High-precision numerical calculation method of solar radiation pressure force for wrinkled solar sails

Abstract

Due to small magnitude of solar radiation pressure (SRP), the area-mass ratio of the solar sail should be large enough to obtain adequate thrust acceleration. Therefore, the membrane structure is usually adopted for solar sails. However, the membrane barely has out-of-plane stiffness; thus, it is necessary to apply in-plane tension on the membrane for maintaining the plane, which may result in wrinkles. The wrinkle will influence SRP force of solar sails. On the one hand, wrinkled regions of the sail are no longer flat, so the angle between the normal vector of the surface in wrinkled regions and the direction of sunlight differ from a flat sail. On the other hand, wrinkles may cause shadow when the solar sail is almost parallel to sunlight and the shadow region cannot generate SRP force. In this paper, the nonlinear buckling theory is used to propose a numerical calculation method to solve the problem of wrinkling analysis of solar sails with complex boundary. Then, a high-precision method for calculating SRP force of wrinkled solar sails is proposed, consisting of two parts: the infinitesimal element SRP force model and the wrinkle shading model. Numerical simulation result verifies the effectiveness of the wrinkling analysis method and the SRP force calculation method. Furthermore, according to calculation result, wrinkles have a certain influence on the SRP force of the solar sail, which will become significant when the solar sail gets parallel to sunlight.

Keywords

solar sail solar radiation pressure force membrane wrinkling analysis wrinkle shading model numerical calculation method

Get full access to this article

View all access options for this article.

References

Tsuda

Mori

Funase

, et al. Flight status of IKAROS deep space solar sail demonstrator. Acta Astronautica 2011; 69: 833–840. DOI: 10.1016/j.actaastro.2011.06.005.

Matsushita

Chujo

Matsumoto

, et al. Solar power sail membrane prototype for OKEANOS mission. Adv Space Res 2021; 67: 2899–2911. DOI: 10.1016/j.asr.2020.10.007.

Johnson

Whorton

Heaton

, et al. NanoSail-D: A solar sail demonstration mission. Acta Astronautica 2011; 68: 571–575.

Johnson

Young

Montgomery

, et al. Status of solar sail technology within NASA. Adv Space Res 2011; 48: 1687–1694.

Spencer

Betts

Bellardo

, et al. The LightSail 2 solar sailing technology demonstration. Adv Space Res 2021; 67: 2878–2889. DOI: 10.1016/j.asr.2020.06.029.

Seefeldt

Spietz

Sproewitz

, et al. Gossamer-1: Mission concept and technology for a controlled deployment of Gossamer spacecraft. Adv Space Res 2017; 59: 434–456.

Seefeldt

. A stowing and deployment strategy for large membrane space systems on the example of Gossamer-1. Adv Space Res 2017; 60: 1345–1362.

Grundmann

Bauer

Biele

, et al. Capabilities of Gossamer-1 derived small spacecraft solar sails carrying Mascot-derived nanolanders for in-situ surveying of NEAs. Acta Astronautica 2019; 156: 330–362.

Fernandez

Visagie

Schenk

, et al. Design and development of a Gossamer sail system for deorbiting in low earth orbit. Acta Astronautica 2014; 103: 204–225.

10.

Wagner

. Flat sheet metal girders with very thin metal webs. Part I, II, III. NACA Tech Memoranda 1929; 20: 200–314.

11.

Friswell

Garvey

Penny

JET

. Model reduction using dynamic and iterated IRS techniques. J Sound Vibrat 1995; 186: 311–323.

12.

Dyka

Ingel

Flippen

. A new approach to dynamic condensation for FEM. Comput Struct 1996; 61: 763–773.

13.

C-H

. Nonlinear wrinkling of nonlinear membranes of revolution. J Appl Mech 1978; 45: 533–538.

14.

Lecieux

Bouzidi

. Experimental analysis on membrane wrinkling under biaxial load – comparison with bifurcation analysis. Int J Sol Struct 2010; 47: 2459–2475.

15.

Vulpetti

Apponi

Zeng

, et al. Wrinkling analysis of solar-photon sails. Adv Space Res 2021; 67: 2669–2687. DOI: 10.1016/j.asr.2020.07.016.

16.

Wong

Pellegrino

. Wrinkled membranes part I: Experiments. J Mech Mater Struct 2006; 1: 1–25.

17.

Bernal

Tassius

Melo

. Elastic response and wrinkling onset of curved elastic membranes subjected to indentation test. Eur Phys J E 2011; 34: 1–5.

18.

Murphy

Macy

. Demonstration of a 10-m Solar Sail System. 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference. CA: Palm Springs, 2004.

19.

Lucchesi

. Reassessment of the error modelling of non-gravitational perturbations on LAGEOS II and their impact in the Lense–Thirring determination. Part I. Planet Space Sci 2001; 49: 447–463.

20.

Bar-Sever

Kuang

. New Empirically Derived Solar Radiation Pressure Model for Global Positioning System Satellites. IPN Progress Report, 2004.

21.

Liu

, et al. A new empirical solar radiation pressure model for BeiDou GEO satellites. Adv Space Res 2016; 57: 234–244.

22.

Nerovny

Lapina

Grigorjev

. Light radiation pressure upon an optically orthotropic surface. J Quant Spectrosc Radiat Transf 2017; 202: 64–73.

23.

Nerovny

Lapina

. Application of a modified generalized sail model on a solar sail with wrinkles. Adv Space Res 2021; 67: 2767–2775. DOI: 10.1016/j.asr.2020.01.020.

24.

Nehrenz

. Initial Design and Simulation of the Attitude Determination and Control System for LightSail-1. 2010, https://digitalcommons.calpoly.edu/aerosp/20/.