A question of winds, geometry, TAS vs GS, and the G1000

[Ragsf15e]

So not in a Mooney, sorry.  But flying home today with a very strong quartering tailwind in cruise (100+kts).  TAS was 250, G1000 says tailwind component was 27, GS was 291.  Wait, isn’t GS just TAS +/- wind??  So my ground speed should be like 277.  Nope, somehow it was in the 290s.  

Anyone know why?

[carusoam]

Interesting pic, Rags...

great focus in most places, and fuzzy near the wind data...

I was expecting that they may break the vector into two parts, xwind and headwind components...

The math would get easier that way...

GS...291 (right screen)

TAS... 249 (left screen)

Wind speed with a quartering arrow... 103

Apparently the tail wind vector of the 103kts of wind is 42kts...

There must be a button to push to display the two wind vector components...

How does that sound?

PP thoughts only, not a CFI...

Best regards,

-a-

[gacoon]

If the compass isnt dead on the wind calculations get really screwed up.  Had same problem with my aspen. 

[Ragsf15e]

10 hours ago, carusoam said:

Interesting pic, Rags...

great focus in most places, and fuzzy near the wind data...

I was expecting that they may break the vector into two parts, xwind and headwind components...

The math would get easier that way...

GS...291 (right screen)

TAS... 249 (left screen)

Wind speed with a quartering arrow... 103

Apparently the tail wind vector of the 103kts of wind is 42kts...

There must be a button to push to display the two wind vector components...

How does that sound?

PP thoughts only, not a CFI...

Best regards,

-a-

The wind is broken down into xwind and tailwind right next to the TAS, just above/left of the hsi.  Shows 27 kts tail and 99 xwind.  I think gacoon is onto something though... a couple degrees on the compass might do it.  There are 2 ahrs, each pfd has its own, and they are normally off a degree or two from each other.

[Bob - S50]

Here's what I think is happening.

The XW/TW are shown relative to your aircraft heading.  GS is NOT relative to your heading, but rather your track along the ground.

Using the Pythagorean principle I get the wind to be 102.6 knots (wind² = XW² + TW²).  Using sin(offset angle) equals 27/99 I get that angle to be 15.255 degrees relative to your heading.  Taking your heading to be 061 degrees, that makes the wind roughly 046 degrees at 102.6.

Taking the angle between the wind (046) and the track (080) I get 34 degrees.  Velocity made good (VMG)/Actual wind = sin(34). Take that times the wind of 102.6 and you get VMG due to the wind of 57.37 knots.

Looking at the HSI, it looks like you have about a 19 degree crab due to crosswind (80 - 61).  Using cos(19) = TAS/VMG, I come up with 235 knots of your TAS actually pushing you along your route.

235 (due to TAS) + 57 (due to wind) and you get 290 knot GS.

Good enough for government work.

[Ragsf15e]

30 minutes ago, Bob - S50 said:

Here's what I think is happening.

The XW/TW are shown relative to your aircraft heading.  GS is NOT relative to your heading, but rather your track along the ground.

Using the Pythagorean principle I get the wind to be 102.6 knots (wind² = XW² + TW²).  Using sin(offset angle) equals 27/99 I get that angle to be 15.255 degrees relative to your heading.  Taking your heading to be 061 degrees, that makes the wind roughly 046 degrees at 102.6.

Taking the angle between the wind (046) and the track (080) I get 34 degrees.  Velocity made good (VMG)/Actual wind = sin(34). Take that times the wind of 102.6 and you get VMG due to the wind of 57.37 knots.

Looking at the HSI, it looks like you have about a 19 degree crab due to crosswind (80 - 61).  Using cos(19) = TAS/VMG, I come up with 235 knots of your TAS actually pushing you along your route.

235 (due to TAS) + 57 (due to wind) and you get 290 knot GS.

Good enough for government work.

That’s definitely plausible.  I’ll try to read some of the g1000 documentation and see if they define exactly what they mean by xw / tw to see if it’s referenced to heading or course.  The Garmin documentation is sometimes very good and other times lacking in things that seem like they should be covered.

[EricJ]

I've had this happen as well.   Here is a TAS of 151 kts, a 61 kt wind with a 12 kt headwind component, and a GS of 151 kts.    Seems weird to me.   I haven't done the trig, but I'd have expected to slow down *some* due to a 12 kt headwind component.   It shows a HDG of 039, winds estimated 320 at 61 kts.    Weird.


 

[Yetti]

We have data and then the computer makes information out of it.  Then the human uses the information.     My second flight I found that with the wind and cross wind data displayed do I need to get the weather from the ground station.     The first airport that I landed at did not have weather, so I just looked at the screen.    Then when coming back I was fiddling around by the airport taking pictures, so forgot to tune in and get the winds.  Which I remembered on Final, so no big deal a quick glance and I had what I needed to know.   Now the other side of that is this conversation and how accurate is it and should it be relied upon.    The other side is I don't really pay that much attention to the radio reported winds past determining which runway.   After that you just fly the airplane to what the winds tell you to.

[Ragsf15e]

46 minutes ago, Bob - S50 said:

Here's what I think is happening.

The XW/TW are shown relative to your aircraft heading.  GS is NOT relative to your heading, but rather your track along the ground.

Using the Pythagorean principle I get the wind to be 102.6 knots (wind² = XW² + TW²).  Using sin(offset angle) equals 27/99 I get that angle to be 15.255 degrees relative to your heading.  Taking your heading to be 061 degrees, that makes the wind roughly 046 degrees at 102.6.

Taking the angle between the wind (046) and the track (080) I get 34 degrees.  Velocity made good (VMG)/Actual wind = sin(34). Take that times the wind of 102.6 and you get VMG due to the wind of 57.37 knots.

Looking at the HSI, it looks like you have about a 19 degree crab due to crosswind (80 - 61).  Using cos(19) = TAS/VMG, I come up with 235 knots of your TAS actually pushing you along your route.

235 (due to TAS) + 57 (due to wind) and you get 290 knot GS.

Good enough for government work.

I actually think you nailed it.  Here’s an excerpt from the G1000nxi manual (mine is not an nxi however).  It doesn’t say “relative to heading”, but it does say “relative to the aircraft”, so close enough for government work as you say.
 

[EricJ]

1 hour ago, EricJ said:

I've had this happen as well.   Here is a TAS of 151 kts, a 61 kt wind with a 12 kt headwind component, and a GS of 151 kts.    Seems weird to me.   I haven't done the trig, but I'd have expected to slow down *some* due to a 12 kt headwind component.   It shows a HDG of 039, winds estimated 320 at 61 kts.    Weird.

So this does actually work out, and it's not intuitive.    I dragged out one of my ancient E6-Bs and was going to work this out on that, but the circle is less than 61kts around.   There are two online sites that work well, though, and that both gave consistent and useful results:

I used the Course, Ground Speed, And Wind Correction Angle box on each.

http://www.csgnetwork.com/e6bcalc.html   

https://e6bx.com/e6b/   

They both indicated a 152 kt GS, course of 069, and a 23 degree wind correction angle.    The 12 kt headwind still sounded funny, but working out the trig, with the winds at 320 at 61 and a heading of 039, the wind is 79 degrees off the nose, so 61*cos(79) = 11.63 kts.   So that works out, too.    As mentioned, in this case there's a big angle between the course and the heading, so the 61 kt wind at 320 is actually a small tailwind to the 069 course.   The wind is actually 13 degrees off the tail of the course, so 61*sin(13) = 13.7 kts tailwind.   The small difference, 13.7 - 11.63 = 2kts.    Rounding errors and other effects make this all pretty consistent.

I have a friend who sails who always kids me about tacking in the wind with the airplane, but apparently you can! 

EDIT:  So the net effect was a 1kt increase in ground speed with a 12 kt wind on the nose.   It works!

Edited January 10, 2020 by EricJ

[Danb]

Nicely done bob btw you have to much time on your hand.

[carusoam]

MS has some applied math geniuses, not just the Prof.

Thank you gents for sharing the calcs!
 

It’s a big Xwind when your plane is pointing a ways off from the direction you are going.... 

Best regards,

-a-

[EricJ]

Another way to look at it is that a crosswind with a small tailwind component relative to a course, if strong enough, will require a large enough correction angle to generate a significant headwind component relative to the aircraft. If the aircraft headwind component with the correction is not as large as the original course tailwind component, you may still have a net increase in ground speed, despite having a "headwind" component.

 

The more I think about this the more it is pretty obvious in hindsight, but I just never thought of it like this before. This was an extreme case for me with essentially a 61 kt crosswind, and still only netted a 1-2 kt increase in ground speed, but with a 12 kt "headwind" relative to the aircraft.

[ArtVandelay]

Trying to follow a geometry discussion is a lot easier with diagrams, ditto with quantum physics (Feynman diagrams).

BTW, this is why we seem to have headwinds most if the time, even if winds are have tailwind component, to get to our destination we have to point into the wind because of the strong cross wind component.

[Ragsf15e]

On 1/10/2020 at 10:54 PM, ArtVandelay said:

Trying to follow a geometry discussion is a lot easier with diagrams, ditto with quantum physics (Feynman diagrams).

BTW, this is why we seem to have headwinds most if the time, even if winds are have tailwind component, to get to our destination we have to point into the wind because of the strong cross wind component.

Sorry to bring this one back to life because I think @Bob - S50 and @EricJ nailed it, but here’s one showing a HW computed but my GS is faster than my TAS?  So usually turning into that wind to hold course makes us slower but…

[Ragsf15e]

On 1/10/2020 at 11:20 AM, EricJ said:

So this does actually work out, and it's not intuitive.    I dragged out one of my ancient E6-Bs and was going to work this out on that, but the circle is less than 61kts around.   There are two online sites that work well, though, and that both gave consistent and useful results:

I used the Course, Ground Speed, And Wind Correction Angle box on each.

http://www.csgnetwork.com/e6bcalc.html   

https://e6bx.com/e6b/   

They both indicated a 152 kt GS, course of 069, and a 23 degree wind correction angle.    The 12 kt headwind still sounded funny, but working out the trig, with the winds at 320 at 61 and a heading of 039, the wind is 79 degrees off the nose, so 61*cos(79) = 11.63 kts.   So that works out, too.    As mentioned, in this case there's a big angle between the course and the heading, so the 61 kt wind at 320 is actually a small tailwind to the 069 course.   The wind is actually 13 degrees off the tail of the course, so 61*sin(13) = 13.7 kts tailwind.   The small difference, 13.7 - 11.63 = 2kts.    Rounding errors and other effects make this all pretty consistent.

I have a friend who sails who always kids me about tacking in the wind with the airplane, but apparently you can! 

EDIT:  So the net effect was a 1kt increase in ground speed with a 12 kt wind on the nose.   It works!

Maybe there’s something to your “tacking into the wind”… with this one I’ve got a headwind that’s giving me added groundspeed??  Since when does a 7kt hw component net a 10kt increase in groundspeed??
 

[exM20K]

@Ragsf15e do they tie out when the winds aloft are light and/or more aligned with the track?

The Acclaim POH has an IAS->CAS adjustment table which adds a knot or three.

-dan

[Ragsf15e]

1 hour ago, exM20K said:

@Ragsf15e do they tie out when the winds aloft are light and/or more aligned with the track?

The Acclaim POH has an IAS->CAS adjustment table which adds a knot or three.

-dan

Yes, they are perfect when more aligned with the track.  The IAS does have a small correction, but it’s basically unnoticeable clean/cruise.  It’s only when there’s a large crosswind component that this becomes noticeable.  I think @EricJ had it right in the way garmin does the trigonometry  doesn’t necessarily work out well between the heading, course, and wind components with a perfect crosswind.