Looking for a math wiz!

"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?

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

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