Data-driven CFD Scaling of Bioinspired Mars Flight Vehicles for Hover.

One way to improve our model of Mars is through aerial sampling and surveillance, which could provide information to augment the observations made by ground-based exploration and satellite imagery. Flight in the challenging ultra-low-density Martian environment can be achieved with properly scaled bioinspired flapping wing vehicle configurations that utilize the same high lift producing mechanisms that are employed by insects on Earth. Through dynamic scaling of wings and kinematics, we investigate the ability to generate solutions for a broad range of flapping wing flight vehicles masses ranging from insects O(10-3) kg to the Mars helicopter Ingenuity O(100) kg. A scaling method based on a neural-network trained on 3D Navier-Stokes solutions is proposed to determine approximate wing size and kinematic values that generate bioinspired hover solutions. We demonstrate that a family of solutions exists for designs that range from 1 to 1000 grams, which are verified and examined using a 3D Navier-Stokes solver. Our results reveal that unsteady lift enhancement mechanisms, such as delayed stall and rotational lift, are present in the bioinspired solutions for the scaled vehicles hovering in Martian conditions. These hovering vehicles exhibit payloads of up to 1 kg and flight times on the order of 100 minutes when considering the respective limiting cases of the vehicle mass being comprised entirely of payload or entirely of a battery and neglecting any transmission inefficiencies. This method can help to develop a range of Martian flying vehicle designs with mission viable payloads, range, and endurance.

Power Benefits of High-Altitude Flapping Wing Flight at the Monarch Butterfly Scale.

The long-range migration of monarch butterflies, extended over 4000 km, is not well understood. Monarchs experience varying density conditions during migration, ranging as high as 3000 m, where the air density is much lower than at sea level. In this study, we test the hypothesis that the aerodynamic performance of monarchs improves at reduced density conditions by considering the fluid-structure interaction of chordwise flexible wings. A well-validated, fully coupled Navier-Stokes/structural dynamics solver was used to illustrate the interplay between wing motion, aerodynamics, and structural flexibility in forward flight. The wing density and elastic modulus were measured from real monarch wings and prescribed as inputs to the aeroelastic framework. Our results show that sufficient lift is generated to offset the butterfly weight at higher altitudes, aided by the wake-capture mechanism, which is a nonlinear wing-wake interaction mechanism, commonly seen for hovering animals. The mean total power, defined as the sum of the aerodynamic and inertial power, decreased by 36% from the sea level to the condition at 3000 m. Decreasing power with altitude, while maintaining the same equilibrium lift, suggests that the butterflies generate lift more efficiently at higher altitudes.

First lift-off and flight performance of a tailless flapping-wing aerial robot in high-altitude environments.

Flapping flight of animals has captured the interest of researchers due to their impressive flight capabilities across diverse environments including mountains, oceans, forests, and urban areas. Despite the significant progress made in understanding flapping flight, high-altitude flight as showcased by many migrating animals remains underexplored. At high-altitudes, air density is low, and it is challenging to produce lift. Here we demonstrate a first lift-off of a flapping wing robot in a low-density environment through wing size and motion scaling. Force measurements showed that the lift remained high at 0.14 N despite a 66% reduction of air density from the sea-level condition. The flapping amplitude increased from 148 to 233 degrees, while the pitch amplitude remained nearly constant at 38.2 degrees. The combined effect is that the flapping-wing robot benefited from the angle of attack that is characteristic of flying animals. Our results suggest that it is not a simple increase in the flapping frequency, but a coordinated increase in the wing size and reduction in flapping frequency enables the flight in lower density condition. The key mechanism is to preserve the passive rotations due to wing deformation, confirmed by a bioinspired scaling relationship. Our results highlight the feasibility of flight under a low-density, high-altitude environment due to leveraging unsteady aerodynamic mechanisms unique to flapping wings. We anticipate our experimental demonstration to be a starting point for more sophisticated flapping wing models and robots for autonomous multi-altitude sensing. Furthermore, it is a preliminary step towards flapping wing flight in the ultra-low density Martian atmosphere.

Effects of abdomen undulation in energy consumption and stability for monarch butterfly.

The flight of monarch butterflies is characterized by a relatively large wing, flapping at a relatively low frequency coupled with abdomen undulation. This paper presents the dynamics of a flapping wing flyer that can be applied to the coupled motion of the wing, body, and abdomen at the monarch butterfly scale, which is formulated directly on the configuration manifold. The resulting thorax and abdomen motion as well as the resultant forces are consistent with the flight of a live monarch butterfly. Based on these, beneficial effects of the abdomen undulation in the flight of monarch butterflies are illustrated. For both hover and forward-climbing trajectories, the abdomen undulation results in a reduction of the energy and power consumption. Furthermore, the Floquet stability analysis shows that the periodic orbits associated with both flight modes are stable. In particular, the abdomen undulation improves the stability. Compared to the dynamics of hawkmoth, bumblebee, and fruitfly models, the monarch possesses superior stability properties.

Kinematic analysis of gait in an underwater treadmill using land-based Vicon T 40s motion capture cameras arranged externally.

Aquatic therapy for rehabilitation can be performed in a variety of environments, which can vary from a traditional swimming pool to a self-contained underwater treadmill. While kinematic analysis has been performed in large volume swimming pools using specific underwater motion capture systems, researchers may only have access to a land-based motion-capture system, which is not waterproof. Additionally, underwater motion capture systems may not fit within the confines of a smaller underwater treadmill. Thus, the purpose of this study was to design and analyze methodology to quantify lower limb kinematics during an aquatic treadmill session, using a land-based motion capture system. Kinematics of lower limb motion at different speeds was studied while walking on an underwater treadmill in comparison to walking on the same treadmill without water (empty tank). The effects of the presence of water on walking kinematics was analyzed and interpreted using parametric and non-parametric testing procedures. The results suggest significant influences of speed on knee and ankle angles (p < 0.05) in both dryland and aquatic scenarios. Knee and ankle angle measures revealed no significant differences between the dryland and water treadmill scenarios (p > 0.05). The increased time requirement in water for the full gait cycle found in this study indicates influence of resistive effects. This finding can be especially suited for muscle strengthening and stabilizing treatments for lower limbs. Also, a framework was developed to realize a potential methodology to use land-based motion capture cameras to successfully analyze the kinematics of gait in constrained aquatic volumes.

Effects of flight altitude on the lift generation of monarch butterflies: from sea level to overwintering mountain.

Aerodynamic efficiency behind the annual migration of monarch butterflies, the longest among insects, is an unsolved mystery. Monarchs migrate 4000 km at high-altitudes to their overwintering mountains in Central Mexico. The air is thinner at higher altitudes, yielding reduced aerodynamic drag and enhanced range. However, the lift is also expected to reduce in lower density conditions. To investigate the ability of monarchs to produce sufficient lift to fly in thinner air, we measured the climbing motion of freely flying monarchs in high-altitude conditions. An optical method was used to track the flapping wing and body motions inside a large pressure chamber. The air density inside the chamber was reduced to recreate the higher altitude densities. The lift coefficient generated by monarchs increased from 1.7 at the sea-level to 9.4 at 3000 m. The correlation between this increase and the flapping amplitude and frequency was insignificant. However, it strongly correlated to the effective angle of attack, which measures the wing to body velocity ratio. These results support the hypothesis that monarchs produce sufficiently high lift coefficients at high altitudes despite a lower dynamic pressure.

Experimental Force and Deformation Measurements of Bioinspired Flapping Wings in Ultra-Low Martian Density Environment.

A Mars flight vehicle could provide a third-dimension for ground-based rovers and supplement orbital observation stations, providing a much more detailed aerial view of the landscape as well as unprecedented survey of the atmosphere of Mars. However, flight on Mars is a difficult proposition due to the very low atmospheric density, which is approximately 1.3% of sea level density on Earth. While traditional aircraft efficiency suffers in the low Reynolds number environment, insect inspired flapping wing flyers on Mars might be able to take advantage of the same lift enhancing effects as insects on Earth. The present work investigates the feasibility of using a bioinspired, flapping wing flight vehicle to produce lift in an ultra-low-density Martian atmosphere. A four-wing prototype, inspired by a prior computational study, was placed in an atmospheric chamber to simulate Martian density. Lift and wing deformation were simultaneously recorded. In Earth density conditions, the passive pitch wing deflection increased monotonically with flapping frequency. On the other hand, in the Martian density environment, the passive pitch deflection angles were very erratic. The measured lift peaked at around 8 grams at 16 Hz. These measurements suggest that sufficient aerodynamic forces for hover on Mars can be generated for a 6-gram flapping wing vehicle. Also, the performance can potentially be improved by better understanding the fluid-structure interaction in ultra-low Mars density condition.

System Analyzer for a Bioinspired Mars Flight Vehicle System for Varying Mission Contexts.

The Marsbee is a novel bioinspired flapping flight vehicle concept for aerial Mars exploration. The Marsbee design addresses the challenges of flying on Mars by mimicking the unsteady lift generation mechanisms seen in terrestrial insects To enable the comparison of the Marsbee system to other flying Mars exploration concepts, a study was performed that employs a Multidisciplinary Design Optimization architecture to analyze and optimize the Marsbee system to suit a wide variety of missions. This study developed an analyzer for a Multidisciplinary Design Feasible (MDF) architecture, as well as explored the design space and attributes necessary in an objective function for Mars flying system missions. The analyzer is based on physical models developed in previous studies. Its functionality was demonstrated by analyzing 100,000 randomly generated designs, with design variables close to a prototype Marsbee tested in Martian density conditions. These results show that by using flexible wings rather than rigid wings the maximum flight times increased from 53 minutes to 114 minutes, and the maximum payload masses increased from 28 grams to 61 grams. These are competing effects and cannot be maximized simultaneously. The results of this study will be used to determine the optimal Marsbee system.

Static accuracy analysis of Vicon T40s motion capture cameras arranged externally for motion capture in constrained aquatic environments.

While the capabilities of land-based motion capture systems in biomechanical applications have been previously reported, the possibility of using motion tracking systems externally to reconstruct markers submerged inside an aquatic environment has been under explored. This study assesses the ability of a motion capture system (Vicon T40s) arranged externally to track a retro-reflective marker inside a glass tank filled with water and without water. The reflective tape used for marker creation in this study was of Safety of Life at Sea (SOLAS) grade as the conventional marker loses its reflective properties when submerged. The overall trueness calculated based on the mean marker distance errors, varied between 0.257 mm and 0.290 mm in different mediums (air, glass and water). The overall precision calculated based on mean standard deviation of mean marker distances at different locations varied between 0.046 mm and 0.360 mm in different mediums. Our results suggest, that there is no significant influence of the presence of water on the overall static accuracy of the marker center distances when markers were made of SOLAS grade reflective tape. Using optical motion tracking systems for evaluating locomotion in aquatic environment can help to better understand the effects of aquatic therapy in clinical rehabilitation, especially in scenarios that involve equipment, such as an underwater treadmill which generally have constrained capture volumes for motion capture.

Scaling Bioinspired Mars Flight Vehicles for Hover.

With the resurgent interest in landing humans on Mars, it is critical that our understanding of the Martian environment is complete and accurate. One way to improve our model of the red planet is through aerial surveillance, which provides information that augments the observations made by ground-based exploration and satellite imagery. Although the ultra-low-density Mars environment has previously stymied designs for achieving flight on Mars, bioinspired solutions for flapping wing flight can utilize the same high lift producing mechanisms employed by insects on Earth. Motivated by the current technologies for terrestrial flapping wing aerial vehicles on Earth, we seek solutions for a 5 gram bioinspired flapping wing aerial vehicle for flight on Mars. A zeroth-order method is proposed to determine approximate wing and kinematic values that generate bioinspired hover solutions. We demonstrate that a family of solutions exists for designs that are O(101) g, which are verified using a 3D Navier-Stokes solver. Our results show that unsteady lift enhancement mechanisms, such as delayed stall and rotational lift, are present in the bioinspired solution for a 5 g flapping wing vehicle hovering in Mars conditions, verifying that the zeroth-order method is a useful design tool. As a result, it is possible to design a family of bioinspired flapping wing robots for Mars by augmenting the adverse effects of the ultra-low density with large wings that exploit the advantages of unsteady lift enhancement mechanisms used by insects on Earth.

Corrigendum: An analytical model and scaling of chordwise flexible flapping wings in forward flight (2016 Bioinspir. and Biomim. 12 016006).

This corrigendum provides a correction to the manuscript. We show that a higher order fluid-structure interaction term that accounts for the transversal flow oscillations, induced by the compliant motion of the airfoil, leads to the Theodorsen's lift equation with a sign reversal for one of the terms. This modified Theodorsen's equation was used in the manuscript.

Chordwise wing flexibility may passively stabilize hovering insects.

Insect wings are flexible, and the dynamically deforming wing shape influences the resulting aerodynamics and power consumption. However, the influence of wing flexibility on the flight dynamics of insects is unknown. Most stability studies in the literature consider rigid wings and conclude that the hover equilibrium condition is unstable. The rigid wings possess an unstable oscillatory mode mainly due to their pitch sensitivity to horizontal velocity perturbations. Here, we show that a flapping wing flyer with flexible wings exhibits stable hover equilibria. The free-flight insect flight dynamics are simulated at the fruit fly scale in the longitudinal plane. The chordwise wing flexibility is modelled as a linear beam. The two-dimensional Navier-Stokes equations are solved in a tight fluid-structure integration scheme. For a range of wing flexibilities similar to live insects, all eigenvalues of the system matrix about the hover equilibrium have negative real parts. Flexible wings appear to stabilize the unstable mode by passively deforming their wing shape in the presence of perturbations, generating significantly more horizontal velocity damping and pitch rate damping. These results suggest that insects may passively stabilize their hover flight via wing flexibility, which can inform designs of synthetic flapping wing robots.

Achieving bioinspired flapping wing hovering flight solutions on Mars via wing scaling.

Achieving atmospheric flight on Mars is challenging due to the low density of the Martian atmosphere. Aerodynamic forces are proportional to the atmospheric density, which limits the use of conventional aircraft designs on Mars. Here, we show using numerical simulations that a flapping wing robot can fly on Mars via bioinspired dynamic scaling. Trimmed, hovering flight is possible in a simulated Martian environment when dynamic similarity with insects on earth is achieved by preserving the relevant dimensionless parameters while scaling up the wings three to four times its normal size. The analysis is performed using a well-validated 2D Navier-Stokes equation solver, coupled to a 3D flight dynamics model to simulate free flight. The majority of power required is due to the inertia of the wing because of the ultra-low density. The inertial flap power can be substantially reduced through the use of a torsional spring. The minimum total power consumption is 188 W kg-1 when the torsional spring is driven at its natural frequency.

Wing-wake interaction destabilizes hover equilibrium of a flapping insect-scale wing.

Wing-wake interaction is a characteristic nonlinear flow feature that can enhance unsteady lift in flapping flight. However, the effects of wing-wake interaction on the flight dynamics of hover are inadequately understood. We use a well-validated 2D Navier-Stokes equation solver and a quasi-steady model to investigate the role of wing-wake interaction on the hover stability of a fruit fly scale flapping flyer. The Navier-Stokes equations capture wing-wake interaction, whereas the quasi-steady models do not. Both aerodynamic models are tightly coupled to a flight dynamic model, which includes the effects of wing mass. The flapping amplitude, stroke plane angle, and flapping offset angle are adjusted in free flight for various wing rotations to achieve hover equilibrium. We present stability results for 152 simulations which consider different kinematics involving the pitch amplitude and pitch axis as well as the duration and timing of pitch rotation. The stability of all studied motions was qualitatively similar, with an unstable oscillatory mode present in each case. Wing-wake interaction has a destabilizing effect on the longitudinal stability, which cannot be predicted by a quasi-steady model. Wing-wake interaction increases the tendency of the flapping flyer to pitch up in the presence of a horizontal velocity perturbation, which further destabilizes the unstable oscillatory mode of hovering flight dynamics.

Effects of spanwise flexibility on the performance of flapping flyers in forward flight.

Flying animals possess flexible wings that deform during flight. The chordwise flexibility alters the wing shape, affecting the effective angle of attack and hence the surrounding aerodynamics. However, the effects of spanwise flexibility on the locomotion are inadequately understood. Here, we present a two-way coupled aeroelastic model of a plunging spanwise flexible wing. The aerodynamics is modelled with a two-dimensional, unsteady, incompressible potential flow model, evaluated at each spanwise location of the wing. The two-way coupling is realized by considering the transverse displacement as the effective plunge under the dynamic balance of wing inertia, elastic restoring force and aerodynamic force. The thrust is a result of the competition between the enhancement due to wing deformation and induced drag. The results for a purely plunging spanwise flexible wing agree well with experimental and high-fidelity numerical results from the literature. Our analysis suggests that the wing aspect ratio of the abstracted passerine and goose models corresponds to the optimal aeroelastic response, generating the highest thrust while minimizing the power required to flap the wings. At these optimal aspect ratios, the flapping frequency is near the first spanwise natural frequency of the wing, suggesting that these birds may benefit from the resonance to generate thrust.

An analytical model and scaling of chordwise flexible flapping wings in forward flight.

Aerodynamic performance of biological flight characterized by the fluid structure interaction of a flapping wing and the surrounding fluid is affected by the wing flexibility. One of the main challenges to predict aerodynamic forces is that the wing shape and motion are a priori unknown. In this study, we derive an analytical fluid-structure interaction model for a chordwise flexible flapping two-dimensional airfoil in forward flight. A plunge motion is imposed on the rigid leading-edge (LE) of teardrop shape and the flexible tail dynamically deforms. The resulting unsteady aeroelasticity is modeled with the Euler-Bernoulli-Theodorsen equation under a small deformation assumption. The two-way coupling is realized by considering the trailing-edge deformation relative to the LE as passive pitch, affecting the unsteady aerodynamics. The resulting wing deformation and the aerodynamic performance including lift and thrust agree well with high-fidelity numerical results. Under the dynamic balance, the aeroelastic stiffness decreases, whereas the aeroelastic stiffness increases with the reduced frequency. A novel aeroelastic frequency ratio is derived, which scales with the wing deformation, lift, and thrust. Finally, the dynamic similarity between flapping in water and air is established.

Correction to 'Aerodynamics, sensing and control of insect-scale flapping-wing flight'.

[This corrects the article DOI: 10.1098/rspa.2015.0712.].

Aerodynamics, sensing and control of insect-scale flapping-wing flight.

There are nearly a million known species of flying insects and 13 000 species of flying warm-blooded vertebrates, including mammals, birds and bats. While in flight, their wings not only move forward relative to the air, they also flap up and down, plunge and sweep, so that both lift and thrust can be generated and balanced, accommodate uncertain surrounding environment, with superior flight stability and dynamics with highly varied speeds and missions. As the size of a flyer is reduced, the wing-to-body mass ratio tends to decrease as well. Furthermore, these flyers use integrated system consisting of wings to generate aerodynamic forces, muscles to move the wings, and sensing and control systems to guide and manoeuvre. In this article, recent advances in insect-scale flapping-wing aerodynamics, flexible wing structures, unsteady flight environment, sensing, stability and control are reviewed with perspective offered. In particular, the special features of the low Reynolds number flyers associated with small sizes, thin and light structures, slow flight with comparable wind gust speeds, bioinspired fabrication of wing structures, neuron-based sensing and adaptive control are highlighted.

Aerodynamic performance of two-dimensional, chordwise flexible flapping wings at fruit fly scale in hover flight.

Fruit flies have flexible wings that deform during flight. To explore the fluid-structure interaction of flexible flapping wings at fruit fly scale, we use a well-validated Navier-Stokes equation solver, fully-coupled with a structural dynamics solver. Effects of chordwise flexibility on a two dimensional hovering wing is studied. Resulting wing rotation is purely passive, due to the dynamic balance between aerodynamic loading, elastic restoring force, and inertial force of the wing. Hover flight is considered at a Reynolds number of Re = 100, equivalent to that of fruit flies. The thickness and density of the wing also corresponds to a fruit fly wing. The wing stiffness and motion amplitude are varied to assess their influences on the resulting aerodynamic performance and structural response. Highest lift coefficient of 3.3 was obtained at the lowest-amplitude, highest-frequency motion (reduced frequency of 3.0) at the lowest stiffness (frequency ratio of 0.7) wing within the range of the current study, although the corresponding power required was also the highest. Optimal efficiency was achieved for a lower reduced frequency of 0.3 and frequency ratio 0.35. Compared to the water tunnel scale with water as the surrounding fluid instead of air, the resulting vortex dynamics and aerodynamic performance remained similar for the optimal efficiency motion, while the structural response varied significantly. Despite these differences, the time-averaged lift scaled with the dimensionless shape deformation parameter γ. Moreover, the wing kinematics that resulted in the optimal efficiency motion was closely aligned to the fruit fly measurements, suggesting that fruit fly flight aims to conserve energy, rather than to generate large forces.

Analytical model for instantaneous lift and shape deformation of an insect-scale flapping wing in hover.

In the analysis of flexible flapping wings of insects, the aerodynamic outcome depends on the combined structural dynamics and unsteady fluid physics. Because the wing shape and hence the resulting effective angle of attack are a priori unknown, predicting aerodynamic performance is challenging. Here, we show that a coupled aerodynamics/structural dynamics model can be established for hovering, based on a linear beam equation with the Morison equation to account for both added mass and aerodynamic damping effects. Lift strongly depends on the instantaneous angle of attack, resulting from passive pitch associated with wing deformation. We show that both instantaneous wing deformation and lift can be predicted in a much simplified framework. Moreover, our analysis suggests that resulting wing kinematics can be explained by the interplay between acceleration-related and aerodynamic damping forces. Interestingly, while both forces combine to create a high angle of attack resulting in high lift around the midstroke, they offset each other for phase control at the end of the stroke.