The wireless sensor network (WSN) technology have been evolving very quickly in recent years. Sensors are constantly increasing in sensing, processing, storage, and communication capabilities. In many WSNs that are used in environmental, commercial and military applications, the sensors are lined up linearly due to the linear nature of the structure or area that is being monitored making a special class of these networks; We defined these in a previous paper as Linear Sensor Networks (LSNs), and provided a classification of the different types of LSNs. A pure multihop approach to route the data all the way along the linear network (e.g. oil, gas and water pipeline monitoring, border monitoring, road-side monitoring, etc.), which can extend for hundreds or even thousands of kilometers can be very costly from an energy dissipation point of view. In order to significantly reduce the energy consumption used in data transmission and extend the network lifetime, we present a framework for monitoring linear infrastructures using LSNs where data collection and transmission is done using UAVs. The system defines four types of nodes, which include: sensor nodes (SNs), relay nodes (RNs), UAVs, and sinks. The SNs use a classic WSN multihop routing approach to transmit their data to the nearest RN, which acts as a cluster head for its surrounding SNs. A UAV moves back and forth along the linear network and transports the data that is collected by the RNs to the sinks located at both ends of the LSN. We name this network architecture a UAV-based LSN (ULSN). In addition, three different UAV movement approaches are presented, simulated, and analyzed in order to measure the system performance under various network conditions.