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Millions of Internet of Thing (IoT) devices have been widely deployed to support applications such as smart city, industrial Internet, and smart transportation. These IoT devices periodically upload their collected data and reconfigure themselves to adapt to the dynamic environment. Both operations are resource consuming for low-end IoT devices. An edge computing enabled unmanned aerial vehicle (UAV) is proposed to fly over to collect data and complete reconfiguration computing tasks from IoT devices. Distinct from most existing work, this paper focuses on flight speed scheduling that allocates proper flight speed to minimize the energy consumption of the UAV with a practical energy model, under the constraints of individual task execution deadlines and communication ranges. We formulate the Energy-Efficient flight Speed Scheduling (EESS) problem, and devise a novel diagram to visualize and analyze this problem. An optimal energy-efficient flight speed scheduling (Offspeeding) algorithm is then proposed to solve the offline version of the EESS problem. Utilizing Offspeeding and the optimal properties obtained from the theoretical analysis, an online heuristic speed scheduling algorithm is developed for more realistic scenarios, where information from IoT devices keeps unknown until the UAV flies close. Finally, simulation results demonstrate our online heuristic is near optimal. This research sheds light on a new research direction, e.g., deadline driven UAV speed scheduling for edge computing with a practical propulsion energy model.