Calculating Headwind/Tailwind component

Most flight computers nowadays calculate wind vector, but only few calculate headwind/tailwind component, which, in my opinion, is almost equally important, since it tells you if your glide over terrain/final glide is going to suffer or benefit from the wind component, as well as help you estimate your task speed. When the vector wind is cross, it is hard to estimate if it results in HW or TW component (as it is factor of wind speed, direction and glider speed).
Thankfully, some flight computers such as 302 provide TAS, so my solution was always to subtract TAS from ground speed to determine HW/TW component, but I am surprised that not all flight computers use this simple calculation to provide instantaneous HW/TW component. After discussing it with some, it was suggested that my assumption is wrong, and that HW != TAS-GS when cross wind is presented. I am not sure why though.
Thoughts?

Thanks,

Ramy

Ramy wrote:
Thankfully, some flight computers such as 302 provide TAS, so my solution was always to subtract TAS from ground speed to determine HW/TW component, but I am surprised that not all flight computers use this simple calculation to provide instantaneous HW/TW component. After discussing it with some, it was suggested that my assumption is wrong, and that HW != TAS-GS when cross wind is presented. I am not sure why though.

This formula is correct:

Wind = TAS - GS

... but only if you use vectors. If you use only the magnitude, you're
wrong, because you're ignoring the direction of these vectors.

Taking an extreme example: your airspeed is 40kt, wind is 30kt from
the right (i.e. no head wind). You would think that your ground speed
is 40kt because you have no head wind. But since the cross wind
displaces you, your ground speed is really 50 kt (according to
Pythagoras: square root of 30^2 + 40^2).

Btw. XCSoar shows head wind component in an InfoBox. The true one.
And if you have airspeed input (e.g. with a CAI302), you get wind in
straight glide nearly instantly.

Max

I gues this is where the confusion is. In your example, you indeed have 10 knots tail wind in the direction you heading. You assumed the wind is 90 degrees, but it is not since you drifting. Now if instead you crab to maintain heading, the tail wind component will change to head wind. So this is proving again that my formula is correct. This is the true head wind/ tail wind component as far as the glider see it, which is ultimately what impact your ground speed and glide perfromance over the terrain.

Ramy

On Tuesday, March 13, 2012 7:51:26 PM UTC-7, Ramy wrote:
I gues this is where the confusion is. In your example, you indeed have 10 knots tail wind in the direction you heading. You assumed the wind is 90 degrees, but it is not since you drifting. Now if instead you crab to maintain heading, the tail wind component will change to head wind. So this is proving again that my formula is correct. This is the true head wind/ tail wind component as far as the glider see it, which is ultimately what impact your ground speed and glide perfromance over the terrain.

Ramy

To clarify more, my formula is not Wind = TAS-GS, it is HW component = TAS-GS. This is the true head wind component as I explained. XCSoar does not currently show the true head wind based on TAS-GS, instead it is calculating it from the vector head wind which is not as accurate.

Ramy

Hi Ramy,

See http://williams.best.vwh.net/avform.htm#Wind
This may clarify it for you.

Your formula is only correct if the wind is parallel to your ground track. It also approximates the correct value when wind speed is much smaller than airspeed.

I think Ramy is correct in this. In his calculation he is basically
assuming that he is flying his true heading - that is, he has adjusted his
true course to compensate for wind. Because of this, all of the vectors
become co-linear.

- Jim




Ramy

To clarify more, my formula is not Wind =3D TAS-GS, it is HW component
=3D
=
TAS-GS. This is the true head wind component as I explained. XCSoar does
no=
t currently show the true head wind based on TAS-GS, instead it is
calculat=
ing it from the vector head wind which is not as accurate.=20

Ramy

On Wednesday, March 14, 2012 12:15:16 AM UTC-7, Jim Wallis wrote:
I think Ramy is correct in this. In his calculation he is basically
assuming that he is flying his true heading - that is, he has adjusted his
true course to compensate for wind. Because of this, all of the vectors
become co-linear.

- Jim




Ramy

To clarify more, my formula is not Wind =3D TAS-GS, it is HW component
=3D
=
TAS-GS. This is the true head wind component as I explained. XCSoar does
no=
t currently show the true head wind based on TAS-GS, instead it is
calculat=
ing it from the vector head wind which is not as accurate.=20

Ramy


Precisely Jim. The formula is based on the glider track relative to the ground. Subtracting GS from TAS (assuming your flight computer provides both) will always give you a precise instantaneous head wind/ Tail wind component in the direction you heading (not the direction your nose is pointing) which is really what matters to your glide performance over the ground, and to your ground speed. The formulas that other mentioned is only relevant if you wanted to calculate the head wind in the direction your nose is pointing, but there is no real value in it.

Ramy

In article m Jim Wallis writes:
I think Ramy is correct in this. In his calculation he is basically
assuming that he is flying his true heading - that is, he has adjusted his
true course to compensate for wind. Because of this, all of the vectors
become co-linear.

- Jim




Ramy

To clarify more, my formula is not Wind =3D TAS-GS, it is HW component
=3D
=
TAS-GS. This is the true head wind component as I explained. XCSoar does
no=
t currently show the true head wind based on TAS-GS, instead it is
calculat=
ing it from the vector head wind which is not as accurate.=20

Ramy




If Ramy is flying due north at 40 kt, with a 10 kt wind from the east,
he will need to be crabbing into the wind to maintain his ground track.

With his true airspeed of 40 ktas, his true heading will be about
14.48 degrees, and his groundspeed will be about 38.73 kts. His true
course will be 0 degrees.

Relative to his true course, his headwind component is 0 kts.
Thus, TAS - GS = 40 - 38.73 = 1.27 kts.


If you convert that wind from the east into components towards his
nose and towards his right wing, then you get 2.5 kts on the nose, and
9.68 kts on the right wing. When you compute his resultant velocity
from 40 - 2.5 kts forward, and 9.68 kts sideways, you get the same
groundspeed as computed before, about 38.73 kts.


The basic problem is that it is generally meangless to compute TAS -
GS, as those are scalar magnitudes of vector values, and the vectors
are rarely colinear.


Alan