Which animals use their energy better during movement? One metric to answer this question is the energy cost per unit distance per unit weight. Prior data show that this metric decreases with mass, which is considered to imply that massive animals are more efficient. Although useful, this metric also implies that two dynamically equivalent animals of different sizes will not be considered equally efficient. We resolve this longstanding issue by first determining the scaling of energy cost per unit distance traveled. The scale is found to be M 2 / 3 or M 1 / 2 , where M is the animal mass. Second, we introduce an energy-consumption coefficient (C E ) defined as energy per unit distance traveled divided by this scale. C E is a measure of efficiency of swimming and flying, analogous to how drag coefficient quantifies aerodynamic drag on vehicles. Derivation of the energy-cost scale reveals that the assumption that undulatory swimmers spend energy to overcome drag in the direction of swimming is inappropriate. We derive allometric scalings that capture trends in data of swimming and flying animals over 10-20 orders of magnitude by mass. The energy-consumption coefficient reveals that swimmers beyond a critical mass, and most fliers are almost equally efficient as if they are dynamically equivalent; increasingly massive animals are not more efficient according to the proposed metric. Distinct allometric scalings are discovered for large and small swimmers. Flying animals are found to require relatively more energy compared with swimmers.cost of transport | Froude efficiency C ost of transport (COT), defined as the energy spent per unit distance traveled, is often used as a measure of the energy efficiency of movement. However, a dimensionless efficiency measure enables comparison across animal sizes for which the scale of COT is required. The weight of the animal could be the scale to nondimensionalize COT (1, 2), but there is no basis in mechanics to do so. Here, we derive the scaling of COT. To that end, we note that it is frequently assumed that a swimming animal spends energy to overcome drag. The assertion that an animal spends power to overcome drag lacks direct evidence in undulatory propulsion. It is well known that animals swimming at low Reynolds number spend power in producing undulatory kinematics (3-5). Even at finite Reynolds numbers it is believed that swimming animals spend power to produce swimming kinematics (6). In this work we formally show that an undulatory swimmer spends power to produce the undulatory kinematics rather than to overcome drag. This result will be used to obtain the scaling of COT. This scale will be used to nondimensionalize COT, which is the new energy-consumption coefficient proposed here. Our analysis also leads to allometric scalings of different variables.Power Spent During Swimming Swimming animals achieve locomotion through the undulatory kinematics of their body. The undulations of the body are predominantly in a direction lateral to the direction of swimming (7-10). In ...

Nearly eighty years ago, Gray reported that the drag power experienced by a dolphin was larger than the estimated muscle power – this is termed as Gray's paradox. We provide a fluid mechanical perspective of this paradox. The viewpoint that swimmers necessarily spend muscle energy to overcome drag in the direction of swimming needs revision. For example, in undulatory swimming most of the muscle energy is directly expended to generate lateral undulations of the body, and the drag power is balanced not by the muscle power but by the thrust power. Depending on drag model utilized, the drag power may be greater than muscle power without being paradoxical.

In the past decade, disinformation has become an increasingly dangerous enemy of public health, scientific advancement, and social stability. To address and counter this trend, it is essential to first identify communities most at risk for disinformation. The Jin-Hafiz Disinformation Index (JHDI) is developed and validated as a tool to counter disinformation and address deficits of good information on a county level in the United States. Once vulnerable communities are identified with the JHDI, targeted interventions with community partnerships can be conducted to address knowledge concerns.

No abstract