Definition
The set of aerodynamic and design factors that determine the published minimum control airspeed (VMC) for a multi-engine airplane with one engine inoperative. VMC is established under specific certification conditions: the critical engine failed and windmilling, the operating engine at takeoff power, flaps in the takeoff position, landing gear retracted, the airplane trimmed for takeoff, center of gravity at the most unfavorable (rearward) allowable position, and the airplane airborne with ground effect negligible. Under these conditions, VMC is the lowest airspeed at which the pilot can maintain straight flight using rudder and no more than 5 degrees of bank toward the operating engine, while holding heading within 20 degrees of the original.
Plain English
VMC is the slowest speed at which a pilot can still keep a twin-engine airplane flying straight after one engine quits. The 'derivation' is simply the list of conditions and design factors used to figure out that speed, so the same number is determined the same way for every airplane.
Context Anchor
Seen in multiengine training when discussing engine-out control, VMC demonstrations, and the red VMC marking on the airspeed indicator.
Derivation
Derivation' comes from the Latin 'derivare', meaning 'to draw off' or 'to trace from a source'. In this context it refers to tracing the published VMC back to the specific conditions and forces it was drawn from. Knowing the derivation tells the pilot what assumptions VMC is built on -- and therefore when those assumptions no longer hold.
Why Pilots Care
Knowing how VMC is derived helps pilots understand why published speeds are conservative and why bank angle and rudder input are critical during an engine failure.
Grounding Statement
Picture a twin-engine airplane with one engine at takeoff power and the other no longer helping: as airspeed drops, the rudder becomes less effective until it can no longer keep the nose straight.
Intuition Check
Do not read VMC here as visual meteorological conditions. In this chapter, VMC means minimum control speed, and derivation means how that speed is determined—not weather conditions and not just the word origin of the abbreviation.
Example Sentence 1
During multi-engine ground school, the instructor walked through the derivation of VMC so students would understand why the published red-line speed assumes takeoff power, gear up, and a rearward center of gravity.
Example Sentence 2
During the oral exam the examiner asked how the derivation of VMC accounts for the 5-degree bank angle.