Can a Laplace PDE Define Air Corridors through Low-Altitude Airspace?

Urban Uncrewed Aircraft System (UAS) flight will require new regulations that assure safety and accommodate unprecedented traffic density levels. Multi- Uascoordination is essential to both objectives. This paper models UAS coordi-nation as an ideal fluid flow with a stream field governed by the Laplace partial differential equation. Streamlines spatially define closely-spaced deconflicted routes through the airspace and define air corridors that safely wrap buildings and other structures so UAS can avoid collision even when flying among low-altitude vertical obstacles and near mountainous terrain. We divide a city into zones, with each zone having its own sub-network, to allow for modularity and assure computation time for route generation is linear as a function of total area. We demonstrate the strength of our proposed approach by computing air corridors through low altitude airspace of select cities with tall buildings. For US cities, we use open LiDAR elevation data to determine surface elevation maps. We select non-US cities with existing high-fidelity three-dimensional landscape models.