  The electric solar wind sail produces thrust by centrifugally spanned high
voltage tethers interacting with the solar wind protons. The sail attitude can
be controlled and attitude maneuvers are possible by tether voltage modulation
synchronous with the sail rotation. Especially, the sail can be inclined with
respect to the solar wind direction to obtain transverse thrust to change the
osculating orbit angular momentum. Such an inclination has to be maintained by
a continual control voltage modulation. Consequently, the tether voltage
available for the thrust is less than the maximum voltage provided by the power
system. Using a spherical pendulum as a model for a single rotating tether, we
derive analytical estimations for the control efficiency for two separate sail
control modes. One is a continuous control modulation that corresponds to
strictly planar tether tip motion. The other is an on-off modulation with the
tether tip moving along a closed loop on a saddle surface. The novel on-off
mode is introduced here to both amplify the transverse thrust and reduce the
power consumption. During the rotation cycle, the maximum voltage is applied to
the tether only over two thrusting arcs when most of the transverse thrust is
produced. In addition to the transverse thrust, we obtain the thrusting angle
and electric power consumption for the two control modes. It is concluded that
while the thrusting angle is about half of the sail inclination for the
continuous modulation it approximately equals to the inclination angle for the
on-off modulation. The efficiency of the on-off mode is emphasized when power
consumption is considered, and the on-off mode can be used to improve the
propulsive acceleration through the reduced power system mass.
