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This study considers a downlink power consumption problem for unmanned aerial vehicles (UAVs)‐assisted wireless communications, in which UAVs are used as aerial base stations to provide service for the ground users and equipped with a directional antenna of fixed beamwidth. Moreover, the on‐board circuit power of UAV is taking into consideration. The authors derive a closed‐form expression for the optimal flying altitude and number of UAVs by minimising the total power consumption under the users' rate requirements in the given coverage area. The numerical simulation and theoretical results show that the optimal flying altitude of UAVs depends on the beamwidth of the directional antenna at UAVs, the on‐board circuit power of UAVs, and the rate constraint of each user.