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VMCA page:
What is Minimum Control speed VMC or VMCA really?
Forgotten knowledge of VMC(A) and its associated conditions cause fatal accidents after engine failure
This page can be downloaded as pdf file here.
Definitions of VMC or VMCA in most Airplane Flight Manuals (AFM) and Pilot's Operating Handbooks (POH) and in multi-engine rating course books suggest that the airplane is controllable at airspeeds down to VMC(A) when one of the engines fails (during takeoff) or is inoperative (in-flight), and the remaining engine(s) is/are set to provide maximum thrust, but this is definitely not true.
Forgotten associated conditions apply for the AFM/POH furnished VMC(A) to be valid and for maintaining control when the airspeed is as low as VMC(A) or even as low as VR, VYSE or V2. This will be explained below.
VMC is defined in FAR/CS 23.149(a) and equivalent regulations which are for airplane design engineers and airworthiness certification: "VMC is the calibrated airspeed at which, when the critical engine is suddenly made inoperative, it is possible to maintain control of the airplane with that engine still inoperative, and thereafter maintain straight flight at the same speed with an angle of bank of not more than 5 degrees". The purpose of the 5° bank and its effect on VMC(A) are explained below.
For pilots this means that a multi-engine airplane is designed and certificated to recover after a (sudden) engine failure and thereafter only to maintain straight flight at the minimum control speed VMC(A) when the asymmetrical thrust is, or is increased to maximum, provided a small bank angle of 5° or little less (as opted by manufacturer) is being maintained away from the inoperative engine. The rudder and ailerons do not have to be sized large enough to make turns at VMC(A), nor at the therewith derived takeoff speeds VR and V2. The VMC must be furnished in the AFM/POH.
Maintaining straight flight and a small bank angle of 5° away from the inoperative engine are the associated conditions for the AFM/POH published VMC(A) to be valid when the asymmetrical thrust is maximum, and are definitely required to be observed to prevent the loss of control and/or collision with the ground.
The small bank angle does not turn the airplane but introduces a side force in the cg which reduces the sideslip due to the asymmetrical thrust, decreasing the drag, and hence increasing the remaining climb performance. It also decreases VMC(A) to a value closer to the AFM/POH furnished value, which also means that when the wings are kept level, the actual VMC(A) increases. This increase is about 6 kt for a small twin, but about 30 kt for a big 4-engine transport airplane. In addition, increasing the bank angle more than 5 degrees into the good engine requires the rudder to be reduced and reversed to confine the sum of the increasing side forces. The VMC(A) increase is much larger when banking further to either side (during turns); a much higher airspeed is required to maintain the equilibrium of forces and moments, and maintain control. Engine-out flight is not coordinated flight.
Although VMC(A) after failure of a non-critical engine is a little lower, the AFM/POH furnished VMC(A) (for the inoperative critical engine) applies in anticipation of and following either engine failure. Failure of a centerline or an inboard engine results in an even lower actual VMC(A), most probably lower than VS (during straight flight). A low VMC(A) is safer.
Reducing asymmetrical thrust a little (during a turn) decreases the required rudder deflection after which the airspeed can be reduced until the rudder is again maximum, the actual VMC(A) is lower.
Hence, the pilot controls VMC(A) with bank angle, thrust and also with the amount of rudder deflection. Asymmetric engine-out flight is not coordinated flight; rudder and/or aileron inputs are continuously required to counteract the thrust and/or sideslip yawing and rolling moments and maintain an equilibrium of forces and moments. When either control is near maximum deflected, Loss of Control is nearby because the equilibrium can no longer be maintained.
An actual VMC(A) does not only apply in anticipation of and following the sudden failure of any engine, but also during the remainder of the engine-out flight, and can be very much higher than the AFM-published VMC(A), as shown below.
FAA Flight Test Guides prescribe how VMC(A) must be determined during experimental flight testing, see the VMC(A) testing paragraph below.
A few relevant paragraphs of these Guides and Regulations are copied into a Background file, in which also a few clarifying notes are included. This file is available for download. Links to these Regulations are on the Links page.
Download this Background file.
Details on VMC(A) are presented in papers on the Downloads page.
TAS, CAS, And IAS Explained
FAR 23.149(a) and equivalent require VMC(A) to be furnished as Calibrated Airspeed (CAS).
As many pilots (and airplane manufacturers) struggle with the difference between Calibrated Airspeed (CAS) and Indicated Airspeed (IAS), these airspeeds will be briefly explained first, as taught at test pilot schools.
Pilots only work with Indicated Air Speed (IAS), don't they? Well, IAS is the speed indicated on the Air Speed Indicator (ASI), but it is not the airspeed at which the airplane is plowing the air, which provides the wing lift and control power, and which is used to furnish limiting and operational speeds in AFM or POH; this speed is called the Calibrated Air Speed (CAS). The Indicated Air Speed (IAS) has/includes unavoidable measuring and instrument errors of up to 9 knots, as allowed by airworthiness regulations. IAS is also the abbreviation of Inaccurate Air Speed; it requires error corrections to be of value for piloting.
Competent pilots work with CAS. For their flying task, pilots read the airspeed on the ASI, but have to apply corrections to be able to find the airspeed at which the airplane and its wings and aerodynamic control surfaces are indeed plowing the air (in CAS), or to find the IAS that corresponds to the limiting and operational speeds, such as VS, VR, V2 or VMC(A), that are furnished as CAS in the POH/AFM. More corrections are required to find the True Airspeed (TAS) and the Ground Speed (GS), both for navigation purposes.
The following airspeeds are used by pilots:
- IAS is the airspeed indicated by an airspeed indicator, and is CAS including the error due to the position of the pitot tube in disturbed air and the ASI instrument error. IAS is an In-Accurate Speed which becomes only valuable when corrected for instrument and position errors; then the IAS corresponds to the CAS of the airplane.
- CAS is the calibrated airspeed, which is the speed of the airplane in the undisturbed airstream with respect to the standard atmospheric pressure and temperature at sea level. The lift of the wings, and the control power of the aerodynamic control surfaces are proportional to the CAS. Limiting and operational speeds are furnished as CAS. CAS is the airspeed for piloting.
- TAS is the true airspeed with respect to the ambient pressure and temperature, and is the CAS corrected for ambient pressure and temperature (at altitude). TAS is the airspeed for navigating.
- GS is the airspeed relative to the ground, and is the TAS corrected for the wind.
These airspeeds, and also the minimum control speed in the air (MC(A)), are often incorrectly defined, explained, and used in Pilot Operating Handbooks and in Airplane Flight Manuals. IASs do not belong in a common generic POH/AFM that applies to a series of airplanes of the same type, because the instrument errors in each individual airplane differ, and VMC(A) and takeoff speeds in IAS might turn out to be too low. This also applies to electronic displays (which should be calibrated and programmed to display CAS).
An IAS always requires the pilot to apply corrections, while a CAS doesn't need corrections and is therefore more convenient to use. Operational and limiting speeds are required to be furnished as CAS in POH/AFMs for a good (safety) reason.
AvioConsult wrote a paper in which these airspeeds are better explained, and proper definitions are provided as taught at universities and test pilot schools. Reference is made to downloadable MSc-level course books but not to books or articles generated by AI, published on Wikipedia, and on forums, or to pamphlets or trash on social media that are written by incompetent writers. Test pilot schools teach all students to calibrate pitot-static systems in theory and in-flight; they know what they are talking about.
Download this paper. Back to top
VMCA As Tail Design Factor
VMC(A) is about forces and moments acting on an engine-out airplane. You will remember that a body is in equilibrium if both the sum of the forces and the sum of the moments (forces times the perpendicular distance to the cg) acting on the body are zero.
When an engine fails or is inoperative in-flight, rudder is required to counteract the asymmetrical thrust yawing moment, and 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 (ρ). So, for given sizes of
the vertical tail with rudder and the ailerons, there is a speed below which the generated
control forces are not large enough anymore to counteract the forces and moments due to asymmetrical thrust, being the speed below which the controls are not effective anymore: the heading and/or bank angle, i.e. the equilibrium of forces and moments, can no longer be maintained by the aerodynamic controls below this speed; control is lost. This speed is called
Minimum Control speed (VMC) or more appropriate: Minimum Control speed in the Air (VMCA). VMC(A) is influenced by all factors that affect the lateral and directional forces and moments that act on the airplane, not only by the asymmetrical thrust.
VMC(A) is already determined (i.e.
assumed and used) by the airplane design engineer for sizing the vertical tail (fin), because a vertical tail may not be made that small that VMC(A) increases above 1.2 VS (during straight flight - FAR/CS 23.149).
On the other side, a large tail results in a lower VMC(A)
but in higher weight and production cost.
FAR/CS 23.149 allows the design engineer to use a small bank angle but maximum 5º
(away from the failed engine) which generates a side force in the cg that can replace the side force due to sideslip when the thrust is asymmetric. This side force acts in the cg and hence, generates no yawing moment. The rudder does not have to overcome the sideslip sideforce and yawing moment anymore, allowing the rudder deflection to be smaller or a smaller vertical tail with maximum rudder at VMC(A). This is illustrated in the figures below for straight flight.
Hence, a small bank angle allows for a smaller – cheaper and lighter – vertical tail, reduces the sideslip (drag) to a minimum for maximum takeoff performance and results in a lower VMC(A) (for straight flight). The effects of other bank angles will be shown below.
Airplane design professor Dr. Jan Roskam (KU) in his college book for sizing control surfaces: "The VMC value ultimately used ties take-off performance to engine-out controllability."
However, the saved hardware weight of a smaller tail needs to be replaced by a quite 'heavy' software condition for pilots (on paper in the AFM/POH) when an engine is inoperative, which is to maintain straight flight only when the asymmetrical thrust is or is increased to maximum, and to maintain a small bank angle away from the inoperative engine for minimum drag and lowest actual VMC(A), hence maximum Rate of Climb.
Read more in this paper, and/or view the video The Real Value of VMC(A) – How to Prevent a Dead Engine from Turning into a Killing Engine:
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A 42 min. video lecture, in which the real value of the minimum control speed airborne (VMC(A)) 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 downloaded here. |
The courses on asymmetric powered flight that two test pilot schools teach can be downloaded from the USArchives via the Links page, click here. Back to top
VMC(A) During Banking
The most important forces and moments acting on an engine-out airplane during banking 15° into and away from the failed engine are shown in the following figure.
For maintaining control, that is for preventing the loss of control, an equilibrium of forces and moments that act on the airplane is required. The aerodynamic forces are proportional to the square of the airspeed. VMC(A) is the lowest airspeed at which an equilibrium of the lateral-directional forces can be maintained, like the stall speed VS is for the longitudinal forces.
VMC(A) in the Limitations Section of the AFM and on the airspeed indicator (red line) is a constant number, which is determined not only for maintaining straight flight, but also for calculating takeoff speeds VR and V2. In-flight though, aerodynamic forces not only vary with airspeed, but also with bank angle, engine thrust, rudder and aileron deflections, and other variables which will change the equilibrium of forces and moments. So, the question is whether and how much (an actual) VMC(A) varies with these variables as well. This is analyzed in this paper using VMC(A) prediction with stability derivatives in lateral-directional equations of motion as taught at the USAF Test Pilot School.
The graphs out of the paper on the left side below show (the actual) VMC(A), the required rudder and aileron deflections, and the resulting sideslip angle versus bank angles between -15° and +15° of a sample airplane after failure of the left engine (#1) while the asymmetrical thrust is maximal.
The airspeed that results from the bank angle for which the sideslip is zero (minimum drag, max. ROC) is the VMC(A) that will be furnished in the AFM (here 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.
The airspeed needs to be increased to prevent the fin from stalling at larger bank angles, hence, the actual VMC(A) increases.
Notice that the actual VMC(A) for wings level (120 kt) of this
sample airplane is 25 kt higher than the AFM-furnished 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 ≈3°, usually 5°), when the airspeed decreases to or is equal to the AFM-furnished VMC(A) 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, as shown in the figure above.
This small bank angle does not result in a turn, but reduces both the drag and (actual) VMC(A). Engine-out flight is never coordinated flight, because control inputs are required to counteract the asymmetrical thrust and side effects. The centripetal force that pilots use to explain turns is reduced or enhanced by the counteracting forces of rudder and/or ailerons. Banking away from the favorable 5° results in sideslip, hence drag, as the figure above proves.
VMC(A) applies after failure of either engine, not only the critical engine.
The right figure above shows the effect of weight and bank angle on VMC(A). When the wings are level, weight has no effect (W·sin 𝜙 = 0). With a 3° bank angle, when the sideslip angle is minimal, VMC(A) is highest at low weight, which is the reason why low weight is used to determine VMC(A), it is the worst-case weight for VMC(A) (for straight flight as required for the AFM-furnished VMC(A) in FAR 23.149). Lockheed C-130 pilots know this figure from their performance manual SMP 777.
Lesson learned (I hope): 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 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 first (in this example by at least 30 kt), or reduce the asymmetrical thrust a little.
At any sign of inadequate remaining control power (near full rudder or max. aileron), i.e. impending loss of control, decrease thrust (a little) and recover to straight flight. After establishing straight flight with the favorable small bank angle, asymmetrical thrust can be increased again. Back to top
How is VMC(A) measured in-flight
The airplane is brought in the VMC(A) test configuration, i.e. lowest weight possible and aft center of gravity, which result in the highest, worst-case VMC(A) 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 VMC(A) (at least VSSE). Then the critical engine is shut down, or set at torque for zero thrust, and the opposite engine at maximum thrust. VMC(A) with the critical engine inoperative is a little higher than VMC(A) while another engine is inoperative, being the worst-case for straight flight. Then the airspeed is slowly decreased until the increasing rudder and/or aileron inputs cannot maintain the heading and/or wings level anymore. The airspeed at which this occurs is VMC(A) 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 can no longer be maintained with rudder and/or ailerons. The airspeed at which this occurs is the VMC(A) of the airplane that will, after extrapolation to sea level, be furnished in the AFM.
This VMC(A) is valid for straight flight only! Regulations do not require the much higher actual VMC(A)'s for other bank angles and during turns to be determined, because of the resulting huge amount of data, the use of which by pilots would be prone to errors.
In some cases, the test pilot also increases the bank angle to the point where the rudder deflection is zero, as indicated in the left figure above; then the required airspeed is larger, and the sideslip/drag is large as well.
Please refer to the formal FAA or EASA Flight Test Guides for the safe conduct of this test, via the Links page. Back to top
VMC(A) Definition for Pilots
The selected tail size imposes a limitation on, i.e. a constraint to pilots. The VMC(A) definition for use by pilots is therefore different than the VMC(A) definition in FAR/CS 23.149 which is for manufacturers, for designing and certification of multi-engine airplanes:
VMC(A) is the minimum speed for maintaining straight flight only when an engine fails or is inoperative and the corresponding opposite engine is set to provide maximum thrust, provided a bank angle is being maintained of 3 – 5 degrees (exact number to be provided by the manufacturer) away from the inoperative engine. VMC(A) increases considerable during banking away from this favorable bank angle, i.e. during turns.
In addition, the manufacturer should specify the bank angle and the configuration (flaps, gear, etc.) for which the AFM-furnished VMC(A) is valid.
Display of VMC(A)
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On the airspeed indicator of Part 23 twin-engine airplanes, the standardized AFM-furnished VMC(A) is indicated by a red radial line, in this example at 80 kt. However, neither a placard on the instrument panel nor a note or warning in the AFM tells the pilot that the redlined VMC(A) is valid only when a bank angle of 3 to 5 degrees (to be specified by the manufacturer) is maintained away from the inoperative engine. A larger bank angle, or a bank angle into the inoperative engine results in a much higher actual VMC(A), a 14 or more-degree sideslip, hence large drag, and to the loss of climb performance and possibly loss of control after which an accident cannot be avoided (when asymmetrical thrust is not reduced). |
The airspeed for maximum single-engine rate of climb VYSE is indicated by a blue radial line, here at 105 kt. In the legend of some Performance Data Tables of Graphs, a note tells the pilot that the presented performance data, including the performance at VYSE, are valid only if a small bank angle is being maintained of 2 - 3 degrees away from the inoperative engine. For other bank angles, the maximum climb performance, or the performance to maintain altitude (i.e. to prevent drifting down) is not guaranteed.
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This note is included in the legend of the Climb Performance Chart - One
Engine Operating in the Piper PA-44 Pilot's Information Manual. It is
included, because not maintaining this bank angle renders the presented
performance data invalid; the airplane might not even be able to maintain
altitude. The bank angle is smaller than 5 degrees, because the presented
performance data requires VYSE, the blue line speed, which is
higher than VMC(A). The vertical tail is more effective at higher
speed. |
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A similar placard is to be installed in full view of pilots of Part 23 commuter airplanes to comply with Aviation Regulations (23.1563). The required small bank angle for the listed VMC(A) to be valid is regrettably not included on the placard, because this is not required by Aviation Regulations, but is essential for flight safety and performance. Not maintaining the small bank angle (i.e. straight flight) at
airspeeds as low as or near VMC, such as VYSE or V2, while the power setting of the
remaining engine is high, is the real cause of most engine failure
related accidents. |
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It is recommended to require a placard like this one in all Part 23 airplanes. KIAS can be used on placards of individual airplanes if both the position and the instrument errors of the installed ASI are used to calculate the VMC(A) as KIAS, as done for the red radial line. More text options are possible. |
VR and V2MIN
The standardized,
AFM-furnished VMC is one of the factors for calculating
the rotation speed VR of all multi-engine airplanes, and
for calculating V1 and minimum takeoff safety speed V2MIN if applicable. Since this VMC is
valid only while maintaining a bank angle of 3 to 5 degrees, as to
be specified by the manufacturer, away from the inoperative engine,
both the calculated VR and V2MIN are also
valid only when maintaining the same bank angle (when the thrust
setting is maximum takeoff). If the pilot does not attain and maintain the small bank angle, the takeoff speeds should be increased for maintaining control.
Refer to the
paper for Investigators and Flight Instructors for a thorough
explanation of takeoff speeds.
VMC(A) For Piloting
Minimum Control speed VMC or VMCA is the lowest calibrated airspeed which can be obtained with full directional and/or lateral control inputs when one (outboard) engine of a multi-engine airplane fails or is inoperative, and the opposite engine is set at maximum thrust.
VMC(A) varies with the magnitude of control inputs, with the level of asymmetrical thrust, with weight, with bank angle, and with asymmetrical drag caused by cowlings, hatches, unfeathered propeller, inadvertent opened thrust reversers, etc., with anything that affects the balance of lateral and directional forces and moments that act on the airplane in-flight. Hence, VMC(A) is a quite complicated airspeed limitation; an airplane has many VMC(A)'s.
To simplify the matter, regulations FAR/CS 23.149 and 25.149, and equivalent, require only one VMC to be determined and furnished in the Limitations Section of the Airplane Flight Manual, the VMC while maintaining straight flight with a small favorable bank angle of 3 to 5 degrees (exact number to be provided by the manufacturer) away from the inoperative engine, for lowest VMC and minimum sideslip and hence, minimum drag, and maximum climb performance, being the VMC which is useful for takeoff, for calculating takeoff speeds. This furnished standardized VMC is therefore valid only for takeoff when both straight flight and a small bank angle away from the inoperative engine are being maintained. At other bank angles, and during the remainder of the engine-out flight, a much higher actual VMC(A) applies, see above.
WARNING: When keeping the wings level, or when banking away from the small favorable bank angle (which is 3 to 5 degrees away from the inoperative engine) to either side, the actual VMC(A) that a pilot will experience in-flight will increase to a much higher value than the AFM-published standardized VMC(A), because VMC(A) varies with the asymmetrical thrust setting and bank angle. Then also the sideslip, hence drag, will increase considerable, further reducing the Rate of Climb. See the figure above.
When banking during takeoff, the actual VMC(A) might increase above V2 or VYSE, causing an unexpected and often fatal loss of control.
It is a myth that the safety margin is larger when turning into the good engine, and that the actual VMC(A) that the pilot will experience in-flight is always as low as the AFM furnished VMC(A). The pilot controls VMC(A) with bank angle, thrust, and amount of rudder.
When the rudder and/or aileron control input is/ are already near maximum for maintaining control, don't further increase the bank angle or the thrust, 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 maintaining the small favorable bank angle for minimum sideslip, hence drag, and lowest actual VMC(A). If a turn is required, increase the airspeed and/or decrease the asymmetrical thrust a little first. Why? To prevent the Loss of Control, reduce the directional forces and moments caused by the asymmetrical thrust, which reduces the required counteracting aerodynamic forces and moments generated by rudder and ailerons; rudder and aileron deflection are then smaller.
If the pointer of the airspeed indicator is at or near the red VMC(A) line and the thrust on the remaining engine(s) is or is increased to maximum, only straight flight should be maintained while maintaining a bank angle of 3 to 5 degrees
away from the inoperative engine.
If the airspeed is at the blue line (VYSE), still a small bank angle is required for minimum sideslip/drag.
When an engine fails during takeoff after V1, bank 5 degrees immediately after liftoff to the same side as rudder pressure. When the airplane starts to bank (unintended) into the dead engine, apply up to maximum rudder and or aileron to counteract. If these controls are ineffective, actual VMC(A) already increased above IAS; control is lost. The only options to save your souls are to reduce asymmetrical thrust a little (temporarily), regain straight flight, attain the small bank angle, and throttle up again, or close the throttles and land wings-level in the dirt, which is more survivable than with a large bank angle.
For turning safely while the asymmetrical thrust is high, gain altitude first during straight flight to allow for some altitude loss during reduced thrust turns, because of the increased sideslip (drag) during turns. It is safer to reduce the thrust a little during the turns to keep the actual VMC(A) low. Also consider a long straight-in approach rather than a tight final turn during which the thrust might have to be increased to maximum for maintaining the glide path (and control will be lost because actual VMC(A) increases above the indicated airspeed). To top
VMC or VMCA?
VMCA, the Minimum Control speed
in the Air (or Airborne), is one of the Minimum Control speeds (VMC's)
of a multi-engine airplane that is published as operational limitation in its
Airplane Flight Manual (AFM). Other
published VMC's are Minimum Control speed on the Ground (VMCG)
and, in some cases, also the Minimum Control speed during approach and Landing (VMCL). VMCA2 for two engines inoperative should still be published for 4- or more engine airplanes.
VMC is often used in (older) manuals in relation to engine failure during takeoff. Regulations,
however, are changing VMC into VMCA, because "VMCA
is more commonly used". A VMCA applies during the whole flight, in anticipation of or following an engine failure, and definitely not only during takeoff. The actual VMC(A) that a pilot will experience in-flight increases considerably during turns, as was shown above. For now, VMCA = VMC.
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This figure, a
safety improving suggestion of AvioConsult, shows that the
actual VMC(A) in this example has become higher than VR
because the wings are kept level. Bank angle and rudder
advisories are presented to decrease the actual VMC(A) to a
safe level to prevent the loss of airplane control. The bank
angle advisory widens up as the airspeed increases. |
Refer to the formal FAA and EASA Flight Test Guides via the Links page. In the reference list on the Downloads page, only the VMC(A) testing paragraphs can be downloaded.
For further details, refer to the paper for investigators and flight instructors presented on the Downloads page.
This page can be downloaded as pdf file here.