Thrust and torque vector characteristics of axially-symmetric E-sail

E-sail attitude control with tether voltage modulation

“…Note that δ n is undefined when kB is parallel to r and, in that case, the pitch angle is α n = 0 (that is, the spacecraft attitude is Sun-facing). Using a more accurate description of the actual E-sail shape [9], each tether bends on the (x k , z B ) plane as a consequence of the combined effects of the centrifugal force and the solar wind dynamic pressure acting on it, as is schematically illustrated in Fig. 4.…”

“…Note that the previous expression of the disturbance torque T d requires the spacecraft spin rate to be sufficiently high [9,10] and, as such, the tether slope to be sufficiently small, or…”

“…Accordingly, the tethers are not perfectly straight, and the uncertainty associated with their actual shape makes it difficult to obtain an estimate of the thrust and torque vectors, which are a necessary information for trajectory analysis and attitude control design. Recent works [9,10] have addressed such a problem with the aim of obtaining approximate closed-form expressions of the E-sail thrust and torque vectors. In particular, the results of Ref.…”

“…In particular, the results of Ref. [9], based on the assumption of a Sun-facing sail [11,12] (that is, a sail whose spin axis is aligned with the Sun-spacecraft line), show that the tether equilibrium shape is well approximated by a natural logarithmic arc when the spacecraft spin rate is sufficiently high and the electrical voltage is uniform. However, in a Sun-facing configuration the E-sail generates a purely radial thrust, while in most cases a trasverse thrust component is necessary for orbital maneuvers, since it allows the orbit angular momentum to be varied [13].…”

Initial Three-Dimensional Trajectory Design for Solar Sails Using Bezier Shaping Approach

“…This type of method is suitable for the initial trajectory design of spacecraft propelled by low-thrust ion engines, whose thrust direction can be arbitrary. However, this type of method is not flexible enough to be used in the initial trajectory design of spacecraft with a thrust constraint, such as a spacecraft propelled by a solar sail [27]- [31], electric solar wind sail [32]- [37], magnetic sail [38], [39], and etc. When there are more than three Bezier orders of coordinate approximation, the shape of the transfer trajectory cannot be determined analytically using only the BCs; there are unknown coefficients that need to be optimized to satisfy certain thrust constraints or to achieve optimal indexes.…”