Keith Moored

Batoid Fishes: Inspiration for the Next Generation of Underwater Robots

For millions of years, aquatic species have utilized the principles of unsteady hydrodynamics for propulsion and maneuvering. They have evolved high-endurance swimming that can outperform current underwater vehicle technology in the areas of stealth, maneuverability and control authority. Batoid fishes, including the manta ray, Manta birostris, the cownose ray, Rhinoptera bonasus, and the Atlantic stingray, Dasyatis sabina, have been identified as a high-performing species due to their ability to migrate long distances, maneuver in spaces the size of their tip-to-tip wing span, produce enough thrust to leap out of the water, populate many underwater regions, and attain sustained swimming speeds of 2.8 m/s with low flapping/ undulating frequencies. These characteristics make batoid fishes an ideal platform to emulate in the design of a bio-inspired autonomous underwater vehicle. The enlargedpectoral finsofeachrayundergoescomplexmotionsthatcouplespanwise curvature with a chordwise traveling wave to produce thrust and to maneuver. Researchersareinvestigatingtheseamazingspeciestounderstandthebiologicalprinciples for locomotion. The continuum of swimming motions—from undulatory to oscillatory—demonstrates the range of capabilities, environments, and behaviors exhibited by these fishes. Direct comparisons between observed swimming motions and the underlying cartilage structure of the pectoral fin have been made. A simple yet powerful analytical model to describe the swimming motions of batoid fishes has been developed and is being used to quantify their hydrodynamic performance. This model is also being used as the design target for artificial pectoral fin design. Various strategies have been employed to replicate pectoral fin motion. Active tensegrity structures, electro-active polymers, and fluid muscles are three structure/actuator approaches that have successfully demonstrated pectoral-finlike motions. This paper explores these recent studies to understand the relationship between form and swimming function of batoid fishes and describes attempts to emulate their abilities in the next generation of bio-inspired underwater vehicles.

The Analysis of Tensegrity Structures for the Design of a Morphing Wing

Current attempts to build fast, efficient, and maneuverable underwater vehicles have looked to nature for inspiration. However, they have all been based on traditional propulsive techniques, i.e., rotary motors. In the current study a promising and potentially revolutionary approach is taken that overcomes the limitations of these traditional methods-morphing structure concepts with integrated actuation and sensing. Inspiration for this work comes from the manta ray (Manta birostris) and other batoid fish. These creatures are highly maneuverable but are also able to cruise at high speeds over long distances. In this paper, the structural foundation for the biomimetic morphing wing is a tensegrity structure. A preliminary procedure is presented for developing morphing tensegrity structures that include actuating elements. To do this, the virtual work method has been modified to allow for individual actuation of struts and cables. The actuation response of tensegrity beams and plates are studied and results are presented. Specifically, global deflections resulting from actuation of specific elements have been calculated with or without external loads. Finally, a shape optimization analysis of different tensegrity structures to the biological displacement field will be presented.

Linear instability mechanisms leading to optimally efficient locomotion with flexible propulsors

We present the linear stability analysis of experimental measurements obtained from unsteady flexible pitching panels. The analysis establishes the connections among the wake dynamics, propulsor dynamics, and Froude efficiency in flexible unsteady propulsion systems. Efficiency is calculated from direct thrust and power measurements and wake flowfields are obtained using particle image velocimetry. It is found that for flexible propulsors every peak in efficiency occurs when the driving frequency of motion is tuned to a wake resonant frequency, not a structural resonant frequency. Also, there exists an optimal flexibility that globally maximizes the efficiency. The optimal flexibility is the one where a structural resonant frequency is tuned to a wake resonant frequency. The optimally tuned flexible panels demonstrate an efficiency enhancement of 122%–133% as compared to an equivalent rigid panel and there is a broad spectrum of wake resonant frequencies allowing high efficiency swimming over a wide range of operating conditions. At a wake resonant frequency we find that the entrainment of momentum into the time-averaged velocity jet is maximized.

Unsteady propulsion by an intermittent swimming gait

Computational results are presented on comparison of intermittently and continuously pitching two dimensional airfoils. In literature, a viscous mechanism proposed by Lighthill (1971) where skin friction of an undulating body can be around 3 - 5 times greater than a rigidly-held coasting body, has been the well adopted explanation of energetic advantage of the intermittent gait over continuous gait. We find that in an inviscid environment, with only involvement of pressure forces, up to 60% of energy is saved by using intermittent swimming. The maximum economy benefit is observed with modified Strouhal number range of 0.15 - 0.5 and the reduced frequency range of 2 - 5. The inviscid mechanism that leads to the superior performance is observed to be coming from the increase of the ratio of thrust generating forces to the induced drag forces. This increase happens as the ratio of swimming to coasting duration is adjusted. In addition, scaling laws predicting the thrust, power, free swimming velocity and cost of transport of two dimensional continuously pitching airfoils are studied for the intermittent swimming gait.

Kinematics of swimming of the manta ray: three-dimensional analysis of open water maneuverability

ABSTRACT For aquatic animals, turning maneuvers represent a locomotor activity that may not be confined to a single coordinate plane, making analysis difficult, particularly in the field. To measure turning performance in a three-dimensional space for the manta ray (Mobula birostris), a large open-water swimmer, scaled stereo video recordings were collected. Movements of the cephalic lobes, eye and tail base were tracked to obtain three-dimensional coordinates. A mathematical analysis was performed on the coordinate data to calculate the turning rate and curvature (1/turning radius) as a function of time by numerically estimating the derivative of manta trajectories through three-dimensional space. Principal component analysis was used to project the three-dimensional trajectory onto the two-dimensional turn. Smoothing splines were applied to these turns. These are flexible models that minimize a cost function with a parameter controlling the balance between data fidelity and regularity of the derivative. Data for 30 sequences of rays performing slow, steady turns showed the highest 20% of values for the turning rate and smallest 20% of turn radii were 42.65±16.66 deg s−1 and 2.05±1.26 m, respectively. Such turning maneuvers fall within the range of performance exhibited by swimmers with rigid bodies. Highlighted Article: Underwater stereovideography detailing the three-dimensional maneuvering performance of the manta ray in its natural environment shows that its turning maneuvers fall within the range of those exhibited by swimmers with rigid bodies.

Inviscid Scaling Laws of a Self-Propelled Pitching Airfoil

Inviscid computational results are presented on a self-propelled virtual body combined with an airfoil undergoing pitch oscillations about its leading edge. The scaling trends of the time-averaged ...

The Swimming of Manta Rays

Manta rays propel themselves by combining oscillating and undulating motions of flexible surfaces. We describe two experiments to study the effects of excitation and flexibility on the wake flowfield: experiments on undulating and flapping three-dimensional fins of elliptical planform, and experiments on pitching two-dimensional panels of rectangular planform with varying flexibility. To interpret the results on thrust and efficiency, we propose scalings for aspect ratio and flexibility, and develop a stability analysis called wake resonance theory. Here we focus on the insights provided by wake resonance theory.

Flow interactions of two- and three-dimensional networked bio-inspired control elements in an in-line arrangement

We present experiments that examine the modes of interaction, the collective performance and the role of three-dimensionality in two pitching propulsors in an in-line arrangement. Both two-dimensional foils and three-dimensional rectangular wings of AR  =  2 are examined. In contrast to previous work, two interaction modes distinguished as the coherent and branched wake modes are not observed to be directly linked to the propulsive efficiency, although they are linked to peak thrust performance and minimum power consumption as previously described (Boschitsch et al 2014 Phys. Fluids 26 051901). In fact, in closely-spaced propulsors peak propulsive efficiency of the follower occurs near its minimum power and this condition reveals a branched wake mode. Alternatively, for propulsors spaced far apart peak propulsive efficiency of the follower occurs near its peak thrust and this condition reveals a coherent wake mode. By examining the collective performance, it is discovered that there is an optimal spacing between the propulsors to maximize the collective efficiency. For two-dimensional foils the optimal spacing of X *  =  0.75 and the synchrony of ϕ  =  2π / 3 leads to a collective efficiency and thrust enhancement of 42% and 38%, respectively, as compared to two isolated foils. In comparison, for AR  =  2 wings the optimal spacing of X *  =  0.25 and the synchrony of ϕ  =  7 π / 6 leads to a collective efficiency and thrust enhancement of 25% and 15%, respectively. In addition, at the optimal conditions the collective lateral force coefficients in both the two- and three-dimensional cases are negligible, while operating off these conditions can lead to non-negligible lateral forces. Finally, the peak efficiency of the collective and the follower are shown to have opposite trends with increasing spacing in two- and three-dimensional flows. This is correlated to the breakdown of the impinging vortex on the follower wing in three-dimensions. These results can aid in the design of networked bio-inspired control elements that through integrated sensing can synchronize to three-dimensional flow interactions.

Unsteady Performance of Finite-Span Pitching Propulsors in Side-by-Side Arrangements

Experimental measurements are presented on the performance of two finite-span pitching wings with an aspect ratio of AR = 2 interacting in a side-by-side arrangement. Experiments are conducted for various synchronies and cross-stream spacings. The thrust, power and lift coefficients as well as the efficiency are reported for both the individual wings and the collective. The collective thrust and power consumption are found to increasewhile the efficiency decreases during out-of-phase oscillations (φ = π) for close spacings of Y∗ ≤ 0.75. Similarly, the collective thrust and power consumption are found to decrease while the efficiency increases during inphase oscillations (φ = 0) for spacings of Y∗ ≤ 1.125. In contrast to this trade-off between improved thrust or efficiency, there are conditions such as at Y∗ = 1 and φ ≈ π/2 and 3π/2 that give a 20% increase in collective thrust and 17% increase in collective efficiency at the same time. It is further demonstrated that the direction of the collective lift shows a dependence on both the synchrony and the spacing.

Disentangling the Relation Between the Planform Shape and Swimming Gait in Cetacean Propulsion

Cetaceans have evolved a broad range of morphological characteristics and swimming gaits associated with enhanced thrust production, high propulsive efficiency, and reduced drag. These variations in their fluke shape and swimming gait influence their force production and energy requirements for swimming. The present study aims to disentangle the relation between the fluke shape and swimming gait in self-propelled swimming. Planform shapes are parametrized by using a NACA-inspired function where the coefficients are fit to different species of cetacea. An unsteady three-dimensional boundary element method is used to model the self-propelled flukes with a drag-producing virtual body. By interchanging the shape and gait parameters, the thrust, power, and efficiency of swimming along with the wake structures are characterized. It is determined that the shape and the gait of the fluke have a considerable influence on the wake topology and in turn the Strouhal number. The force production and power consumption of cetacean swimming is found to follow trends of lift-based propulsion with propulsive efficiencies ranging from 75–85%. It is also discovered that the effect of the shape and gait on the swimming performance are not intertwined and are in fact independent.