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Vminimum control ground
Vmcg is defined as the minimum control speed on the ground, with one engine inoperative (critical engine on two engine airplanes), takeoff power on other engine(s), using aerodynamic controls only for directional control.
Vmcg must be less than V1
Vmcg / Derated Thrust Relationship
To maintain directional control with an inoperative engine, the rudder must be deflected to counteract the adverse yaw. The force that can generated by the rudder is dependent upon the size of the rudder, the amount that the rudder can be deflected and the speed of the airflow across the rudder surface.
In the case of an aircraft fitted with engines that can be derated for takeoff, the reduction in thrust will result in a corresponding reduction in the amount of yaw induced should an engine fail. As the rudder size and deflection capability remain constant, the amount of force required to counter that yaw can be generated at a lower airspeed than would be case during a full thrust takeoff. This results in a reduction in Vmcg and the potential for a reduction in V1.