An aerodynamic brake assembly for use with an airfoil such as the blade of a wind turbine rotor comprises deployable upper and/or lower spoiler plates incorporated in or attached to the airfoil. The spoiler plates can deploy under the influence of centrifugal forces when the rotating airfoil or rotor blade reaches a pre-determined rotational speed. The aerodynamic brake assembly may be integrated within the airfoil or attached to the tip of the airfoil such that, when not deployed, the upper and lower spoiler plates have a profile that approximately conforms to the profile of the part of the airfoil to which it the brake assembly is attached. Thus in a non-deployed state, the spoiler plates have a non-detrimental effect on the performance of the airfoil, and may even contribute to its aerodynamic lift properties. A weighted arm linked to the spoiler plate mechanism can be held in position electromagnetically or by solenoid, until an electrical signal from a controller causes it to release, leading to deployment of the spoiler plates. Failsafe deployment of the spoiler plates can occur either upon loss of power to the mechanism, or when the centrifugal force associated with an overspeed condition of the rotor overcomes the holding force of the electromagnet or solenoid.