Performance-Invariant Scaling of Square Solar Sails

Transcription

1 4th International Syposiu on Solar Sailing Kyoto, Japan, January 17-20, 2017 Perforance-Invariant Scaling of Square Solar Sails Sergey Trofiov Keldysh Institute of Applied Matheatics Russian Acadey of Sciences Mikhail Ovchinnikov Keldysh Institute of Applied Matheatics Russian Acadey of Sciences

2 Contents Square sail systes and their coponents Concept of perforance-invariant scaling Mass scaling laws for the coponents of a square sail syste Payload ass scaling Payload ass fraction scaling and the optial square sail design 2/16

3 Priary designs of solar sails Credit: Surrey Space Centre Credit: R. Bloquist Credit: B. Diedrich Priary types of solar sails: 1. Square sail 2. Disk sail 3. Heliogyro 3/16

4 Sail ebrane structure A solar sail ebrane is usually ade of soe polyiide (Kapton or Mylar). The front surface is aluinized in order to better reflect light. Source: Surrey Space Centre The back surface is usually coated with soe high-eissivity layer or also aluinized for LEO sails and if we do not know a priori what surface will be sunlit. 4/16

5 Types of deployable boos Metallic (e.g., copper-berylliu) Carbon fiber reinforced plastic Source: Surrey Space Centre 5/16

6 Sail deployent echanis Source: Surrey Space Centre 6/16

7 Solar sail perforance characteristics d b p Sail loading A Sail assebly loading Characteristic acceleration P W c L r c s A a c d b 2 P 6 2 N/ at 1 a.u. ( 1 for an ideal sail) L R T J/s is solar luinosity 7/16

8 Perforance-invariant scalability vs. design scalability The design scalability is the ability to anufacture a workable solar sail syste of the sae design as the test prototype, but of different size. The perforance-invariant scalability is the ability to adapt a given sail prototype to the spacecraft of larger or saller ass so that the characteristic acceleration (i.e., the orbital dynaics) reains the sae. 2 2 k A k A k 2 d b?? p const 8/16

9 Boo flexural deflection (bending) boo tip deflection 3 F, EI I E Young s odulus area oent of inertia coefficient defining the distribution of the lateral load F along the boo 2 4 F 3 3 E since F 2 9/16

10 Safe scaling of sail syste coponents Fro the Euler-Bernoulli bea theory: the scaling procedure will be safe (no buckling or plastic bending deforations) if we keep the relative boo tip deflection. To scale the boo thickness is hardly feasible due to violation of the strain liit Δ by a boo in the coiled state. 2 const r dru 4 3 Hence, const k b b b Source: Surrey Space Centre 10/16

11 Payload ass scaling k k b d p b d p k 2 p p b d k k k 1 p 2 PA a p b d c p p d k independent of a when b 1 1 k k c Sailcraft prototype: CubeSail (3U CubeSat) 3 kg 500 g 300 g 581 g d b p 2 k k k if p and vice versa 11/16

12 Payload ass as a function of sail s area Sailcraft prototype: CubeSail (3U CubeSat) A g d 300 g 581 g b 2 3 kg The payload ass achieves axiu at k PA 343 a 12/16 b c b 3

13 Payload ass fraction scaling The payload fraction achieves axiu if 37 k k 3 6 d b k3 2 for CubeSail In general, if b 6, 1 k3 k1, whereas if 6, k1 k3 1 b d 6 k k 1 b d 1 3 In addition, it is always true that k3 k2 13/16 d

14 Effective specific ipulse as a easure of sail syste efficiency Effective specific ipulse of a sail syste: I sp at c g 0 1 ln 1 where is the payload ass fraction For a 2-year flight, CubeSail with noinal and optial (x2) designs would respectively have the following specific ipulse values: I sp I sp s 747 s 9.81 ln s 934 s 9.81 ln % 14/16

15 Accurate consideration of deployent echanis ass and size scaling h 43 height of the boos in the coiled state h If the scale factor k is not too uch, there is an option of changing the subtended angle θ, which increases the cross-sectional oent of inertia. 4 radius of the 4-boo coil 2 r r dru (assuing the Archiedes spiral approxiation) 15/16

16 Conclusions The ass scaling laws are derived for all the coponents of the square sail syste. As a result, the payload ass scaling law is obtained. It is nononotonic (which is intuitively predictable) due to the fact that the boos ass grows faster than the sail area if scaled safely. For a given sail prototype, there exist the axiu payload ass we can potentially eject in orbit with the required level of characteristic acceleration. The payload ass fraction is also scaled non-onotonically. For a given sail prototype, there exist the optial scale: the boos should be about 6 ties as heavy as the deployent echanis. 16/16

17 Acknowledgents Russian Science Foundation (RSF), grant Thank you for your attention

18 Perturbing forces for LEO sailcraft Maxiu values are depicted for a sailcraft with a sail of 25 2 Drag coefficient С D =2.2 18/18