3D photophoretic aircraft made from ultralight porous materials can carry kg-scale payloads in the mesosphere

Exploring Earth's mesosphere and the Martian atmosphere presents significant challenges due to the low atmospheric pressure, hindering the use of traditional propulsion systems. The mesosphere, extending from 50 to 80 kilometers above Earth's surface, is crucial for understanding climate change effects and space debris accumulation, yet its study is limited. Similarly, high-altitude Martian exploration is hampered by decreasing atmospheric density. This paper proposes a novel solution: photophoretic aircraft. Inspired by centimeter-scale microflyers, this work investigates significantly larger, meter-scale, 3D photophoretic vehicles capable of sustained flight in these challenging environments. The use of photophoresis, a light-driven propulsion mechanism, and Knudsen pumping eliminates the need for moving parts, offering a promising path towards long-duration flight and atmospheric data collection in previously inaccessible regions.

Previous research demonstrated the feasibility of photophoretic levitation using porous plates, known as "nanocardboard," composed of ultralight materials like aluminum oxide. These plates levitate due to temperature gradients induced by light absorption on one side, creating a downward jet via Knudsen pumping. This concept has proven successful for centimeter-scale devices. This paper builds upon these advancements, extending the analysis to much larger, 3D structures to enhance lift and operating pressure range. Prior work on solid mylar-CNT composite disks provided analytical tools that informed the design and analysis of the 3D porous structures investigated here. The combination of planar nanocardboard levitation and analytical tools for solid disks allows for a comprehensive understanding of the lift forces generated by the proposed 3D geometries.

To identify optimal 3D geometries for maximizing payload and minimizing operating altitude, the study employs a multi-faceted approach. First, a theoretical expression for the lift force is developed, encompassing both low-Reynolds number (Stokes) and high-Reynolds number (momentum) regimes. This expression is validated through computational fluid dynamics (CFD) simulations using ANSYS Fluent. Three representative geometries—sphere, cone, and rocket—are analyzed. The CFD simulations model fluid flow through the porous structures, considering a wide range of velocities and altitudes (up to 80 km). The reaction forces (equal and opposite to lift force) are determined, and the data are fitted to the developed theoretical lift force expression, yielding geometry-dependent coefficients. A MATLAB code is then developed to numerically optimize geometric parameters (nanocardboard channel width, height, and nozzle radius) as a function of overall aircraft size, considering the altitude-dependent variations in temperature and pressure. The optimization aims to maximize payload or achieve flight at the lowest altitude. The simulations and optimization consider a range of conditions, including variations in sunlight intensity and the effect of Earth's albedo.

The study's key findings demonstrate the feasibility and potential of large-scale 3D photophoretic aircraft. The developed theoretical model accurately predicts lift force across a broad range of Reynolds numbers, interpolating between Stokes and momentum-dominated regimes. Optimization results show that optimal nanocardboard porosity parameters remain consistent across different geometries and sizes, even with significant changes in ambient pressure across altitudes. The maximum areal density required for lift is on the order of a few grams per square meter, emphasizing the critical need for ultralight, high-strength materials like nanocardboard. For 10-meter diameter structures at 80 km altitude, payloads of up to 1 kilogram are achievable. The minimum altitude for flight with zero payload is found to be 55 km. The three geometries exhibit comparable payload capacities for larger sizes. Simulations at reduced sunlight intensity (500 W/m²) indicate payloads approximately four times lower than those under full sunlight (1000 W/m²). The study also highlights the dependence of flight on sunlight exposure, limiting continuous operation to approximately 12 hours at most latitudes; however, extended operation may be possible near the poles due to polar days.

The findings address the research question of whether large-scale photophoretic aircraft are viable for high-altitude flight and payload delivery. The results show clear evidence that such aircraft are feasible, opening up new possibilities for atmospheric research in previously inaccessible regions of Earth's mesosphere and Mars. The ability to carry kilogram-scale payloads, comparable to CubeSats, significantly enhances the potential for scientific instrumentation and data collection. The relatively consistent optimal porosity parameters across altitudes suggest design robustness and adaptability. The study's findings are easily generalizable to Martian atmospheric conditions, using appropriate atmospheric models. The impact extends to various fields, including atmospheric science, climate research, space debris mitigation, and planetary exploration.

This study demonstrates the potential of 3D photophoretic aircraft for carrying kg-scale payloads at high altitudes. The combination of ultralight porous materials, 3D geometry, and photophoretic propulsion enables sustained flight in regions previously inaccessible to traditional aircraft. Future research should focus on material development to achieve even lower areal densities and improved structural integrity for larger aircraft. Further exploration of different geometries and control mechanisms will refine the design and enhance operational capabilities.

The study's limitations primarily stem from the simplifying assumptions made in the theoretical model and simulations. The 100% porosity assumption for the porous walls in the CFD simulations is an idealization. The actual porous structure of nanocardboard is complex, and deviations from this assumption could influence the lift force. The analysis assumes uniform sunlight intensity across the aircraft surface; in reality, variations in sunlight angle and shadows could affect lift. The model also simplifies atmospheric conditions, neglecting factors that could affect flight, such as wind shear and turbulence. Further investigation into material properties and their long-term stability under high-altitude conditions is necessary. Finally, the model assumes ideal Knudsen pumping behavior, neglecting potential complexities in gas flow at these scales.