potential solar sail degradation effects on trajectory and ... · e r and the sail normal direction...

Potential Solar Sail Degradation Effects on Trajectoryand Attitude Control

Bernd Dachwald1 and the Solar Sail Degradation Model Working Group2

1German Aerospace Center (DLR), Institute of Space SimulationLinder Hoehe, 51170 Cologne, Germany, [email protected]

2Malcolm Macdonald, Univ. of Glasgow, Scotland; Giovanni Mengali and Alessandro A.Quarta, Univ. of Pisa, Italy; Colin R. McInnes, Univ. of Strathclyde, Glasgow, Scotland;

Leonel Rios-Reyes and Daniel J. Scheeres, Univ. of Michigan, Ann Arbor, USA; MarianneGorlich and Franz Lura, DLR, Berlin, Germany; Volodymyr Baturkin, Natl. Tech. Univ. ofUkraine, Kiev, Ukraine; Victoria L. Coverstone, Univ. of Illinois, Urbana-Champaign, USA;

Benjamin Diedrich, NOAA, Silver Spring, USA; Gregory P. Garbe, NASA MSFC,Huntsville, USA; Manfred Leipold, Kayser-Threde GmbH, Munich, Germany; Wolfgang

Seboldt, DLR, Cologne, Germany; Bong Wie, Arizona State Univ., Tempe, USA

AAS/AIAA Astrodynamics Specialists Conference7–11 August 2005, Lake Tahoe, CA

Dachwald & SSDMWG (DLR & . . . ) Solar Sail Degradation AAS/AIAA ASC 2005 1 / 42

Outline

The Problem

The optical properties of the thin metalized polymer films that are projectedfor solar sails are assumed to be affected by the erosive effects of the spaceenvironment

Optical solar sail degradation (OSSD) in the real space environment is to aconsiderable degree indefinite (initial ground test results are controversialand relevant in-space tests have not been made so far)

The standard optical solar sail models that are currently used for trajectoryand attitude control design do not take optical degradation into account→ its potential effects on trajectory and attitude control have not beeninvestigated so far

Optical degradation is important for high-fidelity solar sail mission analysis,because it decreases both the magnitude of the solar radiation pressure forceacting on the sail and also the sail control authority

Solar sail mission designers necessitate an OSSD model to estimate thepotential effects of OSSD on their missions


Outline

Our Approach

We established in November 2004 a ”Solar Sail Degradation ModelWorking Group” (SSDMWG) with the aim to make the next steptowards a realistic high-fidelity optical solar sail model

We propose a simple parametric OSSD model that describes thevariation of the sail film’s optical coefficients with time, depending onthe sail film’s environmental history, i.e., the radiation dose

The primary intention of our model is not to describe the exactbehavior of specific film-coating combinations in the real spaceenvironment, but to provide a more general parametric framework fordescribing the general optical degradation behavior of solar sails


Outline

1 Solar Sail Force ModelsIdeal ReflectionNon-Perfect ReflectionSimplified Non-Perfect Reflection

2 Degradation ModelData Available From Ground TestingParametric Degradation Model

3 Degradation Effects on Trajectory and Attitude ControlEquations of Motion and Optimal Control LawMars RendezvousMercury RendezvousFast Neptune FlybyFast Transfer to the HeliopauseArtificial Lagrange-Point Missions

4 Summary and Conclusions

5 Outlook


Solar Sail Force Models

OverviewDifferent levels of simplification for the optical characteristics of a solar sail resultin different models for the magnitude and direction of the SRP force acting onthe sail:

Model IR (Ideal Reflection)

Most simple model

Model SNPR (Simplified Non-Perfect Reflection)

Optical properties of the solar sail are described by a single coefficient

Model NPR (Non-Perfect Reflection)

Optical properties of the solar sail are described by 3 coefficients

Generalized Model by Rios-Reyes and Scheeres

Optical properties are described by three tensors of rank 1, 2, and 3 (19 numbersin total, due to symmetry). Takes the sail shape and local optical variations intoaccount


Solar Sail Force Models Ideal Reflection

SRP Forceon an Ideal Solar Sail

The solar radiation pressure (SRP) at a distance r from thesun is

P =S0

c

( r0r

)2

= 4.563µN

m2·( r0

r

)2

FSRP = 2PA cos α cos α n

Nomenclature

S0: solar constant

(1368 W/m2)

c: speed of light invacuum

r0: 1 astronomical unit(1 AU)

α: sail pitch angle

n: sail normal vector

t: sail tangential vector

FSRP: SRP force

A: sail area


Solar Sail Force Models Ideal Reflection

SRP Forceon an Ideal Solar Sail

The solar radiation pressure (SRP) at a distance r from thesun is

P =S0

c

( r0r

)2

= 4.563µN

m2·( r0

r

)2

incoming radiation

reflected radiation

sail

sun-line

α α

α

α

αSRPFn

t

FSRP = 2PA cos α cos α n

Nomenclature

S0: solar constant

(1368 W/m2)

c: speed of light invacuum

r0: 1 astronomical unit(1 AU)




FSRP: SRP force

A: sail area


Solar Sail Force Models Non-Perfect Reflection

The Non-Perfectly Reflecting Solar Sail

The non-perfectly reflecting solar sail modelparameterizes the optical behavior of the sail film by theoptical coefficient set

P = {ρ, s, εf , εb,Bf ,Bb}

The optical coefficients for a solar sail with a highlyreflective aluminum-coated front side and with a highlyemissive chromium-coated back side are:

PAl|Cr = {ρ = 0.88, s = 0.94, εf = 0.05,

εb = 0.55,Bf = 0.79,Bb = 0.55}

Nomenclature

ρ: reflection coefficient

s: specular reflectionfactor

εf and εb: emissioncoefficients of the frontand back side,respectively

Bf and Bb:non-Lambertiancoefficients of the frontand back side,respectively



The Non-Perfectly Reflecting Solar SailSRP Force in a sail-fixed coordinate frame S = {n, t}

incoming radiation

reflected radiation

sail

sun-line

αα

α

SRPF

n

t

⊥F

||F θφm

FSRP = 2PA cos α [(a1 cos α + a2)n− a3 sinα t]

with the derived optical coefficients

a1 ,1

2(1 + sρ) a2 ,

1

2

"Bf (1 − s)ρ + (1 − ρ)

εfBf − εbBb

εf + εb

#

a3 ,1

2(1 − sρ)

Nomenclature



m: thrust unit vector


FSRP: SRP force

F⊥: SRP forcecomponent along n

F||: SRP force

component along t

θ: thrust cone angle

φ: centerline angle

P: solar radiationpressure (SRP)

A: sail area



The Non-Perfectly Reflecting Solar SailSRP Force on along the radial and sail normal direction

FSRP can also be decomposed along the radial directioner and the sail normal direction n:

FSRP = 2PA cos α [b1er + (b2 cos α + b3)n]

with the derived optical coefficients

b1 ,1

2(1 − sρ)

b2 , sρ

b3 ,1

2

"Bf (1 − s)ρ + (1 − ρ)

εfBf − εbBb

εf + εb

#

Nomenclature

FSRP: SRP force


A: sail area


er : radial unit vector



Solar Sail Force Models Simplified Non-Perfect Reflection

The Simplified ModelSRP Force in a sail-fixed coordinate frame S = {n, t}

Recall that

FSRP = 2PA cos α [(a1 cos α + a2)n− a3 sin α t]

with

a1 ,1

2(1 + sρ)

a2 ,1

2

"Bf (1 − s)ρ + (1 − ρ)

εfBf − εbBb

εf + εb

#

a3 ,1

2(1 − sρ)

Assumptions: s = 1, εfBf = εbBb

FSRP = PA cos α [(1 + ρ) cos α n− (1− ρ) sinα t]

Typically, however, the reflection coefficient ρ is denoted as ηwithin this model

Nomenclature

FSRP: SRP force


A: sail area




ρ: reflection coefficient

s: specular reflectionfactor

εf and εb: emissioncoefficients of the frontand back side,respectively

Bf and Bb:non-Lambertiancoefficients of the frontand back side,respectively


Degradation Model

Overview (Reprise)

Model IR (Ideal Reflection)

Most simple model

Model SNPR (Simplified Non-Perfect Reflection)

Optical properties of the solar sail are described by a single coefficient

Model NPR (Non-Perfect Reflection)

Optical properties of the solar sail are described by 3 coefficients

Generalized Model by Rios-Reyes and Scheeres

Optical properties are described by three tensors of rank 1, 2, and 3 (19 numbersin total, due to symmetry). Takes the sail shape and local optical variations intoaccount

Those models do not include optical solar sail degradation (OSSD)


Degradation Model Data Available From Ground Testing

Data Available From Ground Testing

Much ground and space testing has been done to measure the opticaldegradation of metalized polymer films as second surface mirrors (metalizedon the back side)

No systematic testing to measure the optical degradation of candidate solarsail films (metalized on the front side) has been reported so far andpreliminary test results are controversial

I Lura et. al. measured considerable OSSD after combined irradiationwith VUV, electrons, and protons

I Edwards et. al. measured no change of the solar absorption andemission coefficients after irradiation with electrons alone

Respective in-space tests have not been made so far

The optical degradation behavior of solar sails in the real space environmentis to a considerable degree indefinite


Degradation Model Parametric Degradation Model

Simplifying Assumptions

For a first OSSD model, we have made the following simplifications:

1 The only source of degradation are the solar photons and particles

2 The solar photon and particle fluxes do not depend on time (averagesun without solar events)

3 The optical coefficients do not depend on the sail temperature

4 The optical coefficients do not depend on the light incidence angle

5 No self-healing effects occur in the sail film



Solar radiation dose (SRD)

Let p be an arbitrary optical coefficient from the set P. With OSSD, p becomestime-dependent, p(t). With the simplifications stated before, p(t) is a function ofthe solar radiation dose Σ (dimension

[J/m2

]) accepted by the solar sail within

the time interval t − t0:

Σ(t) ,∫ t

t0

S cos α dt ′ = S0r20

∫ t

t0

cos α

r2dt ′

SRD per year on a surface perpendicular to the sun at 1 AU

Σ0 = S0 · 1 yr = 1368W/m2 · 1 yr = 15.768 TJ/m2

Dimensionless SRD

Using Σ0 as a reference value, the SRD can be defined in dimensionless form:

Σ(t) =Σ(t)

Σ0

=r20

T

∫ t

t0

cos α

r2dt ′ where T , 1 yr



Dimensionless SRD

Using Σ0 as a reference value, the SRD can be defined in dimensionless form:

Σ(t) =Σ(t)

Σ0

=r20

T

∫ t

t0

cos α

r2dt ′

Σ(t) depends on the solar distance history and the attitude history z[t] = (r , α)[t]of the solar sail, Σ(t) = Σ(z[t])

Differential form for the SRD

The equation for the SRD can also be written in differential form:

Σ =r20

T

cos α

r2with Σ(t0) = 0



Assumption that each p varies exponentially with Σ(t)

Assume that p(t) varies exponentially between p(t0) = p0 and limt→∞

p(t) = p∞

p(t) = p∞ + (p0 − p∞) · e−λΣ(t)

The degradation constant λ is related to the ”half life solar radiation dose” Σ(Σ = Σ ⇒ p = p0+p∞

2 ) via

λ =ln 2

Σ

Note that this model has 12 free parameters additional to the 6 p0, 6 p∞ and 6half life SRDs Σp (too much for a simple parametric OSSD analysis)

Reduction of the number of model parameters

We use a degradation factor d and a single half life SRD for all p, Σp = Σ ∀p ∈ P



Reduction of the number of model parameters

We use a degradation factor d and a single half life SRD for all p, Σp = Σ ∀p ∈ P

EOL optical coefficients

Because the reflectivity of the sail decreases with time, the sail becomes morematt with time, and the emissivity increases with time, we use:

ρ∞ =ρ0

1 + ds∞ =

s01 + d

εf∞ = (1 + d)εf 0

εb∞ = εb0 Bf∞ = Bf 0 Bb∞ = Bb0

Degradation of the optical parameters in dimensionless form

p(t)

p0=

(1 + de−λΣ(t)

)/ (1 + d) for p ∈ {ρ, s}

1 + d(1− e−λΣ(t)

)for p = εf

1 for p ∈ {εb,Bf ,Bb}



OSSD Effectson the optical coefficients and the maximum sail temperature

0.020.02

0.04

0.04

0.060.06

0.080.08

0.1

0.1

0.12

0.12

0.14

0.14

0.16

0.16

0.18

0.18

0.2

0.2

Σ

ρ/ρ

0 , s/

s 0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.8

0.85

0.9

0.95

1

0.020.02

0.040.04

0.060.06

0.080.08

0.10.1

0.12

0.12

0.14

0.14

0.16

0.16

0.18

0.18

0.20.2

Σ

εf /ε

f0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

1

1.05

1.1

1.15

1.2

d

d

ρ/ρ0, s/s0, and εf/εf 0

Σ

Tm

ax(α

=0)

[°C

]

0 1 2 3 4

0

100

200

300

400

r = 0.2 AU

r = 1.0 AU

r = 0.8 AU

r = 0.6 AU

r = 0.4 AU

Frame 001 ⏐ 23 Jun 2005 ⏐

Tmax for different solar distances (d = 0.2)



OSSD Effectson the SRP force bubble and the control angles

0.0=Σ

5.0=Σ0.1=Σ0.5=Σ

re

te

FSRP-bubble

0 10 20 30 40 50 60 70 80 90−10

0

10

20

30

40

50

60

Pitch angle [deg]

Con

e an

gle

[deg

] Σ = 5.0

Σ = 1.0

Σ = 0.5

Σ = 0.0

θ(α)

0 0.5 1 1.5 2 2.5 3 3.5 435.2

35.3

35.4

α* [deg

]

0 0.5 1 1.5 2 2.5 3 3.5 424

26

28

30

32

θ* [deg

]

0 0.5 1 1.5 2 2.5 3 3.5 4−30

−20

−10

0

Σ

∆Ft* [%

]

α∗, θ∗, and ∆F ∗t


Degradation Effects on Trajectory and Attitude Control Equations of Motion and Optimal Control Law

Simulation Model

Considerations for trajectorycontrol

Gravitational forces of all celestialbodies

Solar wind

Finiteness of the solar disk

Reflected light from close celestialbodies

Aberration of solar radiation(Poynting-Robertson effect)

The solar sail bends and wrinkles,depending on the actual solar saildesign

Finite attitude control maneuvers

Simplifications for missionfeasibility analysis and to isolatethe effects of OSSD

The solar sail is a flat plate

The solar sail is moving under thesole influence of solar gravitationand radiation

The sun is a point mass and apoint light source

The solar sail attitude can bechanged instantaneously



Problem Statement

Equations of motion

For a solar sail in heliocentric cartesian reference frame:

r = v

v = − µ

r3r + a

where

a = a(r ,n, b1(t), b2(t), b3(t))

is the SRP acceleration acting on the solar sail

Problem

Minimize the time tf necessary to transfer the sail fromx0 = (r0, v0) to xf = (rf , vf ) by maximizing theperformance index J = −tf

Nomenclature

a: propulsive(+ disturbing) accelerationon the sail

r: sail position

r : radius, |r|

v: sail velocity

µ: gravitational parameterof the sun

b1(t), b2(t), b3(t):functions of the sail’soptical parameters


x: sail state

�0: initial value of �

�f : final value of �



Variational Problem

Using standard COV, the optimal direction of n is found by maximizing theHamiltonian H

H = λλλr · v −µ

r3λλλv · r + λλλv · a + λΣ

r20

r2Ter · n

where λλλr , λλλv are the vectors adjoint to the position, and λΣ is the radiation dosecostate

The result is

n =

sin (αλ − α)

sin αλer +

sin α

sin αλeλλλv

for αλ 6= 0

er for αλ = 0

where

er =r

|r|eλλλv

=λλλv

|λλλv |cos αλ = er · eλλλv



Remarks about the Optimal Solution

The optimal control law requires the thrust vector to lie in the planedefined by the position vector r and the primer vector λλλv . Thisgeneralizes a similar conclusion obtained for model IR by C. Sauer andfor model NPR without degradation by G. Mengali and A. Quarta

The equation giving the optimal cone angle as a function of αλ canbe written analytically and solved numerically

The next slide shows, how the optimal solutions typically vary withthe solar radiation dose



Typical Optimal Solutions

0 15 30 45 60 75 900

30

60

90

120

150

180

α [deg]

αλ [deg]

Σ =0, d =0.2

0 15 30 45 60 75 900

30

60

90

120

150

180

α [deg]

αλ [deg]

Σ =0.5, d =0.2

0 15 30 45 60 75 900

30

60

90

120

150

180

α [deg]

αλ [deg]

Σ =1, d =0.2

0 15 30 45 60 75 900

30

60

90

120

150

180

α [deg]

αλ [deg]

Σ =10, d =0.2


Degradation Effects on Trajectory and Attitude Control Mars Rendezvous

Mars Rendezvous

Solar sail with 0.1 mm/s2 ≤ ac < 6 mm/s2

C3 = 0km2/s2

2D-transfer from circular orbit to circular orbit

Trajectories calculated by G. Mengali and A. Quarta using a classicalindirect method with an hybrid technique (genetic + gradient-basedalgorithm) to solve the associated boundary value problem

Degradation factor: 0 ≤ d ≤ 0.2 (0–20% degradation limit)

Half life SRD: Σ = 0.5 (S0 ·yr)Three models:

B Model (a): Instantaneous degradationB Model (b): Control neglects degradation (”ideal” control law)B Model (c): Control considers degradation


Degradation Effects on Trajectory and Attitude Control Mars Rendezvous

Mars RendezvousTrip times for 5% and 20% degradation limit

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5500

1000

1500

2000

2500

3000

ac [mm/s2]

tf [days]

d=0.05

no degradationmodel amodel bmodel c

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5200

300

400

500

600

700

ac [mm/s2]

tf [days]

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5500

1000

1500

2000

2500

3000

3500

4000

ac [mm/s2]

tf [days]

d=0.2

no degradationmodel amodel bmodel c

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5200

300

400

500

600

700

800

900

1000

ac [mm/s2]

tf [days]

OSSD has considerable effect on trip times

The results for model (b) and (c) are indistinguishable close


Degradation Effects on Trajectory and Attitude Control Mercury Rendezvous

Mercury Rendezvous

Solar sail with ac = 1.0 mm/s2

C3 = 0km2/s2

Trajectories calculated by B. Dachwald with the trajectory optimizerGESOP with SNOPT

Arbitrarily selected launch window MJD 57000 ≤ t0 ≤ MJD 57130(09 Dec 2014 – 18 Apr 2015)

Final accuracy limit was set to ∆rf ,max = 80 000 km (inside Mercury’ssphere of influence at perihelion) and ∆vf ,max = 50m/s


Half life SRD: Σ = 0.5 (S0 ·yr)



Mercury RendezvousLaunch window for different d

Launch date (MJD)

Trip

time

[day

s]

57000 57050 57100 57150

350

400

450

Degradation limit:0%

5%

10%

20%

Launch window for Mercury rendezvousSolar sail with ac=1.0mm/s2

Half life SRD = 0.5 (S0*yr)

Frame 001 ⏐ 05 Jul 2005 ⏐ Mercury Launch Window with OSSD

Launch date (MJD)

Trip

time

incr

ease

[%]

57000 57050 57100 571500

5

10

15

20

25

30

35

Half life SRD=0.5 (S0*yr)

Degradation limit:

5%

10%

20%

Launch window for Mercury rendezvousSolar sail with ac=1.0mm/s2

Frame 001 ⏐ 27 Jun 2005 ⏐ Mercury Launch Window with OSSD

Sensitivity of the trip time with respect to OSSD depends considerably on thelaunch date

Some launch dates considered previously as optimal become very unsuitable whenOSSD is taken into account

For many launch dates OSSD does not seriously affect the mission



Mercury RendezvousOptimal α-variation for different d

Time (MJD)

Pitc

han

gle

[rad

]

57000 57100 57200 573000.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Degradation limit:

0%

5%

10%

20%

Mercury rendezvous (solar sail with ac=1.0mm/s2)Launch date = MJD 57000.0


Frame 001 ⏐ 14 Jul 2005 ⏐

Launch at MJD 57000.0

Time (MJD)P

itch

angl

e[r

ad]

57100 57200 57300 574000.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6


Degradation limit:

0%

5%

10%

20%

Mercury rendezvous (solar sail with ac=1.0mm/s2)Launch date = MJD 57030.0

Frame 001 ⏐ 14 Jul 2005 ⏐

Launch at MJD 57030.0

OSSD can also have remarkable consequences on the optimal control angles

Given an indefinite OSSD behavior at launch, MJD 57000.0 would be a veryrobust launch date


Degradation Effects on Trajectory and Attitude Control Fast Neptune Flyby

Fast Neptune Flyby


C3 = 0km2/s2

Trajectories calculated by B. Dachwald with the trajectory optimizerInTrance

To find the absolute trip time minima, independent of the actualconstellation of Earth and Neptune, no flyby at Neptune itself, butonly a crossing of its orbit within a distance ∆rf ,max < 106 km wasrequired, and the optimizer was allowed to vary the launch datewithin a one year interval

Sail film temperature was limited to 240◦C by limiting the sail pitchangle


Half life SRD: 0 ≤ Σ ≤ 2 (S0 ·yr)



Fast Neptune FlybyTopology of optimal trajectories for different d

x [AU]

y[A

U]

-1

-1

0

0

1

1

2

2

-1 -1

-0.5 -0.5

0 0

0.5 0.5

1 1

1.5 1.5

2 2

520510500400300200100

Trip time = 5.80 years

rmin

Tlim

Sail Temp. [K]

Fast Earth-Neptune transfer with solar sail (ac=1.0mm/s2)

= 0.204 AU

= 513.15 K

= 240°C

without degradation

C3=0km2/s2 at EarthFlyby at Neptune orbit within Δr<1.0E6km

d = 0

x [AU]

y[A

U]

-1

-1

0

0

1

1

2

2

-1.5 -1.5

-1 -1

-0.5 -0.5

0 0

0.5 0.5

1 1

1.5 1.5

520510500400300200100

Trip time = 7.87 years

rmin

Tlim

Sail Temp. [K]

Fast Earth-Neptune transfer with solar sail (ac=1.0mm/s2)

= 0.294 AU

= 513.15 K

= 240°C

20% degradation limit, half life SRD = 0.5 (S0*yr)


d = 0.2

With increasing degradation:

Increasing solar distance during final close solar pass

Increasing solar distance before final close solar pass

Longer trip time



Fast Neptune FlybyTrip time and trip time increase for different d and Σ

Sail degradation limit [%]

___

Trip

time

[yrs

]

__

Trip

time

incr

ease

[%]

0 5 10 15 200

1

2

3

4

5

6

7

8

0

10

20

30

40Fast Earth-Neptune transfer with solar sail (ac=1.0mm/s2)Half life SRD = 0.5 (S0*yr)


Frame 001 ⏐ 27 Jun 2005 ⏐ Flight Time

Different degradation factors d (Σ = 0.5 (S0 ·yr))

1 / Half life SRD [1/(S0*yr)]

___

Trip

time

[yrs

]

__

Trip

time

incr

ease

[%]

0 0.5 1 1.5 20

1

2

3

4

5

6

7

8

0

5

10

15

20

25Fast Earth-Neptune transfer with solar sail (ac=1.0mm/s2)Degradation limit = 10%


faster degradationwithoutdegradation

Frame 001 ⏐ 27 Jun 2005 ⏐ Flight Time

Different half life SRDs Σ (d = 0.1)


Degradation Effects on Trajectory and Attitude Control Fast Transfer to the Heliopause

Fast Transfer to the Heliopause


C3 = 0km2/s2

Trajectories calculated by M. Macdonald with AnD-blending (blendingof locally optimal control laws)

Transfer to the nose of the heliosphere at a latitude of 7.5 deg and alongitude of 254.5 deg at 200 AU from the sun

Sail jettison at 5 AU to eliminate any potential interference with theinterplanetary/interstellar medium

Solar distance limited to 0.25 AU


Half life SRD: Σ = 0.5 (S0 ·yr)



Fast Transfer to the HeliopauseTrajectories for different d (Σ = 0.5 (S0 ·yr))

Inner solar system trajectories Variation of solar distance and inclination


Constant solar distance during final close solar pass

Increasing radius of aphelion passage



Fast Transfer to the HeliopauseTrajectories for different d (Σ = 0.5 (S0 ·yr))

21.5

22.0

22.5

23.0

23.5

24.0

24.5

25.0

25.5

26.0

26.5

0 5 10 15 20 25 30

Degradation limit [%]

Trip

tim

e ––

[yrs

]

2.7

2.8

2.9

3.0

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

Aph

elio

n ra

dius

– –

[AU

]

Trip time to 200 AU and radius of aphelion passage

9.5

9.6

9.7

9.8

9.9

10.0

10.1

10.2

10.3

10.4

10.5

10.6

10.7

10.8

10.9

11.0

0 5 10 15 20 25 30

Degradation limit [%]

Velo

city

at 5

AU

––

[AU

/yr]

2.7

2.8

2.9

3.0

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

4.0

Trip

tim

e to

5 A

U –

– [y

rs]

Trip time and velocity at 5 AU (sail jettison point)


Increasing radius of aphelion passage

Longer trip time


Degradation Effects on Trajectory and Attitude Control Artificial Lagrange-Point Missions

Artificial Lagrange-Point Missions

Sun-Earth restricted circular three-body problem with non-perfectlysolar sailSRP acceleration allows to hover along artificial equilibrium surfaces(manifold of artificial Lagrange-points)Solutions calculated by C. McInnes



Artificial Lagrange-Point MissionsContours of sail loading in the x-z-plane

ρ = 1 ρ = 0.9

[1] 30 g/m2 [2] 15 g/m2 [3] 10 g/m2 [4] 5 g/m2




ρ = 1 ρ = 0.8

[1] 30 g/m2 [2] 15 g/m2 [3] 10 g/m2 [4] 5 g/m2




ρ = 1 ρ = 0.7

[1] 30 g/m2 [2] 15 g/m2 [3] 10 g/m2 [4] 5 g/m2


Summary and Conclusions

Summary and Conclusions

Based on the current standard model for non-perfectly reflecting solarsails, we have developed a parametric model that includes the opticaldegradation of the sail film due to the erosive effects of the spaceenvironment

Using this model, we have investigated the effect of differentpotential degradation behaviors on trajectory and attitude control forvarious exemplary missions

All our results show that, in general, optical solar sail degradation hasa considerable effect on trip times and on the optimal steering profile.For specific launch dates, especially those that are optimal withoutdegradation, this effect can be tremendous


Outlook

Outlook

Having demonstrated the potential effects of optical solar saildegradation on future missions, more research on the real degradationbehavior has to be done because the degradation behavior of solarsails in the real space environment is to a considerable degreeindefinite

To narrow down the ranges of the parameters of our model, furtherlaboratory tests have to be performed

Additionally, before a mission that relies on solar sail propulsion isflown, the candidate solar sail films have to be tested in the relevantspace environment

Some near-term missions currently studied in the US and Europewould be an ideal opportunity for testing and refining our degradationmodel


Outlook

Potential Solar Sail Degradation Effects on Trajectoryand Attitude Control

Bernd Dachwald1 and the Solar Sail Degradation Model Working Group2

1German Aerospace Center (DLR), Institute of Space SimulationLinder Hoehe, 51170 Cologne, Germany, [email protected]

2Malcolm Macdonald, Univ. of Glasgow, Scotland; Giovanni Mengali and Alessandro A.Quarta, Univ. of Pisa, Italy; Colin R. McInnes, Univ. of Strathclyde, Glasgow, Scotland;

Leonel Rios-Reyes and Daniel J. Scheeres, Univ. of Michigan, Ann Arbor, USA; MarianneGorlich and Franz Lura, DLR, Berlin, Germany; Volodymyr Baturkin, Natl. Tech. Univ. ofUkraine, Kiev, Ukraine; Victoria L. Coverstone, Univ. of Illinois, Urbana-Champaign, USA;

Benjamin Diedrich, NOAA, Silver Spring, USA; Gregory P. Garbe, NASA MSFC,Huntsville, USA; Manfred Leipold, Kayser-Threde GmbH, Munich, Germany; Wolfgang

Seboldt, DLR, Cologne, Germany; Bong Wie, Arizona State Univ., Tempe, USA

AAS/AIAA Astrodynamics Specialists Conference7–11 August 2005, Lake Tahoe, CA


potential solar sail degradation effects on trajectory and ... · e r and the sail normal direction...

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