Thrust Vectoring of an Electric Solar Wind Sail

The electric solar wind sail is a propulsion system that uses the solar wind proton flow as a source of momentum for spacecraft thrust. The momentum of the solar wind is transferred to the spacecraft by electrically charged light-weight tethers that deflect the proton flow. The sail electrostatic effective area is then much larger than the mechanical area of the tethers, and the system promises high specific acceleration up to about 10 mm per second^2. As the tethers are polarized at a high positive voltage they attract electrons that in turn tend to neutralize the tether charge state. However, only a modest amount of electric power of a few hundred watts is required to operate electron guns to maintain the sail charge state, and the sail can easily be powered by solar panels. The main tethers are centrifugally deployed radially outward from the spacecraft in the sail spin plane. To be tolerant to the micrometeoroid flux each tether has a redundant structure that comprises a number (typically 4) of 20-50 µm metal wires bonded to each other, for example by ultrasonic welding. As a baseline design, the tips of the main tethers host remote units that are connected by auxiliary tethers at the sail perimeter to provide mechanical stability to the sail. As the electric sail offers a large effective sail area with modest power consumption and low mass, it promises a propellantless continuous low thrust system for spacecraft propulsion for various kinds of missions. These include fast transit to the heliopause, missions in non-Keplerian orbit such as helioseismology in a solar halo orbit, space weather monitoring, with an extended warning time (closer to the sun than
L1), multi-asteroid touring mission. Using the electric sail, such missions can typically be accomplished without planetary gravity assist maneuvers and associated launch windows. If planetary swing-bys are planned during the mission, each solar eclipse has to be carefully considered to avoid drastic thermal contraction and expansion of the sail tethers.

In addition to scientific missions, the electric sail can be used for planetary defense as a gravity tractor or an impactor and to rendezvous with such Potentially Hazardous Objects that cannot be reached by conventional propulsion systems. The electric sail has also been suggested as a key method of transportation for products of asteroid mining. Specifically, water from asteroids can be used for in-orbit production of LH2/LOX by electrolysis to provide a cost-efficient way of transporting infrastructure associated with manned Mars missions.

Researchers created a precise model for the electric sail. They derived expressions for the angular thrust and torque densities. They introduced a tether voltage modulation that results in torque-free sail dynamics. They solved the amplitude of the modulation. This amplitude has to be reserved for the sail control and correspondingly the voltage available for thrusting is less than the maximum designed voltage increasing the sail efficiency. This amplitude is 3 times smaller for the sail model introduced here than for that derived using a single tether model. The total thrust to the sail was obtained for the torque-free sail motion. The transverse thrust is somewhat larger (up to about 10%) than that of the single rigid tether model. The reason is that a portion of the sail near the perimeter of the sail is coplanar with the sail spin plane. The thrusting angle was shown to be essentially equal to the fully planar sail being about 20◦
at sail angles higher than 45◦.

The shape of a rotating electric solar wind sail under the centrifugal force and solar wind dynamic pressure is modeled to address the sail attitude maintenance and thrust vectoring. The sail rig assumes centrifugally stretched main tethers that extend radially outward from the spacecraft in the sail spin plane. Furthermore, the tips of the main tethers host remote units that are connected by auxiliary tethers at the sail rim. Here, we derive the equation of main tether shape and present both a numerical solution and an analytical approximation for the shape as parametrized both by the ratio of the electric sail force to the centrifugal force and the sail orientation with respect to the solar wind direction. The resulting shape is such that near the spacecraft, the roots of the main tethers form a cone, whereas towards the rim, this coning is flattened by the centrifugal force, and the sail is coplanar with the sail spin plane. Our approximation for the sail shape is parametrized only by the tether root coning angle and the main tether length. Using the approximate shape, we obtain the torque and thrust of the electric sail force applied to the sail. As a result, the amplitude of the tether voltage modulation required for the maintenance of the sail attitude is given as a torque free solution. The amplitude is smaller than that previously obtained for a rigid single tether resembling a spherical pendulum. This implies that less thrusting margin is required for the maintenance of the sail attitude. For a given voltage modulation, the thrust vectoring is then considered in terms of the radial and transverse thrust component.

SOURCES- Arxiv