To illuminate both the dynamics of eolian grain flows and the controls on their geometry, we conducted experiments on an inclined platform on which grain flows were initiated by broadcasting sand near the top of the platform in a pattern consistent with wind-blown deposition. The growing depositional bumps eventually over-steepened and failed, generating steep headward- and laterally migrating scarps. Mass was fed to the grain flow in this way for approximately 1/4 of the duration of the flow, after which the flows were solitary waves spreading both downslope and cross-slope. The flows abandoned small levees at their widest points, and eventually stopped, commonly before reaching the base of the platform. Our grain flows were typically 2 m long by 20 cm wide, and slightly less than 1 cm thick. The surface velocities at the toe were nearly equal 15 cm/s, increased to nearly equal 20 cm/s at the nose, and then steadily decreased to nearly equal 10 cm/s towards the tail of the flow. The longitudinal velocity gradients created considerable longitudinal strain rates: the toe was in compression with mean strain rates of order -0.1/s, while the tail was in extension with mean strain rates of order 0.1/s. Averaged over many seconds, the velocities were quite steady. Over shorter periods, however, distinct velocity fluctuations dominated the record, with variations up to 100%, and standard deviations 10-20% of the mean. There were both temporal and spatial correlations in velocity histories of surface tracers. We interpret spatial correlations to reflect fixed topographic perturbations at the self-defined bottom boundary, or ramps, and temporal correlations to indicate coherent regions within the flow, or rafts. Ramps were more common than rafts. The longitudinal length scales of these features may be up to many times the thickness of the flow, and endure up to two seconds. Based on the average velocity and the magnitude of the velocity response to perturbations at the bed, the slightly rate-dependent Coulomb rheological model proposed by Savage and Hutter (1991) best describes the general behavior of these flows. Grain flows stop when the toe either thins below a critical thickness or reaches the toe of the slope. The thickness of the nose of a grain flow is controlled by a combination of gradients in longitudinal volume flux and volume losses to the levees at the edge of the flow. The nose eventually thins sufficiently to stop. The initial spatial distribution of velocities is set by the volume flux history of the evolving scarp within the depositional bump. This sets the spatial distribution of strain within the flow, which in turn controls the thickness of the nose. Assuming that the sizes and geometries of depositional bumps are not a function of dune size, we expect a minimum flow thickness to occur on dunes whose lee face length equals the natural runout length of a typical grain flow. For dunes taller than this, grain-flow thickness should increase because of coalescence of flow tongues at some mid-point on the lee face, loading the mid-face region with coalescing grain-flow tongues that subsequently fail as a single large flow.