True heading and Wind direction

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yashvin 2015-7-20

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/230455-true-heading-and-wind-direction

评论： yashvin 2015-9-15

采纳的回答： Star Strider

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

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Star Strider 2015-7-20

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https://ww2.mathworks.cn/matlabcentral/answers/230455-true-heading-and-wind-direction#answer_186637

在 MATLAB Online 中打开

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.

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Star Strider 2015-7-21

在 MATLAB Online 中打开

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.

Star Strider 2015-7-22

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.

Star Strider 2015-8-14

‘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.

Star Strider 2015-8-15

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.

Star Strider 2015-8-16

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.

Star Strider 2015-8-19

‘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 2015-8-21

在 MATLAB Online 中打开

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 2015-8-31

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

yashvin 2015-9-15

Hi Yea,

I mailed you.Please confirm.

thanks

yashvin

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