Dimensionless Speeds Research Articles

Scaling of Gait, Limb Posture, Forces, and Inertial Properties in Terrestrial Locomotion of American Alligators Across a Thousand-Fold Increase in Body Mass

Synopsis Scaling of body shape, gait, limb kinematics, and kinetics can inform about mechanical and energetic constraints influencing animal locomotion on land. However, our knowledge of terrestrial locomotion among tetrapods is biased toward animals that use parasagittal limb postures (mammals and birds). Whether species that use non-parasagittal limb postures (e.g., crocodylians and lizards) share similar scaling principles remains uncertain, especially toward the larger end of the body size spectrum. Here, we compare new data from large adult American alligators (140–223 kg) with previous data from smaller individuals (0.2–5.6 kg) to evaluate the scaling of gait, limb posture, ground reaction forces, and inertial properties of body segments over a size range spanning three orders of magnitude. Larger alligators walked with higher relative stride frequencies and shorter relative stride lengths at equal dimensionless speeds, suggesting that alligators prioritize stance phase mechanical work reduction at the expense of higher costs for swing as they increase in size. Limb posture also changed with body mass: ∼1 kg and larger alligators typically used more adducted and extended limbs, which is expected to mitigate limb muscle forces during stance. Ground reaction forces were increasingly hindlimb dominant as alligators grow to larger size, paralleled by a posterior shift in the center of mass. Counterintuitively, the forelimb grew faster in mass than the hindlimb, possibly because recruited muscle volume is closer to its maximum capacity in the forelimb, compelling larger alligators to keep up with increased mechanical demands via muscle growth more for the forelimb than the hindlimb. These results highlight the numerous changes in body proportions and locomotor performance that are required among animals that use non-parasagittal limb posture, as they grow from neonatal sizes into large adults.

Experiments on the Drag and Lift Coefficients of a Spinning Sphere

The drag and lift coefficients are important parameters that affect the particle motion in a viscous fluid. In the present study, the drag and lift coefficients of a spinning sphere in a water tank were studied experimentally using a high-speed camera. To this end, 22 cases were studied to cover a wide range of dimensionless angular speeds (0.149 < Rr < 3.471) and Reynolds numbers (610 < Re < 3472). Based on the present experimental data and the results obtained from the literature, expressions were developed to calculate the lift and drag coefficients. The performed analyses on lift coefficient show that there is a critical Reynolds number (Rec) at each dimensionless angular speed. When 0 < Re < Rec, the lift coefficient decreases with increasing the Reynolds number, while it is constant when Rec < Re< 3500. The constant lift coefficient corresponding to different spin speeds was defined as the limit value of the lift coefficient. It is found that when 1 < Rr < 12, the limit value of the lift coefficient is 0.37, while the limit value of the lift coefficient increases with increasing dimensionless angular speed at 0 < Rr < 1. It is found that the spin increases the drag coefficient of a spinning sphere only when 0 < Rr < 10. Moreover, the performed analyses show that the drag coefficient of a spinning sphere is less than that of a non-spinning sphere when 10 < Rr < 25. Furthermore, the lift-to-drag ratio of a spinning sphere is discussed in this article.

Do we all walk the walk? A comparison of walking behaviors across tetrapods.

A walking gait has been identified in a range of vertebrate species with different body plans, habitats, and life histories. With increased application of this broad umbrella term, it has become necessary to assess the physical characteristics, analytical approaches, definitions, and diction used to describe walks. To do this, we reviewed studies of slow speed locomotion across a range of vertebrates to refine the parameters used to define walking, evaluate analytical techniques, and propose approaches to maximize consistency across subdisciplines. We summarize nine key parameters used to characterize walking behaviors in mammals, birds, reptiles, amphibians, and fishes. After identifying consistent patterns across groups, we propose a comprehensive definition for a walking gait. A walk is a form of locomotion where the majority of the forward propulsion of the animal comes from forces generated by the appendages interacting with the ground. During a walk, an appendage must be out of phase with the opposing limb in the same girdle and there is always at least one limb acting as ground-support (no suspension phase). Additionally, walking occurs at dimensionless speeds <1 v* and the duty factor of the limbs is always >0.5. Relative to other gaits used by the same species, the stance duration of a walk is long, the cycle frequency is low, and the cycle distance is small. Unfortunately, some of these biomechanical parameters, while effectively describing walks, may also characterize other, non-walking gaits. Inconsistent methodology likely contributes to difficulties in comparing data across many groups of animals; consistent application of data collection and analytical techniques in research methodology can improve these comparisons. Finally, we note that the kinetics of quadrupedal movements are still poorly understood and much work remains to be done to understand the movements of small, exothermic tetrapods.

Propagation of interfacial (Stoneley-type) waves at the joint boundary of two initially-stressed incompressible half-spaces

The presence of initial stress in solids changes the material’s response to finite and infinitesimal deformations. This paper presents a study on the effects of initial stress, finite deformation, and material properties on the speed of interfacial waves which are assumed to travel at the joint boundary of two incompressible half-spaces. The theory of infinitesimal deformations superimposed on finite deformations is used along with the theory of invariants. Boundary conditions at the interface result in an explicit secular equation, which is analyzed generally. For each half-space, a prototype strain–energy function is assumed, which is a function of the deformation gradient and initial stress tensors. The effect of different governing parameters is observed on the wave speed and is analyzed theoretically. Graphical illustrations are also presented to elaborate on the theoretical results. It is observed that for admissible values of parameters, a real wave speed exists and is bounded by values depending on the governing parameters. A comparison between Rayleigh and interfacial wave speeds is also made and supported with graphs of dimensionless wave speeds with respect to initial stresses.

The transient vortex structure in the wake of an axial-symmetric projectile launched underwater

This paper provides refined wake simulations for an underwater projectile launch using an improved delayed detached eddy simulation with the energy equation, volume of fluid, and the overlapping grid technique. Additionally, the projectile wake vortex was analyzed for different Froude numbers and dimensionless transverse flow speeds. Verifications of the numerical method, grid independence, vortex identification method, and time step size are presented. Through a systematic comparison of the wake morphologies, the flow fields and vortex structures in the wakes were analyzed in detail, and the wake vortex evolution mechanisms were explored. The results show that the Kelvin–Helmholtz instability was observed, and the wake flow of the projectile launched underwater contains a complex vortical system that directly determines the wake instabilities. The resulting multiple sub-vortex structures are compact and closely arranged near the central axis without the transverse flow effect. However, compared with cases having no transverse flow, the large-scale double spiral vortex structure in the wake with a transverse flow is more difficult to fracture. In addition, the U-shaped vortex in the secondary vortex is also obviously generated in the wake during the double spiral vortex structure evolution. With an increase in the Froude number, the vortex legs are gradually apparent and, together with the shedding vortex rings in the wake, form a hairpin vortex structure. With an increase in the dimensionless transverse flow speed, the number of sub-vortex rings derived from the shedding vortex in the wake increases significantly, resulting in a more complex interaction mechanism.

Adaptations for bipedal walking: Musculoskeletal structure and three-dimensional joint mechanics of humans and bipedal chimpanzees (Pan troglodytes)

Humans are unique among apes and other primates in the musculoskeletal design of their lower back, pelvis, and lower limbs. Here, we describe the three-dimensional ground reaction forces and lower/hindlimb joint mechanics of human and bipedal chimpanzees walking over a full stride and test whether: 1) the estimated limb joint work and power during the stance phase, especially the single-support period, is lower in humans than bipedal chimpanzees, 2) the limb joint work and power required for limb swing is lower in humans than in bipedal chimpanzees, and 3) the estimated total mechanical power during walking, accounting for the storage of passive elastic strain energy in humans, is lower in humans than in bipedal chimpanzees. Humans and bipedal chimpanzees were compared at matched dimensionless and dimensional velocities. Our results indicate that humans walk with significantly less work and power output in the first double-support period and the single-support period of stance, but markedly exceed chimpanzees in the second double-support period (i.e., push-off). Humans generate less work and power in limb swing, although the species difference in limb swing power was not statistically significant. We estimated that total mechanical positive ‘muscle fiber’ work and power were 46.9% and 35.8% lower, respectively, in humans than in bipedal chimpanzees at matched dimensionless speeds. This is due in part to mechanisms for the storage and release of elastic energy at the ankle and hip in humans. Furthermore, these results indicate distinct ‘heel strike’ and ‘lateral balance’ mechanics in humans and bipedal chimpanzees and suggest a greater dissipation of mechanical energy through soft tissue deformations in humans. Together, our results document important differences between human and bipedal chimpanzee walking mechanics over a full stride, permitting a more comprehensive understanding of the mechanics and energetics of chimpanzee bipedalism and the evolution of hominin walking.

A study on the flow interference characteristics of projectiles successively launched underwater

This paper analyzes the flow interference characteristics of projectiles successively launched underwater with 6 degrees of freedom for different dimensionless launch time intervals and different dimensionless transverse-flow speeds. The realizable k−ε turbulence model and energy equation, as well as the volume of fluid method and overlapping grid technique, are used. Additionally, a verification of the numerical method and a validation of the grid independence are presented. The pressure distribution on the inflow side and backside, the hydrodynamic parameters, the trajectory, and the pitch attitude are studied with the focus on the evolution of hairpin vortex packets in free wake flow. The results show that the hairpin vortex packet in the free wake flow is composed of a multistage hairpin vortex and a low-speed streak region with a stream scale that runs along the interior of the hairpin vortex packet. At higher transverse-flow speeds, the pressure coefficient and hydrodynamic coefficient of the second projectile increase as the launch time interval increases. Due to the effects of transverse flow, when the secondary projectile passes through the core region of the wake vortex, the pressure of uneven distribution characteristics greatly reduces and the trajectory stability increases. To maximize the efficiency and success rate of projectiles successively launched underwater, the second projectile should be launched at ΔT=2.0.

Propulsion of magnetically actuated achiral planar microswimmers in Newtonian and non-Newtonian fluids

Magnetic achiral planar microswimmers can be massively fabricated at low cost and are envisioned to be useful for in vivo biomedical applications. To understand locomotion in representative in vivo environments, we investigated the swimming performance of achiral planar microswimmers in methylcellulose solutions. We observed that these microswimmers displayed very similar swimming characteristics in methylcellulose solutions as in water. Furthermore, this study indicated that the range of precession angles increased as the concentration of MC solution increased. Last, it was demonstrated that achiral planar microswimmers with similar precession angles exhibited nearly the same dimensionless speeds in different concentrations of the methylcellulose solutions. Upon understanding swimmer kinematics, more effective control over the achiral planar microswimmers can be achieved to perform multiple biomedical tasks in in vivo environments.

Numerical treatment of magnetohydrodynamic Carreau liquid with heat and mass transport containing gyrotactic microorganisms

In the current examination, insightful approximations are researched for magnetohydrodynamics Carreau nanofluid having gyrotactic microorganisms over a warmed turning plate. The plate is moving with the steady uniform rakish speed. Administering conditions are gotten by utilizing certain actual presumptions as incomplete differential conditions with limit conditions. These nonlinear types of conditions are changed into coupled standard differential conditions utilizing bunch likeness change. Optimal homotopy investigation strategy (OHAM) is utilized to acquire the graphical outcomes and even qualities for the stream field factors. Graphical portrayal of speeds, temperature, fixation and thickness of gyrotactic microorganisms are examined and clarified. It is tracked down that dimensionless microorganism’s fixation develops for bioconvective Lewis number and focus distinction variable of microorganisms. It is additionally seen that dimensionless speeds diminish because of the attractive impact and Carreau liquid boundary. Contour plots and mathematical outcomes are given for neighbourhood motion boundaries like skin rubbing coefficient, Nusselt number, Sherwood number and thickness number of motile microorganisms.

The loss of the 'pelvic step' in human evolution.

Human bipedalism entails relatively short strides compared with facultatively bipedal primates. Unique non-sagittal-plane motions associated with bipedalism may account for part of this discrepancy. Pelvic rotation anteriorly translates the hip, contributing to bipedal stride length (i.e. the 'pelvic step'). Facultative bipedalism in non-human primates entails much larger pelvic rotation than in humans, suggesting that a larger pelvic step may contribute to their relatively longer strides. We collected data on the pelvic step in bipedal chimpanzees and over a wide speed range of human walking. At matched dimensionless speeds, humans have 26.7% shorter dimensionless strides, and a pelvic step 5.4 times smaller than bipedal chimpanzees. Differences in pelvic rotation explain 31.8% of the difference in dimensionless stride length between the two species. We suggest that relative stride lengths and the pelvic step have been significantly reduced throughout the course of hominin evolution.

Band structure analysis of Green-Naghdi-based thermoelastic wave propagation in cylindrical phononic crystals with energy dissipation using a meshless collocation method

In this paper, a meshless collocation method based on the generalized finite difference (GFD) method is employed for the band structure analysis of thermoelastic waves propagating in the cylindrical phononic crystal (PC). The Green-Naghdi (GN) theory of the generalized coupled thermoelasticity with energy dissipation and the Bloch's theorem are adopted to compute the dispersion relation of thermoelastic waves. The proposed GFD-based meshless collocation method is used to predict the frequency range of the band-gaps and to analyze the effects of the material parameters and the thickness of each layer (sub-cylinder) in a unit-cell on the band-gap property of thermoelastic waves propagating in the cylindrical PCs. The effects of the variations in the layer thicknesses in each unit-cell on the thermoelastic wave band structures are studied in detail. Also, the influences of the key material parameters on the frequency band structures of the thermoelastic waves are investigated. It will be shown that the dimensionless speed of the thermal wave influences the band-gaps more remarkably than other dimensionless parameters such as the dimensionless speeds of the purely elastic dilatational and shear waves, the damping coefficient and the thermoelastic coupling parameter.

Experimental Investigation on the Effect a Rotational Shaft on the Thermal Behavior of a Circular Tube under Constant Heat Flux

Active and passive methods are two main mechanisms of heat transfer improvement. The active methods use external forces to improve heat transfer. This investigation evaluates the thermal and frictional behavior of a circular tube containing a rotational shaft. Constant heat flux was exerted to the circular tube. The fluid inlet and outlet temperature as well as wall temperature of tubes were measured to calculate the hat transfer coefficient. The Re (Reynolds) number was between 800-2000. Also, the dimensionless rotational speed (Rs) had the values of 1,1.5, 2, 2.5 and 3. Results revealed that the rotational shaft could increase the Nu number. Up to %18. Also, the results showed that the rotational shaft could significantly increase the pressure drop and friction factor. The maximum increment of %78 was achieved for friction factor. It was revealed that the use of rotational shaft could be more efficient at low Re numbers and low dimensionless rotational speeds. Also, it was found that by the increment of Reynolds number and being in the transient regime the efficiency of the system would improve.

Low leg compliance permits grounded running at speeds where the inverted pendulum model gets airborne

Animals typically switch from grounded (no flight phases) to aerial running at dimensionless speeds u^ < 1. But some birds use grounded running far above u^ = 1, which puzzles biologists because the inverted pendulum becomes airborne at this speed. Here, we combine computer experiments using the spring-mass model with locomotion data from small birds, macaques and humans to understand the relationship between leg function (stiffness, angle of attack), locomotion speed and gait. With our model, we found three-humped ground reaction force profiles for slow grounded running speeds. The minimal single-humped grounded running speed is u^ = 0.4. This speed value roughly coincides with the transition speed from vaulting to bouncing mechanics in bipeds. Maximal grounded running speed in the model is not limited. In experiments, animals changed from grounded to aerial running at dimensionless contact time around 1. Considering these real-world contact times reduces the solution space drastically, but experimental data fit well. The model still predicts maximal grounded running speed u^ > 1 for low stiffness values used by birds but decreases below u^ = 1 for increasing stiffness. For stiffer legs used in human walking and running, periodic grounded running vanishes. At speeds at which birds and macaques change to aerial running, we found periodic aerial running to intersect grounded running. This could explain why animals can alternate between grounded and aerial running at the same speed and identical leg parameters. Compliant legs enable different gaits and speeds with similar leg parameters, stiff legs require parameter adaptations.

Habitat use and vestibular system's dimensions in lacertid lizards.

The vestibular system is crucial for movement control during locomotion. As the dimensions of the vestibular system determine the fluid dynamics of the endolymph and, as such, the system's function, we investigate the interaction between vestibular system size, head size and microhabitat use in lizards. We grouped 24 lacertid species in three microhabitat types, we acquired three-dimensional models of the bony vestibular systems using micro-computer tomography scanning, and we performed linear and surface measurements. All vestibular measurements scale with a negative allometry with head size, suggesting that smaller heads house disproportionally large ears. As the sensitivity of the vestibular system is positively related to size, a sufficiently large vestibular system in small-headed animals may meet the sensitivity demands during challenged locomotion. We also found that the microhabitat affects the locomotor dynamics: lizards inhabiting open microhabitats run at higher dimensionless speeds. On the other hand, no statistical relationship exists between dimensionless speed and the vestibular system dimensions. Hence, if the vestibular size would differ between microhabitats, this would be a direct effect (i.e. imposed, for instance, by requirements for manoeuvring, balance control, etc.), rather than depending on the lizards' intrinsic running speed. However, we found no effect of the microhabitat on the allometric relationship between head and vestibular system size. The finding that microhabitat is not reflected in the vestibular system size (hence sensitivity) of the lacertids in this study is possibly due to spatial constraints of the skull.

On the vibration of size dependent rotating laminated composite and sandwich microbeams via a transverse shear-normal deformation theory

In this paper, the eigenfrequencies of rotating laminated composite (LC) and sandwich microbeams with different boundary conditions (BCs) are studied. The size-dependent variational formulation of the problem is obtained based on the Modified Couple Stress Theory (MCST) by employing a transverse shear-normal deformable beam theory and finite element method (FEM) formulation. The convergence and verification studies of the developed code are carried out and computed results in terms of dimensionless fundamental frequencies (DFFs) are compared with the available ones in the open literature. Various BCs, aspect ratios, fiber orientation angles, thickness to material length scale parameter (MLSP) ratios, core thickness to face layer thickness ratios, dimensionless rotation speeds (DRSs) and hub ratios are employed for the extensive analyses. It is found that the DFFs of the LC microbeams are highly affected by the small size effect accompanying with the orthotropy ratios, DRSs, hub ratios and fiber orientation angles. The effect of the small size on the DFFs of the rotating clamped-clamped LC microbeams is more pronounced than on those of the rotating clamped-free LC microbeams. The hub ratio has a significant effect on the DFFs of the rotating LC microbeams than the rotation speed.

Dynamic drying transition via free-surface cusps

We study air entrainment by a solid plate plunging into a viscous liquid, theoretically and numerically. At dimensionless speeds $Ca=U\unicode[STIX]{x1D702}/\unicode[STIX]{x1D6FE}$ of order unity, a near-cusp forms due to the presence of a moving contact line. The radius of curvature of the cusp’s tip scales with the slip length multiplied by an exponential of $-Ca$. The pressure from the air flow drawn inside the cusp leads to a bifurcation, at which air is entrained, i.e. there is ‘wetting failure’. We develop an analytical theory of the threshold to air entrainment, which predicts the critical capillary number to depend logarithmically on the viscosity ratio, with corrections coming from the slip in the gas phase.

Three-dimensional kinematics and the origin of the hominin walking stride.

Humans are unique among apes and other primates in the musculoskeletal design of their lower back and pelvis. While the last common ancestor of the Pan-Homo lineages has long been thought to be 'African ape-like', including in its lower back and ilia design, recent descriptions of early hominin and Miocene ape fossils have led to the proposal that its lower back and ilia were more similar to those of some Old World monkeys, such as macaques. Here, we compared three-dimensional kinematics of the pelvis and hind/lower limbs of bipedal macaques, chimpanzees and humans walking at similar dimensionless speeds to test the effects of lower back and ilia design on gait. Our results indicate that locomotor kinematics of bipedal macaques and chimpanzees are remarkably similar, with both species exhibiting greater pelvis motion and more flexed, abducted hind limbs than humans during walking. Some differences between macaques and chimpanzees in pelvis tilt and hip abduction were noted, but they were small in magnitude; larger differences were observed in ankle flexion. Our results suggest that if Pan and Homo diverged from a common ancestor whose lower back and ilia were either 'African ape-like' or more 'Old World monkey-like', at its origin, the hominin walking stride likely involved distinct (i.e. non-human-like) pelvis motion on flexed, abducted hind limbs.

Vibration characteristics of functionally graded graphene reinforced porous nanocomposite cylindrical shells with spinning motion

This paper is concerned with free vibration characteristics of the functionally graded graphene reinforced porous nanocomposite cylindrical shell with spinning motion. It is assumed that the graphene platelet (GPL) nanofillers and internal pores are randomly oriented and uniformly dispersed in each concentric cylindrical shell, and both the GPL weight fraction and the porosity coefficient vary continuously along the thickness direction. Effective material properties of the nanocomposite which are position-dependent are derived employing the modified Halpin-Tsai model and the rule of mixture. Three types of the GPL patterns and four types of the porosity distributions are considered. Frequencies of forward and backward travelling waves and critical spinning speeds are derived from the equations of motion which are established based on the first order shear deformation theory and the Hamilton's principle. Detailed parametric studies on dimensionless natural frequencies and critical spinning speeds of the GPL reinforced porous nanocomposite cylindrical shell are carried out, especially, effect of initial hoop tension on vibration characteristics of the spinning cylindrical shell is numerically discussed.

Free Vibration Analysis of Rotating Functionally Graded Annular Disc of Variable Thickness Using Generalized Differential Quadrature Method

In this paper, free vibration analysis of rotating annular disc made of functionally graded material (FGM) with variable thickness is presented. Elasticity modulus, density and thickness of the disc are assumed to vary radially according to a power low function. The natural frequencies and critical speeds of the rotating FG annular disc of variable thickness with two types of boundary conditions are obtained employing the numerical generalized differential quadrature method (GDQM). The boundary conditions considered in the analysis is the both edges clamped (C-C) and the inner edge clamped and the outer edge free (C-F).The influence of the graded index, thickness variation, geometric parameters and angular velocity on the dimensionless natural frequencies and critical speeds are demonstrated. It is shown that using a plate with a convergent thickness profile, we have a higher critical speed and natural frequency and using a divergent thickness profile, we can lower the critical speed. It is found that increase in the ratio of inner-outer radii could increase the critical speed of the FG annular disk. The results of the present work could improve the design of the rotating FG annular disk in order to avoid resonance condition

Rotation induced flow suppression around two tandem circular cylinders at low Reynolds number

The rotation to a bluff object is known to have a stabilizing effect on the fluid dynamic transport around the body. An unsteady periodic flow can be degenerated into a steady flow pattern depending on the rate of rotation imparted to the body. On the other hand, multiple bodies placed in tandem arrangement with respect to an incoming flow can cause destabilization to the flow as a result of the complicated wake interaction between the bodies. Accordingly, the spacing between the bodies and the rate of rotation have significant impact on the overall fluid dynamic transport around them. The present work aims to understand how these two competing factors are actually influencing the fluidic transport across a pair of identical rotating circular cylinders kept in tandem arrangement in an unconfined medium. The cylinders are subjected to a uniform free stream flow and the gaps between the cylinders are varied as 0.2, 0.7, 1.5 and 3.0. Both the cylinders are made to rotate in the clockwise sense. The Reynolds number based on the free stream flow is taken as 100. A two-dimensional finite volume based transient computation is performed for a range of dimensionless rotational speeds of the cylinders (0 ≤ Ω ≤ 2.75). The results show that the shedding phenomena can be observed up to a critical rate of rotation (Ωcr) depending on the gap spacing. Beyond Ωcr, the flow becomes stabilized and finally completely steady as Ω increases further. Increasing the gap initially causes a slight decrease in the critical rotational speed, however, it increases at a rapid rate for larger gap spacing.