What are VMC and VMCA and how are they determined?

VMC (minimum control speed) is the lowest speed at which directional control can be maintained with critical engine inoperative. VMCA (air minimum control speed) is determined with: Most critical engine inoperative at maximum takeoff thrust, Remaining engines at takeoff thrust, 5 degrees bank toward operating engine allowed, Maximum rudder and aileron applied, and Aircraft trimmed for takeoff. VMCG (ground minimum control speed) considers ground roll. VMC must not exceed 1.2 Vs (stall speed) for certification. Determination involves flight test at decreasing speeds until directional control limit reached. Higher VMC requires longer runways; design goal is low VMC through adequate rudder power and favorable engine placement.