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

Abstract

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.

II. Introduction

Flight on Mars remains a desired, yet still unachieved, goal. In addition to allowing more detailed study of the Martian atmosphere, a reliable Mars flight vehicle could be used to guide rovers and supplement orbital imaging with more detailed local terrain mapping. This would allow for the valuable rover time to be used in the most fruitful way possible, virtually eliminating instances where the rover must back track to avoid obstacles or dangerous terrain. Furthermore, Mars flight vehicles can carry sensors and wireless communication devices in combination with a Mars rover. These enhanced sensing and information gathering abilities can contribute to NASA’s Mars exploration objectives, including determining the habitability of Mars, obtaining surface weather measurements to validate global atmospheric models, and preparing for human exploration on Mars [1].

To date, no man-made device has flown on the Red Planet. NASA’s Jet Propulsion Laboratory has designed the Mars Helicopter which is slated to fly with the 2020 Mars rover, arriving on Mars in early 2021. However, its capabilities are expected to be fairly limited with only 180 seconds of flight time per day [2]. Because the Martian atmospheric density is only around 1% that of Earth’s sea level density [3], the inherent inefficiencies of rotary wing aircraft are amplified by the very low Reynolds number, leading to non-optimal lift generation. Low lift generated by rotary wing aircraft in low Reynolds number ranges means that the helicopter requires a large rotor [2] and thus a large volume to transport it to Mars. This large volume requirement makes the Mars Helicopter an expensive solution to potential flight on Mars.

A. Past Mars Flight Vehicle Concepts

Past Mars flight vehicle concepts are varied and interesting in their own right. They range from traditional fixed wing aircraft powered by a bi-propellant rocket system [4] to balloon type devices potentially capable of months of time aloft [5]. These balloons could be used for long term detailed study of the Martian atmosphere but are uncontrolled, and thus, limited in the scope of supplementing rover operations. One fixed wing aircraft concept is the Aerial Regional-scale Environmental Surveyor (ARES) [6] which would fly around an altitude of 2 km and provide ground scan data to an orbiter that would then return to Earth. This would enable a larger amount of data to be returned than could be relayed through the Mars Reconnaissance Orbiter alone. Primarily due to the short duration of the mission, the ARES system is also limited in its ability to support a rover exploration mission.

Insect-inspired lift production has also been considered to achieve flight on Mars. The Entomopter [7,8] is a flapping wing vehicle that uses a blown wing concept for lift enhancement. The Solid State Aircraft [9] is a solar-powered flapping wing aircraft that employs recent advancements in material science. This prior research in bioinspired flight on Mars employed simplified aerodynamic tools that could not accurately predict the complex, unsteady flow resulting from flapping wing motion [7,8]. For example, the Entomopter required an additional vortex generator to augment the unsteady lift. Most importantly, none of these designs have been realized and thus the goal of flight on Mars is still an open problem.

Our previous work [10–12] described a dynamically scaled, bioinspired flapping wing solution – a Marsbee [10]. These Marsbees take advantage of the unsteady lift generating mechanisms present in low Reynolds number motions by conserving the relevant dimensionless parameters [13]. Due to the extremely low density of the Martian atmosphere, a hovering Marsbee operates in a Reynolds number range of 100 < Re < 5000, similar to the range of Reynolds numbers experienced by hovering fruit flies, crane flies, bumblebees, and hummingbirds on Earth.

B. Current Mars Flight Vehicle Concept - Marsbee

Because of their small size and light weight, a data gathering mission could be accomplished using a large number of Marsbees to provide a reconfigurable and resilient swarm of flying vehicles in combination with a rover. Marsbees could carry a variety of different sensors capable of a wide range of tasks from taking atmospheric readings to recording land topography. This could supplement a rover’s traditionally limited view of the surrounding landscape and allow for more informed choices about direction of travel. An additional advantage of a fleet of Marsbees is that when one fails, another unit can take over its task or a new unit can be added to the active swarm from the reserve. This has the potential to dramatically increase mission duration and the overall system life cycle. For the much larger Mars Helicopter (blade diameter ~1.2 m [2]), when the single unit fails, the mission is permanently ended or postponed until the unlikely event that the unit can be repaired.

In addition to their small size and light weight being advantageous for missions, Marsbees can also benefit from their relatively low wing loading. A comparison of wing loading versus flight time for Mars flight concepts and biological flapping wing fliers on Earth reveals that flying on Mars with flapping wings and low wing loading can result in reusable vehicles with long duration flight times. The supporting data for this trend can be found in Table 1 and is visualized in Fig. 1.

Table 1:

Characteristics of previous Mars flight concepts and selected insects with wing loadings presented in Martian N. Flight times are estimated by the researchers who proposed each concept.

System	Wingspan (m)	Wing Area (m2)	Mass (kg)	Wing Loading (N/m2)	Flight Time (min)
AME [ 14 ]	12	12	200	62	528*
Minerva [ 14 ]	6.2	6.7	140	79	75*
ARES [ 14 ]	6.3	7.1	160	82	68
Argo VII [ 14 ]	6.7	7.3	160	83	87*
Astroplane [ 14 ]	21	20	300	56	600*
Canyon Flyer [ 14 ]	2.2	0.77	15	70	15*
Mars Flyer [ 14 ]	1.6	0.63	12	70	20*
Entomopter [ 7 ]	1.0	0.17	1.0	13	10
Mars Helicopter	1.1	0.95†	1.8	7.0	3
Mesicopter [ 15 ]	N/A	4.9×10−4†	1.7×10−2	31	N/A
Hoverfly [16]	1.7×10−2	1.6×10−5	1.7×10−5	1.0	N/A
Fruit Fly [17]	6.0×10−3	1.6×10−6	1.0×10−6	2.4	N/A
Monarch butterfly [18]	1.0×10−2	2.6×10−3	4.2×10−4	0.60	600
Hawkmoth [19]	1.9×10−1	7.9×10−3	1.1×10−2	1.4	360
Cicada [19–21]	1.0×10−1	1.2×10−3	1.1×10−3	3.7	17
Bumblebee	2.8×10−2	2.0×10−4	5.0×10−4	9.4	89
Hummingbird [19]	1.4×10−1	2.9×10−3	1.1×10−2	14	1200
Marsbee	2.4×10−2	2.8×10−2	6.0×10−3	0.80	348

^†Indicates rotary wing disk area

^*Indicates single use vehicles; Underline highlights biological data points.

Fig. 1.

Plot of wing loading vs flight time data from Table 1. Some of the higher wing loading flyers are able to maintain a long flight endurance with a high aspect ratio. However, they come with the significant drawback of being single use, while Marsbees and Mars Helicopters are reusable. It is also clear that the significantly lower wing loading of an optimal Marsbee corresponds to a longer flight time.

C. Objective and Scope

Using multi-fidelity numerical tools including 2D and 3D rigid Navier-Stokes equation (NS) solutions, we showed in earlier work [10–12] that bioinspired wing shapes and motions can yield sufficient lift to sustain a Marsbee in the Martian density condition. While each of these computational models has its range of validity and merits as an aerodynamic tool, we seek to explore the realization of a physical Marsbee and its ability to achieve lift in a Martian environment.

The main objective of this paper is to experimentally test the hypothesis that bioinspired flight mechanisms can produce sufficient lift to fly on Mars via a physical, robotic Marsbee. As such, a Marsbee prototype was designed with wings and kinematics based on our earlier numerical solutions [12]. The Marsbee was then placed in a variable pressure chamber, where the air density was reduced to the Martian density level of 1.42×10⁻² kg/m³. Aerodynamic forces as well as wing deformations were recorded at various flapping frequencies. The resulting forces and wing motions will be used to later inform and improve the computational models still being developed for flapping wing flight in Mars atmospheric conditions.

In this paper, we first present the experimental setup and methods in Section III. This provides an explanation of the Marsbee flapper and the vacuum chambers used, as well as the force and motion tracking measurements. Section IV contains the results and discussion of the flapping wing forces and wing motion captured in the vacuum chambers simulating a Mars density environment. Finally, Section V contains the conclusions and potential next steps in the design of the Marsbee flapping wing robot.

III. Methodology

Based on previous numerical calculations [22], we suspected that it is possible for a bioinspired flapping wing flight vehicle to fly in a Martian density environment. To confirm this theory, we initially placed a modified Chiba flapper [23] in a large vacuum chamber and qualitatively measured wing deformation in the low density environment using a high speed camera. Subsequently, we placed the Marsbee flappers in a smaller vacuum chamber to measure forces with a rigidly attached ATI Nano 17Ti force transducer. We then recorded the lift generated at various frequencies to determine whether the robotic Marsbee could generate sufficient lift on Mars. With this experimental setup, we could determine the required flapping frequency, as well as any additional payload the system could carry.

Several factors contribute to lift generation with flapping wings. These include flapping frequency, f, flapping amplitude, Φ, angle of attack, α, and wing area S. Figure 2 shows the relevant quantities on a flapper. Because the flapper relied on passive pitching, there was no direct control over the pitch angle, and the flapping amplitude was likewise restrained by the gear mechanism. The main method of controlling the force produced was to change the flapping frequency f.

Fig. 2.

Flapper shown with relevant parameters. Flapping amplitude Φ, wing pitch angle α, wingspan R, chord c, flapping frequency f, leading LE and trailing TE edge. Force transducer axis also indicated.

A. High Speed Visualization of Flexible Wing Motions in Martian Density

For visualization purposes, the wing motion of a modified flapper [23] from Chiba University was recorded in the Large Vacuum Test Facility (LVTF) chamber at the University of Alabama Huntsville’s Propulsion Research Center (PRC). The modified Chiba flapper uses a slightly different flapping mechanism than the Marbsee prototype (Section III.B), but maintains the same wing shape, size, and material. The LVFT has a test section diameter of 1.8 m and a length of 4 m (Fig. 3). It uses a convection vacuum gauge sensor (InstruTech CVG101 Worker Bee) which is capable of very low vacuum including the pressure and density levels required for simulating Mars atmospheric conditions. The motion was recorded using a high-speed camera capable of shooting 960 frames per second. This allowed us to gain a quick, qualitative understanding of the wing deformation at different densities and wing flapping frequencies, which could not be done in the smaller Plasma and Electrodynamics Research Lab pressure chamber (Section III.B) due to viewing constraints. As seen in Fig. 4, there is a notable difference in the wing pitch motion when the Marsbee is flapping at a constant frequency in the ambient Earth atmospheric density condition (1.168 kg/m³) versus flapping in the Mars density condition (1.42×10⁻² kg/m³).

Fig. 3.

Marsbee experimental setup in the LVTF large vacuum chamber. a) Schematic representation and b) Marsbee test stand inside the chamber.

Fig. 4.

Snapshots of the wing and passive pitch motion in a) ambient Earth and b) Martian atmospheric conditions. In the ambient Earth density condition, the trailing edge follows the leading edge as the pairs of upper and lower wings come together, similar to insect wing motions [13]. However, the trailing edge leads the leading edge in the Martian density condition.

In the ambient Earth conditions, the pitching motion mimics the pitching motion of flexible insect wings, namely in the way that the trailing edge always lags behind the leading edge for each wing stroke. However, in the low-density Martian environment, during some strokes, the pitching motion can be opposite of what is desired – i.e. the trailing edge can precede the leading edge, resulting in lift being generated in an undesired direction. Specifically, at 30% of the flapping period when the upper and lower wings are coming together, the Earth density condition (Fig. 4a) is characterized by the leading edges coming together first, followed by the trailing edges of the wings. However, at the corresponding time instant in the Martian density condition (Fig. 4b), the trailing edge of the upper wing is coming together with a nearly ‘flat’ lower wing, followed by the leading edge of the upper wing meeting the lower wing, resulting in low-lift-producing motion. This motion motivated using the Vicon motion capture system and ATI Nano force transducer to quantify the wing deformation and corresponding aerodynamics. Understanding the wing fluid-structure-interaction will allow for developing higher fidelity flexible wing models for efficient bioinspired flight on Mars.

B. Marsbee Flapper and Plasma and Electrodynamics Research Lab Vacuum Chamber

The experimental setup consisted of the Marsbee robotic prototype mounted on a custom test stand that allowed for measurements of the unsteady forces produced by the flexible flapping wings. This test stand was placed inside a vacuum chamber located at the PRC. This chamber in the Plasma and Electrodynamics Research Lab (PERL) has a test section measuring 0.3 m diameter and 0.6 m length. It uses a convection vacuum gauge sensor (InstruTech CVG101 Worker Bee) and is capable of very low vacuum including the pressure and density levels required for simulating Mars atmospheric conditions. The experimental setup is shown in Fig. 5.

Fig. 5.

Marsbee experimental setup in the smaller (PERL) vacuum chamber. a) Schematic of vacuum chamber and motion tracking cameras. b) Outside view of the vacuum chamber with the Vicon motion tracking cameras looking through the chamber’s side viewing window. c) Interior view of the vacuum chamber housing the Marsbee test stand.

We selected a four-wing flapper configuration similar to the hummingbird-inspired micro air vehicle (MAV) [23]. The four-wing configuration was driven via the readily available flapping wing mechanism sold by MicronWings, which could support the required wing size, as well as achieve a reasonable flapping frequency. Similar to the successful design of a the hummingbird-inspired MAV [23], the wings were constructed using a 25 μm polyethylene film with a 1.0 mm diameter carbon fiber rod at the leading edges. The wing size and the flapping kinematics are based on our numerical solution [12] that predicted a lift that can offset a 6 g flapping wing vehicle that is similar to the Marsbee robotic prototype. Each of the four Marsbee wings has a single wing planform area of S=0.0070 m² with a wing length of R=12 cm and mean chord of c=5.5 cm, resulting in a single-wing aspect ratio of AR=2. The wing size is based on doubling the total wing area of the previous computational results for a 6-gram, two-wing flapper configuration [12] to make up for the constrained flapping kinematics of the MicronWings mechanism. The peak-to-peak flapping amplitude of the upper set of wings is kinematically restricted to Φ_u≅35 deg and to Φ_l≅30 deg for the lower pair of wings. Similarly, the flapping frequency is restricted to f < 20 Hz (see Section IV Fig. 7).

Fig. 7.

Experimental force measurements as a function of flapping frequency at simulated Martian atmospheric conditions (red) and near vacuum (black). The near vacuum conditions demonstrate that the inertial forces of the wings are much less than the aerodynamic forces present even in the Martian density.

C. Force and Optical Wing Motion Measurement Setup

The forces were measured using the ATI-Nano-17 Titanium force transducer. Before the start of each trial, the transducer was setup such that the load due to the flapper’s own weight was zeroed. The motion of the flapper was actuated by supplying a series of input voltages to the drive motor. For each trial, forces were recorded for five seconds. The mean lift was calculated by time-averaging the force in the lift direction over the five second interval.

Nine small reflective tape markers were placed on one of the wings (D-L in Fig. 6), with markers A, B, and C being placed on the mounting bracket used to secure the Marsbee to the force transducer. Because of this, markers A, B, and C were inserted digitally in Fig. 6 in locations representing where they were relative to the flapper during testing. Markers A and B were used to form the flapper axis, with marker C serving as a third point to generate a reference plane. The 3D position of each marker was recorded using an array of Vicon T40s cameras placed outside of the small vacuum chamber (Fig. 5a,b). Each reflective marker was 3×5 mm in size and weighed approximately 3.9×10⁻³ g. The total mass of all nine markers was around 9% of the mass of the individual wing. We previously used this same optics-based method to measure the three-dimensional wing kinematics and the body motion of freely flying Monarch butterflies [24].

Fig. 6.

Position of the reflective markers on the Marsbee wing. Markers A, B, and C are shown in representative locations.

The five Vicon cameras were positioned outside the chamber and calibrated such that the marker positions on the wing could be clearly recorded through a glass viewing window located on the side of the chamber. The marker distribution on the wing was chosen such that both chordwise deformation of the wing as well as the three-dimensional shape of the wing could be measured. In addition to the wing markers, two more markers (A and B in Fig. 6) were placed on the flapper body as a reference line. The wing flapping angle was determined using the position of markers A and G (Fig. 6). The flapping frequency was obtained by taking the FFT of the time history of the flapping angle. The wing pitching angle was calculated as the angle between line joining G and I with respect to longitudinal axis of the flapper formed by markers A and B. Wing flexibility in the chordwise direction was not considered in the calculation. The chordwise deformation of the wing was determined using the line connecting wing markers G and I. The experimental setup enables simultaneous measurements of flapping wing kinematics and the resulting time history of forces in Earth and Martian atmospheric density condition at various flapping frequencies. The wing motion was recorded at a sampling rate of 400 Hz and the forces were recorded at a sampling rate of 2000 Hz. Both the Marsbee flapper and the force transducer were located inside the chamber and powered using externally located power supply units. The input voltage to the flapper was supplied using a Tekpower TP3005P power supply. The force transducer output was connected to a National Instruments Data Acquisition (DAQ) board and the measured data was saved to an external computer. Any gaps in the recorded marker position data were interpolated using cubic spline interpolation. The wing motion data were smoothed using a low pass filter with a cut off frequency of 50 Hz. The recorded force data, which included higher frequency oscillations, were filtered using a low pass filter with a cut off frequency of 100 Hz.

IV. Results and Discussion

The forces and wing motion of the flapper were first recorded at Earth atmospheric density condition inside the PERL chamber, followed by Martian density condition as described in Section III.A. The density inside the chamber was controlled by changing the pressure and recording the temperature. At Earth conditions, the temperature and pressure inside the chamber were 23° C and 99325 Pa, respectively, resulting in an air density of 1.2 kg/m³. At simulated Martian density, the temperature inside the chamber was 23° C for all tests. We varied the pressure between 1133.4 Pa and 1333.2 Pa, resulting in an air density between 1.333×10⁻² kg/m³ and 1.568×10⁻² kg/m³ during the tests, which is within the Martian atmospheric density range [2,3,25].

A. Inertial Force Separation

We followed a well-documented procedure to separate the inertial force from the aerodynamic force [26]. This was required to ensure that the forces read by the force transducer are a result of aerodynamic forces acting on the wing instead of inertial forces due to the motion of the wing’s mass attached to the force transducer. To perform this measurement, the vacuum chamber was brought to a near-vacuum level of O(10⁻³) torr. The flapper was placed on the force transducer and forces were averaged over multiple flapping periods for a large range of flapping frequencies. The mean resultant forces are shown in Fig. 7. The inertial forces generated by the flapping motion in near vacuum are an order of magnitude lower at O(10⁰) mN compared to the mean aerodynamic forces at O(10¹) mN.

B. Lift Force Measurements in the Martian Density Condition

The forces and wing motion of the flapper were first recorded at Earth atmospheric density condition inside the chamber followed by Martian density condition. The wing motion and forces generated by the flapper were recorded over a range of input voltages resulting in different flapping frequencies. At Earth conditions, we varied the input voltage to the flapper between 0.5 V and 2 V in 0.5 V increments and between 2 V to 2.6 V in 0.2 V increments. The input voltage for Martian conditions was varied between 0.8 V and 2.6 V in 0.2 V increments in order to achieve a range of frequencies comparable to the frequencies achieved in Earth density condition. Three repeated measurements were acquired at each voltage.

Figure 8 shows the mean lift as a function of the flapping frequency based on three repeated measurements at Earth and Martian conditions. The Marsbee flapper generates positive lift in both conditions. The mean lift in Earth density condition increases with the flapping frequency. The magnitude of lift (in grams) in Earth density condition, was around 11 g of lift at 17 Hz. The mean lift normalized with Martian gravity increases between 8 Hz and 14 Hz and then nonlinearly fluctuates with a maximum of around 8 g at 16 Hz, which is comparable with the lift observed when using the same wings in the Earth density condition. In Fig. 8b, the lift trends for the flapper are normalized by their respective gravities. These results indicate that the Marsbee flapper at Martian conditions is capable of producing lift comparable to its weight.

Fig. 8.

Experimental measurements as a function of flapping frequency at Earth and simulated Martian atmospheric conditions. a) Measured lift in mN; b) Measured lift in grams. The mean lift at Earth and Martian densities are normalized with 9.8 m/s² and 3.26 m/s², respectively.

C. Wing Deformation Measurements in the Martian Density Condition

The mean lift trend in Fig. 8 can be explained with the wing deformation measurements. A key mechanism in generating positive lift is the passive pitch angle resulting from wing deformation. This deformation is the result of a dynamic balance of the wing inertia, elastic restoring force, and aerodynamic force. For flexible wings, passive pitch angle plays the role of angle of attack. A pitch angle of 45 deg is known to produce the highest lift [27]. The passive pitch angle is measured using the mean chord line and is relative to a plane formed by markers A, B, and C in Fig. 6. The values for the mid-stroke passive pitch angles can be found Fig. 9.

Fig. 9.

Comparison of passive pitch angle due to wing deformation at Earth and Martian density condition.

For the Marsbee wing in Earth density condition, the mid-stroke passive pitch angle increases with flapping frequency, reaching 23 deg at 15 Hz (Fig. 9). Therefore, the associated lift shown in Fig. 8 generally increases with pitch angle. On the other hand, in Martian density condition, the wing deforms in a nonlinear way, producing a mean lift trend (Fig. 8) that is qualitatively different than the trend in Earth density condition. The trend of mean lift as a function of flapping frequency still appears to be similar to the passive pitch angle trend (Fig. 8 and Fig. 9). With an increase in frequency, the mid-stroke passive pitch angle remains nearly constant in the Mars conditions.

Figure 10 shows the phase delay between flapping and passive pitching. In the Earth density condition, the phase lag and the pitch angles increase with flapping frequency. Increased phase lag between the pitching angle and flapping is one of the key requirements for generating optimal lift for hovering wings. However, in the Mars density condition, phase delay decreases and even becomes negative at some frequencies.

Fig. 10.

Passive pitch phase delay vs wing flapping frequency. In the Earth density condition, the delay increases with flapping frequency. However, in the Mars density condition, the phase delay decreases and even becomes negative at higher flapping frequencies, contributing to the inconsistent lift observed during the trials.

In order to determine the relationship between the flapping frequency and the passive pitching frequency, an FFT of the time history of the x component (see Fig. 2) of the flapper wing markers G and I was taken. Data from the Earth density condition and Mars density condition were analyzed and are found in Fig. 11. In the Earth density condition the flapping and passive pitch frequencies are about the same, indicating the passive pitch motion peaks once per half-stroke as seen in insect flight. However, in the Martian density condition, the passive pitch motion switches between the first order and higher order frequency modes.

Fig. 11.

Comparison of passive pitching frequency and flapping frequency in Earth density (1.168 kg/m³) and Mars density (1.42×10⁻² kg/m³). The passive pitching frequency increases nearly linearly with flapping frequency in Earth conditions, but in Martian conditions, the passive pitch frequency is not consistent with the flapping frequency.

Figure 12 shows snapshots of wing mean chord pitch angle during a stroke cycle with a flapping frequency of 12.7 Hz in the Earth condition and 14.3 Hz in the Mars density condition. In Earth density condition (Fig. 12a), the trailing edge lags the leading edge, resulting in a motion that is similar to flying insects [13]. This pitching motion produces high lift in an efficient manner. In Martian density condition (Fig. 12b), the trailing edge leads the leading edge. This produces non-optimal lift. These contrasting pitch angle behaviors are consistent with the high-speed video wing snapshots in Fig. 4.

Fig. 12.

Representative chordwise wing shape snapshots at a) Earth and b) Martian density condition.

In summary, the resulting combination of the flapping and pitching motion is able to generate positive lift in the Martian density condition. However, the resulting pitch motion due to the larger wings is not optimal, suggesting that the bioinspired lift generation in Martian conditions can be improved by taking into account the fluid-structure interaction in the ultra-low Martian density condition.

V. Conclusion

Despite the suboptimal passive pitch angles observed in the low-density Martian environment, the Marsbee flapper was experimentally shown to generate lift in excess of its weight. This partially validated the Marsbee concept and encouraged us to use bioinspired dynamically scaled flight mechanisms. It was demonstrated that the flapper could generate approximately 8-grams of lift while only weighing around 6-grams. The primary limitations of the current flapper design are its small motor, weak structural integrity, and lack of flapping kinematics control. While the target flapping frequency could not be reached in this experiment, the concept was proven to be feasible.

The resulting combination of the flapping and pitching motion is able to generate positive lift in the Martian density condition. However, the resulting pitch motion due to the large wings is not optimal, suggesting that bioinspired lift generation in Martian conditions can be improved by taking into account the fluid-structure interaction in the ultra-low Martian density condition. While the flapper was able to generate sufficient lift to offset its weight, it was producing much less than it theoretically could produce if the passive pitching and the phase delay were optimized for the Mars density environment.

I. Nomenclature

AR	=	wing aspect ratio (single wing)	[1]
c	=	mean wing chord	[m]
f	=	flapping frequency	[Hz]
LE	=	lead edge	[1]
R	=	wing span (single wing)	[m]
Re	=	Reynolds number	[1]
S	=	wing planform area	[m2]
TE	=	trailing edge	[1]
Φl	=	peak-to-peak flapping amplitude, lower wing	[deg]
Φu	=	peak-to-peak flapping amplitude, upper wing	[deg]