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Falling paper flutters and tumbles through air, whereas a paper airplane glides smoothly if its leading edge is appropriately weighted. We investigate this transformation from ‘plain paper’ to ‘paper plane’ through experiments, aerodynamic modelling and free flight simulations of thin plates with differing centre of mass (CoM) locations. Periodic modes such as fluttering, tumbling and bounding give way to steady gliding and then downward diving as the CoM is increasingly displaced towards one edge. To explain these observations, we formulate a quasi-steady aerodynamic model whose force and torque coefficients are informed by experimental measurements. The dependencies on angle of attack reflect the transition from attached to separated flow and a dynamic centre of pressure, effects that prove critical to reproducing the observed motions of paper planes in air and plates in water. Because the model successfully accounts for unsteady and steady flight modes, it may be usefully applied to further problems involving actuated motions, feedback control and interactions with ambient flows. 

Abstract Modern day aerobic respiration in mitochondria involving complex I converts redox energy into chemical energy and likely evolved from a simple anaerobic system now represented by hydrogen gas-evolving hydrogenase (MBH) where protons are the terminal electron acceptor. Here we present the cryo-EM structure of an early ancestor in the evolution of complex I, the elemental sulfur (S 0 )-reducing reductase MBS. Three highly conserved protein loops linking cytoplasmic and membrane domains enable scalable energy conversion in all three complexes. MBS contains two proton pumps compared to one in MBH and likely conserves twice the energy. The structure also reveals evolutionary adaptations of MBH that enabled S 0 reduction by MBS catalyzed by a site-differentiated iron-sulfur cluster without participation of protons or amino acid residues. This is the simplest mechanism proposed for reduction of inorganic or organic disulfides. It is of fundamental significance in the iron and sulfur-rich volcanic environments of early earth and possibly the origin of life. MBS provides a new perspective on the evolution of modern-day respiratory complexes and of catalysis by biological iron-sulfur clusters.