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 use stochastic geometry to characterise the behaviour of a network of UAV access points that intelligently position themselves above user hotspots, and we evaluate the performance of such a network against cases where the UAVs are positioned in a rectangular grid or according to heuristic positioning algorithms.