A transportable rig apparatus provides for well completion operations while also providing a rig apparatus that readily resists or negates the effects of dynamic wind forces or other weather phenomenon. More particularly, the transportable rig apparatus provides a mast assembly that can extend in a generally vertical direction, e.g. perpendicular to the rig carrier and/or ground surface, such that the rig can be placed directly adjacent to a wellbore, the mast assembly providing a mast apparatus that readily resists or negates the effects of strong winds or other weather phenomenon.