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SOAR - Satellite for Orbital Aerodynamics Research

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Citation for published version (APA):Crisp, N., Roberts, P., Edmondson, S., Haigh, S., Huyton, C., Livadiotti, S., Abrao Oiko, V. T., Smith, K., Worrall,S., Becedas, J., Gonzalez, D., Gonzalez, G., Dominguez, R., Bay, K., Ghizoni, L., Jungnell, V., Morsbøl, J., Binder,T., Boxberger, A., ... Schwalber, A. (2018). SOAR - Satellite for Orbital Aerodynamics Research. In 69thInternational Astronautical CongressPublished in:69th International Astronautical Congress

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SOAR { Satellite for Orbital Aerodynamics Research

N.H. Crispa,�, P.C.E. Robertsa, S. Edmondsona, S.J. Haigha, C. Huytona, S. Livadiottia, V.T.A. Oikoa, K.L. Smitha,S.D. Worralla, J. Becedasb, D. Gonz�alezb, G. Gonz�alezb, R. Dom��nguezb, K. Bayc, L. Ghizonic, V. Jungnellc,

J. Morsb�lc, T. Binderd, A. Boxbergerd, S. Fasoulasd, G.H. Herdrichd, F. Romanod, C. Traubd, D. Garcia-Almi~nanae,S. Rodriguez-Donairee, M. Suredae, D. Katariaf, R. Outlawg, B. Belkouchih, A. Conteh, J.S. Perezh, R. Villainh,

A. Hei�ereri, A. Schwalberi

aThe University of Manchester, Oxford Rd, Manchester, M13 9PL, United KingdombElecnor Deimos Satellite Systems, Calle Francia 9, 13500 Puertollano, Spain

cGomSpace AS, Langagervej 6, 9220 Aalborg East, DenmarkdUniversity of Stuttgart, Pfa�enwaldring 29, 70569 Stuttgart, Germany

eUPC-BarcelonaTECH, Carrer de Colom 11, 08222 Terrassa, Barcelona, SpainfMullard Space Science Laboratory (UCL), Holmbury St. Mary, Dorking, RH5 6NT, United Kingdom

gChristopher Newport University, Newport News, Virginia 23606, USAhEuroconsult, 86 Boulevard de S�ebastopol, 75003 Paris, France

iconcentris research management gmbh, Ludwigstra�e 4, D-82256 Furstenfeldbruck, Germany

Abstract

SOAR (Satellite for Orbital Aerodynamics Research) is a CubeSat mission designed to investigate the interaction betweendi�erent materials and the atmospheric ow regime in Very Low Earth Orbits (VLEO) and to demonstrate aerodynamicattitude and orbit control manoeuvres. Improving knowledge of the gas-surface interactions is important for the designof future satellites operating in lower altitude orbits and will enable the identi�cation of materials which can minimisedrag or improve aerodynamic control, a key aim of the Horizon 2020 DISCOVERER project. In order to achieve theseobjectives, SOAR features two payloads: i) a set of steerable �ns which provide the ability to expose di�erent materialsor surface �nishes to the oncoming ow with varying angle of incidence whilst also providing variable geometry toinvestigate aerostability and aerodynamic control; and ii) an Ion and Neutral Mass Spectrometer with Time-of-Flightcapability which enables accurate measurement of the in-situ ow composition, density, and thermospheric wind velocity.Using precise orbit and attitude determination information and the measured atmospheric ow characteristics the dragand side-force experienced by the satellite in orbit can studied and estimates of the aerodynamic coe�cients calculated.This paper �rst presents the scienti�c design and operational concept of the SOAR mission, focusing on the stabilityand control strategy which enables the spacecraft to maintain the ow-pointing attitude required by the payloads. Themethodology for recovery of the (relative) aerodynamic coe�cients from the measured orbit and in-situ atmosphericdata is then presented. Finally, the uncertainty of the resolved aerodynamic coe�cients is estimated statistically usingsimulations.

Keywords: Orbital Aerodynamics; Drag Coe�cient; Gas-Surface Interactions; Thermospheric Wind; CubeSat.

1. Introduction

SOAR (Satellite for Orbital Aerodynamics Research)is a scienti�c CubeSat mission designed to investigate theinteractions between the atmospheric ow regime in VeryLow Earth Orbits (VLEO) and di�erent materials andsurface-coatings. Secondary objectives of the SOAR mis-sion are to provide new in-situ measurements of the atmo-spheric density and composition and variation of the ther-mospheric wind velocity over the range of altitudes belowapproximately 400 km. SOAR will also demonstrate novelattitude and orbit control manoeuvres using the aerody-

�Corresponding author.Email address: nicholas.crisp@manchester.ac.uk

(N.H. Crisp)

namic forces and torques which can be generated at thesealtitudes.

The SOAR mission is a key component of to Horizon2020 funded DISCOVERER project [1], which aims to rad-ically redesign Earth Observation satellites for sustainedoperation at signi�cantly lower altitudes. Improving theknowledge and understanding of the Gas-Surface Interac-tions (GSIs) at these low orbital altitudes is an importantstep in the identi�cation of novel and interesting materialswhich can reduce atmospheric drag or improve aerody-namic control capability.

The experiments performed by SOAR will be used toprovide valuable validation data for further ground-basedexperiments on materials and GSIs which will be per-formed in the ROAR (Rare�ed Orbital Aerodynamics Re-search) Facility [1] at The University of Manchester. The

IAC-18.B4.2.2x43107

Nomenclature

� Energy accommodation coe�cient

� Rotational acceleration

x Linear acceleration

� Atmospheric density

~vrel Relative atmospheric ow vector

Aref Reference area

CF Force Coe�cient

CT Torque Coe�cient

I Moment of inertia

lref Reference length

m Mass

Ra Earth equatorial radius

ROAR Facility is a unique set-up which is aimed at theidenti�cation of novel materials for satellite applicationswith a focus on improved aerodynamic properties and atomicoxygen resistance. The facility is principally comprised ofa UHV environment, an atomic oxygen source capable ofproviding representative orbital velocities and surface in-teractions, and a sensor suite including Ion and NeutralMass Spectrometers (INMS) which enable measurementand characterisation of the incident and reemitted gas-owon sample materials.

1.1. The VLEO Environment

Very Low Earth Orbits can be de�ned as those belowwhich the atmosphere begins to have a meaningful e�ecton the orbital and attitude dynamics of a spacecraft. Incomparison to Low Earth Orbits (LEO), typically de�nedas any orbit below 2000 km, VLEO is generally de�nedas below 500 km to 450 km. However, this de�nition maybe somewhat deceptive as in reality the range of VLEOvaries with density and the expansion and contraction ofthe atmosphere and is therefore highly dependent on thesolar cycle. The lower-end of the VLEO range is boundedby orbits which can be sustained for a very short period oftime as a result of the signi�cant atmospheric drag whichwill be acting at these altitudes, typically between 100 kmto 150 km.

In VLEO the atmosphere is signi�cantly less densethan the ground or conventional ight altitudes and isconsidered to be rare�ed such that the mechanics of con-tinuum ow regimes can no longer be applied. The non-dimensional Knudsen number can be used to classify dif-ferent ow-regimes and is de�ned as the ratio between themean free path (the average distance between successivecollisions) of the constituent molecules in a ow and a char-acteristic physical length (eg. the length of a body in that

ow). When the Knudsen number is high (ie. Kn > 10)the gas-surface interactions along the length of a body areof much greater signi�cance than any gas-gas interactions,including those with reected particles [2]. This regime istermed Free Molecular Flow (FMF), and generally appliesacross the VLEO range for spacecraft of typical size [3].

In the FMF regime of VLEO the interactions betweenmolecules (incident and reected) are considered to have

a negligible e�ect on the ow. The forces which act on abody can therefore be determined by considering only theinteractions between the molecules and the body, and inparticular the momentum and energy transfer which oc-curs at the surface. It is known that these interactions aredependent on surface roughness and cleanliness (particu-larly related to altitude-dependent atomic oxygen adsorp-tion and accommodation), surface composition and latticestructure, surface temperature, gas composition, and theincident particle temperature, velocity, and incidence an-gle [4, 5, 6]. However, whilst numerous models for theseGSIs and the associated force coe�cients have been de-veloped [2, 7, 8, 9, 10], most of these factors have thusfar been neglected. A key element of this current de�citin GSI modelling is the lack of experimentation which cano�er insight into the e�ect that each of these factors has onthe momentum and energy transfer in a GSI and thereforethe forces which act on a body in the VLEO ow regime.

1.2. On-Orbit Investigation of Gas-Surface Interactions inVLEO

Previous investigation of gas-surface interactions in theFMF regime has included both experimentation performedin laboratories and on-orbit, review of which is principallyprovided by Moe et al. [4], Moe and Moe [11] and Pilin-ski [12]. Some studies have used indirect measurementtechniques, for example investigating adsorption on pres-sure gauge and mass spectroscopy instruments [13], or pas-sive detection of scattered remission angle [14, 15]. How-ever, systematic and sustained experimental campaignshave not yet been carried out and measurement of exter-nal spacecraft surface accommodation has not yet been ap-proached. Whilst direct measurement of the experienceddrag forces using accelerometers has been performed dur-ing the transitional re-entry phase of the Space Shuttle[16, 17], further experiments in the wider LEO range havenot yet been pursued.

Other studies have used observational methods to in-fer �tted accommodation and drag coe�cients of di�erentspacecraft or materials from the attitude motion or orbitaltrajectory. These experiments have notably included Pad-dlewheel [18] and spherical [5, 19] satellites, but have alsoincluded more complex geometries [20, 21, 22]. However,

2

the results obtained using these methods have thus far re-lied on modelled atmospheric densities and are thereforesubject to their inherent biases and uncertainties.

By analysis of the ODERACS radar calibration satel-lites, [19] suggest that the variation in �tted drag coe�-cient for similar spherical geometries with varying surfacecomposition or treatment is less than 5 % in VLEO at so-lar minimum and that this variation reduces with altitudeas a result of increased atomic oxygen adsorption.

1.3. Scienti�c Objectives

The principal scienti�c objective of SOAR is to inves-tigate the variation of the aerodynamic coe�cients of dif-ferent materials and surface �nish at di�erent incidenceangle to the oncoming ow and at di�erent orbital al-titudes. In-situ measurement techniques will be used toprovide knowledge of the incident ow environment in ad-dition to the attitude and orbital parameters from whichthe forces and torques experienced by the body can be re-covered. By providing in-situ density measurements of theoncoming ow which can be used directly in the recoveryof the �tted aerodynamic coe�cients and associated ac-commodation coe�cients, this experimental methodologypresents a signi�cant advantage over previous observation-based studies.

The additional mission objectives for SOAR are as fol-lows, but beyond the scope of this paper.

� Perform measurements of the thermospheric windspeed and vector.

� Perform measurement of atmospheric density andcomposition.

� Demonstrate the ability to control the spacecraft at-titude using aerodynamic torques.

� Demonstrate the ability to control the spacecraft or-bit using aerodynamic forces.

2. Satellite Design

SOAR takes the form of a 3U CubeSat developed fromthe �Dsat design of Virgili Llop and Roberts [23], previ-ously proposed for the QB50 programme for lower ther-mospheric exploration and research. The basic geometryand con�guration of SOAR is shown in Fig. 1.

In order to provide in-situ information about the owconditions, including thermospheric winds, the spacecraftfeatures a forward-facing Ion and Neutral Mass Spectrom-eter (INMS). This sensor, improved since the developmentof the QB50 satellites, includes new Time-of-Flight (ToF)capability, enabling assessment of the incoming ow veloc-ity in addition to the total atmospheric density and owcomposition.

To maintain accuracy of the INMS instrument, thespacecraft must be pointed in the direction of the oncom-ing ow to within a given acceptance angle. Simply, this

Figure 1: Geometry and con�guration of the SOARsatellite with steerable �ns and INMS payloads.

requires that the spacecraft nominally ies in an attitudewhich is aligned with the direction of the ow. SOARtherefore features a similar design of four aerodynamicpanels as �Dsat, providing natural aerostability to thespacecraft. These panels can also be rotated to achievethe scienti�c objectives of the mission and are thereforetermed steerable-�ns herein.

The surfaces of these steerable-�ns will coated with dif-ferent materials and surface �nishes and will be exposedto the ow at varying angles of incidence to perform theproposed investigation of the drag and lift coe�cients. Asdescribed by Virgili Llop and Roberts [23], the steerable-�ns can be operated in pairs in two di�erent ways; co-rotation and counter-rotation. Under stable ow-pointingconditions, co-rotation of a single pair of the steerable-�nscreates a net lift or side force and therefore a torque (inyaw for the vertical �ns or pitch for the lateral �ns). Thespacecraft will therefore rotate to y at an angle to the

ow. Contrastingly, counter-rotation of a pair of oppos-ing �ns generates no net side-force, but creates a torque-couple in roll, causing the spacecraft to spin about the

ow-pointing direction.

Attitude control of the spacecraft is principally enabledby a three-axis reaction wheel assembly (tetrahedral con-�guration of four wheels). A three-axis magnetorquer isalso speci�ed to perform initial detumbling operations fol-lowing launch and to enable desaturation and momentummanagement of the reaction wheels. SOAR also carries ananosatellite-class star-tracker and Earth and sun sensors

3

to provide precise attitude knowledge. An on-board GPSreceiver provides the precise position and velocity of thespacecraft and removes dependency of the experiment onobservational tracking information.

3. Experimental Design

A body exposed to an oncoming ow will produce forceof an aerodynamic nature, the magnitude and direction ofwhich will be dependant on the orientation with respectto the ow vector. This force is often decomposed intothree mutually perpendicular forces; drag, normal, andside force. An alternative term, lift force, is often usedto refer to either the normal or side force depending onthe convention used the chosen coordinate system. UsingEq. (1) each of these forces can be associated with a dimen-sionless force coe�cient CF which relates the magnitudeof the force or accelerations produced with the dynamicpressure of the surrounding ow and the spacecraft geom-etry.

F =1

2�v2rel

~vrelj ~vrelj

ArefCF = mx (1)

where � is the local atmospheric density, vrel the space-craft velocity relative to the oncoming ow, and Aref thereference area.

Equivalently, an associated aerodynamic torque or ro-tational acceleration experienced can be described by Eq. (2)in which CT is the aerodynamic torque coe�cients (in ei-ther roll, pitch, or yaw) and lref is an additional referencelength.

T =1

2�v2rel

~vrelj ~vrelj

Aref lrefCT = I � (2)

The primary scienti�c objective of SOAR is to providein-situ measurements of the GSI characteristics of di�erentmaterials and surface-coatings in the VLEO environment.These GSI characteristics will be investigated by consid-ering the the variation in drag and lift forces producedby the steerable-�ns which can be observed when di�erentmaterials are individually exposed to the oncoming owat varying incidence angle and at di�erent altitudes as theorbit of SOAR decays.

Reconciliation of these force and torque coe�cientswith the true GSI mechanics still requires a model for theexchange of energy and momentum of the gas species withthe surface and the associated reemission pattern. How-ever, experimental determination of these aerodynamic co-e�cients provides valuable in-situ validation data for theexperiments which will be performed in the ROAR Facil-ity.

3.1. Drag Coe�cient

Investigation of the drag coe�cient of di�erent mate-rials exposed to the ow by the steerable �ns was pro-posed by Virgili Llop and Roberts [23] for the �Dsat mis-

sion. In this method, opposing steerable-�ns are counter-rotated, nominally producing no net lift/side-force, but anet torque in roll, thus allowing the drag coe�cient to bedetermined from the resulting spacecraft trajectory.

For SOAR both co-rotated and counter-rotated con-�gurations of the steerable �ns can be considered to per-form experiments on the variation in drag coe�cient withincidence angle and altitude. Using the reaction wheels,torques generated by aerodynamics or other disturbancescan be compensated and thus the nominal direction of thesatellite controlled for a period of time during an experi-ment or test-run.

During these test-runs the orbital parameters or trajec-tory of the spacecraft will vary depending on the oncom-ing ow conditions and spacecraft geometry with respectto the ow. For example, as the incidence angle of theof the steerable �ns is increased towards the normal, thepanel area exposed to the ow will also be increased. Thedrag experienced by the spacecraft for a given ow con-dition will also therefore increase and will be reected inthe rate of orbital decay. The drag coe�cient for a givenorbital altitude and con�guration of the steerable �ns cansubsequently be recovered by considering the relationshipbetween the produced drag force and the acceleration ofthe spacecraft, expressed by Eq. (1). However, it should benoted that the drag coe�cient determined by this methodis representative of the whole spacecraft in the given con-�guration and not speci�c to only the surfaces or materialsof the steerable �ns exposed to the ow.

In practice, this analysis can be performed by usingan orbit determination process which is informed by theatmospheric density and spacecraft position and velocitywhich are measured over the period of the test-run. Aparameter-�tting process is used to to �nd the best-�t dragcoe�cient which provides convergence between the mea-sured trajectory and a mathematical model for the motionof the spacecraft.

The accuracy to which the drag coe�cient can be de-termined by such a method is primarily dependent onthe quality of the experimental data which can be ob-tained during each test-run (characterised by uncertaintyor noise) and the �delity of the mathematical model towhich this will be compared to. Therefore, to measure thedrag coe�cient of two di�erent con�gurations, it is nec-essary that the measured trajectories of the two test-runscan be distinguished from each other. E�ectively, this im-poses a minimum requirement on the noise or uncertaintyin the measured data and the duration of each test-run.

The �delity of the mathematical model used by the or-bit determination process can also have an e�ect on thequality of the recovered drag coe�cient. In order to pro-vide convergence towards the measured trajectory usingthe free parameter �tting it is necessary that the modelincorporates the relevant perturbations and their spatialand temporal variations over the duration of the test-run. However, the selection of necessary perturbationsand modelling �delity are related to the noise in the mea-

4

sured position and velocity. Perturbations which wouldcause variation in the trajectory of the spacecraft of lessthan the noise in the measured values can be safely ne-glected, simplifying the form of the mathematical model.The selection of these perturbations is explored further inSection 6.

3.2. Lift Force Coe�cient

As various de�nitions and conventions for the forcesacting on a vehicle exist, the term lift force will be usedherein to describe any force which acts perpendicular tothat of the drag force in the body-axes of a notional space-craft. This also provides commonality in terminology forboth the vertical and lateral �ns for SOAR which are sym-metrical in roll (about the z-axis) with respect to the satel-lite.

Similarly to the drag coe�cient, the lift force coe�cientof the di�erent materials and surfaces exposed to the owby the steerable �ns will be investigated by analysis ofthe resulting spacecraft motion and a parameter �ttingmethod to recover the aerodynamic coe�cient.

For a counter-rotated con�guration of opposing steerable-�ns can be used to analyse the lift force coe�cient. Theequal but opposing lift forces produced by the opposing�ns act as a couple to generate a net rolling torque onthe spacecraft. The lift force coe�cient can therefore berecovered by considering the evolution of the spacecraftattitude, principally in roll.

Alternatively, for a co-rotated con�guration of oppos-ing steerable �ns, both a net lift force and pitch/yaw torquewill be produced. Two methods for recovery of the liftforce coe�cient can therefore be considered. The �rst usesthe produced lift force and can be performed by coordi-nated analysis of the orbital trajectory of the spacecraftrequiring simultaneous parameter �tting of the drag co-e�cient and the lift force coe�cient. However, as the liftforce of known materials is typically a fraction of the drag-force, the ability to e�ectively infer the lift force coe�cientfrom the measured orbital data may be limited. The sec-ond method exploits the pitch/yaw torque produced by theco-rotated con�guration of the steerable �ns and utilisesboth the resulting attitude motion of the spacecraft andangular momentum of the reaction wheels to determinethe lift force coe�cient.

Use of the attitude dynamics of the spacecraft to de-termine the lift force coe�cient requires an expression re-lating the torque T produced by the steerable �ns to theangular acceleration � about a given axis of the spacecraft,given by Eq. (3).

T = FLlF =1

2�v2rel

~vrelj ~vrelj

Aref lFCF = I � (3)

where the produced torque or couple can also be de-�ned by the lift force FL and associated moment arm lF .

Assuming that the body of the spacecraft does not con-tribute any additional roll torques, the lift force coe�cient

can be recovered by considering the evolution of attitude inthe roll-axis of the spacecraft in combination with knowl-edge of the control inputs, and reaction wheel rates orangular momentum.

Free-parameter �tting of the lift force coe�cient fromthe attitude evolution of the spacecraft requires an at-titude dynamics model including models for the torqueswhich act on the spacecraft. The orbit trajectory and per-turbation models used in the drag coe�cient analysis arealso required to provide the correct spatial and temporalreference for the selected torque models.

4. Attitude Stability and Control Analysis

The presence and use of the steerable �ns on SOARproduces a number of di�erent forces and torques whichneed to be carefully considered to ensure stability andpointing accuracy of the spacecraft throughout its life-time. Interaction of the spacecraft with the residual at-mosphere in LEO, solar radiation, and the magnetic andnon-spherical gravity �elds of the Earth must principallybe considered. The capability to control the attitude andstability of the spacecraft using on-board actuators also re-quires consideration as the orbital altitude decreases andthe aerodynamic torques experienced increase in magni-tude.

The concept of aerostability is employed by SOAR toprovide passive pointing towards the oncoming ow direc-tion in orbit. This aerostability is provided by the steer-able �ns which are located towards the aft of the spacecraftand thus generate a restoring aerodynamic torque in pitchand/or yaw in response to any misalignment of ow direc-tion with the longitudinal axis of the spacecraft. Wheneach steerable �n is oriented parallel to the longitudinalbody axis of the spacecraft a minimum drag con�gurationis generated for the nominal spacecraft attitude. Similarly,when the steerable �ns are all oriented normal to the space-craft longitudinal axis the maximum drag con�guration isachieved.

As the material and surface coatings which will be ap-plied to the steerable �ns are yet to be selected for themission, this creates uncertainty in the attitude perfor-mance and control capability of the satellite. Di�erentmaterials will have varying GSI performance, and maytherefore result in the production of signi�cantly di�er-ent forces and torques when exposed to the ow. In thefollowing analyses Sentman’s model [2] for GSIs is usedin which the energy accommodation coe�cient � and sur-face (wall) temperature Tw principally govern the qualityof particle reection/reemission.

4.1. Static Stability

The static stability of provided by di�erent con�gura-tions of the steerable �ns can be investigated by consider-ing the torque generated by the interaction of the space-craft geometry with the oncoming ow.

5

Figure 2: Pitch/Yaw moment coe�cient of SOAR withvarying angle of incidence with respect to the ow in theminimum (steerable �ns parallel to body) and maximum(steerable �ns perpendicular to body) dragcon�gurations. Assuming Sentman GSI model at 300 kmaltitude, 56:1� inclination

Modelling of the aerodynamic moment coe�cients forSOAR has been performed using ADBSat [24], an analyti-cal panel-method tool for convex satellite geometries whichcan encompass di�erent gas-surface interaction models andbasic shadowing analysis. In this study Sentman’s model isapplied throughout with accommodation coe�cient � = 1and Tw = 300 Kelvin unless otherwise stated.

The static pitching/yawing moment coe�cient of SOARin the minimum and maximum drag con�gurations is pre-sented in Fig. 2. The negative slope of the pitch/yawmoment coe�cient with angle of incidence indicates theaerostable nature of these con�gurations. The conceptof aerodynamic stability derivatives, or aerodynamic sti�-ness, for spacecraft at orbital altitudes, can be used to fur-ther investigate the expected attitude behaviour for vary-ing geometry and ight conditions [25]. The static pitch/yawstability derivative CT� , can be calculated from the gradi-ent of CT over a small range about the nominal attitude(� = 0). The variation in static pitch/yaw stability deriva-tive for steerable �n angles over the range of minimum tomaximum drag con�gurations is shown in Fig. 3, notingthat the steerable �ns are counter-rotated and thus demon-strate symmetry between pitch and yaw. The increase instability derivative with increasing incidence angle demon-strates that a greater static stability is achieved when alarger panel area is presented to the ow.

In order to characterise the performance of di�erentmaterials and surface-coatings in orbit, during the exper-imental periods only one pair of steerable �ns will be ro-tated with respect to the ow at any given time. With thiscon�guration a total of four materials or surfaces can becharacterised during the mission, two per pair of opposingsteerable �ns.

When a single pair of steerable �ns is counter-rotated

Figure 3: Aerodynamic sti�ness, static stabilityderivative, of SOAR with varying steerable �n angle withrespect to the ow. Assuming Sentman GSI model at200 km altitude, 56:1� inclination

with the spacecraft pointing into the direction of the on-coming ow a net rolling torque is generated but no netpitch or yaw torques are created. However, if the rela-tive direction of the ow changes (for example due to at-mospheric co-rotation or thermospheric winds) or the at-titude of the satellite is perturbed, induced torques aregenerated due to a variation in the projected area of thecounter-rotated �ns to the ow. In Fig. 4 the vertical �nsare counter-rotated and the spacecraft attitude is o�setwith respect to the oncoming ow in sideslip with an an-gle of 5�. Under these conditions, contrary to either themaximum or minimum drag con�gurations, a net pitch-ing torque arises due to the di�erence in area presentedto the ow by the vertical �ns. The plot of net torquesin pitch and yaw for this con�guration, shown in Fig. 5,demonstrate that induced torques in pitch due to angleof sideslip have a positive gradient about the equilibrium,and are therefore disturbing rather than restoring. Fur-thermore, these torques grow at a faster rate than therestoring torques generated by the lateral �ns due to pitchangle. If the ow is therefore o�set with respect to thespacecraft body in yaw the spacecraft responds by rotat-ing in the pitching axis as a result of the set angle of thesteerable �ns. Equivalent behaviour is demonstrated forcounter-rotated lateral �ns and an o�set in angle of at-tack. This e�ect is therefore termed pitch-yaw couplinghenceforth.

Co-rotation of a pair of opposing steerable �ns gener-ates a net torque in pitch or yaw, but no net torque in roll.Fig. 5 shows the torques in pitch and yaw for a con�gura-tion in which the lateral �ns are co-rotated, demonstratinga small bias in pitch torque when the spacecraft is alignedwith the direction of the oncoming ow. However, as thepitch (angle of attack) is increased by a small amount (�3�in Fig. 5) the pitch torque crosses zero with a negative gra-dient. The spacecraft therefore demonstrates stability in

6

Figure 4: SOAR geometry with vertical �nscounter-rotated at 45�. The 5� sideslip angle of the owproduces a variation in projected area between thevertical �ns and results in a disturbing pitch torque.

pitch at this small angle with respect to the ow. Thespacecraft is also shown to be stable in yaw about theoncoming ow direction.

4.2. Dynamic Stability

In order to understand the evolution of attitude overtime and in the presence of perturbing torques the dy-namic response of the spacecraft must be considered. Forrotationally symmetric con�gurations the previous analy-ses showed that aerostability ensures that restoring torqueswill be produced in response to changes in the oncoming

ow direction. However, due to the FMF nature of thesurrounding atmospheric environment, natural dampingof the generated angular velocity is not generated. There-fore, without any additional damping input or further per-turbation to the system, the spacecraft will oscillate aboutan equilibrium point. The amplitude and frequency of thisoscillation are dependant on the initial disturbance, stabil-ity derivative, and the environmental conditions Mostaza-Prieto and Roberts [25].

The response of SOAR in the minimum and maximumdrag con�guration for varying orbital altitude and in theabsence of further perturbing torques is presented in Fig. 7.The responses demonstrate the aerostable nature of thespacecraft con�guration and that the amplitude and pe-riod of oscillation both decrease with increasing aerody-namic sti�ness and dynamic pressure.

This oscillatory mode can be critically damped, sig-ni�cantly reducing the range over which the attitude ofthe spacecraft varies, as discussed by Virgili Llop et al.[26]. However, due to the presence of further perturbingtorques in the real orbital environment (eg. thermosphericwinds, solar-radiation pressure, gravity gradient), and er-rors or incompatibilities associated with real attitude ac-

tuator systems (eg. magnetorquer availability and cross-coupling), the true dynamic response is more complex.

Further control methods for aerostable spacecraft arepresented in the literature, but have not yet been testedbeyond simulation. Psiaki [27] presents a compass-likePID control method which utilises magnetorquers to pro-vide three-axis stabilised nadir-pointing capability to a1U CubeSat with a shuttlecock con�guration of deployed‘feathers’. Auret and Steyn [28] subsequently applied thismethod to an extended 3U CubeSat geometry which in-cluded a pair of actuating ‘paddles’, provide control capa-bility about the roll axis. Further control methods utilisingreaction wheels were also investigated, including a 3-axisquaternion feedback control law providing pointing perfor-mance for imaging applications.

A further issue with active control of a ow-pointingspacecraft is that the true oncoming ow vector is notknown a priori. A reference vector for true three-axis ow-pointing control using proportional control inputs is there-fore missing. A predicted vector can be used including thee�ect of atmospheric co-rotation, however the integrationof thermospheric winds using available models is associ-ated with much greater uncertainty.

5. Mission Simulations

The orbit and attitude response of SOAR in the VLEOenvironment can be investigated a 6-DOF orbital propa-gator, simulating periods of the planned mission. In thesesimulations this tool incorporates the forces and torquesassociated with the Earth gravitational potential (analyt-ical J4 or EGM2008 [29]), solar radiation pressure, resid-ual magnetic dipole interactions (IGRF-11 [30]), varyingatmospheric density (NRLMSISE-00 [31]), and thermo-spheric winds (HWM93 [32] and HWM07 [33]).

As above, the ADBSat tool [24] is used to calculatealtitude-dependent aerodynamic coe�cients using Sent-man’s GSI model. However, it is important to recall thatthe results presented herein will be subject to the assump-tions and limitations of the implemented GSI model andthe input parameters used and therefore may di�er sub-stantially from the true behaviour in orbit.

Control of the spacecraft in these simulations is pro-vided by modelled reaction wheel actuators which are con-�gured in a tetrahedral formation providing redundancyand a dedicated wheel in the roll-axis. The inputs to thereaction wheels are provided by a proportional-derivativecontroller (without knowledge of the true oncoming owdirection). The implemented control gains are currentlyset empirically as the development of other control meth-ods, including adaptive and optimal control, will be ex-plored in future work. Desaturation of the reaction wheelswill be performed if necessary during the idle operationsand between experimental test-runs using the magnetor-quer actuators.

7

Figure 5: Pitch-Yaw coe�cient response for SOAR with vertical �ns counter-rotated at incidence angle of 20�

Figure 6: Pitch-Yaw coe�cient response for SOAR with lateral �ns co-rotated at incidence angle of 20�

5.1. Idle Operations

At the beginning of the mission SOAR will be deployedfrom the ISS to an altitude of approximately 400 km ap-proximately 400 km. As this deployment is expected tobe Q1 2020, expected to be the beginning of a very lowactivity solar minimum, the atmospheric density at thisaltitude will extremely low compared to later in the mis-sion lifecycle and aerodynamic torques experienced by thespacecraft will be relatively small in comparison to the ex-pected solar radiation pressure, residual magnetic dipole,and gravity gradient torques. The natural attitude re-sponse of SOAR without any active actuation under theseconditions is shown in Fig. 8, indicating ow-pointing an-gular errors generally within �30� in pitch and yaw whenin the minimum-drag condition. The maximum drag con-�guration is shown to reduce the amplitude of oscillationby increasing the aerodynamic sti�ness of the satellite, re-sulting in ow-pointing angular errors within �10� for thesame conditions. Fig. 8 also shows that a greater en-ergy accommodation coe�cient slightly increases the at-

titude angle range experienced by SOAR in these con�g-urations, demonstrating the e�ect that di�erent materialsor surface-coatings can have on the attitude dynamics ofthe spacecraft.

The results of these simulations suggest that it maybe necessary at the beginning of the mission (assuming aninsertion altitude of 400 km and low solar activity condi-tions) to increase the stability of the satellite by operatingin the maximum drag con�guration, albeit at the expenseof total orbital lifetime. As the satellite descends in al-titude the atmospheric density will increase and aerosta-bility in the the minimum drag con�guration will improvesuch that it can be utilised whilst maintaining small ow-pointing angular errors.

The active attitude actuators (reaction wheels and mag-netorquers) on SOAR can be used to further reduce theoscillatory motion of SOAR and provide �ner ow-pointingattitude. However, as the perturbing torques are not allperiodic in nature, in particular those due to solar ra-diation pressure, the angular momentum of the reaction

8

Figure 7: Uncontrolled and aerostable pitch/yaw attitude response of SOAR geometry for varying altitude andsteerable �n con�guration. Attitude simulation performed considering only aerodynamic torques in an equatorial orbit.

wheels requires management in order to avoid saturation.Furthermore, the typical disadvantages of cross-couplingand limited availability of magnetorquers must also be ac-commodated whilst the the power consumption of the ac-tuators must be considered for extended use and througheclipse periods.

5.2. Experimental Operations

During the experimental operation of SOAR, both theco-rotated and counter-rotated con�gurations of the steer-able �ns can be considered.

In the counter-rotated con�guration the spacecraft isnominally pointed towards the oncoming ow direction asno torques are in generated in pitch or yaw. A net torque inroll is however produced, which if uncontrolled will causethe spacecraft to spin up. As a result of natural aerosta-bility, oscillations in the pitch and/or yaw attitude will beproduced when the spacecraft is disturbed from its equilib-rium ow pointing con�guration. The e�ect of pitch-yawcoupling will then also act to disturb the attitude of thespacecraft from the ow-pointing direction.

During drag coe�cient experiments, the attitude willbe controlled in three axes avoiding roll-up of the space-craft. Contrastingly, two alternative methods for the in-vestigation of the lift-force coe�cient are proposed. The�rst can be performed alongside the experiments on thedrag-coe�cient under three-axis attitude control and utilisesthe principal of conservation of momentum between the

reaction wheels and the spacecraft body to recover theaerodynamic torque in the roll axis and therefore the co-e�cient of lift-force. The second allows the roll axis toremain uncontrolled allowing the acceleration in roll to bemeasured by the attitude-determination system.

Control of the roll torque and pitch-yaw coupling ef-fects causes build-up in the angular momentum in the re-action wheels towards saturation. Similar to the previ-ous analyses, these e�ects are strongly linked to the at-mospheric density or dynamic pressure. However, as thedensity increases the magnitude of the pitch-yaw couplingand roll torques also increase and the spacecraft becomesmore di�cult to control with the attitude actuators. How-ever, in general the counter-rotated con�guration ensuresthat the INMS device is pointed towards and oscillatesacross the oncoming ow direction and can be operatedwithin its angular acceptance range. The counter-rotatedmode is therefore preferable for the use of the INMS tomeasure the in-situ atmospheric density and ow velocitysuccessfully during the experimental periods.

In the alternative co-rotated con�guration, pitch oryaw torques are generated by the common incidence angleof the two opposing steerable �ns, causing the spacecraft to

y at an angle to the oncoming ow. This behaviour is alsoassociated with an oscillatory motion about an equilibriumattitude, resulting from the aerostability of the spacecraft.However, as the nominal attitude of the satellite will bebiased in either pitch or yaw, control actuators must be

9

Figure 8: Nominal uncontrolled attitude response of SOAR in the minimum drag and maximum drag con�gurationwith two di�erent accommodation coe�cients � = 0:6 and � = 1 at 400 km altitude and under low solar activityconditions. Aerodynamic coe�cients calculated using ADBSat and Sentman’s model with Tw = 300 K.

10

used to correct the nominal pointing direction such thatthe INMS will be aligned towards the ow, ensuring theaccuracy of the measured density and ow velocity infor-mation. As a bias in the pitch or yaw torques exists, an-gular momentum will build-up in the reaction wheels andeventually cause saturation of the control system.

5.2.1. Three-axis Attitude Control

The response of SOAR under three-axis attitude con-trol with one set of steerable �ns counter-rotated at anangle of 45� is shown in Fig. 9 for two di�erent altitudes.At the lower altitude of 250 km the limit of the reactionwheel assembly is reached as the rates increase to satura-tion after 20 min. This results in a loss of control actuationand subsequent roll-up of the satellite. The magnitude ofthe pitch and yaw oscillations of the spacecraft also beginincrease to above 20�, beyond the acceptance range of theINMS.

At the higher altitude of 350 km attitude control canbe sustained by the reaction wheels for a much longer pe-riod with less build-up of angular momentum, a product ofthe lower density atmosphere and therefore aerodynamictorques of smaller magnitude. The attitude in pitch andyaw of the spacecraft is also shown to be maintained withina much smaller angular range (

Figure 9: Attitude response of SOAR at 250 km and 350 km altitude with vertical steerable panels counter-rotated at45� and three-axis reaction wheel control under low solar activity conditions. Aerodynamic coe�cients calculated usingADBSat and Sentman’s model with � = 1 and Tw = 300 K.

12

Figure 10: Attitude response of SOAR at 250 km and 350 km altitude with vertical steerable panels co-rotated at 45�

and three-axis reaction wheel control under low solar activity conditions. Aerodynamic coe�cients calculated usingADBSat and Sentman’s model with � = 1 and Tw = 300 K.

13

Figure 11: Attitude response of SOAR at 250 km and 350 km altitude with vertical steerable panels counter-rotatedat 45� and pitch-yaw reaction wheel control under low solar activity conditions. Aerodynamic coe�cients calculatedusing ADBSat and Sentman’s model with � = 1 and Tw = 300 K.

14

Figure 12: Attitude response of SOAR at 250 km and 350 km altitude with vertical steerable panels co-rotated at 45�

and pitch-yaw reaction wheel control under low solar activity conditions. Aerodynamic coe�cients calculated usingADBSat and Sentman’s model with � = 1 and Tw = 300 K.

15

The performance and data output of the the INMS issimulated prior to use in the free parameter �tting pro-cess. The measured density is �rst produced using theNRLMSISE-00 [31] atmosphere model, informed by orbitand attitude data previously modi�ed for GPS and ADCSsensor and acquisition errors and noise. This density isthen subsequently transformed using the INMS instrumentuncertainty, also reported in Table 1. Finally, data pointsfor which the spacecraft would be pointing outside the an-gular acceptance range of the INMS are rejected and themissing values replaced by interpolation between neigh-bouring valid data-points.

The free-parameter �tting process utilises a least-squaresorbit determination algorithm which seeks to minimise theerror between the reference and modelled trajectories byvarying the free values of the aerodynamic coe�cients.This process is iterative and is terminated by convergencecriteria. Finite- or central-di�erencing methods are usedto account for the errors in the initial condition of the statevector.

The expected experimental performance at di�erent or-bital altitudes and steerable-�n con�gurations can be ob-tained by considering the standard deviation or con�denceinterval of the returned aerodynamic coe�cient after anumber of Monte Carlo iterations. Overlap in the stan-dard deviation for two con�gurations suggests that the dif-ference in �tted drag coe�cient for these two results maynot be statistically signi�cant and therefore may not iden-ti�able from each other in the current experiment. Theimpact of the use of the Monte Carlo simulations can alsobe investigated by considering the con�dence interval onthe �tted drag coe�cient or the standard deviation.

Reducing this standard deviation, e�ectively the res-olution of the experiment, can be achieved by increasingthe signal-to-noise ratio, for example by increasing the testrun time or reducing the uncertainties associated with theutilised data.

Table 1: Summary of expected satellite sensorperformance.

Instrument 1� Uncertainty

GPS Position [m] 2:5GPS Velocity [m s�1] 45� 10�3ADCS Angle [rad] 0:2� 10�3ADCS Angular Velocity [rad s�1] 25� 10�3INMS Number Density [cm�3]

p�N + 0:7

Steerable Fin Rotation Angle [rad] 0:0175

Fig. 13 shows the returned drag coe�cients from thisdata reduction process for SOAR operating with a rangeof di�erent steerable-�n (counter-rotated) incidence anglesand at several altitudes below 400 km. For these drag-coe�cient experiments an experimental period of 120 minis targeted, encompassing more than a single orbital pe-riod, and three-axis reaction wheel attitude control is im-

plemented. The test-run is aborted if the angular range inpitch or yaw exceeds the INMS acceptance limit of 10� orthe reaction wheels approach 90 % saturation. Referencelines for the GSI-based drag coe�cient at each altitudeand con�guration have been provided.

These results indicate that experimentally determineddrag coe�cients for the di�erent steerable �n incidence an-gles are likely to be identi�able and distinguishable withinaltitude range of 250 km to 350 km, with the exceptionof high-incidence angles (60� to 90�) at 350 km. Aboveand below this altitude range the expected uncertaintyis much greater and the experimentally determined dragcoe�cients many not be distinguishable from other con�g-urations. Variation in the experimentally determined re-sults and the reference (GSI-based) drag-coe�cients ariseprimarily from the variation in cross-sectional area andsteerable �n incidence angle which occurs as the satelliteoscillates in pitch and yaw. Additional sources of errorcan be attributed to the sensor characteristics and noiseparameters and the least-squares �tting process.

The variation of the drag coe�cient with altitude foreach steerable �n con�guration also does not appear to beidenti�able from the expected experimental performance.This is due to the relatively small variation in drag coef-�cient which is expected over the available altitude rangeand the experimental uncertainties arising from the space-craft dynamics and sensor characteristics. However, Sent-man’s GSI model with a single accommodation coe�cient(� = 1) has been used to generate these results and theyare therefore subject to the inherent assumptions and sim-pli�cations of the model. These results are also thereforenot representative of the di�erent materials which will beused to cover the steerable �n surfaces. Signi�cantly, thesematerials may demonstrate variation in atomic oxygen ac-commodation with orbital altitude which would increasethe corresponding drag coe�cient.

The corresponding standard deviation of the drag coef-�cient is shown in Fig. 14. These results indicate that theexperimental uncertainty �rst decreases with reducing alti-tude. This is a result of the increasing atmospheric densityand therefore greater aerodynamic forces which generatea variation in the trajectory that can be identi�ed againstthe noise in the measured parameters. The 200 km and225 km altitude runs with non-minimum or maximum dragcon�gurations also show signi�cantly higher uncertainty.This results from very short experimental runs (average of17:8 min) as the spacecraft dynamics at the low altitudeand higher atmospheric density cause the reaction wheelsto saturate quickly. However, at these altitudes the life-time will be very short and it is not expected that dragcoe�cient experiments will principally performed in thisrange.

7. Concluding Remarks

The simulated dynamics of the SOAR spacecraft demon-strate the aerostable nature of the design and the capabil-

16

200 220 240 260 280 300 320 340 360 380 400

Altitude in km

0.2

0.4

0.6

0.8

1

1.2 Deflection 0 degDeflection 15 degDeflection 30 degDeflection 45 degDeflection 60 degDeflection 75 degDeflection 90 deg

Figure 13: Simulated �tted drag coe�cient for varyingsteerable-�n counter-rotation angle and altitude.Error-bars represent the expected 95 % con�denceinterval on the �tted drag coe�cient calculated from a 25sample Monte Carlo simulation.

200 220 240 260 280 300 320 340 360 380 400

Altitude in km

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Deflection 0 degDeflection 15 degDeflection 30 degDeflection 45 degDeflection 60 degDeflection 75 degDeflection 90 deg

Figure 14: Expected standard deviation of simulated�tted drag coe�cient for varying steerable-�ncounter-rotation angle and altitude. Error-bars representthe 95% con�dence interval on this standard deviationcalculated from 25 sample Monte Carlo simulation.

ity to operate successfully with the steerable-�ns in bothcounter-rotated and co-rotated modes over a range of or-bital altitudes in VLEO.

The combination of the INMS and steerable �n pay-loads are shown to enable experimental assessment of thedrag coe�cient of di�erent materials exposed to the owat varying incidence and over a range of altitudes as thespacecraft descends due to orbital decay. Methods for therecovery of the lift coe�cient have also been proposed butrequire further mission analysis.

Simulations of the expected experimental performancedemonstrate constraints on both the maximum and min-imum altitudes at which the drag coe�cient for di�erentcon�gurations can be successfully recovered from the mea-sured orbital parameters. At high altitudes longer testruns or larger steerable �ns are be required to improve theexperimental uncertainty due to the expected noise asso-

ciated with the GPS position and velocity measurements.At lower altitudes saturation of the reaction wheels cansigni�cantly limit the experimental period.

Implementation of more complex attitude control meth-ods, for example using adaptive or model-predicted meth-ods, may be able to extend the capabilities of the reac-tion wheels and therefore the experimental uncertainty atlower altitudes. However, uncertainty and variability inthe oncoming ow direction will remain a challenge. Ac-tive tracking of the ow direction by the steerable �nscould also be utilised to reduce the variation in cross-sectional area and therefore also improve the experimentalperformance.

Acknowledgements

The DISCOVERER project has received funding fromthe European Union’s Horizon 2020 research and innova-tion programme under grant agreement No 737183.

References

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