We present a method to define a clustering of terminals connected to a backhauled network provided by aerial platforms, such as drones or balloons. Our novel optimization method optimizes the choice of clusters. We reduce the former energy consumption achieved by the state of the art. We manage to formulate this problem as an explicit linear optimization program. Thus, by decomposing the energy consumption into a constant and a variable part, we obtain an energy reduction of the variable part from 20% up to almost 50%, when compared with the best known method. We prove that we reach the best lower bound in term of energy consumption. Our method performs 10% to 90% of energy saving compared to an unclustered network.