# The Wind Vector Triangle

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I hope that this post is considered within the scope of this forum, but I figured that this is where I would be most likely to find someone with the skill and interest to help me with my problem.Solving the wind vector triangle, I came up with this formula: Ground speed = Square root of (wind speed squared + true airspeed squared - 2 x wind speed x true airspeed x cosine (wind direction - track))On a flight where TAS 250, Wind 270/55, Track 139With a calculator I get an answer of Ground speed = 288.7 kts.This agrees with a solution worked out on my Aristo AVIAT 617 (Wizz wheel) nav computer which showed 289 kts.My Sporty's E6B "Electronic Flight Computer" comes up with an answer 282.2 kts.An Active Sky (B174) Navlog report shows 282 kts.While in flight on the sim under these conditions I achieved 282 kts.It seems that unlike me, the clever Active Sky chaps can do their sums right. In spite of being in the illustrious company of the inventor of the trusty old wizz wheel, what is wrong with my formula?

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Are you using True wind direction or Magnetic wind direction?Hope this helps,JimActiveSky Sales and Supporthttp://www.hifisim.com/images/as2004proudsupporter.jpg

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It's been a while since I've done any real-world flight planning, but as I recall, winds aloft are always forecast and reported using True North. Surface wind METARs and TAFs are of course magnetic. I'd never thought about this, but I wonder if the wind vector shown in Active Radar is mag or true.

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I believe it is True North.Hope this helps,JimActiveSky Sales and Supporthttp://www.hifisim.com/images/as2004proudsupporter.jpg

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In both the real world and the sim, surface winds are reported Mag and winds aloft are reported True.In the Sim, there is a "surface layer", which has a ceiling (stored in metres, oddly enough), below which the ambient wind is Mag, and above which it is True. The little red numbers you see if you press "Shift-Z" are always Mag, with magnetic Variation applied above the "surface layer".I have proven this with an FSBUS CCC circuit that considers the surface layer and the Magnetic variation as required, and have a "cheat gauge" on my panel that consistently shows Magnetic wind direction and speed whether on the ground or high in the sky.The Active Sky TAFs METARs and Nav Log correctly report surface winds Mag and winds aloft True.When I set the Active Sky Aloft Predictability to 100%, my gauge agrees with the TAF/Nav Log. I need no more proof than that, that my opening statement in this little tirade is true.Whether winds aloft are true or mag, however, is not my question.If you attempt to solve a wind vector problem using magnetic course (track) and true wind direction you will never be able to solve for ground speed unless you consider magnetic variation. Agreed? Or am I being stupid here?I need help to fix my flawed formula. In it I use Mag course (track) being the path over the ground that the aircraft follows in flight, irrespective of where the nose is pointed, derived from the Active Sky Nav Log. I also use Mag wind direction, where the local Magnetic variation is applied to the Active Sky Nav Log True wind direction. I should be able to solve for ground speed using trig.So with my formula in the one camp we have my answer, and the Aristo wheel. In the other camp, we have Active Sky, the Sporty's E6B, and what actually happens in the Sim.You can see why I prefer the Active Sky groundspeed, I just can't seem to see what I am doing wrong.

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