Optical Solar Sail Degradation Modeling

Bernd Dachwald1, Giovanni Mengali2, Alessandro A. Quarta2,Malcolm Macdonald3, Colin R. McInnes4

1German Aerospace Center (DLR), Oberpfaffenhofen, Germany2University of Pisa, Italy3SciSys Ltd., Bristol, UK

4University of Strathclyde, Glasgow, Scotland, UK

1st International Symposium on Solar Sailing27–29 June 2007, Herrsching, Germany

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 1 / 27

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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 2 / 27

Outline

Our Approach

We established in November 2004 a ”Solar Sail Degradation ModelWorking Group”1 (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

1the authors and Volodymyr Baturkin, Victoria L. Coverstone, Benjamin Diedrich,Gregory P. Garbe, Marianne Gorlich, Manfred Leipold, Franz Lura, Leonel Rios-Reyes,Daniel J. Scheeres, Wolfgang Seboldt, Bong WieDachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 3 / 27

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:

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. Takes the sail shape and local opticalvariations into account

Refined Model by Mengali, Quarta, Circi, and Dachwald

Optical properties depend also on light incidence angle, surface roughness, and temperature

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 4 / 27

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:

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. Takes the sail shape and local opticalvariations into account

Refined Model by Mengali, Quarta, Circi, and Dachwald

Optical properties depend also on light incidence angle, surface roughness, and temperature

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 4 / 27

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:

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. Takes the sail shape and local opticalvariations into account

Refined Model by Mengali, Quarta, Circi, and Dachwald

Optical properties depend also on light incidence angle, surface roughness, and temperature

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 4 / 27

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:

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. Takes the sail shape and local opticalvariations into account

Refined Model by Mengali, Quarta, Circi, and Dachwald

Optical properties depend also on light incidence angle, surface roughness, and temperature

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 4 / 27

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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 5 / 27

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. Takes the sail shape and local opticalvariations into account

Refined Model by Mengali, Quarta, Circi, and Dachwald

Optical properties depend also on light incidence angle, surface roughness, and temperature

Those models do not include optical solar sail degradation (OSSD)Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 6 / 27

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

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

◮ 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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 7 / 27

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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 8 / 27

Degradation Model Parametric Degradation Model

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 withinthe 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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 9 / 27

Degradation Model Parametric Degradation Model

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 withinthe 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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 9 / 27

Degradation Model Parametric Degradation Model

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 withinthe 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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 9 / 27

Degradation Model Parametric Degradation Model

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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 10 / 27

Degradation Model Parametric Degradation Model

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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 10 / 27

Degradation Model Parametric Degradation Model

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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 11 / 27

Degradation Model Parametric Degradation Model

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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 11 / 27

Degradation Model Parametric Degradation Model

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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 11 / 27

Degradation Model Parametric Degradation Model

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∞ =

s0

1 + dεf∞ = (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}

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 12 / 27

Degradation Model Parametric Degradation Model

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∞ =

s0

1 + dεf∞ = (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}

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 12 / 27

Degradation Model Parametric Degradation Model

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∞ =

s0

1 + dεf∞ = (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}

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 12 / 27

Degradation Model Parametric Degradation Model

OSSD Effectson the optical coefficients and the SRP force bubble

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

0.08

0.08

0.1

0.1

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

“degradation” of optical coefficients

0.0=Σ

5.0=Σ0.1=Σ0.5=Σ

re

te

“degradation” of SRP force bubble

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 13 / 27

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:

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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 14 / 27

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 0.5

500

1000

1500

2000

2500

3000

ac [mm/s

2]

tf [days]

d=0.05

no degradation

model amodel b

model 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 0.5

500

1000

1500

2000

2500

3000

3500

4000

ac [mm/s

2]

tf [days]

d=0.2

no degradation

model amodel b

model 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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 15 / 27

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

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

Half life SRD: Σ = 0.5 (S0 ·yr)

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 16 / 27

Degradation Effects on Trajectory and Attitude Control Mercury Rendezvous

Mercury RendezvousLaunch window for different d

Launch date (MJD)

Tri

ptim

e[d

ays]

57000 57050 57100 57150

350

400

450

Degradation limit:0%

5%

10%

20%

Launch window for Mercury rendezvous

Solar sail with ac=1.0mm/s

2

Half life SRD = 0.5 (S0*yr)

Launch date (MJD)

Tri

ptim

ein

cre

ase

[%]

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 rendezvous

Solar sail with ac=1.0mm/s

2

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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 17 / 27

Degradation Effects on Trajectory and Attitude Control Mercury Rendezvous

Mercury RendezvousOptimal α-variation for different d

Time (MJD)

Pitch

an

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/s

2)

Launch date = MJD 57000.0

Half life SRD = 0.5 (S0*yr)

Launch at MJD 57000.0

Time (MJD)P

itch

an

gle

[rad

]57100 57200 57300 57400

0.3

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

Half life SRD = 0.5 (S0*yr)

Degradation limit:

0%

5%

10%

20%

Mercury rendezvous (solar sail with ac=1.0mm/s

2)

Launch date = MJD 57030.0

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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 18 / 27

Degradation Effects on Trajectory and Attitude Control Fast Neptune Flyby

Fast Neptune Flyby

Solar sail with ac = 1.0 mm/s2

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

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

Half life SRD: 0 ≤ Σ ≤ 2 (S0 ·yr)

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 19 / 27

Degradation Effects on Trajectory and Attitude Control Fast Neptune Flyby

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

520

510

500

400

300

200

100

Trip time = 5.80 years

rmin

Tlim

Sail Temp. [K]

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

2)

= 0.204 AU

= 513.15 K

= 240°C

without degradation

C3=0km

2/s

2at Earth

Flyby at Neptune orbit within ∆r<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

520

510

500

400

300

200

100

Trip time = 7.87 years

rmin

Tlim

Sail Temp. [K]

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

2)

= 0.294 AU

= 513.15 K

= 240°C

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

C3=0km

2/s

2at Earth

Flyby at Neptune orbit within ∆r<1.0E6km

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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 20 / 27

Degradation Effects on Trajectory and Attitude Control Fast Neptune Flyby

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

Sail degradation limit [%]

__

_T

rip

tim

e[y

rs]

__

Tri

ptim

ein

cre

ase

[%]

0 5 10 15 200

1

2

3

4

5

6

7

8

0

10

20

30

40Fast Earth-Neptune transfer with solar sail (a

c=1.0mm/s

2)

Half life SRD = 0.5 (S0*yr)

C3=0km

2/s

2at Earth

Flyby at Neptune orbit within ∆r<1.0E6km

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

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

__

_T

rip

tim

e[y

rs]

__

Tri

ptim

ein

cre

ase

[%]

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 (a

c=1.0mm/s

2)

Degradation limit = 10%

C3=0km

2/s

2at Earth

Flyby at Neptune orbit within ∆r<1.0E6km

faster degradationwithoutdegradation

Different half life SRDs Σ (d = 0.1)

Comparable results have been found by M. Macdonald for a mission to theheliopause.

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 21 / 27

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 sail

SRP acceleration allows to hover along artificial equilibrium surfaces(manifold of artificial Lagrange-points)

Solutions calculated by C. McInnes

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 22 / 27

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

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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 23 / 27

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

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

ρ = 1 ρ = 0.8

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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 24 / 27

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

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

ρ = 1 ρ = 0.7

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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 25 / 27

Summary and Conclusions

Summary and Outlook

All our results show that optical solar sail degradation has aconsiderable 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

Having demonstrated the potential effects of optical solar saildegradation on future missions, more research on the real degradationbehavior has to be done

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

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 26 / 27

Summary and Conclusions

Optical Solar Sail Degradation Modeling

Bernd Dachwald1, Giovanni Mengali2, Alessandro A. Quarta2,Malcolm Macdonald3, Colin R. McInnes4

1German Aerospace Center (DLR), Oberpfaffenhofen, Germany2University of Pisa, Italy3SciSys Ltd., Bristol, UK

4University of Strathclyde, Glasgow, Scotland, UK

1st International Symposium on Solar Sailing27–29 June 2007, Herrsching, Germany

Dachwald et al. (27–29 June 2007) Degradation Modeling ISSS 2007, Herrsching 27 / 27