathematical optimum but also meets safety requirements for eVTOL take-off, departure climb, final approach, and landing phases. The methodology, model, and conclusions can provide decision support for urban planners in the initial stages of UAM planning.
本研究提出了确定深圳 VTOL 场址的综合流程和方法。由于在各种公共交通方式中，交通拥堵对乘坐出租车的影响很大，本研究将出租车乘客视为换乘 UAM 的潜在用户。我们利用地理信息系统工具确定满足二维平面可用性的地点，并建立障碍物评估模型进一步筛选满足三维空间可用性的地点。通过根据 UAM 的特点对传统的 HLP 进行调整，我们开发了一个整数编程模型来确定 VTOL 站点的位置。该模型将从处理后的出租车出行数据中得出的潜在 UAM 行程、利用地理信息系统和障碍物评估确定的 VTOL 站点的潜在位置以及相关参数设置作为输入。最大限度地节约旅行成本，并求解 VTOL 站点的位置、UAM 旅行次数以及进入和离开 VTOL 站点地面段的每次旅行的交通方式选择。考虑到位置的三维空间可用性，可确保每个 VTOL 场址的位置不仅代表数学最佳值，还能满足 eVTOL 起飞、离场爬升、最终进场和着陆阶段的安全要求。该方法、模型和结论可为城市规划者在 UAM 规划的初始阶段提供决策支持。

However, a limitation of this research is the lack of detailed income data, which led to setting the time value parameter based on average annual wages. In reality, everyone's time value varies, and different time values significantly impact UAM demand. Those with lower time value may opt for cheaper transportation modes, having greater tolerance for traffic congestion, whereas those with higher time value are more likely to choose time-saving UAM. The high time value suggests that they might be willing to pay several times more than ground transportation prices to save time by taking eVTOL. Considering VTOL site capacity limits and eVTOL fleet size limits presents another avenue for improvement. Capacity restrictions might lead to eVTOL ground waiting or hovering due to high demand, while adding eVTOL fleet size limitations could result in passengers waiting despite being at the VTOL site, reducing UAM's time-saving benefits. Moreover, factors such as the introduction of ride-sharing services for eVTOL similar to taxi pooling, considering uncertainties arising from congestion when entering and leaving VTOL site ground segments, and adding noise when selecting VTOL site locations, can be explored as future research directions.
然而，这项研究的局限性在于缺乏详细的收入数据，因此只能根据年平均工资来设定时间价值参数。实际上，每个人的时间价值都是不同的，不同的时间价值会对 UAM 需求产生重大影响。时间价值较低的人可能会选择更便宜的交通方式，对交通拥堵有更大的容忍度，而时间价值较高的人则更有可能选择节省时间的 UAM。高时间价值表明，他们可能愿意支付比地面交通价格高出数倍的费用，通过乘坐 eVTOL 来节省时间。考虑到 VTOL 场址容量限制和 eVTOL 机队规模限制，也是一种改进途径。容量限制可能会导致 eVTOL 因需求量大而在地面等待或盘旋，而增加 eVTOL 机队规模限制可能会导致乘客尽管已在 VTOL 现场但仍在等待，从而降低 UAM 节省时间的优势。此外，未来的研究方向还包括为 eVTOL 引入类似出租车拼车的共享服务、考虑进出 VTOL 站点地面段拥堵造成的不确定性以及在选择 VTOL 站点位置时增加噪音等因素。

Replication and data sharing
复制和数据共享

The data and codes that support the findings of this study are available at https://doi.org/10.26599/ETSD.2023.9190024.
支持本研究结果的数据和代码见 https://doi.org/10.26599/ETSD.2023.9190024。

Declaration of competing interests
利益冲突声明

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
作者声明，他们没有任何可能会影响本文所报告工作的已知经济利益或个人关系。

Acknowledgement 鸣谢

This research was supported by the National Natural Science Foundation of China (Grant Nos. U2033203 and 52272333) and the Fundamental Research Funds for Central Universities of Nanjing University of Aeronautics and Astronautics (Grant No. 3082022NS2022067).
本研究得到了国家自然科学基金（批准号：U2033203和52272333）和南京航空航天大学中央高校基本科研业务费（批准号：3082022NS2022067）的资助。

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Cited by (0)

Chenhao Guo is currently pursuing his M.S. degree in transportation engineering at College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, China. His research interests include urban air mobility, air traffic management, and air traffic big data visualization, analysis and modeling.

Jianxiong Nie is with Air Traffic Management Bureau of Central-South China. He is an expert in air traffic control and airspace operations, as well as a construction project consulting expert. He has extensive work experience and a remarkable track record in air traffic management, having participated in scientific and technological research and development projects involving various aspects of air traffic operations, earning high recognition in the industry.

Xu Hang received his M.S. degree in transportation engineering in Nanjing University of Aeronautics and Astronautics in 2013. He has 11 years of experience in air traffic control and 12 years of experience in airspace management, with strong scientific research and management skills. He is a senior engineer and director of airspace management office of Central-South Regional Air Traffic Management Bureau (ATMB), Civil Aviation Administration of China (CAAC). He is also a specialist for preparing ICAO on-site Universal Safety Oversight Audit Programme (USOAP) audit in ANS. His expertise includes airspace planning, management, assessment, and new technology for air navigation.

Yanjun Wang is an associate professor of the College of Civil Aviation, Nanjing University of Aeronautics and Astronautics (NUAA), China. He received his B.S. degree in air traffic management and dispatch and his M.S. degree in transportation engineering from NUAA in 2004 and 2007, respectively. He was a doctoral researcher at EUROCONTROL Experimental Center from 2009 to 2012, and received his Ph.D. degree in information and network science from Télécom ParisTech (ENST), France. He was a visiting faculty at Massachusetts Institute of Technology from December 2018 to April 2020. His research interests cover human factors in aviation, big-data analytics, and network flow optimization and network resilience.

Yanyan Chen is an associate professor of Civil Aviation Management Institute of China. He was the technical officer of the International Civil Aviation Organization in Air Navigation Bureau, and a senior engineer of air traffic control strategic planning. He serves as the editor-in-chief of Journal of Air Traffic Control.

Daniel Delahaye received his B.S. degree in engineering from the Ecole Nationale de l'Aviation Civile (ENAC, French Civil Aviation University); his M.S. degree in signal processing from the National Polytechnic Institute of Toulouse, in 1991; his Ph.D. degree in automatic control from the Aeronautics and Space National School, in 1995, under the co-supervision of Marc Schoenauer; and his Ph.D. degree from the Department of Aeronautics and Astronautics, MIT, in 1996, under the supervision of Prof. Amedeo Odoni. He is currently the Head of the Optimization and Machine Learning Team, ENAC Research Laboratory. He is also in charge of the research chair “AI for ATM and Large-Scale Urban Mobility” in the new AI institute Artificial and Natural Intelligence Toulouse Institute (ANITI), Toulouse. He conducts research on mathematical optimization and artificial intelligence for airspace design and aircraft trajectories optimization. He actively collaborates with MIT, Georgia Tech, and NASA on development of artificial intelligence algorithms for air traffic management applications.

¹: These authors contributed equally.

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Outline 概要

Figures (8) 数字 (8)

Tables (1) 表格 (1)

Communications in Transportation Research
交通研究通讯

Abstract 摘要

Keywords 关键词

1. Introduction 1.导言

2. Literature review 2.文献综述