, which explains our experimental data well. The dashed and dashed-dot lines in Figure are plots of Equation for Black Si and Glaco surfaces with α = 1.1×10 -4 and 2.9×10 -3 values calculated based on θ and ∆ cos θ values obtained in previous sections with no other fitting parameters. Equation 6 also predicts an expression for the the critical speed the droplet must have to overcome contact-line pinning, namely Ũcrit = (6α) 1/2 = (3/2 ∆ cos θ) 1/2 sin θ (Results summarized in Table ). Note that here we assume that ∆ cos θ is independent of U I and contact-line speed, which we have verified in Figure . At high impact velocity Ũ ≫ 1, we ignore the effects of contact-line pinning. Instead, iner-Table : Summary of the parameters obtained (experimentally) for the two surfaces and used to plot dashed/dashed-dot lines in Figure . 1.1×10 -4 0.025 Glaco 148 • 4.6×10 -2 2.9×10 -3 0.13 tial effects dominate, and the droplet spreads into a thin disc with maximum contact radius r max ∼ R Ũ 1/2 and a resulting surface area of 2πr 2 max (to account for top and bottom surfaces, ignoring the sides) upon impact; at which point, the kinetic energy of the impacting droplet is converted to interfacial energy 2πγr 2 max ∼ 2πγR 2 Ũ . After rebound, the interfacial energy is converted back to kinetic energy (albeit at a lower value) 2 mU 2 R ∼ 2πγR 2 Ũ , which can be rearranged to give e ∼ 1/ Ũ 1/2 for Ũ ≫ 1 (7) , consistent with the data obtained by our group and Wang et al. ( ) (See gray full line in Figure ). Note that in our analysis, we have ignored the effects of viscous dissipation, which is important for more viscous droplets (e.g., glycerin), but not for pure water droplets. See also further discussion of e in Supporting Figure .