[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/pro...p?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