The Feasibility of Insect-Based Flight as a Means of Extraterrestrial Exploration

Abstract

Efforts in the past have been made to investigate the feasibility of entomopters, insect-inspired flapping-wing aircraft, as a means of extraterrestrial planetary flight [1, 13]. The main mission objectives were to explore different planets and in the process, collect and retrieve samples in support of scientific research. Historically, the lack of adequate technology limited the prospects of creating an untethered entomopter capable of independent flight. Specifically, the lack of a proper simulation environment and an inadequate ability to replicate the complex kinematics of insect flight were two main hindering factors [1]. However, the progression of technology and recent developments, especially with an increased understanding of insect flight, have given entomopters a second chance [2]. In this research, we attempt to properly scale an entomopter prototype designed for past NASA/NIAC research to optimize its performance in different extraterrestrial conditions while retaining its original design constraints such as its innate Reynolds number value. Specifically, we provide calculations regarding the weight, wing area, and size of said prototype to allow it to operate in different extraterrestrial atmospheric conditions.

Keywords: entomopters, flapping-wing flight, extraterrestrial flight

Nomenclature

Note: All variables will have units defined in this section unless a unit conversion was applied. Unit conversions are clearly outlined when they happen.

I. Introduction

A reasonable question to ask is why flapping-wing flight should be considered a viable solution to flight in extraterrestrial atmospheres. After all, while rotary and fixed-wing flight have had great success on Earth, relatively little effort was put into the development of flapping-wing aircraft due to technological limitations, a lack of practical use, or a combination of both. To answer this, it is imperative to first understand how atmospheric conditions affect different modes of flight.

Fixed-wing flight through a fluid relies on a mixture of laminar and turbulent flow. While an exclusively laminar flow can offer advantages such as predictability, it also reduces the amount of lift able to be created by an airplane. Similarly, an exclusively turbulent flow presents advantages such as a high degree of lift, but it also comes with a high degree of drag. Therefore, for a fixed-wing aircraft to operate in normal performance envelopes, it must be flown through a fluid medium that allows it to operate in the Reynolds number range it was designed for. Reynolds number is a dimensionless quantity that can help predict if the fluid flow will be laminar, turbulent, or a mixture of both. From a formulaic point of view, this is represented as follows:

From the above formula, it can be observed that the Reynolds number is directly correlated to fluid density. This means that to maintain the same Reynolds number through a decrease in fluid density, there needs to be an increase in either the flow (operating) velocity, characteristic length, or a combination of both. It should also be noted that out of the eight planets in our solar system, Earth ranks second in terms of atmospheric density [3]. The only planet that outcompetes Earth in terms of atmospheric density is Venus, and it is also a planet with an atmospheric pressure that is more than 90 times that of Earth’s [4]. This imposes a high degree of structural challenge on any craft wishing to visit Venus, making atmospheric density calculations the least of worries when trying to create a vehicle that can sustain itself under such high pressures. Therefore, Venus will be excluded from the scope of this study. As mentioned above, changes to atmospheric pressure require a change in velocity or characteristic length. Such modifications are technologically impractical due to the high degree of atmospheric density difference between Earth and other planets. For example, compensating for the loss of atmospheric density with operating velocity would present many obstacles in takeoff and landing and would make mission objectives such as collecting precise planetary samples very difficult. At the same time, compensation through an increased characteristic length risks having an oversized aircraft that cannot be easily transported to other planets from Earth (at the time of this research, there are no known extraterrestrial human settlements). Since fixed-wing flight on 6 out of 8 planets (excluding Venus and Earth) would require this type of modification, it can be concluded that this mode of flight is not ideal for extraterrestrial flight.

One alternative is rotary-wing flight. Indeed, the most recent breakthrough in extraterrestrial flight was in 2021 when the NASA Ingenuity drone, which employed contra-rotating rotor blades, set the record for the first-ever controlled, powered flight on another planet [5]. Rotary-wing flight has the advantage of a relatively simple design structure and the ability to fly at very low speeds, hover, and have vertical takeoff and landing (VTOL) capabilities. However, it is especially vulnerable to foreign object damage (FOD), and flight at higher speeds is unstable and inefficient [6]. The Ingenuity also fell victim to FOD after a series of flights (72), highlighting the vulnerability of rotary-wing flights.

Given that extraterrestrial environments are not always aircraft-friendly, the vulnerability of rotary-wing flight is a huge setback in terms of the practicality of this mode of flight. The third mode of flight is flapping-wing flight. This mode of flight offers the advantage of having favorable characteristics of both fixed-wing and rotary-wing flight: the ability to fly fast and slow, hover, and possess VTOL capabilities. Flapping wing flight also allows for a high degree of maneuverability, as observed in nature by birds and insects [7]. The disadvantages of fixed-wing and rotary-wing flight, the inability to match adequate Reynolds number values, and the vulnerability against FOD, respectively, are both resolved in flapping-wing flight. Because flapping-wing flight inherently operates at low Reynolds numbers, the decrease in Reynolds number due to a thinner atmosphere does not present a drastic challenge to this mode of flight. Therefore, unlike fixed-wing flight, flapping-wing flight is not as drastically impacted by a less dense atmosphere. At the same time, research has shown that flapping wing flight is highly resistant to FOD [1], fixing the problem with rotary-wing flight. In combination, these factors make flapping-wing flight a viable if not competitive candidate for extraterrestrial flight. Entomopters, which get their name from entomo – insect and pteron – wing, are a prime example of flapping wing aircraft. The latest concept of extraterrestrial flapping-wing flight was a 2017 NASA project titled Marsbee that sought to carry out extraterrestrial discovery by employing a swarm of bee-like flapping-wing drones [8]. That project shares similar prospects to what this research sees in flapping-wing flight. Combining an extensive data library for insect flight and standard formulas for flight characteristics, we can obtain estimates for the requirements of entomopter flight on different planets within and beyond our solar system.

II. Baseline Calculations

By isolating the specific model of an entomopter, we can calculate the relationship between wing area and body mass as well as wing beat frequency and body mass. The entomopter chosen for this research was a breakthrough design by a research team led by Michelson at Georgia Tech Research Institute that took inspiration from the hawk moth (Manduca sexta) [9] and Hummingbirds [1]. Select design parameters of this entomopter appear in research [1]. By finding and scaling the relationships between body mass and wing area as well as body mass and wing beat frequency of the moth family, the same relationships could be found for the entomopter.

Fig. 1. (a) and (b) show Body Mass vs. Wing Area and Body Mass vs. Wing Beat Frequency plots (in log scale and on Earth) for different insects [10]. The red tick marks and blue lines were added to measure the precise value of each moth (Heterocera) dot. Only moths were considered since the entomopter in question is based on moths. The measurements for each dot were taken through a digital ruler and the values were put into a matrix for calculations. Figures (a) and (b) reproduced under academic fair use.

Values from Fig. 1(a) and (b) were put into matrices. The description of Fig. 1 shows how the values were measured. By using matrix inversion through GNU Octave, the least-squares line for log body mass vs. log wing area was calculated to be:

Through unit conversion for body mass from (g) to (kg), wing area from (cm²) to (m²) and removing the logarithm, the true relationship between wing area (in m²) and body mass (in kg) of the moth family on Earth was calculated:

Similarly, the same process was used to calculate the least-squares line for log body mass vs. log wing beat frequency:

Again, removing the logarithm and converting the unit for body mass from (g) to (kg) and removing the logarithm, the true relationship between wing f = beat frequency (in Hz) and bm = body mass (in kilograms) on Earth is shown:

These lines approximate relationships between wing area and body mass as well as wing beat frequency and body mass within the moth family. Notice that the graphs in Fig. 1 also provide the rough spread of mass for the moth family. This information was used to calculate the Martian weights for each mass value:

Next, the lines were used to calculate entomopter flight characteristics on Mars. Mars was chosen because Michelson’s entomopter was originally designed with Martian conditions in mind. Later in the paper, we will discuss how these calculations can be furthered to other planets.

III. Martian Calculations – Wing Area

Utilizing the lines of best fit, we can calculate the wing area of the entomopter on Mars. This was done through utilizing formulas in research [1, 10]. First, the fundamental equation for lift is:

Here, weight is equal to lift since we are most interested in calculating the amount of lift required to maintain level flight, and this is when the lift generated by an aircraft is equal to its weight. For the entomopter in Research [1], the air density and maximum coefficient of lift are provided:

Combining the least-squares line for Wing Area vs. Body Mass on Earth and the general lift formula, we can derive the relationship between velocity and mass. The velocity vs. mass relationship can then be used to solve for the relationship between Wing Area vs. Body Mass on Mars:

This relationship is plotted in Fig 4. With this relationship in mind, the minimum and maximum wing area of the entomopter on Mars and Earth were calculated:

Notice that since the Martian atmosphere is thinner, the wing area is larger overall on Mars than on Earth. However, as stated in the introduction, flapping wing flight is not drastically impacted by atmospheric changes, and the increase in wing area from Earth to Mars is well within modern technological constraints. This is especially true since entomopters on Earth are small in size to begin with.

IV. Martian Calculations – Wing Flap Velocity

Utilizing the line of best fit, we can calculate the wing flap velocity of the entomopter on Mars. Similar to how the wing area was calculated, this calculation involves relationships derived from research [1, 10].

Define one full stroke to be the wing starting at a point, flapping down and up, and ending up at the starting position. We can first find the minimum and maximum wing beat frequencies for each body mass:

One interesting phenomenon to note here is that wing beat frequency decreases as body mass increases. That is, there is an inverse relationship between wing beat frequency and body mass. This is consistent with nature, where larger insects and birds tend to flap slower than smaller ones. Thus the calculation for wing flap velocity is split between the smallest and the largest mass possible for Heterocera. In both cases, the wing shape will assumed to be a square to promote simplicity in calculations. The ideal amplitude for the entomopter’s wing flap was found to be +- 60º [2].

In summary, Michelson’s entomopter can have a mass of anywhere between 10^−4.26kg and 10^−2.265kg. On Mars, with the least mass, the entomopter would have an overall wing area of 0.0077m² with a wing beat frequency of 43.918Hz. Its wing flap velocity would be 11.419m/s. With the most mass, the entomopter would have an overall wing area of 0. 067m² with a wing beat frequency of 20.675 Hz. Its wing flap velocity would be 15.858m/s.

V. Expanding Calculations – All Planets

Sections III and IV have shown how baseline relationships between different properties of Michelson’s entomopter can be used to derive critical values such as wing area and wing flap velocity for safe flight on Mars. These calculations can be repeated for other planets as well. There are exactly three modifications necessary to repeat such calculations for other planets.

First, the air density, measured in kg/m³, within the wing area calculations in Section III needs to be replaced with the desired planet’s air density. Next, in the same formula, the gravity needs to be replaced with the desired planet’s gravity. Last, with the new minimum and maximum wing areas, replace Wa_MarsMin and Wa_MarsMax in Section IV that appear in wing flap velocity calculations. As long as the atmospheric density and gravity on Earth remain the same, the simple 3-step process should yield accurate results for entomopter properties for planets within, and even beyond, our solar system.

VI. Conclusions

Flapping-wing flight has great potential as a means of extraterrestrial flight because it offers the combined advantage of fixed-wing and rotary-wing flight, making it exceptionally adaptable and versatile. However, there are still technological developments that need to happen for this mode of flight to be confidently feasible. One main constraint is power. Fig. 5 shows that out of the three modes of flight investigated in this research – fixed-wing, rotary-wing, and flapping-wing – flapping-wing flight consistently requires the largest amount of power input to sustain flight at different velocities. In Michelson’s prototype, a reciprocating chemical muscle (RCM) was used to allow flapping-wing flight [1, 12]. An RCM is regenerative and also does not require oxygen to operate, making it ideal for low-power flights in extraterrestrial atmospheres. In a different research conducted by Wood, an innovative actuator found within a fly-inspired entomopter demonstrated a power density of 400 W/kg. For comparison, biological estimates of power densities of insects’ muscles range between 80 W/kg and 83 W/kg. According to Wood, this was “the first example of where a subsystem of the microrobotic fly [entomopter] exceeds the performance of its biological counterpart” [2]. Such technological advancements show a promising progression towards the feasibility of flapping-wing flight, and it makes the calculations made in this research relevant.

References

1. [1]  G. L. P. T., “Extraterrestrial Flight: Entomopter-Based Mars Surveyor,” Typeset.io, 2023. [Online]. Available: https://typeset.io/pdf/extraterrestrial-flight-entomopter-based-mars-surveyor-495gpkrva0. pdf.
2. [2]  G. A. R. et al., “A High-Performance Electromechanical Actuator for a Miniature Flight System,” in 2007 IEEE Aerospace Conference, Big Sky, MT, USA, 2007, pp. 1-8. doi: 10.1109/AERO.2007.4457871.
3. [3]  NASA, “Planetary Fact Sheet,” National Space Science Data Center. [Online]. Available: https://nssdc.gsfc.nasa.gov/planetary/planetfact.html.
4. [4]  NASA, “NASA’s DAVINCI Explores Ten Mysteries of Venus,” 2023. [Online]. Available: https://www.nasa.gov/solar-system/nasas-davinci-explores-ten-mysteries-of-venus/#:~:te xt=The%20surface%20of%20Venus%20is,times%20hotter%20than%20an%20oven.
5. [5]  NASA, “Mars 2020 Perseverance: Ingenuity Mars Helicopter,” 2023. [Online]. Available: https://science.nasa.gov/mission/mars-2020-perseverance/ingenuity-mars-helicopter/.
6. [6]  G. J. B. and S. P. K., “Quadrotor Dynamics and Control,” 2007. [Online]. Available: https://ai.stanford.edu/~gabeh/papers/Quadrotor_Dynamics_GNC07.pdf.
7. [7]  H. W. and B. P., AIAA Guidance, Navigation, and Control Conference, Reston, VA: American Institute of Aeronautics and Astronautics, 2007, doi: 10.2514/4.862502.
8. [8]  NASA, “MarsBee: Swarm of Flapping Wing Flyers for Enhanced Mars Exploration,” 2023. [Online]. Available: https://www.nasa.gov/general/marsbee-swarm-of-flapping-wing-flyers-for-enhanced-mars-exploration/.
9. [9]  C. R. et al., Neurotechnology for Biomimetic Robots. Cambridge, MA: MIT Press, 2021. doi: 10.7551/mitpress/9780262536691.001.0001.
10. [10]  R. J. R., The Biomechanics of Insect Flight. Princeton, NJ: Princeton University Press, 2001. doi: 10.1515/9780691094915.
11. [11]  AIAA, “Paper 2007-6498: AIAA Guidance, Navigation, and Control Conference,” 2007. [Online]. Available: https://arc.aiaa.org/doi/abs/10.2514/6.2007-6498.
12. [12]  R. C., “RCM Generations,” 2023. [Online]. Available: http://angel-strike.com/entomopter/RCM-Generations.jpg.
13. [13]  C. L. and S. T., “Final Report on the NIAC Study: Flapping Wing Micro Air Vehicle,” NASA Innovative Advanced Concepts, 2020. [Online]. Available: https://www.niac.usra.edu/files/studies/final_report/522Colozza.pdf.

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