An aerodynamic seal assembly for a rotary machine includes multiple sealing segments disposed circumferentially intermediate to a stationary housing and a rotor. Each of the segments includes a shoe plate with a forward load-bearing section and an aft load-bearing section configured to generate an aerodynamic force between the shoe plate and the rotor. The shoe plate includes at least one labyrinth teeth facing the rotor and positioned between the forward load-bearing section and the aft load-bearing section. The sealing segment also includes at least one spring connected to a pedestal located about midway of an axial length of the shoe plate and to a stator interface element. Further, the sealing segment includes a rigid segmented secondary seal attached to the stator interface element at one first end and in contact with the pedestal of the shoe plate at one second end.