E-Sail Three-Dimensional Interplanetary Transfer with Fixed Pitch Angle

The electric solar wind sail (E-sail) is a propellantless propulsion system concept based on the use of a system of very long and thin conducting tethers, which create an artificial electric field that is able to deflect the solar-wind-charged particles in order to generate a net propulsive acceleration outside the planetary magnetospheres. The radial rig of conducting tethers is deployed and stretched by rotating the spacecraft about an axis perpendicular to the nominal plane of the sail. This rapid rotation complicates the thrust vectoring of the E-sail-based spacecraft, which is achieved by changing the orientation of the sail nominal plane with respect to an orbital reference frame. For this reason, some interesting steering techniques have recently been proposed which are based, for example, on maintaining the inertial direction of the spacecraft spin axis or on limiting the excursion of the so-called pitch angle, which is defined as the angle formed by the unit vector perpendicular to the sail nominal plane with the (radial) direction of propagation of the solar wind. In this paper, a different control strategy based on maintaining the pitch angle value constant during a typical interplanetary flight is investigated. In this highly constrained configuration, the spacecraft spin axis can rotate freely around the radial direction, performing a sort of conical motion around the Sun-vehicle line. Considering an interplanetary Earth–Venus or Earth–Mars mission scenario, the flight performance is here compared with a typical unconstrained optimal transfer, aiming to quantify the flight time variation due to the pitch angle value constraint. In this regard, simulation results indicate that the proposed control law provides a rather limited (percentage) performance variation in the case where the reference propulsive acceleration of the E-sail-based spacecraft is compatible with a medium- or low-performance propellantless propulsion system.