Perpetual Endurance Flight

Introduction

Fig. 1: Solar Impulse 2, the first piloted aircraft to circumnavigate the globe on only solar power, takes off in Switzerland. (Source: Wikimedia Commons)

Current unmanned aircraft are limited to the amount of fuel they can carry onboard. This limitation inhibits many interesting applications for long endurance aircraft such as high-altitude communication transceivers, precision agriculture, long-term scientific studies, and even the exploration of other planets. With recent advances in our knowledge of aerodynamics, materials, structures, and energy harvesting technologies, the idea of perpetual endurance flight is more in reach than ever before.

The Physics of Perpetual Flight Endurance

The governing equations behind perpetual flight endurance for fixed wing aircraft are relatively simple to derive. For an unpowered aircraft gliding in still air, the aircraft will sink with some sinking velocity. Thus, the power to keep the aircraft aloft is [1]

Therefore, we can approach this problem from a combination of three avenues, by supplying sufficient power to the aircraft, minimizing aircraft weight, and minimizing the aircraft's sinking velocity. An aircraft's sinking velocity can be written in terms of the aircraft's lift/drag ratio and velocity: [2]

Therefore, to minimize sinking velocity, we can minimize the lift/drag ratio and/or minimize velocity. Since lift is a function of the coefficient of lift, wing area, and velocity and must equal weight for sustained flight, per

we can minimize velocity by maximizing wing area.

Therefore, we conclude that the keys to achieving perpetual flight are a sufficient power source, low weight, high lift/drag ratio, and high wing area. [1] Weight and wing area are largely problems in structural engineering, where engineers are developing novel ways to fabricate large wings at low weight. Lift/drag ratio is a problem in aeronautical engineering, where engineers design airfoils that produce high lift forces with low drag penalties. Finally, perpetual power sources are a more broad and undefined area. The remainder of this report will cover three potential ways for an aircraft to perpetually harness energy from our environment.

Power Sources For Perpetual Flight Endurance

The most widely explored area of perpetual flight endurance is solar power. The concept of using solar power relies on the aircraft storing reserve energy during the day, either by climbing altitude or storing energy in onboard batteries, and slowly draining these energy stores at night when solar power is not available. While the efficiency of photovoltaics are only around 25%, advances in lightweight thin-film silicon photovoltaic cells and lithium batteries have allowed a few projects to achieve the capability for perpetual flight. [2] In 2016, Solar Impulse 2 (Fig. 1) was the first piloted fixed-wing aircraft to circumnavigate the Earth using only solar power. [3] Making solar-based perpetual flight work at smaller scales has been more difficult, as the current flight endurance record for aircraft below 50 kg is 81 hours. [4]

Another method to power perpetual flight endurance is through thermal soaring. This method is mostly inspired by soaring birds that find and navigate updrafts that have vertical speeds faster than their sinking speed. Radio control hobbyists have long practiced thermal soaring with manually-piloted sailplanes, but making this work autonomously has been a challenge. Several projects have attempted to develop algorithms that can model the location of thermals, and very recent developments in reinforcement learning have allowed a project to train a small glider to autonomously learn and navigate atmospheric thermals. [5] While no thermal soaring glider has autonomously navigated for more than a few hours, advances in computer science algorithms are bound to enable significant progress in this area in the near future.

One final potential method for perpetual flight endurance is dynamic soaring. Also inspired by birds, namely albatrosses, dynamic soaring involves extracting energy from horizontal non-uniform wind fields called wind shear. To our knowledge, no autonomous aircraft has successfully used this technique to extend its flight range, although many have proposed it as a future avenue to explore as unmanned aerial robot technology continues to advance. [2]

© Eric Chang. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

References

[1] H. Ross, "Fly Around the World with a Solar Powered Airplane," American Institute of Aeronautics and Astronautics, AIAA-2008-8954, 14 Dec 08.

[2] X.-Z. Gao et al., "Reviews of Methods to Extract and Store Energy for Solar-Powered Aircraft," Renew. Sustain. Energy Rev. 44, 96 (2015).

[3] F. Fawnzy, "Solar Impulse 2: Around the World with Zero Fuel", CNN, 26 Jul 16.

[4] P. Oettershagen et al., "Design of Small Hand-Launched Solar-Powered UAVs: From Concept Study to a Multi-Day World Endurance Record Flight," J. Field Robotics 34, 1352 (2017).

[5] G. Reddy et al., "Glider Soaring via Reinforcement Learning in the Field," Nature 562, 236 (2018).