Filming sport videos from an aerial view has always been a hard and an expensive task to achieve, especially in sports that require a wide open area for its normal development or the ones that put in danger human safety. Recently, a new solution arose for aerial filming based on the use of Unmanned Aerial Vehicles (UAVs), which is substantially cheaper than traditional aerial filming solutions that require conventional aircrafts like helicopters or complex structures for wide mobility. In this paper, we describe the design process followed for building a customized UAV suitable for sports aerial filming. The process includes the requirements definition, technical sizing and selection of mechanical, hardware and software technologies, as well as the whole integration and operation settings. One of the goals is to develop technologies allowing to build low cost UAVs and to manage them for a wide range of usage scenarios while achieving high levels of flexibility and automation. This work also shows some technical issues found during the development of the UAV as well as the solutions implemented.