Relations between morphology, buoyancy and energetics of requiem sharks

Sharks have a distinctive shape that remained practically unchanged through hundreds of millions of years of evolution. Nonetheless, there are variations of this shape that vary between and within species. We attempt to explain these variations by examining the partial derivatives of the cost of transport of a generic shark with respect to buoyancy, span and chord of its pectoral fins, length, girth and body temperature. Our analysis predicts an intricate relation between these parameters, suggesting that ectothermic species residing in cooler temperatures must either have longer pectoral fins and/or be more buoyant in order to maintain swimming performance. It also suggests that, in general, the buoyancy must increase with size, and therefore, there must be ontogenetic changes within a species, with individuals getting more buoyant as they grow. Pelagic species seem to have near optimally sized fins (which minimize the cost of transport), but the majority of reef sharks could have reduced the cost of transport by increasing the size of their fins. The fact that they do not implies negative selection, probably owing to decreased manoeuvrability in confined spaces (e.g. foraging on a reef)

Energetic and physical limitations on the breaching performance of large whales

The considerable power needed for large whales to leap out of the water may represent the single most expensive burst maneuver found in nature. However, the mechanics and energetic costs associated with the breaching behaviors of large whales remain poorly understood. In this study we deployed whale-borne tags to measure the kinematics of breaching to test the hypothesis that these spectacular aerial displays are metabolically expensive. We found that breaching whales use variable underwater trajectories, and that high-emergence breaches are faster and require more energy than predatory lunges. The most expensive breaches approach the upper limits of vertebrate muscle performance, and the energetic cost of breaching is high enough that repeated breaching events may serve as honest signaling of body condition. Furthermore, the confluence of muscle contractile properties, hydrodynamics, and the high speeds required likely impose an upper limit to the body size and effectiveness of breaching whales

Longitudinal Stability Criteria for a Propeller-Driven Aircraft

The Routh criterion is used to assess longitudinal dynamic stability of a propeller-driven aircraft. Under a few plausible assumptions on possible ranges of the pertinent stability derivatives, it reduces to a pair of simple conditions imposing a traditional aft limit (the forward of the maneuver and the neutral-speed-stability points) on the center-of-gravity position and an upper limit on the longitudinal moment of inertia. It is demonstrated that most aircraft have sufficiently small inertia to remain stable as long as their center-of-gravity is properly placed. At the same time, sailplane-like aircraft (as, e.g., long endurance UAVs), with an engine installed at the rear extremity of the aircraft, may have sufficiently high inertia to become unstable regardless of their center-of-gravity placement