atmospheric drag - upmocw.upm.es/ingenieria-aeroespacial/modeling-the-space-environment/... ·...

Atmospheric Drag

Modeling the Space Environment

Manuel Ruiz Delgado

European Masters in Aeronautics and SpaceE.T.S.I. Aeronauticos

Universidad Politecnica de Madrid

April 2008

Atmospheric Drag – p. 1/29

Atmospheric Drag

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Atmospheric Drag

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Effects of Air Drag: MIR Station Reentry March 22, 2001Watch MIR deorbit video on Youtube (simulation by AGI)


Aerodynamic Drag

Space AerodynamicsPerturbations of Keplerian motionFree molecular flowBallistic coefficientDrag computation

High atmosphereStructure of the atmosphereSun influence:F10.7

Geomagnetic activity influence:Kp

Atmospheric ModelsStatic: Exponential, Harris-Priester, US StandardDynamic: Jacchia, MSISE, COSMOS


Perturbations of Keplerian Motion

1e−008

1e−006

0.0001

0.01

1

100

10000

1e+006

0 100 200 300 400 500 600 700 800 900

Acc

eler

atio

n (m

/s2 )

Height (km)

Accelerations of the Satellite (BC=50)

Shuttle

ISS

KeplerJ2

C22Sun

MoonDrag (low)

Drag (high)Prad


Perturbations of Keplerian Motion

1e−008

1e−006

0.0001

0.01

1

100

10000

1e+006

0 5000 10000 15000 20000 25000 30000 35000 40000

Acc

eler

atio

n (m

/s2 )

Height (km)

Accelerations of the Satellite (BC=50)

GEOGPS

KeplerJ2

C22Sun

MoonDrag (low)

Drag (high)Prad


Space Aerodynamics

Free molecular flow: Knudsen No. ≫ 1

Molecules interact one by one with the body: incident flow notdisturbedby the body.

Space Aerodynamics



Kn =L

d=

Ma

Re

L : Mean free path of the moleculesd : Characteristic longitude of satellite

Space Aerodynamics



Kn =L

d=

Ma

Re

L : Mean free path of the moleculesd : Characteristic longitude of satellite

Kn ≫ 1 Free molecular flow Space environmentKn ∼ 1 Transition (Complex: reentry)Kn ≪ 1 Continuum flow Classical aerodynamics

ECSS-E-10-04A definesKn > 3 as free molecular regime

Free molecular flow over 150 km (small satellites) or 250 km(shuttle, ISS)


Impact Types

θ θp1 p2

n

Elastic impact: p2 = p1 + 2p1 cos θn

Drag coefficient: CD = 4

p1p2

n

Diffuse refflection: p2 = p1/2

Drag coefficient: CD = 2 − 4

Impact Types

θ θp1 p2

n

Elastic impact: p2 = p1 + 2p1 cos θn


p1p2

n

Diffuse refflection: p2 = p1/2

Drag coefficient: CD = 2 − 4

p1

Absorption (diffuse emission later): p2 = 0


p1

Abrasion: p2 =?Atmospheric Drag – p. 8/29

Atmospheric Drag

xy

z dA⊥

v

θ

v∆t

Force over the surfacedA⊥, incidence angleθ:

∆m = ρvdA⊥∆t ⇒ dF =∆p

∆t= ρv2[1 + f(θ)]dA⊥

Atmospheric Drag

xy

z dA⊥

v

θ

v∆t



∆t= ρv2[1 + f(θ)]dA⊥

Integrating over the whole surface gives the dragacceleration:

aD =D

m= −

1

2

CDA

mρ |vrel|vrel

Atmospheric Drag

xy

z dA⊥

v

θ

v∆t



∆t= ρv2[1 + f(θ)]dA⊥

Integrating over the whole surface gives the dragacceleration:

aD =D

m= −

1

2

CDA

mρ |vrel|vrel

Lateral drag: CD = CD⊥ + CD‖A‖

A⊥

vrel

vt Orbital speed:vrel ∼ 8 km/s

Thermal speed:vt ∼ 1 km/s (12mv2 = 3

2kT )

Important for light or svelte craft


Atmospheric Drag

aD =D

m= −

1

2

CDA

mρ |vrel| vrel

vrel Speed relative to the atmosphere Rotation, winds

Atmospheric Drag

aD =D

m= −

1

2

CD A

mρ |vrel|vrel


CD Drag Coefficient: difficult to measure

CD ∼ 2 − 2.4 (1-4)

Atmospheric Drag

aD =D

m= −

1

2

CD A

mρ |vrel|vrel



CD ∼ 2 − 2.4 (1-4)

A Frontal area depends on attitude

Atmospheric Drag

aD =D

m= −

1

2

CDA

mρ |vrel|vrel



CD ∼ 2 − 2.4 (1-4)


ρ Atmospheric density: ∼ 15% error

Atmospheric Drag

aD =D

m= −

1

2

CDA

mρ |vrel|vrel



CD ∼ 2 − 2.4 (1-4)


ρ Atmospheric density: ∼ 15% error

β =m

CDABallistic coefficient: (β ↑, aD ↓)

Some authors use the opposite form: BC=CDA

m


Computing Drag

4 problems:

Calibrating CD or β : Differential Correction MapleOD

Propagating orbits with drag:atmospheric model

Computing satellite lifetime: averaged equations King-Hele

Atmospheric research

Computing Drag

4 problems:

Calibrating CD or β : Differential Correction MapleOD

Propagating orbits with drag:atmospheric model

Computing satellite lifetime: averaged equations King-Hele

Atmospheric research

Effects on the orbit

Seculars:a ↓, e ↓→ Reentry Spiral Maplanim

Circularization phase Mir ISS

Spiral phase: reenty Mars

Periodic:Ω, ω, i (through atmospheric rotation)


Structure of the Atmosphere

km

100

101

102

103

Sea Level

Tropopause

Stratopause

Mesopause

Thermopause

Troposphere

Stratosphere

Iono

sphe

re

Mesosphere

Thermosphere

Exosphere

Mt Everest

Clouds↑

ISS, Shuttle

Dominant constituent

N2

O

He


Constituents - Solar low

1e−010

1e−005

1

100000

1e+010

1e+015

1e+020

1e+025

1e+030

0 100 200 300 400 500 600 700 800 900

Den

sity

(m

olec

/m3 )

Height (km)

Constituents: Low Solar Activity

N2O

O2HeArHN


Exospheric TemperatureT∞ vs Solar Activity

0

200

400

600

800

1000

1200

1400

1600

1800

0 100 200 300 400 500 600 700 800 900

T (

ºK)

Height (km)

HighMeanLow


Density vs Solar Activity

1e−016

1e−014

1e−012

1e−010

1e−008

1e−006

0.0001

0.01

1

100

0 100 200 300 400 500 600 700 800 900

Den

sity

(kg

/m3 )

Height (km)

HighMeanLow


Location-Related Changes

In Static Models,properties change only withlocation:



*** Height: Hydrostatic equilibrium⇒ ρ = ρ0eh0−h

H hell




H hell

** Latitude:change ofheight through flattening φg

Height over the Ellipsoidchanges with longitude:∆hell = 0 − 21 km ⇔ ∆ρ

S

S

h

h'' S

h'

φg

E

ell

ell

ell

hcir




H hell

** Latitude:change ofheight through flattening φg

Height over the Ellipsoidchanges with longitude:∆hell = 0 − 21 km ⇔ ∆ρ

S

S

h

h'' S

h'

φg

E

ell

ell

ell

hcir

* Longitude: λg

Temporal change (day/night) Subsolar hump

Small space variation (seas, mountains→ atmosphere), mainlyat low heights.


Causes of Time-Related Changes

In Time-varying Models,properties change withlocationandtime:

Solaractivity

Internalgeomagnetic

field

Sunspots

UV/EUVradiation

Solarwind

Geomagneticactivity Index

Kp / Ap

IndexF10.7

Densityρ(t)


Time Changes Due to the Sun

Sunspot 11 year cycle: ∼ 85%Sunspot Number∼ EUV (10-120 nm)⇒ T∞ ⇒ ρ

EUV not measurable: PROXYF10,7 ,(

F10.7

)

81

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Time Changes: Sun and Geomagnetic Field

Diurnal variations: ∼ 15%

Solar UV radiation heats up the atmosphere:ρ ↑

Max: subsolar hump, delayed 2-2:30 pm. Antipod MinDensity ρ depends on:

Apparent local solar time LHA⊙ of satellite jach/hed

Solar declination δ⊙

Geodetic latitude φg of satellite

Time Changes: Sun and Geomagnetic Field

Diurnal variations: ∼ 15%

Solar UV radiation heats up the atmosphere:ρ ↑

Max: subsolar hump, delayed 2-2:30 pm. Antipod MinDensity ρ depends on:

Apparent local solar time LHA⊙ of satellite jach/hed

Solar declination δ⊙

Geodetic latitude φg of satellite

Magnetic storms:

Earth field’s fluctuations: small effectSolar storms: short but large effect: Up to30%

Influence ρ through the geomagnetic indicesKp or Ap


Other Changes

Solar rotation period of 27 days: Variable 0 − 10%Visible sunspots change

EUV radiation changes

Affects ρ through F10.7 and(

F10.7

)

81(81 day average)

Other Changes

Solar rotation period of 27 days: Variable 0 − 10%Visible sunspots change

EUV radiation changes

Affects ρ through F10.7 and(

F10.7

)

81(81 day average)

Semi-annual variation:Sun distance changes. Small

Cyclical variations:11-year cycles are not regular.ESA’s standardcycle. Small

Atmospheric rotation:difficult to know. Decreases with height.Co-rotation is a good estimate. < 5%

Winds: Not well known. Models not mature. Low orbits. Small

Tides:The atmosphere also suffers tides. Models. Small


Data Sources

Before Space Age: nothing known about the properties of theatmosphere above 150 km

Early satellites: orbit tracking. AssumeCD, computeρ

Careful with NORAD TLE’sn: may include other accelerations

On-board accelerometers: non-gravitational accelerations

On-board mass spectrometers: chemical composition, temperature

Incoherent scatter ground-based radar: electron and ion distribution,which is related to neutral density and composition


Static Models

Properties

Simple, low computation time, reasonable results

Good for theoretical or long-range studies (averaged)

Errors up to 40% (Mean Sun) or 60% (High Sun)

Time-varying models also have errors (∼15%)

Static Models

Properties

Simple, low computation time, reasonable results

Good for theoretical or long-range studies (averaged)

Errors up to 40% (Mean Sun) or 60% (High Sun)

Time-varying models also have errors (∼15%)

Exponential structure:

Spherical symmetry, co-rotating with Earth

Hydrostatic equilibrium + perfect gas:ρ = ρ0eh0−h

H

Reference density and height,ρ0, h0

Scale heightH (changes withh!)


Static Models

US Standard Atmosphere 62, 76 (0-1000 km)

Tabulated

Ideal, stationary atmosphere, at 45oN, moderate solar activity

CIRA 65-90 (0-2500 km)

COSPAR-International Reference Atmosphere.

CIRA-72 and -86 incorporate dynamic models forh > 100km

Harris-Priester (0-1000 km)

Static. Fast. Tabulated forT∞ ⇒ Interpolate

Includessubsolar hump(only LHA⊙ , equinoctial)


Time-Varying Models

Comprehensive: include all the main effects

Inherent errors: unpredictable Sun, proxies, data fit ∼ 15%

Better with past measured data. Reasonable predictions

Numerically intensive

Time-Varying Models

Comprehensive: include all the main effects

Inherent errors: unpredictable Sun, proxies, data fit ∼ 15%

Better with past measured data. Reasonable predictions

Numerically intensive

Jacchia-Roberts (65,71,77, 81) (70-700 km)

The first.Uses satellite data. Late, also ISR

Profile for T∞(F10,7, F 10,7,Kp, φg, λ, δ⊙, LHA⊙, MJD, UT)

Numerical int.diffusion PDE of each constituent:ρ(h) .

Roberts:Integrate several profiles, tabulated polynomial fit

Computationally intensive FORTRAN: MET/71, 77

ValladoandMontenbruckdescribe different modifications of the Jacchia model


Time-Varying Models

MSIS 83, 86, MSISE 90, 2000 (0-2000 km)

Mass Spectrometer & Incoherent Scatter +satellite tracking

Profile T∞(JD, hel, λg, φg, LST, F10.7, F10.7, Api, Api)

Diffusion PDE for each constituent:1ni

dni

dh + 1

Hi+ 1+αi

TdTdh = 0 ,

series integration (faster)

Add partial densities:ρ(h) =∑

ρi

More recent, faster, exact;J-R still better in some cases

ESA recommended standard/ Mean cycle for predictions

FORTRAN code available/ Indices data sources:• ftp://ftp.ngdc.noaa.gov/STP/GEOMAGNETIC_DATA/INDICES/KP_AP/

• http://celestrak.com/SpaceData/ (AverageF107 computed)


ftp://ftp.ngdc.noaa.gov/STP/GEOMAGNETIC_DATA/INDICES/KP_AP/

http://celestrak.com/SpaceData/

Time-Varying Models

COSMOS (160-600 km)

Tracking data fit of the COSMOS satellites

ρ = ρn k1 k2 k3 k4

ρn - Night density profile: exponential

k1 - Solar activity correction,F10.7, 4 values

k2 - Day/Night correction

k3 - Semi-annual correction (small)

k4 - Geomagnetic correction,ap

Very simple, modular, fast, available(cf. Vallado)

Good for orbits similar to the COSMOS satellites

“Density Model for Satellite Orbit Predictions.” GOST 25645-84


Comparison of Time-Varying Models

Model CPU ∆ρ ∆ρmax

Jacchia 71 1,00 - -Jacchia-Roberts 0,22 0,01 0,03Jacchia-Lineberry 0,43 0,13 0,35Jacchia-Gill 0.11 0,02 0,08Jacchia 77 10,69 0,13 0,35Jacchia-Lafontaine 0,86 0,13 0,36MSIS 77 0,06 0,18 0,53MSIS 86 0,32 0,21 1,45TD88 0,01 0.91 7,49DTM 0,03 0,40 1,22

Data from Montenbruck, p. 100


Conclusions

Atmospheric Drag is significant between 200-700 km

Uncertainties inCD, ρ, A

Static models have large erros

Time-varying models’ typical error is about15%Because of the model: indirect proxyBecause of the Sun’s uncertaintyBecause of the fast solar storms

Density is the heaviest computation load of orbit propagation

Use the simplest model within the required precision

New models coming, error down to5% : Solar-2000, HASDM

Space sensors allow direct measuring of EUV, without proxies


COWELL with drag acceleration

Begin y = f(y, t)

Input data KB/File

Initializations Load Indices Common block

ITRF / H, Lat-Long Density

ODE Integrator Call Int step Call Derivs Drag Accel

Save Data FILE Other Accel

End

rGCRF Hell, φg , λ


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