Extended Data Fig. 4: Restitution mechanics and empirical fit.

References for the observations are given on the bottom right, where markers with shaded interiors signify experiments not using standard Earth conditions or field data, markers with solid interiors signify explicit measurements of the restitution coefficients outside wind tunnels. Magenta and yellow markers are from studies where the restitution coefficient is measured or noted, values for the vertical-axes of markers with other colors are inferred from simulated trajectories. All horizontal-axes are the Galileo number \({{{\mathcal{G}}}}\). (a) The ratio of the ejection to impact velocity of a characteristic saltating grain, that is the restitution coefficient e. (b) The angle the grain impacts the bed, with the theoretical fixed ejection angle denoted (cyan line). (c) The restitution coefficient normalized such that it impacted the bed at a fixed angle (θ↓ = − 10∘), e10, with the empirical relationship used in the main text relating the two axes (cyan line) (Methods).