An Analysis of the Factors Influencing the Capacity of Constrained Urban Airspace

Abstract

The traffic density of small aerial vehicles operating within urban environments is expected to increase significantly in the near future. This urban environment is highly constrained due to being limited to the low-altitude airspace directly above the existing road network. To increase understanding of the factors influencing the capacity of urban airspace, multiple empirical studies have been performed using fast-time simulations. However, the empirical nature of these simulations hampers the extrapolation of their results beyond the specific conditions that have been tested. At the same time, the emergent behaviour of aircraft in constrained urban airspace, such as queueing and local hotspots, yields the existing analytical models for general airspace invalid. In this paper, we derive and validate an analytical model approximating the relationship between the mean flow rate and mean density in a two-dimensional orthogonal grid network airspace, expressed in the so-called Macroscopic Fundamental Diagram. This analytical model is based on road transportation queueing theory and can explain the different interactions occurring in constrained urban airspace compared to general airspace. Notable findings show that the entire airspace can become unstable when the maximum capacity of a single intersection only is reached. Furthermore, the maximum airspace density is found to be unaffected by cruise speed. The results demonstrate how the derived analytical model for the Macroscopic Fundamental Diagram provides an increased understanding of the factors that influence capacity of constrained urban airspace, thereby offering an effective tool for urban airspace design applications. Moreover, this model lays the groundwork for the derivation of more expanded models, including the altitude dimension and non-orthogonal or non-four-way intersections, that can further improve comprehension of constrained urban airspace.