Help Calculating True Heading

[eyeball11]

Hi All,

I am trying to build a spreadsheet for calculating various pre-flight measures. The only one I have left giving me difficulty is True Heading. I know what variables are going into the equation but not how they are being calculated. If I do it on a flight calculator, the inputs are: TCrs (the direction of course as found on a map), TAS (which we usually have around 100), Wind Direction and Wind Speed. As an example, sometimes my TCrs may be say 180 degrees and the True Heading will come out as 180 or it may come out as 184 depending on the other input values.

Can anyone explain to me the exact formula it is using? Once I have that I can probably piece together how to input it in a spreadsheet. Thanks!

[Kurwa]

Are you talking about Sine and Cosine ratios? Soh Cah Toa? Right angle triangle, the Sine function of the angle the wind makes with your track equals the magnitude of the opposite side of the triangle over the adjacent? You would have been forced to learn this somewhere prior to being allowed to use the calculator I would think?

[Strega]

Once again Im amazed at the lack of understanding of such basic things as calculating wind correction!!

All you are doing when you add your true course to the wind, is adding vectors.


It is my opinion that if a pilot cannot calculate wind corrections, groundspeed withought a flight computer(includes a whiz wheel) , they shouldnt be flying.

[HS-748 2A]

Once again Im amazed at the lack of understanding of such basic things as calculating wind correction!!

All you are doing when you add your true course to the wind, is adding vectors.


It is my opinion that if a pilot cannot calculate wind corrections, groundspeed withought a flight computer(includes a whiz wheel) , they shouldnt be flying.

I didn't notice where 'eyeball11' said he / she was flying. He's building a spread sheet. Why don't you piss off?

Or, if you're so gawd damn smart, give him a breakdown on the math, like he asked for so he can input it into his computer program.

It should be no problem for you, as I'm sure you learned something when you asked
this question a couple months ago.

[eyeball11]

Once again Im amazed at the lack of understanding of such basic things as calculating wind correction!!

All you are doing when you add your true course to the wind, is adding vectors.


It is my opinion that if a pilot cannot calculate wind corrections, groundspeed withought a flight computer(includes a whiz wheel) , they shouldnt be flying.

I didn't notice where 'eyeball11' said he / she was flying. He's building a spread sheet. Why don't you piss off.

Or, if you're so gawd damn smart, give him a breakdown on the math, like he asked for so he can input it into his computer program.

It should be no problem for you as I'm sure you learned something when you asked
this question a couple months ago.

Well at least SOMEBODY doesn't jump to conclusions like others do. You are completely correct. I am not a pilot whatsoever, I am building a spreadsheet for somebody. I have figured out how to make it produce the appropriate results for every other factor but don't understand the basic math the flight calculator is using for that one category.

For the record, I'm pretty sure those who think it is simple would be amazed. For example, this is the formula required to make it work for Groundspeed: Formula = ROUND("TAS"*SQRT(1-(("wind velocity"/"TAS")*SIN(RADIANS("wind direction"-"true track")))^2)-"wind velocity"*COS(RADIANS("wind direction"-"true track")),0)

Sooooo, I'll ask again: does anyone know the basic formula being used to calculate what I asked for?

[Kurwa]

A simple way is Wind Velocity/True Airspeed x 60. This would give you a maximum drift correction angle assuming a 90 degree crosswind. If the wind angle meets your track at less than 90 degrees, then apply a Sine ratio to that angle (enter the angle then press SIN on a calculator). Or , you can resolve a rough number by applying the following rounded Sine ratios: 90 to 75 degrees equals 1, 60 degrees is 0.9, 45 degrees is 0.7, 30 degrees is 0.5, 15 degrees is 0.3.
Is this what you're looking for? Googling Trigonometry may help with the concept

[Strega]

Once again Im amazed at the lack of understanding of such basic things as calculating wind correction!!

All you are doing when you add your true course to the wind, is adding vectors.


It is my opinion that if a pilot cannot calculate wind corrections, groundspeed withought a flight computer(includes a whiz wheel) , they shouldnt be flying.

I didn't notice where 'eyeball11' said he / she was flying. He's building a spread sheet. Why don't you piss off?

Or, if you're so gawd damn smart, give him a breakdown on the math, like he asked for so he can input it into his computer program.

It should be no problem for you, as I'm sure you learned something when you asked
this question a couple months ago.

actually I asked about a window in an old whiz wheel, not how to add vectors..

[Strega]

Sooooo, I'll ask again: does anyone know the basic formula being used to calculate what I asked for

the basics are to break everything down into x and y components, and then add them.

[eyeball11]

A simple way is Wind Velocity/True Airspeed x 60. This would give you a maximum drift correction angle assuming a 90 degree crosswind. If the wind angle meets your track at less than 90 degrees, then apply a Sine ratio to that angle (enter the angle then press SIN on a calculator). Or , you can resolve a rough number by applying the following rounded Sine ratios: 90 to 75 degrees equals 1, 60 degrees is 0.9, 45 degrees is 0.7, 30 degrees is 0.5, 15 degrees is 0.3.
Is this what you're looking for? Googling Trigonometry may help with the concept

Thanks. I'll try working with that and see if it works in Excel (I'll let you know). Googling trigonometry likely won't help (my problem isn't with math, I have several courses in calculus, trigonometry, linear algebra, etc.). My problem is in that I don't fly so I don't really know what I am trying to compute here. Your explanantion above makes what I am trying to compute more visual and should help me come up with a formula that will work.

[eyeball11]

Sooooo, I'll ask again: does anyone know the basic formula being used to calculate what I asked for

the basics are to break everything down into x and y components, and then add them.

To paraphrase, you don't know the formula (or a formula)?

[Strega]

Thanks. I'll try working with that and see if it works in Excel (I'll let you know). Googling trigonometry likely won't help (my problem isn't with math, I have several courses in calculus, trigonometry, linear algebra, etc.). My problem is in that I don't fly so I don't really know what I am trying to compute here. Your explanantion above makes what I am trying to compute more visual and should help me come up with a formula that will work.

you have 2 vectors to add,

1) wind velocity
2)Aircraft velocity
=
3)ground velocity

[Strega]

To paraphrase, you don't know the formula (or a formula)?

work back from first principles, plug and chug formulas are for morons

[Louis]

Eyeball, maybe this will come in handy:

Aviation Formulary: http://williams.best.vwh.net/avform.htm

Otherwise you can always show us what you have so far as an attachment.

Goodbye,

Louis

[eyeball11]

Thanks. I'll try working with that and see if it works in Excel (I'll let you know). Googling trigonometry likely won't help (my problem isn't with math, I have several courses in calculus, trigonometry, linear algebra, etc.). My problem is in that I don't fly so I don't really know what I am trying to compute here. Your explanantion above makes what I am trying to compute more visual and should help me come up with a formula that will work.

you have 2 vectors to add,

1) wind velocity
2)Aircraft velocity
=
3)ground velocity

I'm looking for a direction.

[Invertago]

Strega = quick on the trigger slow on the draw lol

[Strega]

I'm looking for a direction

last time I checked, velocity was a vector quantity..

[mcrit]

I'd suggest that you use vector projections. Project the wind vector along your track to get a head/tailwind component, and then project the wind at 90 degrees to your track to get the x-wind component. Once you have these you can firgure out ground speed and drift correction.
If you are not sure about how to do vector projections PM me and I'll see what I can dig up for you.

[eyeball11]

I think I may have figured it out. I'll have to verify but it seems to be producing the same numbers he came up with on the sheet he gave me:

True Heading = Course+DEGREES(ASIN(Wind Strength/TAS*SIN(RADIANS(Course-Wind Direction+180))))

When he can get me some more numbers I'll let you know if the above works and anyone who wants to use it (those of you who don't worry about being called "morons" by some) can fill your boots.

[Strega]

Here you go:

Course to steer =Desired track+DEGREES(ASIN(wind speed/true airspeed*SIN(RADIANS(desired track-wind direction+180))))

Ground speed =(true airspeed*COS(RADIANS(Desired track-course to steer)))+(wind speed*COS(RADIANS(desired track-wind direction+180)))

[JigglyBus]

Once again Im amazed at the lack of understanding of such basic things as calculating wind correction!!

and then......

Here you go:

Course to steer =Desired track+DEGREES(ASIN(wind speed/true airspeed*SIN(RADIANS(desired track-wind direction+180))))

Ground speed =(true airspeed*COS(RADIANS(Desired track-course to steer)))+(wind speed*COS(RADIANS(desired track-wind direction+180)))

??????????


I'm amazed as well Strega, I don't know how anybody with a grade two education couldn't understand that.

You are officially now on my list of personal heroes.

[Aviatard]

This site may be of some help:
http://williams.best.vwh.net/avform.htm

Ed Williams' Aviation Formulary.

Cheers.

[TTJJ]

Here is a simple spread sheet to calculate what you want.

TR is Track, Wd is Wind Direction, Ws is Wind Speed, HD is Heading

Input values in the yellow cells. The green cells are calculated values. The colourless cells are just used for calculations

For the Answers in E2 and F2 use:
WCA= ASIN(D2/B2*SIN((C2-A2)/180*PI()))/PI()*180
G/S = SQRT(B2^2+D2^2-2*B2*D2*COS((C2-A2-E2)/180*PI()))
These formulas are from Wikipedia.org under E6B.
There is an error in their ground speed calculation. Where they say +WCA, it should be -WCA.

These values have been worked out using the above formulas and compared to what some call a "whiz wheel", but which I refer to lovingly as a "Vector Detector", on this marvellous site: http://www.vandeenensupport.com/projects/rs/index.html

The WCA gives you a direction for the correction (+ or -).
Off to the side or hidden somewhere you will need the K -P columns to fix any numbers that are less than 0 or more than 360:

L2 = A2 + E2. M2 = IF(L2<0,L2+360,IF(L2>360,L2-360,L2)). O2 = IF(I2="E",G2-H2,G2+H2). P2 = IF(O2<0,O2+360,IF(O2>360,O2-360,O2))
Make G2=M2 and J2 = P2 to guarantee a valid number for headings.

You can add distances later to get times etc.

If it is an extremely slow sex week, you can do the same with Deviation.
Hope this helps

I am done...Miller Time...

[TTJJ]

I am sitting in Faro, Portugal on a fight from Brazil, and the bar has closed( buggers) so I thought I'd add a bit to the spread sheet above.

This spread sheet uses Lat/Long and calculates distances and times in Rhumb line and Great Circle routes. You will notice that the distances are almost the same for any normal flight. In this example, the distances from Thompson to Toronto are only 2.4 miles apart. (B8)
The times use the R L distances. The G C distance is just for reference.

(note. The formula for G C assumes that the World is a perfect sphere, so distances to China may be out about 3 miles. It just goes to show that you can't assume anything about the World these days)

The spread sheet for RL works anywhere on Earth except the North and South Poles.
So if you are stuck up (or down) there and need to use this spreadsheet to save your sorry ass with the last gasps of your computer's battery ...you are SOL. Sorry, life sucks.

The only convention that must be used when inputting data is that South Latitudes and East Longitudes are negative. However, just make the Degrees part negative. The spreadsheet converts the minutes to a negative value as needed.



These are the formulas that go into cells A10:B23

Lat1 =RADIANS(C2+IF(C2<0,D2*-1,D2)/60)
Long 1 =RADIANS(E2+IF(E2<0,F2*-1,F2)/60)
Lat 2 =RADIANS(C4+IF(C4<0,D4*-1,D4)/60)
Long 2 =RADIANS(E4+IF(E4<0,F4*-1,F4)/60)
dlon W =MOD(B13-B11,2*PI())
dlon E =MOD(B11-B13,2*PI())
q =IF(ABS(B12-B10)=0,COS(B10),(B12-B10)/B17)
dphi =LN(TAN(B12/2+PI()/4)/TAN(B10/2+PI()/4))
TR True =IF(B14<B15,MOD(ATAN2(B17,-B14),2*PI()),MOD(ATAN2(B17,B15),2*PI()))*180/PI()
Dist R L =IF(B14<B15,SQRT(B16^2*B14^2+(B12-B10)^2),SQRT(B16^2*B15^2+(B12-B10)^2))*((180*60)/PI())
Dist G C =2*ASIN(SQRT((SIN((B10-B12)/2))^2+COS(B10)*COS(B12)*(SIN((B11-B13)/2))^2))*180*60/PI()
True HD =C7+B25
True HD Corr =IF(B21<0,B21+360,IF(B21>360,B21-360,B21))
Mag HD =IF(L7="W",I7+K7,I7-K7)
Mag HD Corr =IF(B23<0,B23+360,IF(B23>360,B23-360,B23))
WCA =ASIN(F7/D7*SIN((E7-C7)/180*PI()))/PI()*180

This is for the GS in H7 =SQRT(D7^2+F7^2-2*D7*F7*COS((E7-C7-G7)/180*PI()))

And this is for the Fuel in O7 =J7*N7*24

The red lettering in Row 5 is to informe you where to copy the calculated data from.

Area number "2" are the calculations for area "1"

Areas "3" and "4" are just ideas for a different setup.
(It seems everyone these days is carrying a PDA, Blackberry etc that can do spreadsheets. Having something like number "3" in your pocket along with a CFS for coordinates gives you a pretty powerfull means of planning a flight, giving a charter quote...or just while chatting over a beer...damn bar).

Area "5" are just some coordinates of airports in the US and Canada to play with.

The formulas can be copied and pasted right into the spreadsheet avoiding typing errors and basically...effort. It should take you all of 10 minutes to build the thing.

Giving credit where credit is due, the basic formulas are from http://williams.best.vwh.net/avform.htm

Have fun. I have to go find some more beer somewhere.
Closing the bar when there are thirsty pilots about. Can you imagine the nerve??

[TTJJ]

I should have thought of this before, but the alchohol just wasn't letting me listen to my brain over the screaming demands of my liver.
Ah, those long layovers...

You can download the above file from here.
It ain't pretty. It is like this so you can cut 'n paste to make your own layout.
I suppose it could be used as a teaching aid.

http://www.adrive.com/public/bc732644c1 ... 887f8.html

Any way, it is free.
I am really bad at this internet/file stuff. Let me know if it works.

[TTJJ]

Slow...sex...week

In the "All knowledge is good" category we have this spread sheet.
Maybe this should be moved over to the Instructing Forum after a few days.



I can not think of a practical use for this but maybe some enterprising Instructor or Geography teacher might find one.

The coordinates are input into the top left corner. Across the bottom you can see the alphabet. Each letter is is the first letter of a country. Airports are listed by Country - City - then name if there are more than one.
There is easily more than 1000 airports listed from around the world. Just copy and paste them in.

The spreadsheet calculates both a Rhumb Line and a Great circle solution to the Nav problem. It then compares the two and shows the difference.

The chart gives the crossing Latitude for each 5 degrees of Longitude on the Great Circle. That makes it easy to draw a Great Circle Route on a Mercator Projection in class.

The chart also gives the course change, distance and ETE between each 5 degrees of Longitude. Remember that the distance required to travel 1 degree of Longitude changes as one changes Latitude.
The chart values are correct. I have checked them against routes drawn on Google Earth to within 1 minute of Lat.

The Spreadsheet assumes that the wind will be the same for the whole trip. I know, I know...it is just easier that way.

The graph... Well the graph is just a somewhat weak representation of the route. I tried to find a Mercator Projection for free without luck. The graph also goes nuts if the flight crosses 180 degrees West/East or for trips less than 5 degrees Longitude between DEP and DEST. If someone out there could find a fix I would be much obliged.
It works nicely for a "normal" trip to say Europe from Canada.

The graph shows the Equal Time Point for the trip. It can be used to show the effect of wind on the ETP.

Numbers 1, 2, 3 are the same "group". They need to stay together. There are a whole bunch of cells used for calculation way off to the right out of view.

Numbers 4 and 5 are separate stand alone calculators.

Number 4 is a completely self contained Time/Dist/Fuel calculator using Lat/Long. (You need both sides of the number "4") It can be cut and pasted to different areas as is. It is sized to fit on the screen of a PDA

Number "5" is a stand alone navigation checker. It is not a Nav Log. It was made for harried Instructors to quickly check the work of students going on x-country trips without getting Carpel Tunnel Syndrome from using the Whiz Wheel. You can cut and paste this calculator anywhere as well.

One note, the model of the world is spherical. We all know that the world is not a sphere. Therefore distances upwards of 5000 miles between airports will be off by about 15 miles. If one day you decide that you are going to use this spreadsheet to try and fly non-stop from Thompson to Shanghai in your little C-152, then you should probably take those extra 15 miles into consideration when calculating your fuel load......and don't forget the 406 ELT...

If nothing else it is interesting to see the differences in courses needed to fly a Great Circle route. Also unless you are going WAY FAR, there is really no difference between the two. In the this example Vancouver to Toronto, only a 23.7nm difference.

Anyway have at it. If you fix the graph let me know.

The spread sheet can be downloaded from here.
Aviation Spreadsheets 1 backup.xlsx

Have fun
I gotta find a girl friend...