We develop a simple model for steady, uniform transport in aeolian saltation over a horizontal bed that is based on the computation of periodic particle trajectories in a turbulent shearing flow. The wind and the particles interact through drag, and the particles collide with the bed. We consider collisions with both rigid and erodible beds. The impact velocity in a periodic trajectory over a rigid bed is unconstrained, while that over an erodible bed must have a value that produces a single rebounding particle. The difference in the nature of the collisions results in qualitative differences in the nature of the solutions for the periodic trajectories and, in particular, to differences in the dependence of the particle flow rate on the strength of the turbulent shearing.