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Recent progress of electric systems has raised attention towards hybrid-electric and full-electric aircraft. Nevertheless, the current low battery energy density limits the application of these propulsive architectures to large transport aircraft. In the context of the general aviation category, full-electric aircraft for the so-called Urban Air Mobility scenario are gaining increasing interest. These air taxis, also called e-VTOL, are conceived to exploit vertical take-off and landing capabilities, to carry people from one point to another, typically within the same city. In this paper, a new conceptual design methodology for urban air vehicles is presented and applied to an innovative convertiplane, called TiltOne, based on a box-wing architecture coupled with tilt-wing mechanisms. Several TiltOne configurations have been designed according to the current regulations imposed by European Union Aviation Safety Agency, and sensitivity analyses have been carried out on the varying main design parameters, such as wing loading and propellers’ disk loading, as well as main top-level aircraft requirements. The results provide an overview for today’s operational capabilities of such aircraft and, in addition, depict possible scenarios for a near-future horizon, based on the assumption of increased performance levels for the electric powertrain components. In such scenario, two different concepts of operations are analysed and discussed: the first is based on a given design range, long enough to cover the urban distances; the second is conceived to exploit the capability of flying multiple shorter missions with a single battery charge. The designed TiltOne configurations derived from these different approaches are presented, highlighting their potential capabilities and possible drawbacks.