# Performance Estimate of a Spin-Stabilized Drag Sail for Spacecraft Deorbiting
## 1 Introduction
The latter are propellantless propulsion systems that produce thrust by exploiting solar radiation pressure acting on a low-mass, highly reflective membrane [33; 34]. Therefore, drag sails can rely on technological advances in the solar sailing field in terms of architecture, manufacturing, and deployment. It is worth noting that the higher area-to-mass ratio of a spacecraft equipped with a drag sail entails some critical issues because it increases the probability of impact with untracked debris [35; 36]. However, good deorbiting capabilities in a reasonably short time and low collision energy with the membrane significantly alleviate the previously mentioned problem [30; 31]. The great interest in drag sails is confirmed by several on-orbit tests that are yielding promising results. The first experimental validation of the drag sail concept came from test missions focused on the problem of deploying a solar sail. Specifically, NASA's NanoSail-D2, launched in 2010 after the failure of NanoSail-D [37], deployed a 10 m\({}^{2}\) square reflective sail in LEO, which deorbited after 240 days due to atmospheric drag. Similarly, LightSail-1, designed by the Planetary Society [38], completed its test flight in 2015 by making a rapid reentry from a highly elliptical LEO with a perigee altitude of about 350 km [39]. The Gama Alpha mission, designed by the French company Gama Space and launched in January 2023, is expected to perform a spin-deployment test of a solar sail in LEO [40]. However, the first technological test of a true drag sail, i.e., a sail aimed at deorbiting the satellite, can be traced back to 2012, when RAIKO, a 2U CubeSat designed by Tohoku and Wakayama Universities, was released to an altitude of 420 km, then decayed in less than three months thanks to a 0.25 m\({}^{2}\) square drag sail [41]. More recently, in 2017, InflateSail, a CubeSat designed by the Surrey Space Center for the Von Karman Institute, tested the deployment in LEO of a 10 m\({}^{2}\) square drag sail by means of an inflatable mast [42]. The drag sail was supported by four composite arms and deorbited after 72 days. A 4 m\({}^{2}\) square drag sail was also equipped on the Canadian Advanced Nanospace eXperiment-7 (CanX-7) satellite, a 3U CubeSat designed by the University of Toronto. The drag sail had a thickness of 0.0127 mm and was made of Upilex-S (a Kapton-like material) and coated with aluminum to protect the substrate from atomic oxygen erosion [43]. CanX-7 was launched to a Sun-synchronous orbit with an altitude of 700 km in September 2016. The sail was deployed in May 2017, and the satellite completed its deorbiting after five years, in April 2022. The operating principle of a drag sail is to exploit atmospheric drag to accelerate the deorbiting of the satellite. Therefore, the most favorable attitude of the sail is the one that exposes the maximum surface area to atmospheric particle flow, which is basically equivalent to imposing that the spacecraft's orbital velocity vector is constantly perpendicular to the sail surface (assuming that the surface itself is flat), i.e., that it maintains a fixed orbital attitude. A three-axis attitude control system could in principle be used for this purpose; however, the fixed attitude condition may not be met on a spacecraft at end-of-life due to sensor or actuator failures, or due to lack of propellant. One possible alternative is offered by sail architectures that can passively maintain the desired attitude, such as spherical [44] or pyramidal [45; 46; 47; 48] drag sails. Such configurations are very promising, but they significantly increase the complexity of the system compared to the well-known and widely tested square sails. Based on the above considerations, this paper focuses on square drag sails, and proposes a spin-deployed and spin-stabilized configuration. Indeed, spin-deployment and spin-stabilization for solar sails (conceptally similar to drag sails) have been studied for different architectures.