Looking for a math wiz!

[Chad Speer]

Okay, I know I've seen a lot of engineers and technical folks on here.
I have a complex math problem relating to the classic wind triangle
that I posted on sci.math and received little response. I don't know
if they're stumped or just not interested. :-)

Here is a copy of my original post and the only useful response I
received. Anyone have a solution?

(For the controllers here, this is an enhancement we are trying to add
to the Falcon program that centers will see next year, which was
developed by a controller here at ZKC.)


Chad Speer
PP-ASEL, IA
ATCS, Kansas City ARTCC



************************************************** *
************************************************** *

My original post:
*****
I am helping someone with a program that estimates wind speed and
direction using radar data from aircraft. I need help finding a
formula that can determine the wind speed and direction when given the
following information for multiple aircraft:

direction of travel
speed across the ground
speed through the air

The direction of travel and the speed across the ground are taken from
the radar data. The speed through the air is taken from the pilot's
flight plan. We're air traffic controllers trying to improve our
training tools, so we get access to all the goodies.

I know that with information from just one aircraft, the possibilities
are endless for the wind speed and direction. I think it is possible
to use the same data from two or more aircraft to determine the wind
speed and direction.

I thought I could come up with a formula to solve this, but the need to
reference everything to north in order to achieve actual directions
instead of just angles took it way above my head.

Basically, you are given the lengths of two adjacent sides of many
different triangles. You also know the angle of one of those sides
(aircraft direction) with respect to a known reference (north). The
properties common to all of the triangles, which are unknown, are the
length of the third side (wind speed) and the angle of that third side
(wind direction) with respect to a known reference (north).

If I have not described this well enough, I can upload some diagrams to
a web page to simplify the problem. I would really be grateful if
someone is able to solve this!
*****



A useful response:
*****
Interesting problem.

For the single aircraft, case, let:
Wd, Ws be wind direction and speed.
Ad, As be aircraft direction and speed (relative to the air, not the
ground).
Gd, Gs be aircraft direction and speed (relative to the ground).

Representing each vector as a 2-tuple of (direction, magnitude) gives:
(Gd, Gs) = (Ad, As) + (Wd, Ws)

The unknowns are Ad, Ws, and Wd. (Note that As is known due to filed
information, i.e. a pilot will know how fast his aircraft cruises.)

Splitting into x- and y-components will result in 2 equations with 3
unknowns. I agree that there are infinitely many solutions in the
single-aircraft case.

For the two-aircraft case (and I'll just suffix with 1 and 2), we have:
(Gd1, Gs1) = (Ad1, As1) + (Wd, Ws)
(Gd2, Gs2) = (Ad2, As2) + (Wd, Ws)

where of course we assume that the wind affecting each aircraft (since
they are presumably not too many tens of miles apart) is the same.
Breaking into x- and y-components leads to 4 equations and 4 unknowns
(Ad1, Ad2, Wd, Ws). The 2-aircraft case probably has a unique solution.
We have:

Gs1 * cos(Gd1) = As1 * cos(ad1) + Ws * cos(Wd)
Gs1 * sin(Gd1) = As1 * sin(ad1) + Ws * sin(Wd)
Gs2 * cos(Gd2) = As2 * cos(ad2) + Ws * cos(Wd)
Gs2 * sin(Gd2) = As2 * sin(ad2) + Ws * sin(Wd)

One can probably square equations, add, and make use of the
relationship that sin^2(x) + cos^2(x) = 1. I'm not sure what the form
of the solution would be. I'm too lazy to work it out. It will be
messy.

I believe at first glance that the 2-aircraft case has a single unique
solution (4 equations, 4 unknowns).

However, moving on to more than 2 aircraft ...

If there are more than 2 aircraft, the system is "overspecified" (there
is a mathematical term for this, but it has been so long ...). You
probably want a way to pick a single best solution among the infinitely
many, assuming that you have some "noise" in the data.

The style of solution you want is probably about the same as a
"least-squares" solution to a system of linear equations, i.e.

http://www.mathresource.iitb.ac.in/linear%20algebra/mainchapter8.5.html

I would need to do some thinking about how to phrase this problem as a
least-squares problem (the sines and cosines above put doubts in my
head), but there is probably a way to do it. So, out of a group of
data for at least 2 aircraft, you should be able to grind out a
solution that is unique according to some constraints and assumptions.

To summarize my thoughts:

a)1 aircraft --> system not solvable.
b)2 aircraft --> system has one solution, but I'm too lazy to do the
algebra.
c)3 or more aircraft --> system is overspecified, and some least
squares approach should give a solution.

One more thought: I've spent a fair amount of time in little Cessnas.
It has been my experience that wind direction and speed won't vary too
much over distance, but may vary EXTREMELY with altitude. I've flown
on days when the winds at 3,000 feet were 15 knots and the winds at
6,000 feet were 50 knots (or at least this is my memory). I accept the
assumption that winds affecting aircraft at the same altitude that are
within maybe 20NM of each other are about the same. But I do not
accept the assumption that winds at different altitudes are similar --
my experience says otherwise. If you agree, this adds yet another
dimension to the problem.

(BTW, near the end of my student training, I used to like to fly in
heavy crosswinds to practice technique. We have an airport about 20NM
North of our local airport with a roughly perpendicular runway, and I
discovered that if the wind was blowing straight down the runway here I
could get a perfect crosswind to practice with just by going N and
using the other airport. The surface winds were always about the same
at both airports. That is why I'm comfortable with the assumption that
winds don't vary much over relative short distances.)

Good problem.

I am not a mathematician. I hope others can add more insight.
*****

[d&tm]

"Chad Speer" > wrote in message
ups.com...
> Okay, I know I've seen a lot of engineers and technical folks on here.
> I have a complex math problem relating to the classic wind triangle
> that I posted on sci.math and received little response. I don't know
> if they're stumped or just not interested. :-)
>
> Here is a copy of my original post and the only useful response I
> received. Anyone have a solution?
>
> (For the controllers here, this is an enhancement we are trying to add
> to the Falcon program that centers will see next year, which was
> developed by a controller here at ZKC.)
>
>
> Chad Speer
> PP-ASEL, IA
> ATCS, Kansas City ARTCC
>
>
>
> ************************************************** *
> ************************************************** *
>
> My original post:
> *****
> I am helping someone with a program that estimates wind speed and
> direction using radar data from aircraft. I need help finding a
> formula that can determine the wind speed and direction when given the
> following information for multiple aircraft:
>
> direction of travel
> speed across the ground
> speed through the air
>
> The direction of travel and the speed across the ground are taken from
> the radar data. The speed through the air is taken from the pilot's
> flight plan. We're air traffic controllers trying to improve our
> training tools, so we get access to all the goodies.
>
> I know that with information from just one aircraft, the possibilities
> are endless for the wind speed and direction. I think it is possible
> to use the same data from two or more aircraft to determine the wind
> speed and direction.
>
> I thought I could come up with a formula to solve this, but the need to
> reference everything to north in order to achieve actual directions
> instead of just angles took it way above my head.
>
>snip

Chad
if you know HDG ( ie where you are pointing), GS and TAS then there is only
1 possibility for the wind speed and direction. these can be calculated
from the cosine rule. If you know the cosine rule and the sine rule for
triangles you can calculate a lot of things.
to apply both of these rules draw yourself a little triangle and mark the
sides small a,b and c.
then mark the angles capital A,B and C where angle A is opposite side a
and angle B is opposite side b.
cosine rule a^2 = b^2 +c^2 - 2bc cos( A)
sine rule a/sin A = b/sin B = c /sin C

in the case of the NAV triangle

WS= SQRT( GS^2+TAS^2 =2*GS*TAS*cos(HDG-TR))
where WS= windspeed
GS = ground speed
TAS = airspeed
HDG = heading(where you are pointing)
TR = track ( where you are going)

If you want I can email you an excel spreadsheet that has this already
coded. you just enter your TAS, GS and HDG and it will give you the WS and
Wind direction.

Terry
PPL

[Stefan]

d&tm schrieb:

> if you know HDG ( ie where you are pointing), GS and TAS then there is only
> 1 possibility for the wind speed and direction.

Actually, there are two.

But the question was a different one. It has already been answered
pretty well, all what remains is to do the dirty work and shuffling some
formulas.

Stefan

[Chad Speer]

Terry - thanks for the reply, but heading is not known.

Stefan - we need to be able to plug these known values into a formula
and kick out a result. Assuming the original responder was on the
right track, I still don't know what to do with his suggestion. Any
ideas on that? I'm not lazy, this just went over my head a long time
ago. :-)


Chad Speer
PP-ASEL, IA
ATCS, Kansas City ARTCC



On Dec 16, 4:13 pm, Stefan > wrote:
> d&tm schrieb:
>
> > if you know HDG ( ie where you are pointing), GS and TAS then there is only
> > 1 possibility for the wind speed and direction.Actually, there are two.
>
> But the question was a different one. It has already been answered
> pretty well, all what remains is to do the dirty work and shuffling some
> formulas.
>
> Stefan

[Kev]

Stefan wrote:
> d&tm schrieb:
>
> > if you know HDG ( ie where you are pointing), GS and TAS then there is only
> > 1 possibility for the wind speed and direction.
>
> Actually, there are two.

Eh? Not to sidetrack the thread too much, but how could there be two
wind answers?

For example on the E-6B, to solve this, you'd set TRACK up, grommet
over GS, and then look for where your TAS arc meets your drift
correction angle (HDG-TRACK). The vector back to the grommet is the
single direction and speed for the wind.

Thanks, Kev

[d&tm]

"Stefan" > wrote in message
...
> d&tm schrieb:
>
> > if you know HDG ( ie where you are pointing), GS and TAS then there is
only
> > 1 possibility for the wind speed and direction.
>
> Actually, there are two.

I give up, can you please explain how there can be 2 ?

[Stefan]

Kev schrieb:

> Eh? Not to sidetrack the thread too much, but how could there be two
> wind answers?

Mathematically: There are always two square roots which solve the
equation: A positive and a negative.

Physically: If you only know GS, TAS and HDG, then you don't know
whether the wind blows from the let or from the right. (If you also know
the track, then of course there's only one solution.)

Stefan

[Michael Ware]

"d&tm" > wrote in message
...
>
> "Stefan" > wrote in message
> ...
>> d&tm schrieb:
>>
>> > if you know HDG ( ie where you are pointing), GS and TAS then there is
> only
>> > 1 possibility for the wind speed and direction.
>>
>> Actually, there are two.
>
> I give up, can you please explain how there can be 2 ?
>

There are two possible situations for the wind correction. You do not know
the direction of the correction for wind ( i.e. is the plane crabbing left
or right to compensate for x-wind) you only know the magnitude (wind speed).
Think of the triangle that is formed by vectors on the e6b. Without the
direction, you have an ambiguous answer, looks like two similar triangles, a
lefty and a righty.
Someone else could probably explain this better, that's the basic idea.

Mike

[Aluckyguess]

Can you email that to me also.




"d&tm" > wrote in message
...
>
> "Chad Speer" > wrote in message
> ups.com...
>> Okay, I know I've seen a lot of engineers and technical folks on here.
>> I have a complex math problem relating to the classic wind triangle
>> that I posted on sci.math and received little response. I don't know
>> if they're stumped or just not interested. :-)
>>
>> Here is a copy of my original post and the only useful response I
>> received. Anyone have a solution?
>>
>> (For the controllers here, this is an enhancement we are trying to add
>> to the Falcon program that centers will see next year, which was
>> developed by a controller here at ZKC.)
>>
>>
>> Chad Speer
>> PP-ASEL, IA
>> ATCS, Kansas City ARTCC
>>
>>
>>
>> ************************************************** *
>> ************************************************** *
>>
>> My original post:
>> *****
>> I am helping someone with a program that estimates wind speed and
>> direction using radar data from aircraft. I need help finding a
>> formula that can determine the wind speed and direction when given the
>> following information for multiple aircraft:
>>
>> direction of travel
>> speed across the ground
>> speed through the air
>>
>> The direction of travel and the speed across the ground are taken from
>> the radar data. The speed through the air is taken from the pilot's
>> flight plan. We're air traffic controllers trying to improve our
>> training tools, so we get access to all the goodies.
>>
>> I know that with information from just one aircraft, the possibilities
>> are endless for the wind speed and direction. I think it is possible
>> to use the same data from two or more aircraft to determine the wind
>> speed and direction.
>>
>> I thought I could come up with a formula to solve this, but the need to
>> reference everything to north in order to achieve actual directions
>> instead of just angles took it way above my head.
>>
>>snip
>
> Chad
> if you know HDG ( ie where you are pointing), GS and TAS then there is
> only
> 1 possibility for the wind speed and direction. these can be calculated
> from the cosine rule. If you know the cosine rule and the sine rule for
> triangles you can calculate a lot of things.
> to apply both of these rules draw yourself a little triangle and mark the
> sides small a,b and c.
> then mark the angles capital A,B and C where angle A is opposite side a
> and angle B is opposite side b.
> cosine rule a^2 = b^2 +c^2 - 2bc cos( A)
> sine rule a/sin A = b/sin B = c /sin C
>
> in the case of the NAV triangle
>
> WS= SQRT( GS^2+TAS^2 =2*GS*TAS*cos(HDG-TR))
> where WS= windspeed
> GS = ground speed
> TAS = airspeed
> HDG = heading(where you are pointing)
> TR = track ( where you are going)
>
> If you want I can email you an excel spreadsheet that has this already
> coded. you just enter your TAS, GS and HDG and it will give you the WS
> and
> Wind direction.
>
> Terry
> PPL
>
>
>
>

[d&tm]

"Stefan" > wrote in message
...
> Kev schrieb:
>
> > Eh? Not to sidetrack the thread too much, but how could there be two
> > wind answers?
>
> Mathematically: There are always two square roots which solve the
> equation: A positive and a negative.
>
> Physically: If you only know GS, TAS and HDG, then you don't know
> whether the wind blows from the let or from the right. (If you also know
> the track, then of course there's only one solution.)
>
Of course you are correct, I meant to include Track in the knowns, (
afterall if you dont know the track whether you are the pilot or the ATC you
are really in trouble.)
terry

[[email protected]]

[followups set to r.a.piloting]

In rec.aviation.piloting Chad Speer > wrote:
> Anyone have a solution?

I don't know what the solution is but I can certainly admire the
problem. :)

Actually, I think I pretty much agree with the one response you posted,
in part:

>> a)1 aircraft --> system not solvable.
>> b)2 aircraft --> system has one solution, but I'm too lazy to do the
>> algebra.

I worked out a little of the algebra for b) and the equations just
seem to be getting longer and longer instead of heading for a solution,
so I stopped.

>> c)3 or more aircraft --> system is overspecified, and some least
>> squares approach should give a solution.

I may be saying the same thing he is, but here is possibly another way
to look at case for 3 or more aircraft. If you know how to solve the
problem for 2 aircraft, and you have more aicraft than that, you can
pick any two and solve the problem for those two aircraft, yielding
a wind speed and direction. Then you can pick a different pair of
aircraft and solve the problem again -- you should get something close
to the same answer you got the first time. If you do this for all the
possible pairs of aircraft, you will _probably_ end up with a range of
answers that are somewhat grouped around a middle point. This does
result in a lot of calculations - 380 pairs for 20 aircraft or 9900
pairs for 100 aircraft - but this is the kind of thing computers are
good at.

>> It has been my experience that wind direction and speed won't vary
>> too much over distance, but may vary EXTREMELY with altitude.

I definitely agree with this. When you are picking pairs of airplanes,
it may be helpful (in terms of coming up with meaningful numbers) to
pick ones that are sort of close to the same altitude.

[from earlier in your post:]
> I have a complex math problem relating to the classic wind triangle
> that I posted on sci.math and received little response.

Here is some complete speculation on why it didn't get much response:

1) The folks there saw the magic words "air traffic control" in your
post and figured that if they helped you with it, they'd probably
get sued any time a plane crashes for the next 50 years.

2) The folks there saw the magic words "air traffic control" in your
post and figured out that you really do work for the FAA and
therefore have unlimited amounts of money and should give them a
grant to study this problem, rather than them answering for free on
Usenet.

Understand that I'm not saying that you shouldn't have said the magic
words - it's often quite helpful to understand the basic problem
somebody is trying to solve. And maybe neither of my speculations are
accurate.

Some other ideas on places to ask for help:

The halls of academentia. Go down to UMKC, find the math department,
and see if one of the professors can help you. They might also refer
you to a grad student who is good at turning food into solved math
problems. :) One minor problem with this is timing - they may have
all bugged out for the holidays.

NWS/NOAA. They might have solved this problem themselves at some point
and might be able to give you some code. My first two guesses at where
to try would either be the regular office in Pleasant Hill, MO, or the
Severe Storms Lab in Norman, OK.

You probably know about this, but you can cheat by pointing a radar
straight up and letting it figure out what the winds are doing:
http://www.profiler.noaa.gov/npn/profiler.jsp?options=full
But it sounds like you might be working on a (partially?) "canned"
training scenario and current real-world data is not exactly what
you need.

I hope this helps!

Matt Roberds

[Everett M. Greene[_2_]]

"Michael Ware" > writes:
> "d&tm" > wrote
> > "Stefan" > wrote
> >> d&tm schrieb:
> >>
> >> > if you know HDG ( ie where you are pointing), GS and TAS then there is
> >> > only 1 possibility for the wind speed and direction.
> >>
> >> Actually, there are two.
> >
> > I give up, can you please explain how there can be 2 ?
>
> There are two possible situations for the wind correction. You do not know
> the direction of the correction for wind ( i.e. is the plane crabbing left
> or right to compensate for x-wind) you only know the magnitude (wind speed).
> Think of the triangle that is formed by vectors on the e6b. Without the
> direction, you have an ambiguous answer, looks like two similar triangles, a
> lefty and a righty.
> Someone else could probably explain this better, that's the basic idea.

And a simple explanation of the whole process is that
the wind triangle has three (vector) components:
heading, course, and wind. The vector sum of heading
and wind gives course which is the problem that pilots
are accustomed to solving. Rearranging the equation
so as to compute wind given heading and course is not
at all difficult. The law of cosines allows determination
of the third side of a triangle given two sides and
the included angle. The law of sines allows determining
the other two angles given the three sides. There is no
left/right ambiguity given the course and heading.

[Chad Speer]

Matt wrote:

*****
If you know how to solve the problem for 2 aircraft, and you have more
aicraft than that, you can pick any two and solve the problem for those
two aircraft, yielding a wind speed and direction. Then you can pick a
different pair of aircraft and solve the problem again -- you should
get something close to the same answer you got the first time. If you
do this for all the possible pairs of aircraft, you will _probably_ end
up with a range of answers that are somewhat grouped around a middle
point. This does result in a lot of calculations - 380 pairs for 20
aircraft or 9900 pairs for 100 aircraft - but this is the kind of thing
computers are good at.
*****

Exactly how I hope this plays out.

*****
When you are picking pairs of airplanes, it may be helpful (in terms of
coming up with meaningful numbers) to pick ones that are sort of close
to the same altitude.
*****

I didn't specify in my original post because I didn't expect the
question to be raised, but we will be using aircraft within a 2000 foot
window. At the higher altitudes, that rarely involves a difference of
more than a few degrees and maybe six knots of wind.

*****
1) The folks there saw the magic words "air traffic control" in your
post and figured that if they helped you with it, they'd probably get
sued any time a plane crashes for the next 50 years.
*****

I hadn't considered that. Hell, even *I* don't trust the FAA. :-)

*****
2) The folks there saw the magic words "air traffic control" in your
post and figured out that you really do work for the FAA and therefore
have unlimited amounts of money and should give them a grant to study
this problem, rather than them answering for free on Usenet.
*****

I wish I could offer someone money. This whole system was designed by
a controller who realized the data was just sitting there and decided
to make something useful with it. Now, it's being deployed nationwide.
If the FAA really gets involved, this will be a useless program. Never
fails.

I really have no involvement in this. He briefed me on his work and I
told him I thought I could produce a formula for the wind. We'll see.
I may have bitten off too much. :-)

*****
The halls of academentia. Go down to UMKC, find the math department,
and see if one of the professors can help you. They might also refer
you to a grad student who is good at turning food into solved math
problems. :) One minor problem with this is timing - they may have
all bugged out for the holidays.
*****

This was my original thought. We even have an aerospace engineering
program nearby (University of Kansas) where I could probably shame
someone into a solution. "The guys in the math department said you
couldn't handle the trigonometry."

I really like the open discussion of Usenet and would love to make this
solution an eternal part of rec.aviation. If that doesn't happen, I'll
bribe some grad students...

*****
NWS/NOAA. They might have solved this problem themselves at some point
and might be able to give you some code. My first two guesses at where
to try would either be the regular office in Pleasant Hill, MO, or the
Severe Storms Lab in Norman, OK.
*****

Now there's an idea I will consider. We even have meteorologists on
staff who could probably grease some wheels there.

Thanks for the discussion!

Chad Speer
PP-ASEL, IA
ATCS, Kansas City ARTCC

[Jim Carter[_1_]]

> -----Original Message-----
> From: Everett M. Greene ]
> Posted At: Sunday, December 17, 2006 11:05 PM
> Posted To: rec.aviation.ifr
> Conversation: Looking for a math wiz!
> Subject: Re: Looking for a math wiz!
>
....
> And a simple explanation of the whole process is that
> the wind triangle has three (vector) components:
> heading, course, and wind. The vector sum of heading
> and wind gives course which is the problem that pilots
> are accustomed to solving. Rearranging the equation
> so as to compute wind given heading and course is not
> at all difficult. The law of cosines allows determination
> of the third side of a triangle given two sides and
> the included angle. The law of sines allows determining
> the other two angles given the three sides. There is no
> left/right ambiguity given the course and heading.

The problem given one aircraft has many solutions because neither
heading nor wind vector can be determined by radar. Two unknowns for the
3 factor problem. Heading will change as a function of wind vector and
vice-versa.

As a sidebar: is this just an exercise or is the goal to empower the
controllers to provide accurate real-time winds aloft?

[Kev]

> "Stefan" > wrote in message
> ...
> > Mathematically: There are always two square roots which solve the
> > equation: A positive and a negative.
> >
> > Physically: If you only know GS, TAS and HDG, then you don't know
> > whether the wind blows from the let or from the right.

While that statement is true, it doesn't cover all the possibilities.
We're talking about the case of a single aircraft? We know its HDG,
GS, TAS, but nothing else? That's only three of the six wind triangle
variables. We must know at least four to get an exact answer. With
only three knowns, there are a whole range of possible answers, since
we don't know what the wind correction angle is without knowing a CRS.

For example, for the following HDG, TAS and GS:

HDG 0
TAS 120
GS 100

All the following CRS, WD an WS are valid solutions, plus many more
in-between:

CRS WD WS
=== === ===
310 054 095
330 056 060
350 039 028
000 000 020 CRS=HDG
010 321 028
030 304 060
050 306 095

I think you were visualizing a triangle, and thought of the two obvious
solutions. But there are a lot more. Again, use the E6B method and
you'll see that any drift angle along the TAS arc contains a valid WS
and WD answer.

Regards, Kev

[Danny Deger]

"Chad Speer" > wrote in message
ups.com...

> Chad Speer
> PP-ASEL, IA
> ATCS, Kansas City ARTCC
>
>
>
> ************************************************** *
> ************************************************** *
>
snip

> direction of travel
> speed across the ground
> speed through the air
>

If you can get heading also, it is a fairly simple equation as others have
posted.

Danny Deger

[Travis Marlatte]

Chad,

I think that some clarification of the use might help. I can imagine two
scenarios:

1) enroute - in this case, you know the track and ground speed from radar.
You have the filed TAS. You have no idea of the crab angle or heading. This
sounds like the information you presented in your question. However,
enroute, who cares what the wind correction is. I am having trouble
imagining how this would help a controller - in training or not.

2) terminal - in this case, you still know the track and ground speed from
radar. However, now the filed TAS is probably no longer valid since it is
probably at a lower altitude than filed and used to compute the TAS. The
plane may also be under speed constraints. On the other hand, the controller
may be vectoring so now you have an assigned heading and maybe even an
assigned speed. You also have the pressure for the area and the TAS can be
computed from that and radar data. If this were an automated computation, it
could be done on every plane that was given an assigned speed (or even IAS
queried from the pilot) and an assigned heading (or even queried from the
pilot). Now maybe not every plane can provide all of the data but certainly
some could. Enough to update the calculated wind periodically.

Scenario 2 seems to me the one that would make knowledge of the wind most
desirable. It is also the scenario that could provide additional data and
certainly provides different data than what was posed in your question.

What say you?

--
-------------------------------
Travis
Lake N3094P
PWK

[Chad Speer]

Travis wrote:
*****
I think that some clarification of the use might help. I can imagine
two scenarios:

1) enroute - in this case, you know the track and ground speed from
radar. You have the filed TAS. You have no idea of the crab angle or
heading. This sounds like the information you presented in your
question. However, enroute, who cares what the wind correction is. I am
having trouble imagining how this would help a controller - in training
or not.
*****

This is for enroute training, Travis. It is not the crab angle we are
after, but the winds aloft. If we could pull the actual (or even just
forecast) winds aloft into this system, we'd be set. Unfortunately,
I'm told that data cannot be used for this purpose. I don't know if it
is inaccessible or if there is a contractual reason we can't get to it.
The bottom line is that we have only radar data to estimate the winds.

I see no other way of estimating the winds with this data. I hope that
this eventually provides us a workable solution. I've seen too many
trainees make bad decisions because they didn't consider the effects of
the wind to discount the usefulness of this information. A fair number
of operational errors occur because controllers don't use the wind to
their advantage.

By the way, my wife fell in love with Chicago on our trip last weekend,
so I'll be in your neck of the woods much more often. Atlantic
Aviation at Midway made us feel very welcome. :-)


Chad Speer
PP-ASEL, IA
ATCS, Kansas City ARTCC

[Chad Speer]

Jim wrote:
*****
As a sidebar: is this just an exercise or is the goal to empower the
controllers to provide accurate real-time winds aloft?
*****

This is just a training tool, Jim. Basically a replay system that
allows us to take control of an aircraft an demonstrate how a situation
could have been handled differently by a trainee. It should be really
cool, but none of this will be used on live traffic.


Chad Speer
PP-ASEL, IA
ATCS, Kansas City ARTCC

[Stefan]

Kev schrieb:

> I think you were visualizing a triangle, and thought of the two obvious
> solutions. But there are a lot more.

Frankly, I didn't contemplate very much and just posted the obvious.

Stefan

[Everett M. Greene]

"Jim Carter" > writes:
> > Everett M. Greene ]
> ....
> > And a simple explanation of the whole process is that
> > the wind triangle has three (vector) components:
> > heading, course, and wind. The vector sum of heading
> > and wind gives course which is the problem that pilots
> > are accustomed to solving. Rearranging the equation
> > so as to compute wind given heading and course is not
> > at all difficult. The law of cosines allows determination
> > of the third side of a triangle given two sides and
> > the included angle. The law of sines allows determining
> > the other two angles given the three sides. There is no
> > left/right ambiguity given the course and heading.
>
> The problem given one aircraft has many solutions because neither
> heading nor wind vector can be determined by radar. Two unknowns for the
> 3 factor problem. Heading will change as a function of wind vector and
> vice-versa.

I recall the original posting said that heading was known
as it would be in many approach/departure scenarios.

> As a sidebar: is this just an exercise or is the goal to empower the
> controllers to provide accurate real-time winds aloft?

[Kobra]

>
> I recall the original posting said that heading was known
> as it would be in many approach/departure scenarios.

No...the OP said the GROUND TRACK was known. The heading would not be known
unless the controller asked the pilot for his heading.

>> As a sidebar: is this just an exercise or is the goal to empower the
>> controllers to provide accurate real-time winds aloft?

I was thinking that controllers should have an accurate knowledge of the
winds aloft direction and speed while vectoring aircraft to the localizer.
On a couple of occasions a controller assigned me a heading to intercept the
localizer that did not allow me to intercept the localizer until after the
FAF due to his misunderstanding of how the winds were carrying me downwind.

Kobra

[Doug[_1_]]

This is why ground track (and ground speed) is actually now perferable
to heading and airspeed. But what with all the FAA certification and
all planes not having GPS (or SOME kind of rnav), we're stuck using the
antiquated heading and indicated airspeed.
Ah, I pine for the days a good old 4 course range....when all pilots
were men...........

Kobra wrote:
> >
> > I recall the original posting said that heading was known
> > as it would be in many approach/departure scenarios.
>
> No...the OP said the GROUND TRACK was known. The heading would not be known
> unless the controller asked the pilot for his heading.
>
> >> As a sidebar: is this just an exercise or is the goal to empower the
> >> controllers to provide accurate real-time winds aloft?
>
> I was thinking that controllers should have an accurate knowledge of the
> winds aloft direction and speed while vectoring aircraft to the localizer.
> On a couple of occasions a controller assigned me a heading to intercept the
> localizer that did not allow me to intercept the localizer until after the
> FAF due to his misunderstanding of how the winds were carrying me downwind.
>
> Kobra