Water entry impact dynamics of diving birds

Effect of feathers on drag in plunge-diving birds

This study explores the impact of feathers on the hydrodynamic drag experienced by diving birds, which is critical to their foraging efficiency and survival. Employing a novel experimental approach, we analyzed the kinematics of both feathered and nonfeathered projectiles during their transition from air to water using high-speed imaging and an onboard accelerometer. The drag coefficients were determined through two methods: a direct calculation from the acceleration data and a theoretical approach fitted to the observed velocity profiles. Our results indicate that feathers significantly increase the drag force during water entry, with feathered projectiles exhibiting approximately double the drag coefficient of their smooth counterparts. These findings provide new insights into the role of avian feather morphology in diving mechanics and have potential implications for the design of bioinspired aquatic vehicles in engineering. The study also discusses the biological implications of increased drag due to feathers and suggests that factors such as body shape might play a more critical role in the diving capabilities of birds than previously understood.

Leger J, Goldbogen JA. Spin-leap performance by cetaceans is influenced by moment of inertia

Cetaceans are capable of extraordinary locomotor behaviors in both water and air. Whales and dolphins can execute aerial leaps by swimming rapidly to the water surface to achieve an escape velocity. Previous research on spinner dolphins demonstrated the capability of leaping and completing multiple spins around their longitudinal axis with high angular velocities. This prior research suggested the slender body morphology of spinner dolphins together with the shapes and positions of their appendages allowed for rapid spins in the air. To test whether greater moments of inertia reduced spinning performance, videos and biologging data of cetaceans above and below the water surface were obtained. The principal factors affecting the number of aerial spins a cetacean can execute were moment of inertia and use of control surfaces for subsurface corkscrewing. For spinner dolphin, Pacific striped dolphin, bottlenose dolphin, minke whale and humpback whale, each with swim speeds of 6-7 m s-1, our model predicted that the number of aerial spins executable was 7, 2, 2, 0.76 and 1, respectively, which was consistent with observations. These data implied that the rate of subsurface corkscrewing was limited to 14.0, 6.8, 6.2, 2.2 and 0.75 rad s-1 for spinner dolphins, striped dolphins, bottlenose dolphins, minke whales and humpback whales, respectively. In our study, the moment of inertia of the cetaceans spanned a 21,000-fold range. The greater moments of inertia for the last four species produced large torques on control surfaces that limited subsurface corkscrewing motion and aerial maneuvers compared with spinner dolphins.

Slamming dynamics of diving and its implications for diving-related injuries

In nature, many animals dive into water at high speeds, e.g., humans dive from cliffs, birds plunge, and aquatic animals porpoise and breach. Diving provides opportunities for animals to find prey and escape from predators and is a source of great excitement for humans. However, diving from high platforms can cause severe injuries to a diver. In this study, we demonstrate how similarity in the morphology of diving fronts unifies the slamming force across diving animals and humans. By measuring a time-averaged impulse that increases linearly with the impact height, we are able to estimate the unsteady hydrodynamic forces that an average human body experiences during the slamming phase of a feet-first, hand-first, or head-first dive. We evaluate whether the unsteady forces put the diver at risk of muscle or bone injuries for a particular diving height. Therefore, this study sheds light on a hydrodynamics-based protocol for safe high diving and an evolutionary driver for animal morphology.

Jerk within the Context of Science and Engineering—A Systematic Review

Rapid changes in forces and the resulting changes in acceleration, jerk and higher order derivatives can have undesired consequences beyond the effect of the forces themselves. Jerk can cause injuries in humans and racing animals and induce fatigue cracks in metals and other materials, which may ultimately lead to structure failures. This is a reason that it is used within standards for limits states. Examples of standards which use jerk include amusement rides and lifts. Despite its use in standards and many science and engineering applications, jerk is rarely discussed in university science and engineering textbooks and it remains a relatively unfamiliar concept even in engineering. This paper presents a literature review of the jerk and higher derivatives of displacement, from terminology and historical background to standards, measurements and current applications.

Investigations on the buckling and dynamics of diving-inspired systems when entering water

This work provides comparative modeling approaches to determine the velocities and natural frequencies of plunge-diving bird and bioinspired drone systems when entering water. These systems are chosen to further explain the survival of diving birds as they impact water and to provide insight into the design geometry and material choice of bioinspired diving drones. A nonlinear reduced-order model is developed and utilized to analyze the dive at impact considering both Timoshenko and Euler-Bernoulli beam theories. Using Hamilton's principle, the equations of motion are first derived. Then, static and dynamic buckling analyses are conducted. For this study, a geometrically simplified cone-beam system is considered, where the cone represents the head and the beam represents both the neck and body of the plunge-diving systems. The first study is to analyze the effects different diving drone materials and cone dimensions play on the sensitivity of the system. The second study applies geometric parameters to the cone-beam system representative of a plunge-diving bird (Northern gannet) and a surface-diving bird (Double-crested cormorant). The results show that choosing a material with a higher Young's modulus and a cone with a smaller half angle increase the velocity at which buckling occurs. The buckling velocities of the predicted Northern gannet model appear to be much greater than the average recorded diving speeds, suggesting that the bird is capable of plunge-diving at more extreme conditions. The natural frequencies are found for the aforementioned plunge-diving systems to predict failure if any external frequencies are known to act on the system while on a mission, such as conditions dependent on the climate or environment. It is shown in all buckling studies that the Euler-Bernoulli beam theory consistently overestimates the responses when compared with the Timoshenko beam theory. In the dynamic responses, Euler-Bernoulli beam theory overestimates for the pre-buckling region, then underestimates at the start of the post-buckling region until a point where the two theories cross paths. The amount of error with Euler-Bernoulli beam theory depends heavily on the slenderness ratio of the beam due to the theory being a simplification of the Timoshenko beam theory. It is noted that as the development of a more realistic bird model improves, the thickness will become significant and the use of Euler-Bernoulli beam theory at the point of impact will no longer be a valid assumption.