Realistic Solar Sail Thrust

Abstract

Before a solar sail will be used as a primary propulsion system for a space flight mission, many technical areas must be developed further. One of these areas concerns understanding the propulsion performance of a realistic solar sail well enough so that solar sail orbits can be confidently predicted to meet defined mission requirements. This paper identifies major contributors to solar sail thrust uncertainty, and analyzes the most significant ones to provide a better understanding of thrust generation by a “realistic” solar sail. Performance of representative “realistic” sailcraft are compared to similar “ideal” and “non-ideal” sailcraft to illustrate the differences.

Appendix A. The PSS Solar Sail Module

A MATLAB-based software tool, called the Solar Sail Module (SSM), was developed by Princeton Satellite Systems (PSS) for the NASA In-Space Propulsion Technology (ISPT) Solar Sail Program to provide solar sail analysis, design and simulation capabilities. SSM is based upon, and takes advantage of, the capabilities in Princeton Satellite Systems’ existing Spacecraft Control Toolbox (SCT) that has been commercially available since 1995. SCT is composed of the following modules:

• Core: Orbit and attitude dynamics, computer-aided modeling, sensor and actuators

• Attitude Control: Complete attitude control design examples

• Orbit: Precision orbit propagator, mission planning, formation flying

• Estimation: Attitude and orbit estimators

• Propulsion: Propulsion system modeling

• Thermal: Thermal system modeling

• Link: Link and radar analysis

• Spin Axis Attitude Determination: Attitude determination with horizon and sun sensors

• Formation Flying: Control and estimation of satellite formations

The PSS Solar Sail Module is based on functions from several of these modules with the addition of numerous solar sail specific functions and scripts. The SSM is self-contained and only requires basic MATLAB 5.2 or later. Simulink is not used. It has a number of interactive Graphical User Interfaces but the core simulation capability is based on MATLAB scripts. The Solar Sail Module includes all source code (scripts) and no dll or p-code files are used. All functions follow a consistent format, have many comments, and can be easily customized by the user.

Simulations are script-based. MATLAB’s ode113, a variable order, variable step size integrator, is used to propagate the kinematical and dynamical equations. The right-hand-side function called by ode113 is created by the user in a standard format script. This script can be configured to use a selected disturbance model, attitude dynamics model and orbital dynamics model. Several sail-specific attitude dynamics models are available and configurable. The controller is called from the simulation script. Controllers are implemented digitally and are not part of the simulation right-hand-side.

The software includes functions for multi-body dynamic modeling, attitude control systems design, thrust vector control design, orbit analysis, solar sail mission analysis, thermal analysis and power subsystem analysis. Sailcraft models can be created, analyzed and simulated without the need to deal with any other software tools. The software couples attitude and orbit dynamics into the same simulations. The user can choose from several different attitude dynamics models, including specially-developed multibody models for moving mass and gimbaled boom control systems, and from several orbit models including point mass, n-body and non-spherical earth.

Sailcraft models are created using a graphical computer-aided design package that is included in the software. The component information defined in the computer aided design (CAD) package is used to generate mass properties and for all disturbance (force) calculations. Component-level data includes optical and thermal properties for the surfaces; mass, center-of-mass, and inertia; and magnetic dipoles, RF sources, etc. Additional information can also be stored with each component so that the CAD file serves as a database for all model data.

A disturbance modeling package is included which can be used independently or integrated with the solar sail simulations. Disturbances on a sailcraft include:

• Solar pressure force and torque

• Earth radiation force and torque

• Earth albedo force and torque

• Aerodynamic force and torque

• Gravity gradient torque

• Thermal emission force and torque

• Magnetic torque

• Radio frequency emission force and torque

• Outgassing force and torque

This list includes some disturbances only applicable to a sailcraft in a planetary orbit, and does not include disturbances caused by actuators on the spacecraft.

The PSS Solar Sail Module includes a number of scripts associated with developing a sailcraft model for use within the simulations. The user creates a separate script that provides the information input to the Module scripts. Within the user script, the Module script BuildCADModel.m sets up the sailcraft model data structure and collects all of this data into a saveable file. After initializing BuildCADModel, the user uses additional SSM scripts, such as CreateBody, and CreateComponent to define the parts of the sailcraft that will be incorporated into the overall model. These scripts define the properties of each component, including shape, size and mass, as well as important solar sail properties such as optical and thermal coefficients. The Module scripts include many generic shapes, such as “box”, “sphere” and “cylinder” that make inputting components easier. Figure A-1 shows the component model for a triangular sail quadrant. In this example, the quadrant includes a defined amount of billow, and the surface is broken up into a number of “triangles” that can be used as individual sub-components for computing radiation, aerodynamic, and even magnetic forces on each element.

Of equal importance, these “create” scripts define the orientation and placement of each component, with respect to the body as a whole. When brought into the overall sailcraft model, using the “add” command, BuildCADModel uses this information to rotate and displace the component into its proper place. For instance, the quadrant above would need to be rotated such that the side visible in the figure (associated with the reflective side of the sail) would have the axis normal to this surface pointed in the “X” direction, and also rotated and displaced to its proper quadrant position.

At the same time it adds the component, BuildCADModel computes the component mass properties, and updates the overall sailcraft properties (total mass, total inertia, etc.). When completed, the user can save the overall model structure into a separate file that can be called for use in simulations, and can use several Module display and analysis scripts to analyze the final sailcraft model. Figure A-2 shows the 100 × 100 meter square, non-ideal sail with billow model used for many of the simulations conducted in this dissertation.

Once the model is created, it can be used in simulations. Once again, the user creates a stand-alone script that calls and provides information to a number of Module scripts. The most used of these is FSailCombined.m. This script (function) creates the data structure used for each step in the simulation. As inputs, the user specifies the Sun and planet (if applicable) ephmerides to be used and the orbit gravity model, the environment the sail is to operate in (in terms of planetary atmospheric density, radiation, magnetic fields, etc.), the attitude dynamics and guidance for the sailcraft—including initial orbital elements, and the sail disturbances (forces) to be considered during the simulation.

As in BuildCADModel, several existing Solar Sail Module scripts can be used within FSailCombined to incorporate standard quantities easily. The most demanding for the user is specification of the sailcraft dynamics (multiple moving bodies, such as moving masses or tip vanes for attitude control can be accommodated) and specification of the sailcraft guidance. The guidance can be simply a result of the reaction of the system to the sailcraft dynamics (moving masses, etc.—set up by a user-defined control logic) based on calculations each step of the iteration, or simply a specification of the sail attitude profile over time. Of particular interest to the user, the SailDisturbance.m script (function) is where the forces and torques on the sailcraft are computed each iteration. When specified, and where applicable, these calculations are performed on each “triangle” of the components created in the sailcraft CAD model. The SolarPressureForce script (function) is called upon to calculate the combined thermal and optical forces on the sail. If in a planetary orbit (with specified characteristics) aerodynamic, albedo, and even magnetic field forces can be calculated.

Once the required information is input, the simulation can be run using an iterative differential equation integration method. One of the standard MATLAB methods is ode113, which calls the values and functions within FSailCombined to compute the new sailcraft state at each specified time step. These state parameters at each time step are saved within FSailCombined and can be retrieved, graphed, and/or plotted by the user-created simulation script. Many of these products are visible throughout this paper.