Variable geometry turbines having a turbine housing with an inlet and an outlet, a turbine wheel rotatably mounted between the inlet and the outlet, a movable wall member having an inlet passageway between the inlet of the turbine housing and the turbine wheel, and a plurality of vanes circumferentially spaced and extending across the inlet passageway, the plurality of vanes having a specified shape. Methods for designing configurations of vanes for variable geometry turbines.