Accurately predicting the size-dependant sinking rate of diatoms is necessary to fully understand the cycling of oceanic carbon and silicon. Stokes' law predicts that sinking velocity should be proportional to the square of a diatom's radius (a scaling exponent of 2), which does not agree with empirically measured sinking speeds (scaling exponents of 1.2-1.6). We offer an alternative model for sinking speed that separately accounts for the different densities of a diatom's frustule (its siliceous cell armor) and its cytoplasm. The ratio of frustule to cytoplasm volume changes with size and, thereby, affects the scaling relationship between velocity and radius. The resulting model predicts a scaling exponent between 1 and 2 depending on the size and shape of the diatom, more accurately predicting the upper bound of measured sinking speeds and offering an analytical formula for the prediction of the maximum sinking speed of diatoms.

Given sufficient space, it is possible for gliding animals to reach an equilibrium state with no net forces acting on the body. In contrast, every gliding trajectory must begin with a non-steady component, and the relative importance of this phase is not well understood. Of any terrestrial animal glider, snakes exhibit the greatest active movements, which may affect their trajectory dynamics. Our primary aim was to determine the characteristics of snake gliding during the transition to equilibrium, quantifying changes in velocity, acceleration, and body orientation in the late phase of a glide sequence. We launched 'flying' snakes (Chrysopelea paradisi) from a 15 m tower and recorded the mid-to-end portion of trajectories with four videocameras to reconstruct the snake's body position with mm to cm accuracy. Additionally, we developed a simple analytical model of gliding assuming only steady-state forces of lift, drag and weight acting on the body and used it to explore effects of wing loading, lift-to-drag ratio, and initial velocity on trajectory dynamics. Despite the vertical space provided to transition to steady-state gliding, snakes did not exhibit equilibrium gliding and in fact displayed a net positive acceleration in the vertical axis, an effect also predicted by the analytical model.

Despite their lack of appendages, flying snakes (genus Chrysopelea) exhibit aerodynamic performance that compares favorably to other animal gliders. We wished to determine which aspects of Chrysopelea's unique shape contributed to its aerodynamic performance by testing physical models of Chrysopelea in a wind tunnel. We varied the relative body volume, edge sharpness, and backbone protrusion of the models. Chrysopelea's gliding performance was surprisingly robust to most shape changes; the presence of a trailing-edge lip was the most significant factor in producing high lift forces. Lift to drag ratios of 2.7-2.9 were seen at angles of attack (α) from 10-30°. Stall did not occur until α>30°and was gradual, with lift falling off slowly as drag increased. Chrysopelea actively undulates in an S-shape when gliding, such that posterior portions of the snake's body lie in the wake of the more anterior portions. When two Chrysopelea body segment models were tested in tandem to produce a two dimensional approximation to this situation, the downstream model exhibited an increased lift-to-drag ratio (as much as 50% increase over a solitary model) at all horizontal gaps tested (3-7 chords) when located slightly below the upstream model and at all vertical staggers tested (±2 chords) at a gap of 7 chords.