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Can someone explain why V1 increases with headwind and decreases with tailwind? I read such a phrase in my ATPL(A) performance textbook, but without further explanation.

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V1 is the maximum airspeed you can accelerate to and then stop again without running out of runway. For the sake of simplicity, let’s assume that happens at the midpoint of the runway.

If there is a headwind, i.e. your airspeed before starting the takeoff roll is positive, then you will achieve a higher airspeed at the midpoint.

Likewise, if there is a tailwind, i.e. your airspeed before starting the takeoff roll is negative, then you will achieve a lower airspeed at the midpoint.

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    $\begingroup$ What you describe as V1 is actually only an upper limit on V1. The actual value for V1 could be lower and it could be limited by other speeds, like e.g. VR (which does not depend on wind) or Vmbe (which depends on wind speed since kinetic energy w.r.t. the ground is relevant for braking). $\endgroup$
    – Bianfable
    Nov 11 '21 at 9:31
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    $\begingroup$ You can even see that effect in a realistic simulator like X-Plane when using a glider that has a rather sensitive (regarding low air speeds) speed indicator. Or, even in more simple words: That's how kites work ;-) $\endgroup$
    – U. Windl
    Nov 12 '21 at 12:44
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Some additions to StephenS answer, here is a more detailed picture:

  • VR is the speed at which you should take off your aircraft, as defined by the aircraft weight, altitude, temperature. This is provided by aircraft performance tables.
  • V1 is the maximum speed at which you may still abort take-off while expecting a stopping before end of pavement. This depends on your aircraft ability to accelerate (thus depends on its performance: power, weight, altitude) and then to decelerate (depending on aircraft weight, brakes capacity, and (mostly!) remaining runway length).

Said otherwise, V1 is basically based on the runway length and aircraft performance-of-the-day. The closer V1 is from VR the better, as it means less time between V1 and VR for bad things to happen (e.g. engine failure).

And then, considering the wind:

  • Some headwind means your aircraft needs less time and runway distance to reach VR, leaving more runway length to decelerate in case of rejected take-off; V1 is then higher (which is good).
  • On the contrary, with some tailwind your aircraft will take more runway length to reach VR, leaving less distance (and time) for deceleration in case of rejected take-off; V1 is then lower (which is not so good).
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    $\begingroup$ indeed! updated $\endgroup$
    – Joël
    Nov 11 '21 at 9:37
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    $\begingroup$ A headwind will also decrease braking distance somewhat, while a tailwind will increase it. $\endgroup$
    – jamesqf
    Nov 11 '21 at 15:56
  • $\begingroup$ lol thanks @jamesqf i was literally about to ask that! heh $\endgroup$
    – Fattie
    Nov 12 '21 at 12:17
  • $\begingroup$ @Fattie: Don't know how much it would affect a commercial airliner, but it's very noticable in a small plane. $\endgroup$
    – jamesqf
    Nov 12 '21 at 17:40
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    $\begingroup$ @Codebling At first order of magnitude, yes, headwind does not really change the aircraft acceleration (*). But the take-off distance will significantly vary, as the time/distance to reach VR is the integration of acceleration from initial airspeed; therefore if airspeed is already positive at take-off start thanks to headwind, the aircraft will need less time and distance to reach VR. Note (*): aircraft acceleration is very likely not constant with airspeed, depending on engine type, propeller setting, etc. $\endgroup$
    – Joël
    Nov 14 '21 at 10:48
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Don't count on it, though, on turbine airplanes big enough to use "Flex" takeoffs. This is when an aircraft has "more runway than it needs" for a full-thrust takeoff at its weight, temperature, wind, etc. Therefore, they reduce thrust somewhat, trading a longer runway roll for much reduced turbine engine wear and tear.

A lot of math goes into this, since Flex is actually implemented by lying to engine computers about ambient air temperature, making it over-estimate engine pressure and temperature values, and rollback somewhat to protect the engine.

V1 is all about your last chance to abort a takeoff and still be able to stop before the end of the runway. The point along the runway varies by all the above plus your momentary ground speed.

If I were king, there'd be a rail on runway edge with a trolley, moving toward you, marking your "last abort point" at your data and ground speed. But instead, they use above data (plus assumptions about your acceleration) to capture that "last chance" point not even as a ground speed, but as an airspeed. That is V1.

Getting from "Harper's trolley" to an air speed computed prior to start of takeoff roll is also a whole lot of math.

A takeoff roll starts at a ground speed, but ends at an air speed. As such, a plane with a nice headwind has less actual accelerating to do.

Conversely a rejected takeoff starts at an air speed, but ends at a ground speed (of 0). Thus, a good headwind means less actual decelerating to do, which can happen in less runway distance. So right off the bat, V1 can happen later down the runway with a head wind.

However, other answers are only correct (V1 being higher) if you always say "who cares about turbine maintenance". As soon as Flex enters the picture, all bets are off. A runway you can use effectively in a strong tailwind will certainly warrant Flex in a strong headwind. You have two complex calculations - V1 and Flex - both using a lot of parameters. V1 may remain the same or even lower a bit.

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Simple. V1 is the airspeed that you can accelerate to and still stop on the remaining runway. Except for minor effects wind has on aircraft acceleration, a headwind or tailwind is not relevant to the groundspeed/runway remaining when this is no longer possible (this is determined more by braking/reverse thrust).
So this will occur at pretty much the same point on the runway, and at the same groundspeed regardless of the wind. Therefore, with a headwind, you will have a higher airspeed when you get to this same point on the runway.

Except for the fact that we have always done it this way, and as in all things, accepted practices resist change, it might be argued that with ground speed indicators as ubiquitous as they are today, ground speed might be a better determinant for V1 than airspeed. I would be curious to see what a more detailed analysis might indicate about that.

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