# V2 variables

## Clearing obstacles after takeoff means flying by the numbers

April 1, 2011

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Many of the new V-speeds taught to first-time jet pilots are only used in the event of an engine failure. V 2, V FS, V ENR, V AC—depending on the aircraft manufacturer and phase of flight (takeoff, go-around, et cetera)— a pilot will calculate several speeds for each takeoff and landing that he will almost certainly not need to use. Most pilots quickly learn to compute the speeds in initial training and use them in nearly every simulator session during one simulated engine failure after another; however, many pilots harbor misunderstandings about what the speeds represent.

### April 2011 AOPA Pilot Turbine Edition

V 2, for example, is often mistakenly thought to be the jet equivalent of V XSE, or single-engine best angle of climb speed. Pilots of piston and turboprop multiengine aircraft learn not only the speeds for best rate and angle of climb when both engines are working, VY and VX respectively, but those for best rate and angle with one engine failed. For most nonjet twins, these speeds are provided for one weight and altitude combination, and the pilot never ventures beyond these default values.

In contrast, before every takeoff in a jet, the pilot will typically calculate four V-speeds based on criteria such as weight, altitude, temperature, and flap setting. The first two of these speeds, V 1 and V R, determine how late into the takeoff a pilot may abort the takeoff, and when the pilot begins the transition to flight. The other two speeds, V 2 and a “final” climb speed (which goes by different names depending on the aircraft manufacturer; we’ll call it V FINAL), are only used if an engine fails during the takeoff, when an abort no longer can be completed safely.

During initial sim training, for nearly every simulated engine failure on takeoff, the pilot is presented with a textbook—that is to say, worst-case—event. The engine is programmed to fail just before V 1, the pilot reacts, rotates the aircraft at V R, and climbs to a safe altitude above obstructions at V 2. Once above immediately threatening obstacles, the pilot accelerates to the final climb speed and retracts flaps. From this sequence many pilots develop a logical but fallacious correlation of V 2 to V XSE, and V FINAL to V YSE.

In fact, it is V FINAL that correlates much more closely to V XSE. So what does V 2 represent? In short, a compromise. For most circumstances a jet will encounter, certification requirements define takeoff distance as the longer of the distance to either bring an airplane up to V 1 and initiate an aborted takeoff, or continue on one engine so that the aircraft reaches V 2 speed at 35 feet agl. Clearly the higher the V 2 speed defined by the manufacturer, the longer the distance that will be necessary to accelerate from V 1 to V 2 on only one engine. Because of the desire to minimize published takeoff distances, the manufacturer often sets V 2 to be the minimum allowed by certification requirements, based on minimum allowable ratios of V 2 to stall speed and V MC.

So what’s the implication of V 2 being a bit lower than V XSE? A brief review of basic aerodynamics will illustrate the drawback to this minimum V 2 approach. Rate of climb is determined by the excess power an aircraft has available; however, angle of climb is determined by the amount of excess thrust available. For given atmospheric conditions, the thrust output of a jet engine is nearly constant if plotted against airspeed, while the thrust required by the aircraft follows the familiar “J” curve. Given these two curves, it is apparent that the greatest distance between the two lines, or the point of maximum excess thrust, occurs at minimum thrust required speed—which is to say, the minimum drag point of the curve.

At any speed slower than this point, the increase in induced drag means that climb angle will suffer. So by selecting a V 2 that lies below minimum drag speed, the aircraft manufacturer is giving up some possible climb gradient in favor of a reduced takeoff distance. As most jet aircraft have an abundance of extra thrust, this is an acceptable tradeoff, and even during a nonoptimal climb at V 2, most jets will turn out adequate, or even impressive, single-engine climb angles.

Although not common in light jets, some larger jet aircraft have software or performance charts that allow for an optimized, rather than minimum, V 2. If takeoff distance is calculated as 4,000 feet, but 9,000 feet of runway is available, it is easy to see that by increasing the V speeds until optimal V 2 is reached, extra runway can be converted into better engine-out climb performance.

What is common in light jets is the ability to depart with a reduced, or even zero, flap setting when runway available is not a limit, but engine-out climb performance may be. By departing with reduced flaps, the aircraft must accelerate to a higher speed before rotation, which brings the aircraft closer to true V XSE.

Also, the reduced drag of a lower flap extension means that the thrust-required curve shifts down—for any given speed, less thrust is required simply to maintain level flight—so more thrust is excess, and can contribute to a relatively greater climb angle.

Nearly all engine failures in the simulator occur just prior to V 1, but a real engine failure can occur at any point in the takeoff roll.

Beyond the performance implications of knowing what V 2 really represents, there is also a practical flight application. Nearly all engine failures in the simulator occur just prior to V 1, but a real engine failure can occur at any point in the takeoff roll.

When I conduct in-aircraft training, for example, I typically retard one thrust lever to idle just as V R is reached. With the two- to three-second spool-down time of a jet engine, by the time the pilot recognizes the engine has failed, the airspeed is often five to 10 knots above V 2. Most pilots just out of sim training exhibit a strong desire to pitch the aircraft up until V 2 is reached, then hold V 2 until clean-up altitude is attained.

Keeping in mind the drag curve, it becomes apparent that a pilot who has attained a speed higher than V 2 before recognizing an engine failure would be better served by maintaining that higher speed until at clean-up altitude, provided the aircraft hasn’t accelerated so much as to be faster than V FINAL. Doing so will result in lower drag, and thus a better climb angle.

Neil Singer is a Master CFI and a mentor pilot in Cessna and Embraer light jets. Photography by Mike Fizer.