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The design of effective routing protocols in airborne networks (ANs) relies on suitable mobility models that capture the movement patterns of airborne vehicles. As airborne vehicles cannot make sharp turns as easily as ground vehicles do, the widely used ground-based mobile ad hoc network (MANET) mobility models are not appropriate to use as the analytical frameworks for airborne networking. In this paper, we introduce a novel mobility model, which is called the smooth-turn (ST) mobility model, that captures the correlation of acceleration of airborne vehicles across temporal and spatial coordinates. The proposed model is realistic in capturing the tendency of airborne vehicles toward making straight trajectories and STs with large radii, yet is tractable enough for analysis and design. We first describe the mathematics of this model and then prove that the stationary node distribution is uniform. Furthermore, we introduce a metric to quantify the degree of model randomness, and using this, we compare and classify several mobility models in the literature. We conclude this paper with several possible variations to the basic ST mobility model.