We report a theoretical study of the optical centrifuge acceleration of an asymmetric top molecule interacting with an electric static field by solving the time-dependent Schrödinger equation in the rigid rotor approximation. A detailed analysis of the mixing of the angular momentum in both the molecular and the laboratory fixed frames allow us to deepen the understanding of the main features of the acceleration process, for instance, the effective angular frequency of the molecule at the end of the pulse. In addition, we prove numerically that the asymmetric superrotors rotate around one internal axis and that their dynamics is confined to the plane defined by the polarization axis of the laser, in agreement with experimental findings. Furthermore, we consider the orientation patterns induced by the dc field, showing the characteristics of their structure as a function of the strength of the static field and the initial configuration of the fields.