Looking for a math wiz!

"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

"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

"Denny" wrote in message
oups.com...
Lots of fun to play with the formulas... But, the fly in the ointment
here is that the airspeed filed by the pilot is a canned number and has
nothing to do with reality... I fly IFR, I file the same airspeed - 130
kt - for all flights regardless of load, altitude, and what the power
setting winds up to be... If the actual airspeed in your problem is
within 15% of the filed number you will be lucky...

denny


Now I see why heading is not known. I agree, calculating wind on filed
airspeed would not be a good idea. Maybe taking the average of many
airplanes might be OK, but the difference between filed and actual can be
HUGE.

Danny Deger

"Chad Speer" wrote in message
ps.com...
Denny wrote:
*****
Lots of fun to play with the formulas... But, the fly in the ointment
here is that the airspeed filed by the pilot is a canned number and has
nothing to do with reality... I fly IFR, I file the same airspeed - 130
kt - for all flights regardless of load, altitude, and what the power
setting winds up to be... If the actual airspeed in your problem is
within 15% of the filed number you will be lucky...
*****


You're right, Denny. When you get down to the piston single/twin
level, there is great variation. This will be used mostly with high
altitude traffic where, with the exception of an occasional turboprop,
the true speeds are 400 knots plus. Most commercial operators file to
the knot and, in my experience, fly within ten knots. That is probably
going to be an acceptable variation, but time will tell. We will also
be polling some pilots initially to determine their heading, true
airspeed, and observed winds to validate our results.

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

Each plane gives you an estimate of the head/tail wind, but no information
on the cross wind. You need a way to combine all the different airplanes
wind data into a single estimate of the wind. The error in filed airspeed
vs. actual airspeed could be averaged out over many airplanes.

I am sure a Kalman filter would work (I think :-), but it has been a while
since I have worked on a Kalman Filter. The math is not trivial, and this
particular filter would definately not be trivial. You could start the
filter with the estimate of wind from the weather guy -- or would this be
considered cheating.

Danny Deger

"d&tm" wrote in message
...

"Chad Speer" wrote in message
oups.com...
Terry - thanks for the reply, but heading is not known.

snip

TAS1^2=WS^2+GS1^2-2WSGS1COS(180-ABS(WD-TR1)
TAS2^2=WS^2+GS2^2-2WSGS2COS(180-ABS(WD-TR2)

WHERE TAS1 AND TAS2 ARE TRUE AIRSPEEDS FOR AIRCRAFT 1 AND 2
WS = WIND SPEED
WD =WIND DIRECTION IN DEGREES MAG
TR1 AND TR2 ARE TRACKS MAGNETIC FOR AIRCRAFT 1 AND 2
GS1 AND GS2 ARE GROUND SPEEDS FOR AIRCRAFT 1 AND 2.
(180-ABS(WD-TR) WILL GIVE YOU THE ACTUAL ANGLE BETWEEN WIND DIRECTION AND
TRACK.

Now we have 2 equations with 2 unknowns ( WS and WD) which should be
solvable but I am stuggling to get it out. However I did a little
exercise
which suggests the end result may not be very useful. because small errors
in the ground speeds will cause very large errors in the calculated wind
speed.

I think the head/tail wind portion of the estimate should be pretty good,
but the crosswind component would have so much error as to be useless. We
need a way to use the head/tail wind components from different airplanes,
flying different headings and NOT use the less acurate crosswind estimates.
I think a Kalman filter would work.

Danny Deger

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

It is common for a new (or weak)
controller to turn an aircraft behind another, only to see that same
aircraft pick up a bunch of speed. The turn has nearly no effect on
separation, so they turn them some more. Within minutes, the turn is
fifty degrees and the controller is sucking up a seat cushion. Fun to
watch, but it would be nice to train that kind of stuff out of the
workforce. :-)

With even a close approximation of the winds, the realism is greatly
enhanced. Otherwise, the what-if's are reduced to a bland simulation
and utility is reduced.

Do the controllers know (and have easily available, say, on the
terminal) the wind speed forecasts? Would they be sufficient to greatly
reduce the above scenario?

Jose
--
"There are 3 secrets to the perfect landing. Unfortunately, nobody knows
what they are." - (mike).
for Email, make the obvious change in the address.

I really like the open discussion of Usenet

Try some of the math and CS newsgroups. You might get more traction.

Jose
--
"There are 3 secrets to the perfect landing. Unfortunately, nobody knows
what they are." - (mike).
for Email, make the obvious change in the address.

Now I see why heading is not known.

Yanno, each airplane that has GPS could transmit its data to Center,
which could then sort it out. This is possibly much more useful than
the Mode S ID or the N-number.

Jose
--
"There are 3 secrets to the perfect landing. Unfortunately, nobody knows
what they are." - (mike).
for Email, make the obvious change in the address.

Chad Speer wrote:
This tool is basically meant to be a replay of a high altitude training
session, where the trainer can say "Okay, let's see what would have
happened if you had turned AAL460 fifteen left rather than descending
him." As it exists now, it is really cool, but a bit unrealistic. If
the winds are strong enough, a fifteen degree turn can easily add
twenty knots to a groundspeed. [..]

Chad, I think we need to stop and get the requirements, so we can help
better. I'm guessing how the program will work:

You have data from a training session. It has a recording of many
aircraft movements that you can play back. Perhaps you add one new
and controllable craft to the mix (AAL460 above?) and that's the one
that gets vectored by the trainee, to see what kind of trouble he can
get in/out of. Since all the other aircraft had been affected by wind,
the controllable plane needs the same flight input. Is this a good
description?

If so, I'm thinking that the wind within the 2000' block you talked
about, is a single fixed value for the entire training session. Would
that be fair to say? If that is true, then you don't need to
calculate the wind except once at the beginning. Can this be stored
for later use each time?

Just trying to get a handle on things,
Kev