The Wind Vector Triangle

[Guest bluepilot]

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?

[JSkorna 137]

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

[Guest bluepilot]

Good question, I should have specified - I'm using all Magnetic (ie: track and wind). I guess the trig should pan out ok as long as one is consistent, ie: stick to mag or true.Some background to my question:I have a little fuel planning spreadsheet into which I plug the True Wind Direction (from the Active Sky Nav Log), and the magnetic variation (from FS Nav) at the approx. midpoint of each route leg, giving me the Magnetic Wind Direction.It seems a long way around, but until I can figure out how to automate this I'll keep plugging away.Using the Magnetic Track from the Active Sky Nav Log, and my TAS from performance data based on Density Altitude (which raises a temperature question that I will ask another time) and power setting (both part of my spreadsheet), I'm attempting to calculate ground speed in order to ultimately calculate fuel burn.I started the spreadsheet before I purchased Active Sky, (part of my motivation in making the purchase was to thoroughly test the spreadsheet under "real" conditions) so I wasn't aware of the availability of the GS on the Nav Log. As a brief digression - using Active Sky has opened up a whole new world and this is the most fun I've had trying to prove a silly algorithm. I now approach flight planning on the sim exactly as I do in the real world. Brief-Plan-Go-Debrief.I'm very impressed that you guys get the right answer, and not overly surprised that my answer is wrong.I was hoping to pick your brains as to how you went about it as long as the basis of your GS calc isn't considered proprietary.

[Guest DNelson]

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.

[JSkorna 137]

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

[Guest bluepilot]

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.