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Aerodynamic properties, such as the drag and lift coefficients (CD & CL), are key parameters for Low Earth Orbiting (LEO) spacecraft when determining lifetime propellant consumption, predicting deorbit maneuvers, and determining aerodynamic disturbance torque. The drag and lift coefficients for complex shapes is difficult to compute analytically, so a method was developed to determine values these coefficients using a finite plate element method. By superimposing the effect of individual elements, the drag and lift coefficients for a complex object can be determined. Characteristics of the flat plate element are modeled using either experimental data or theoretical models based on hypersonic gassurface interactions. It is the goal of this chapter to show examples of how the satellite drag coefficient can be determined using a finite plate element model. This information can then be used to help determine spacecraft trajectories and aerodynamic disturbance torques as a function of the spacecraft attitude. The internal workings of the modeling tools are not addressed here but instead example results for simple satellite shapes are presented 1. A separate chapter will address results for the lift coefficient and aerodynamic force vector in the future. This chapter describes a method for determining the drag coefficient of spacecraft in orbits significantly affected by aerodynamic forces. A spacecraft configuration and mission orbit is required for this method to be useful. An effective drag coefficient is determined that is useful for both attitude control disturbance torque and orbital mechanics perturbation force modeling. By using finite plate elements, used to approximate the shape of spacecraft in three dimensions, complex shapes can be readily modeled for high-accuracy computations. The net force created on the shape at any attitude can be readily computed along with the disturbance torque if the mass properties of the shape are also known. This model is validated using experimental data for hypersonic molecular beams and Direct Simulation Monte Carlo (DSMC) methods. Examples of spacecraft drag coefficient mapping in three dimensions are included for both simple shapes and a hypothesized spacecraft. It is the goal of this chapter to show examples of how the satellite drag coefficient can be determined using a finite plate element model and to demonstrate some results using simple shapes.

Aerodynamic Disturbance Force and Torque Estimation for Spacecraft and Simple Shapes Using Finite Plate Elements – Part I: Drag Coefficient