NADIR workshop - October 25-26, 2011 page 1 / 15

Drag coefficients

Sean BruinsmaCNES

Marcin PilinskiCU Boulder

NADIR workshop - October 25-26, 2011 page 2 / 15

The drag coefficient, CD, quantifies the atmospheric drag of an object. It depends on surface material, speed, temperature, atmospheric temperature and mean mass.

The drag acceleration of a spacecraft is computed as follows:

i.e., the drag coefficient scales density inferred from perturbation analysis or accelerometer data directly.

But CD is not modelled according to standards…

The problem

adrag 12CDAm

v 2

2adragmCDAv

2

NADIR workshop - October 25-26, 2011 page 3 / 15

GOCE: drag

Simplest macro-model:Frontal area A = 0.70 m2

Mass = 1038 kgOptical properties: ‘GRACE’Drag coefficient CD = 2.65(Accommodated diffuse=2.01Specular: 0.64)

Using these values resultedin the densities to the right

NADIR workshop - October 25-26, 2011 page 4 / 15

GOCE: dragHowever, more realistic values appear to be:

- A = 1.10 m2

- CD = 3.65

- Densities are 32% smaller when using the larger frontal area - Densities are 37% smaller when using the larger CD

- Densities are 69% smaller when using larger frontal area and CD

Difference with JB2008 increases!

NADIR workshop - October 25-26, 2011 page 5 / 15

GOCE: satellite model

NADIR workshop - October 25-26, 2011 page 6 / 15

GOCE: drag coefficient

NB: ESOC uses CD=3.7, and this gave good station acquisition results

Computed speed ratio:9.0 – 10.3

CD=3.5-3.6

NADIR workshop - October 25-26, 2011 page 7 / 15

Satellite: StellaLaunched: 26 September 1993Mean altitude: 800 - 835 kmEccentricity: 0.02Inclination: 98.6°Diameter: 24 cmMass: 48 kg

Drag coefficient: high altitude

We selected an easy object for the study: a sphere

NADIR workshop - October 25-26, 2011 page 8 / 15

Previous WorkHarrison and Swinerd 1995: estimated CD based on multi-satellite analysis

quasi-specular modelCD=2.52

Pardini et al. 2006: Estimated basedon literature review, some adsorption considerations, and Cook’s model

diffuse modelCD=2.2 - 2.8

[Pardini et al. 2006]

Drag coefficient: high altitude

NADIR workshop - October 25-26, 2011 page 9 / 15

Diffuse Reflection With Incomplete Accommodation

Drag coefficient: high altitude

NADIR workshop - October 25-26, 2011 page 10 / 15

Quasi-Specular Reflection and Goodman’s Model of Accommodation

cosine reflection

Adapted from Gregory and Peters

1987

ν=2.215

Drag coefficient: high altitude

NADIR workshop - October 25-26, 2011 page 11 / 15

Semi-Empirical Satellite Accommodation Model (SESAM)

[Pilinski, 2011]

Drag coefficient: high altitude

NADIR workshop - October 25-26, 2011 page 12 / 15

Model bias estimated by Bowman and Moe (2005)

Drag coefficient: high altitude

NADIR workshop - October 25-26, 2011 page 13 / 15

Harrison and Swinerd, 1995

Drag coefficient: high altitude

NADIR workshop - October 25-26, 2011 page 14 / 15

Pardini et al., 2006

Drag coefficient: high altitude

NADIR workshop - October 25-26, 2011 page 15 / 15

Conclusions

Due to the large uncertainty in model inputs (i.e. accommodation coefficient), lack of surface reflection data, and the significant differences in model results (±15%), one could state that the problem of physical drag coefficients at 800 km remains largely unsolved

Fitted ballistic coefficients corrected for model bias result in a CD between 2.3 to 2.7

SESAM predicts a CD between 2.8 and 3.0

Accommodation values of 0.9 or higher will probably result in incorrect CD at altitudes around 800 km. Therefore a value of 2.2 is likely to be too low.

Drag coefficient: high altitude