An aerodynamic braking device for a payload casing intended to be ejected from a projectile on its trajectory including at least one parachute connected to the casing by hangers, the parachute and the parachute hangers being housed in a sleeve. The sleeve is wound around an axis of winding perpendicular to its longitudinal direction and attached to a cylindrical housing the axis of which is parallel to the axis of winding, which housing is itself secured to a shell base that closes off the projectile, the hangers being connected to the casing by an extension cable which is wound around the axis of the housing and attached thereto by at least three peripheral break lines which are uniformly angularly distributed.