Drag Effector

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Description

This module computes the forces and torques on a Spacecraft object based on its interaction with an atmospheric model, such as the Atmosphere Exponential Planet Model model. The computed forces/torques are then applied as external effectors to the spacecraft object. These values may be computed in one of the following modes:

• Fixed: Drag force computed anti-parallel to the spacecraft velocity vector. Optional torques due to the user-specified center of pressure. The default center of pressure is at the system center of mass (i.e. no torques).
• Lookup Table: Forces and torques are evaluated using a simple nearest neighbor lookup table that searches for the velocity pointing vector entry most closely aligned with the simulation.

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Example Use Cases

• Aerodynamic Perturbation Modelling: Aerodynamic perturbations contribute to satellite drift in LEO after J2 gravity perturbations and the largest non-conservative contribution. Add this model to consider these effects. Note: typically, the largest source of errors when modelling aerodynamic perturbations is around assumptions in drag coefficient and atmospheric density predictions.
• End-of-Life Assessment Study aerodynamic de-orbit options for end-of-life management. Note: This aerodynamic model is only valid where the free-molecular flow assumption is valid (i.e. the mean free path between particle collisions is much larger than the spacecraft dimensions). Below 300 km where this assumption starts to break down, consider using an appropriate method (e.g. DSMC) to generate lookup tables.

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Module Implementation

Fixed

In this mode, the module computes the aerodynamic drag and torque on a body in the body frame $\mathcal{B}$. Given the velocity of the body in the inertial frame ${}^{\mathcal{N}}{\mathbf{v}}_{BN}$, the force on the body in the inertial frame can be written as,

$${}^{\mathcal{N}}{\mathbf{F}}_{BN}=-0.5C_D\rho A|v_{BN}{|}^2{\hat{\mathbf{v}}}_{BN}$$

Where $C_D$ is the drag coefficient, $A$ is the projected area and $\rho$ is the local atmospheric density. The body frame $\mathcal{B}$ drag force is then simply,

$${}^{\mathcal{B}}{\mathbf{F}}_{BN}=[BN{]}^{\mathcal{N}}{\mathbf{F}}_{BN}$$

The body frame torque ${}^{\mathcal{B}}{\tau }_{BN}$ is then simply,

$${}^{\mathcal{B}}{\tau }_{BN}=({\mathbf{r}}_{CtB}-{\mathbf{r}}_{CoP}){\times }^{\mathcal{B}}{\mathbf{F}}_{BN}$$

Where ${\mathbf{r}}_{CoP}$ is a user-defined center of pressure defined relative to $\mathcal{B}$ and ${\mathbf{r}}_{CtB}$ is the position of the spacecraft total center of mass relative to $\mathcal{B}$.

$${}^{\mathcal{B}}{\mathbf{v}}_{BN}=[BN{]}^{\mathcal{N}}{\mathbf{v}}_{BN}$$

Lookup Table

In this mode, the module accepts a look-up table in .csv format where entries are defined as follows:

${}^{\mathcal{B}}{\mathbf{v}}_{BN}$	${}^{\mathcal{B}}{\mathbf{F}}_{BN}$	${}^{\mathcal{B}}{\mathbf{r}}_{CoP}$
Body velocity in the body frame	Body force in the body frame	Centre of Pressure in the body frame

The mode will then perform a nearest neighbors lookup where the entry that minimizes the error between the actual velocity vector is selected i.e.

$$\mathrm{index}=\min {(}^{\mathcal{B}}{\mathbf{v}}_{BN}\cdot {}^{\mathcal{B}}{\mathbf{v}}_{\mathrm{lookup},BN}[\mathrm{index}])$$

The mode follows the same method in the Fixed mode, without the frame transformation step as results are already pre-computed in the body frame.

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Assumptions/Limitations

• Fixed: Contributions for aerodynamic lift and sideslip are not computed. By convention, these are assumed to be negligible but this is only sometimes true depending on spacecraft geometry and area-to-mass ratio.
• Lookup: The lookup method in this mode becomes computationally intensive for tables with a large number of entries. Consider optimization strategies if needed e.g. gradient search and linear interpolation. As with the Fixed method, lift and sideslip contributions are not accounted for.
• The validity of this approach is contingent on the appropriate modelling of $C_D$ or look-up table elements. It is not designed for use for re-entry modelling and landing envelope analysis.
• The density of the atmosphere is evaluated at the location of the spacecraft in inertial coordinates and is computed on the atmosphere models, and not on the drag effector.
• Area: For a fixed model, the projected area is assumed to be static and unchanging. The area is a constant parameter and not affected by the position and rotation of the spacecraft.
• For the default atmosphere to be connected with the drag information, an Atmosphere Exponential Planet Model or Atmosphere NRLMSIS Planet Model model must be enabled.