Wednesday, April 16, 2014

Understanding V2



Many of the new V-speeds first time jet pilots are exposed to are only used in the event of an engine failure.  V2, VFS, VENR, VAC- depending on the aircraft manufacturer and phase of flight (takeoff, go-around, etc.), a pilot will calculate several speeds for each takeoff and landing that he will almost certainly not need to use.  While most pilots quickly learn to compute the speeds in initial training, and use them nearly every simulator session during one simulated engine failure after another, many pilots harbor misunderstandings about what the speeds represent.

V2, for example, is often mistakenly thought to be the jet equivalent of VXSE, or single engine best angle of climb speed.  Pilots of piston and turbo-prop multi-engine 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 non-jet twins, these speeds are given 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 settings.  The first two of these speeds, V1 and VR, 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, V2 and a "final" climb speed (which goes by different names depending on the aircraft manufacturer- we'll call it VFINAL), are only used if an engine fails during the takeoff, after the point at which an abort can be safely completed.

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 V1, the pilot reacts, rotates the aircraft at VR, and climbs to a safe altitude above obstructions at V2.  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 V2 to VXSE, and VFINAL to VYSE.

In fact, it is VFINAL that correlates much more closely to VXSE.  So what does V2 represent then? 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 V1 and initiate an aborted takeoff, or continue on one engine so that the aircraft reaches V2 speed at 35' AGL.  Clearly the higher the V2 speed defined by the manufacturer, the longer the distance that will necessary to accelerate from V1 to V2 on only one engine.  Due to the desire to minimize published takeoff distances, the manufacturer often sets V2 to be the minimum allowed by certification requirements, based on minimum allowable ratios of V2 to stall speed and VMC. 

So what's the implication of V2 being a bit lower than VXSE? A brief review of basic aerodynamics will illustrate the drawback to this minimum V2 approach.  While rate of climb is determined by the excess power an aircraft has available, 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 V2 which lies below minimum drag speed, the aircraft manufacture 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 non-optimal climb at V2, most jets will turn out adequate, or even impressive, single-engine climb angles.

While not common in light jets, some larger jet aircraft have software or performance charts that allow for an optimized, rather than minimum, V2.  If takeoff distance is calculated as 4000', but 9000' of runway is available, it is easy to see that by increasing the V speeds until optimal V2 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 VXSE.  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.

Beyond the performance implications of knowing what V2 really represents, there is also a practical flight application.  While nearly all engine failures in the simulator occur just prior to V1, 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 VR 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 ten knots above V2.   Most pilots just out of sim training exhibit a strong desire to pitch the aircraft up until V2 is reached, then hold V2 until clean up altitude.

Keeping in mind the drag curve, it becomes apparent that a pilot who has attained a speed higher than V2 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 VFINAL.  Doing so will result in lower drag, and thus a better climb angle.

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