True heading and Wind direction

Hello,

Given I have wind value, wind direction and true direction

May i know if in matlab, we have a function which resolves the wind into components parallel and perpendicular to my true direction?

In the end, I want to know if we have headwind or tailwind component?

Thanks

Answer 1

[Star Strider]

There isn’t one specifically, but you can create one easily enough:

windhx = @(C,W,S) S*[sind(abs(C-W)); cosd(abs(C-W))];       % [Crosswind; Headwind] = windhx(Course, WindDirection, WindSpeed)

This takes aircraft course ‘C’ (the direction of intended flight), wind direction ‘W’, both in degrees, and windspeed ‘S’, in whatever units you want (usually knots). It produces a (2x1) vector of crosswind component in the first row, and headwind component in the second row. Negative values indicate a Left crosswind and a Tailwind, respectively.

See the Wikipedia article on Tailwind for more information.

[yashvin]

Hi thanks for your suggestion.

I tried the Wikipedia example. Find below my codes

How do we run it? This "@" is new to me. Is it a function?

windhx = @(C,W,S) S*[sind(abs(C-W)); cosd(abs(C-W))];      

[Crosswind Headwind] = windhx(Course, WindDirection, WindSpeed)

Course=240
WindDirection=90
WindSpeed=15

[yashvin]

And does it apply for any wind direction and course? Any general formula you would suggest?

[yashvin]

I was trying for many combinations of course and wind direction. If its in the same direction of my course, I simply want to add it and otherwise subtract it.

I am trying to make it work irrespective of the difference between the course and the wind direction ( even when the difference is greater than 90)

Any suggestion?

[Star Strider]

My pleasure.

The ‘@’ denotes a function handle, in this instance, to an anonymous function. (See the documentation on Anonymous Functions for details.) It applies to any wind direction and course, with the exception that 360° must be entered into the function as 0°.

The function I posted is entered on one line. The comment to the right of it on the same line (denoted by the beginning ‘%’) is documentation to show how the function should be used, and is not part of the code.

For your arguments, it gives an appropriate answer:

Course=240
WindDirection=90
WindSpeed=15

CrossWind_Headwind = windhx(Course, WindDirection, WindSpeed)

CrossWind_Headwind =

       7.5000
     -12.9904

So the airplane is flying southwest with an easterly wind 09015, resulting in a easterly crosswind component of 7.5 and a tailwind of 12.99.

One clarification from my earlier post that sorts all ambiguities about Left and Right crosswinds is in this slight revision of my earlier function:

windhx = @(C,W,S) [S; S].*[sind(abs(C-W)).*sign(C-W); cosd(abs(C-W))];  % Course, WindDirection, WindSpeed = [Crosswind; Headwind]

Here, a positive crosswind is always a left crosswind, and a negative crosswind is always a right crosswind. I tested it with a number of different courses and wind directions. A negative headwind component is a tailwind regardless.

As for a general formula, this is about as general as it gets.

[yashvin]

HI

I had a look at the documentation for the Anonymous handle documentation.

My main aim was to calculate the True Air Speed given ground speed and wind value and direction. So, once I know whether it is a headwind or a tailwind, I can do the necessary calculation with it.

Find below the codes that I had written. It is in a function though.

function [Tas]= GS_to_Tas(True_heading,Wind_direction,Wind_speed,Ground_Speed)

Wind_parallel=Wind_speed.*[cosd(abs(True_heading-Wind_direction))]

GS_length=length(Ground_Speed)

Tas=zeros(1,GS_length)

for i=1:GS_length

if (Wind_parallel(i) > 0) % headwind case

      Tas(i)=Ground_Speed(i)-Wind_parallel(i);

else % tail wind

      Tas(i)=Ground_Speed(i)+Wind_parallel(i);

end

end

All my input parameters are an array of numbers.

Is my approach correct for selecting whether it is a headwind or a tailwind?

Thank

yashvin

[yashvin]

One more question, for the computation of the headwind/tailwind component via

cosd(abs(C-W))

removing the absolute will not have impact , right?

[Walter Roberson]

Removing the abs() will have an impact if complex quantities are involved.

[Star Strider]

First, true airspeed (TAS) is a complicated calculation involving indicated airspeed (IAS) and density altitude. Groundspeed incorporates that and the wind direction and velocity at altitude. Note that to fly a particular course, you not only have to account for headwind, but to adjust the airplane heading, ‘crabbing’ into the crosswind. This will decrease your groundspeed, because some of your indicated airspeed is going to counter the crosswind component. If you fly an uncorrected course, you will be off course by whatever the crosswind component is and the length of your flight. Don’t ignore the crosswind component in any of your calculations.

GPS will of course give you groundspeed without having to do all the TAS calculations. If you’re flying a GPS course, you don’t have to bother with any of the other calculations. Just adjust your heading to fly your chosen course.

I don’t understand the code you posted. It’s not how I would calculate TAS. See the Wikipedia article on True airspeed for a full discussion.

Note that my most recent ‘windhx’ function is designed to be vectorised. If you give it row vectors of course, wind direction, and wind speed (all the same length), it will produce a matrix with the crosswind in the first row and headwind in the second row for each triplet of input arguments.

Second, removing the absolute from both headwind and crosswind calculations will have impact. At least it did when I experimented with it. That’s the reason I wrote the function as I did.

[yashvin]

Thx. You are perfectly right. I was ignoring the crosswind. It is going to have an impact on the TAS. The correct approach i guess i using the Mach number. Thx again : )

[Star Strider]

My pleasure!

The Mach number for a jet is likely the most accurate indication of TAS. Groundspeed necessarily incorporates the headwind or tailwind, and correction for the crosswind component. If you consider the headwind and crosswind components as a right-triangle, the hypotenuse is the indicated airspeed (or TAS or Mach number if you have those data). Make the appropriate transformations to calculate groundspeed.

When you have the time, learn to fly, preferably getting your Instrument Rating so you will fully understand the Air Traffic Control system and high-altitude flight. It’s fun, and it will give you a practical understanding of everything you are currently studying in your research.

[yashvin]

Yea I am trying to learn flying in parallel! I am trying to use both the Mach number approach(using the static temperature) and wind velocity triangle approach to get the TAS. Theoretically I believe both results should be same! Let me check and confirm with you.

Initially, I was resolving the wind component and taking only the component that is parallel (either head or tail) and do the addition with the GS. I was neglecting the crosswind component.

Keep you posted and thanks for your word of encouragement!

Yashvin

[Star Strider]

Go for your Instrument Rating! It took me about 1½ years to go from my first flying lesson to passing my Instrument check-ride (on the first go!), and filing IFR allowed me to fly anywhere the airplane could manage.

They should be the same, but you have to know the air density at altitude as well as the winds at altitude.

Thank you! I’m interested in what you’re doing.

[yashvin]

I have been also trying to understand the airspeed.

From IAS-CAS(Calibrated)-TAS- GS. I am currently doing data decoding (from flight) and from your experience, is the calibrated airspeed and the computed airspeed the same?

I tried looking on the net but from IAS to CAS (computed) , the say only compensate for instrument errors. IS the COMPUTED airspeed the same as the CALIBRATED air speed?

[Star Strider]

‘Computed’ airspeed is new. It must be new to Wikipedia as well, since it doesn’t appear there either, and isn’t in any of the FAA and AOPA references I usually use. My impression is that it is airspeed calculated from GPS data, including speed and altitude, as well as ambient pressure and temperature. I can’t find a good, quantitative or mathematical definition of it. (For some of the others, the Simulink Aerospace Blockset documentation has interesting information you might want to explore. I was aware of it, but I never looked through it, since I don’t have the software.) See Ideal Airspeed Correction for details.

This site Airspeed Indicator has the clearest discussion I’ve been able to find:

• ‘The computer compensates also for position errors which is called the Computed airspeed. The Computed airspeed is used the calculate the CAS.’

The rest of the article puts this in context.

So my impression is that the calibrated airspeed and computed airspeed might yield the same numbers, but they are arrived at differently. I would say they are not the same.

One thing I’ve learned from our discussions is that airspeed is not as straightforward as I always thought it was. I knew of TAS, CAS, and IAS, but never needed to go much beyond those in my flight planning and flying.

[yashvin]

Thanks for your tips regarding the computed air speed. Yes, I had trouble finding out the computed airspeed definition on the net! Even as you noticed, in Wikipedia, its not defined.

Currently, I have my true heading, true wind direction, wind speed. Using the formula you showed me previously, I can obtain either the headwind/tail wind and the crosswind.

Given I do have my groundspeed, I can find my effective TAS but my real TAS can obtained only if i include the crosswind component.

Lets take an example

Course=330.7324
WindDirection=190.5469
WindSpeed=25

windhx = @(C,W,S) [S; S].*[sind(abs(C-W)).*sign(C-W); cosd(abs(C-W))];  % Course, WindDirection, WindSpeed = [Crosswind; Headwind]
CrossWind_Headwind = windhx(Course, WindDirection, WindSpeed)

My groundspeed is

GroundSpeed=483

And the result is

CrossWind_Headwind =

    16.007602765057563
   -19.203037616901174

This means I am having a tail wind

So

Eff_tas=483+19.20

And my

real_tas=sqrt(Eff_tas^2 + 16.007^2)

Is it correct?

[yashvin]

Sorry I corrected the last lines

So

Eff_tas=483-19.20

real_tas=sqrt(Eff_tas^2 + 16.007^2)

[Star Strider]

TAS is simply the aerodynamics of the aircraft in flight, with IAS corrected for air density (density altitude). Wind doesn’t enter into the calculation.

Your ‘real_tas’ calculation seems more like groundspeed to me.

[yashvin]

[yashvin]

From above pic, please confirm

GS=174
TAS=182
True Wind direction=234
WindSpeed=10
TrueHeading=195

Crosswindcomponent=10sin(39)

Wind_parallel=10cos(39)

Eff_tas=174+10*cos(39)=181.7715
Crosswind=10sin(39)=6.2932

And

real_tas=sqrt(Eff_tas^2 + Wind_parallel^2)=181.88 (almost 182)

Can you please confirm my true heading is really 195 from the PFD?

[Star Strider]

Your calculations seem consistent with those that the flight management system (FMS) is reporting.

I never flew with a FMS, only the more prosaic ‘T’ instrument cluster, and a hand-held GPS for backup.

The heading indicator (HI) on the right here, is always magnetic, not true. This dates back to the ‘whiskey compass’ days before gyros, and all runway headings are numbered as being the closest integer 10° to their compass heading (so RWY 17-35 would be about 170°-350° magnetic). Wind directions at altitude are given in true directions, so you have to correct the wind direction for the local magnetic deviation.

This jet has just intercepted the glideslope at 2000 feet above the runway TDZ elevation (given by the GPS), and is flying the localizer on a magnetic heading of 195° to land on RWY 19. At that elevation, is is still crabbing into the wind. It will transition to a sideslip into the wind at about 200 feet above the TDZE.

I can’t tell if the wind direction is true or magnetic, although while upper level winds are always reported as true, the control tower (and ATIS) give the local wind direction as magnetic.

The problem is that I don’t know what the FMS knows. My GPS calculates true and magnetic direction, reckoning true from my location w.r.t. the true north pole, and magnetic from its own magnetic compass. So is the FMS calculating and reporting true or magnetic wind direction? You would have to determine that from the FMS documentation.

With those reservations, I agree with your observations. I just cannot determine how it is reporting wind direction (calculating from the airplane’s crab angle and airspeed). From the pilot’s perspective, the pilot is flying the localizer and glideslope and adjusting the airplane’s attitude and power settings appropriately. It is helpful to know the crosswind velocity, but only if it close to the maximum certified crosswind component for the airplane, usually about 15 kts. (The highest crosswind I ever landed in was 12 kts. It was fortunately steady and not gusting, but exciting nonetheless!) Keeping the upwind wingtip from being the first part of the airplane to touch down is the challenge in a crosswind landing.

[yashvin]

Thanks again for your detailed explanation. The data i decoded are "true" one. Be it the wind direction and my true heading. For the FMS, i need to check which one they are displaying. Any particular link you know which helps to know this. I had a look a some online doc from Airbus regarding the Flight Instrument. But so far no clue.

If my heading shown on the FMS was "true", then we could have nailed it down.

I am learning the Instrument by myself though i would want some guidance be it online sources. I really appreciate your practical experience insights.

[Star Strider]

My pleasure.

I’m not sure what to suggest with respect to information on flight management systems (FMS). See the Wikipedia pages for Flight Management Systems and Electronic Flight Information Systems. Beyond that, I would see the individual manufacturers’ sites, such as these from Bendix-King and Rockwell-Collins. They also have downloadable desktop trainer software, although I’ve not used them. Still another option are flight simulators by Microsoft and others. Since I’ve not flown with and EFIS system, your best option is probably to ask someone at your airport who has experience with it. (My EFIS was a handheld E6B electrionic calculator!)

However, all aircraft navigate using magnetic directions, not true directions. This creates a bit of confusion only when distinguishing ‘true direction’ (with reference to the geographic north pole, not the magnetic north pole, in addition to considering magnetic deviation that changes with geographic location) from ‘true airspeed’ (that has nothing to do with compass direction) and other such. They have different meanings in different contexts.

[yashvin]

I manage to find a snapshot with true heading mentionned on it. I was examining the the function above which takes as input the "course"(intended direction of flight as you have mentionned). During flight is the true heading and course same.?

I am using the true heading for this course parameter. The other variable i do have is my true track.

I came across this in wiki:

In the event of a headwind or tailwind, heading and course in an aircraft are the same. For a ship at sea, if a current is running parallel to the heading, then the course is the same as the heading.

https://en.wikipedia.org/wiki/Wind_triangle

Using the values from the 2 pic above and the function, I did get approx the same TAS values.

Please do confirm

Thanks for all your help!

[Star Strider]

‘True’ directions may be given for transoceanic flights, but since I don’t have an Airline Transport Pilot Certificate (where I would be required to know that information), I will defer to your assessment that the heading indicator gyro is indeed flying a true — and not magnetic — course, as the electronic flight information system (EFIS) indicates.

I don’t know what the EFIS is reporting in terms of course or heading. I suspect the airplane is on autopilot, following the GPS course and displaying only the course and not the heading, but I don’t know for sure. That would probably be at the pilot’s discretion.

Course and heading are not necessarily the same. Course is the path over the ground (or ocean) that the airplane is flying, and heading is the orientation of the airplane with respect to true (or magnetic, as applicable) north pole. So with a crosswind, heading will be different from course. With no crosswind, they will be the same. The Wikipedia article is slightly ambiguous on that point in the sentence you quoted.

Your airplane seems to be flying over northern Canada on a 067° true course, with a 46 kt tailwind. If that’s a YouTube video, I’d be interested in the URL for it.

[yashvin]

Hi

There you go for the youtube url :

https://www.youtube.com/watch?v=K3oRKmZ5qQg

I will get back to you for more updates :)

Thanks

Yashvin

[Star Strider]

My pleasure.

Thanks for the link.

[yashvin]

One more question for your last comment:

"Your airplane seems to be flying over northern Canada on a 067° true course, with a 46 kt tailwind. "

From wikipedia, the relationship between groundspeed, tailwind and headwind is:

Ground speed can be determined by the vector sum of the aircraft's true airspeed and the current wind speed and direction; a headwind subtracts from the ground speed, while a tailwind adds to it.

The last line from Wiki was a little bit confusing.

Suppose the tailwind was 46 kt and the GS=621 knots. I was thinking then my TAS was 46+621 knots which was wrong!

I came across this in a forum

Ground Speed = Air Speed (plus or minus) Wind Speed.

If you get a head wind, then you have to subtract the wind speed and if you have a tail wind, you add it to your airspeed. Thus, in your case, the air speed on the Boeing 737 was 520 mph, and your tail wind was 228 mph giving you a ground speed of 748 mph. A 228 mph tailwind is not impossible in a jet stream

This was from

http://www.askcaptainlim.com/flying-the-plane-flying-90/75-were-we-breaking-the-sound-barrier-or-was-this-a-false-reading.html

May be you can share your experience regarding the relationship with the displayed TAS, GS and wind

Thanks

yashvin

[Star Strider]

Those references are talking about a pure headwind or tailwind, and in that regard, they’re correct. ‘Airspeed’ flying a given course however is not TAS unless the wind is a pure headwind or tailwind.

If you have a crosswind component, you have to ‘crab’ into it to stay on course, reducing your effective airspeed. Your indicated TAS is the hypotenuse of the wind triangle, and your actual airspeed is the ‘adjacent’ side of the triangle. You then add the headwind or tailwind component to the ‘adjacent’ value to get your groundspeed.

If you can get hold of an old-fashioned mechanical E6B calculator, you can get a graphical interpretation of this idea. This E6B instruction manual from Sporty’s Pilot Shop will explain it. (Come to think of it, since you’re learning to fly, buy an E6B and learn to use it. It’s an education all its own.)

[yashvin]

You know right now, after decoding the data, I am only having GS, true wind direction and wind speed. I need to do the opposite i.e identify the crosswind and then substract or add the "adjacent" component to the ground speed and get the corresponding TAS (hypotenuse)-thats the indicated one as you said.

Our data that are being decoded do not contain the TAS. Thats why i need to validate the calculation from a known TAS result and eventually apply it to our data.

The next step is integration of the TAS with time leading to the air distance flown because once again this do not form part of our decoded data. Thanks for your recommendation! I hope I can order it online !

[yashvin]

One more thing I can add is that from the decoded data, the parameters are listed as :

1. true heading

2. true track angle

I believe by track they means course . Is it ambiguous?

[yashvin]

In the E6B page,

I tried for these combinations-pg 32

GS=120

Wind Speed=104

True heading=160

True course=180

Tas=140

Using the same steps:

TAS_calculated=sqrt((120+50*cosd(76))^2+(50*sind(76))^2) leads to 140.7234

One important thing is that of if i use the heading instead of the course, I would get the wrong result -which is fully justified.

So in my decoded data, I believe i should be using the true track angle instead of the true heading!

Correct?

[Star Strider]

I’m not sure what ‘track angle’ is. Do you mean ‘course’?

As I understand what you wrote, you have wind speed and direction at altitude, course (direction over the ground the airplane is flying), and groundspeed.

You want to calculate airspeed and heading (direction the airplane is flying to maintain course in the presence of a crosswind). The secd function may be helpful here to calculate the hypotenuse of the wind triangle.

[yashvin]

Thanks for your suggestion!

Yes, I believe by "true track angle" they actually meant course. I compared the "true heading" to the "track angle" values. They are almost the same..sometimes with a deviation of at most 5 degrees. So, as you explained, sometimes the true heading and the course might different due to effect of the wind.

So by true track angle , they are meaning course!

I will analyse the data and compare the values and get back to you!

Thanks and Keep you posted

[Star Strider]

My pleasure.

The terminology is indeed confusing. Does your source define their terms anywhere? It will help greatly if they do.

[yashvin]

No they dont! Thats why I was somehow crazy with it! After decoding, i tried to infer from the data.

I believe they must have defined it somewhere but it is not openly available!

Stay in touch Yashvin

[Star Strider]

That is indeed regrettable!

What sort of flights are you studying? What data are you analysing? What is your objective?

I can’t promise anything, but I may be able to do research online to figure this out and discover at least some of the necessary information if I know what I’m looking for. I understand that if this is your research, you may not want to go into detail, but the more I know, the more I may be able to help.

[yashvin]

Hi

The kind of data i am dealing is very sensitive. I doubt I can write it here since it is an open forum.

I can discuss with you personally if you wish.

Let me know

Its super interesting!

Thanks Yashvin

[Star Strider]

If you trust Gmail, my contact information listed on my File Exchange profile is <mailto:[e-mail] [e-mail]>.

[yashvin]

thanks for providing your contact detail.

I will write to you :)

Yashvin

[Star Strider]

Be sure to put MATLAB-Yashvin as the first words in the ‘Subject’ line so I won’t miss it.

[yashvin]

Hi Yea,

I mailed you.Please confirm.

thanks

yashvin