Capacity of a constrained urban airspace: Influencing factors, analytical modelling and simulations

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. Multiple studies have addressed factors influencing the capacity of urban airspace. These have used simulations of aircraft, yet the empirical nature of these simulations limits their use beyond the specific conditions that have been tested. Analytical models would not have this limitation, but they are only developed for general airspace, while the emergent patterns in constrained urban airspace are different than in general, unconstrained conditions. For instance, queuing and local congestion are patterns that are unique to the heavily-constrained environment. Therefore, in this paper, we derive an analytical model for air traffic in a confined airspace to find the influencing factors for its capacity. By means of a simulation of aerial vehicles, we verify the analytical model and show a relationship between the mean flow rate and mean density in a two-dimensional orthogonal grid network airspace. Results show that the entire airspace can become unstable when the maximum capacity of just one intersection is reached. Furthermore, the maximum airspace density is found to be unaffected by cruise speed. The results demonstrate how the derived analytical model provides an effective tool to predict the effect of several design parameters on the capacity of constrained urban airspace. Moreover, this model can form the basis for further extensions, including the altitude dimension and non-orthogonal or non-four-way intersections.