In this work, we propose a methodology for the energy-efficient placement of an unmanned aerial system (UAS) deployed to collect data from a set of ground user equipments (UEs). The data-communication between the UEs and the UxNB, a radio access node carried by an unmanned aerial vehicle (UAV), of the UAS follows a non-orthogonal multiple-access (NOMA) scheme; in which all the UEs share the same time and frequency resources. The receiver removes the inter-UE interference from the co-channel UEs through joint implementation of a powerreduction technique at the UEs and the successive interference cancellation (SIC) at the receiver. Firstly, a new energy-efficiency metric, area energy efficiency (AEE) representing the total area covered by a UxNB per Watt-Hour (Wh) of energy consumed, is introduced. Then, the optimal hovering altitude of the UxNB that maximizes the AEE is determined using the proposed algorithm. Numerical evaluations show that the obtained solution using the proposed algorithm matches the globally optimal solution, and the proposed NOMA scheme prevails over an equivalent orthogonal multiple access (OMA) scheme, in terms of the AEE.