Vmca Speed

[Lavonna Baldree]

Vmcais defined as the minimum speed, whilst in the air, that directional control can be maintained with one engine inoperative (critical engine on two engine aerolanes), operating engine(s) at takeoff power and a maximum of 5 degrees of bank towards the good engine(s).

When an engine, on a multi engine aircraft, fails or is inoperative in flight, the asymmetric thrust creates a yawing moment which causes the aircraft to turn towards the failed engine. Rudder is used to counteract this yaw and adverse roll effects are negated by use of the ailerons. There is a minimum speed at which, by using full rudder deflection, it is possible maintain a constant heading with level wings. This speed is reduced if the aircraft is banked towards the live engine(s). The speed that corresponds to full rudder deflection in combination with a 5 degree bank angle is defined, by regulations, as the minimum control speed and is referred to as Vmca (Velocity of Minimum Control in the Air).

For a given size of vertical tail with rudder, at speeds below Vmca, the generated rudder side force is not large enough to counteract the asymmetrical thrust. As a consequence, heading cannot be maintained at speeds below Vmca with the critical engine failed and the other engine(s) operating at maximum thrust. Vmca was calculated (assumed) by the design engineer when determining the size of the vertical tail. Whilst a large tail will result in a reduced Vmca, it will also have adverse consequences in terms of weight, production costs and hangar accessability. A small vertical tail can mitigate those issues but will result in an increase in Vmca. Regulations prohibit Vmca values greater than 1.2 Vs.

Vmca is a manufacturer determined speed which will be published in the Aircraft Flight Manual (AFM). The speed is mathematically calculated during aircraft design and verified as part of the certification test flight process. Conditions and criteria for determination of Vmca include the following:

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 Vmca.

VMC(A) easily becomes a ruthless killer that strikes unexpected and merciless if a multi-engine rated pilot is not (made) aware of the really simple defenses against its killing potential. During the past 25 years, at least 600 pilots of small and big multi-engine airplanes did not know how to deal with the forceful, striking impact that VMC(A) can have when an engine fails or is inoperative, and do regrettably not live anymore to learn what exactly happened. Most accident or safety investigators, manual writers and their inspectors do not know either (which is also why such accidents continue to occur). AvioConsult learned about VMC(A) at the USAF Test Pilot School and in college books, and teaches the defenses below and in downloads, for free.

VMC, or more specifically VMCA, is the AFM-published Minimum Control speed in the Air for maintaining straight flight only when either engine of a multi-engine airplane fails or is inoperative and the corresponding opposite engine is set to provide maximum thrust, provided a small favorable bank angle is being maintained of 3 to 5 degrees (exact number to be provided by the manufacturer) away from the inoperative engine. A VMC or VMCA applies after failure of either engine, and during the whole flight, not only during takeoff.

WARNING: The actual VMCA that the pilot will experience when banking away from the small favorable bank angle will increase to a much higher actual value than the AFM-published VMCA, because the actual VMCA varies with asymmetrical thrust setting, bank angle and weight. When keeping the wings level, or banking away from the favorable 5 bank angle, the sideslip, hence drag, will increase considerable, further reducing the Rate of Climb. In addition, the actual VMCA will increase much above V2 or VYSE, causing an unexpected and often fatal loss of control.

The defense? When the rudder and/or aileron control input is/ are near maximum for maintaining control, don't further increase the bank angle, but maintain straight flight while banking 5 into the good engine (same side as the rudder pedal) or reduce asymmetrical thrust (a little to stop the yawing or rolling). Safest is to climb straight ahead to a safe altitude while maintaing the small favorable bank angle; then increase speed and turn, if required. Why? To prevent the Loss of Control.

When an engine fails or is inoperative in-flight, rudder is required to counteract the asymmetrical thrust yawing moment; roll effects are to be counteracted by the ailerons. The counteracting forces generated by these aerodynamic control surfaces are proportional to the square of the airspeed (V2), to the area of the surfaces (S) and to the air density. So, for given sizes of the vertical tail with rudder and the ailerons, there is a speed below which the generated rudder side force ("horizontal lift") is not large enough anymore to counteract the asymmetrical thrust, or below which the ailerons are not effective anymore: the heading and/or bank angle cannot be maintained ("controlled") below this speed. This speed is called Minimum Control speed (VMC) or more appropriate: Minimum Control speed in the Air (VMCA).

A 42 min. video lecture, in which the real value of the minimum control speed airborne (VMCA) is explained as taught at all formal Test Pilot Schools and most aeronautical universities, including the review of two accidents using views from the cockpit, is available on YouTube. Click here.

A pdf file with slides and script used in this video can be downloadedhere. Courses on asymmetric powered flight that test pilots and flight test engineers receive at formal Test Pilot Schools can be downloaded from the USArchives via the Links page, click here.

This figure shows the airspeed required for maintaining control of this sample airplane for bank angles between 15 left and 15 right when engine #1 is inoperative and #2 is at max. thrust, for rudder and aileron deflections to stay within their mechanical limits (enabling control).

When the Indicated Airspeed is near AFM-published VMC(A), then bank 4 away from the inoperative engine to avoid loss of control and for minimum drag, i.e. for max. Rate of Climb. Do not turn!

The figure is calculated in this paper.

VMCA is a constant number, but only in the Limitations Section of the AFM and on the airspeed indicator (red line). In flight, the actual VMCA varies with bank angle, engine thrust, rudder deflection, and other variables. This graph shows (the actual) VMCA, and the required rudder and aileron deflections, and the resulting sideslip angle versus bank angle of a sample airplane after failure of the left engine (#1) while the asymmetrical thrust is maximal and control can just be maintained (control deflections are less than or equal to their mechanical maximum, and sideslip is max. 14).

The airspeed that results from the bank angle for which the sideslip is zero (minimum drag, max. ROC) is the VMCA that will be published in the AFM (95 kt). At bank angles larger than 6 away from the failed engine, for this sample airplane, the rudder needs to be reversed to limit the sideslip angle which, nevertheless, increases to 14, being the fin stall angle of attack (with deflected rudder). The airspeed needs to be increased to prevent the fin from stalling at larger bank angles, hence, the actual VMCA increases.

Notice that the actual VMCA for wings level (120 kt) of this sample airplane is 25 kt higher than the AFM-published VMC(A).

This leads to the limitation that the pilot should not turn, but maintain the exact bank angle that was used to design the vertical tail and at which the drag is minimal (in this example 4, usually 5), when the airspeed decreases to or is equal to the AFM-published VMCA while the asymmetrical thrust is maximal.

At higher airspeeds, the bank angle can be smaller; at VYSE, 3 of bank might result in minimum drag.

This small bank angle does not result in a turn, but reduces both the drag and (actual) VMCA. Engine-out flight is never coordinated flight. VMCA applies after failure of either engine, not only the critical engine.

Lesson learned: The vertical tail with rudder and/or the ailerons are not designed large enough for maintaining control during turns into or away from the inoperative engine when the airspeed is, or is close to VMCA while maximum asymmetrical thrust is set, but only for maintaining straight flight. Therefore, before turning to either side, even at small bank angles, increase the airspeed by at least 30 kt.

At any sign of inadequate remaining control power (near full rudder or max. aileron), i.e. impending loss of control, decrease thrust (a bit) and recover to straight flight. After establishing straight flight with the favorable bank angle, asymmetrical thrust can be increased again.

The airplane is brought in the VMCA test configuration, i.e. lowest weight possible and aft center of gravity, which result in the highest, worst case VMCA at which straight flight can be maintained. In-flight, at a safe altitude of 5000 ft AGL, an airspeed is attained well above the anticipated VMCA (at least VSSE). Then the critical engine is shut down, or set at torque for zero thrust, and the opposite engine at maximum thrust. The airspeed is slowly decreased until the increasing rudder and/or aileron cannot maintain the heading and/or wings level anymore. The airspeed at which this occurs is VMCA with the wings level; also mind the large unavoidable sideslip, i.e. drag. Then, the bank angle is slowly increased into the operating engine, to a maximum of 5 or until the sideslip is zero, and the airspeed is further decreased until again the heading cannot be maintained with rudder and/or aileron. The airspeed at which this occurs is the VMCA of the airplane that will be published in the AFM, after extrapolation to sea level. VMCA when any other engine is inoperative is a little lower than VMCA with the critical engine inoperative.

Regulations do not require the much higher actual VMCA during turns to be determined.

Please refer to the formal FAA or EASA Flight Test Guides for the safe conduct of this test, via the Links page.

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