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Wireless access points on unmanned aerial vehicles (UAVs) are being considered for mobile service provisioning in commercial networks. To be able to efficiently use these devices in cellular networks it is necessary to first have a qualitative and quantitative understanding of how their design parameters reflect on the service quality experienced by the end user. In this paper we set up a scenario where a network of UAVs operating at a certain height above ground provide wireless service within coverage areas shaped by their directional antennas. We provide an analytical expression for the coverage probability experienced by a typical user as a function of the UAV parameters and demonstrate the performance trade-offs that occur as these parameters are varied.