Calculation of windspeed and wind direction without circling:

Here's my understanding. If it's not correct, doubtless someone will
straighten me out and I will have learned something. DISCLAIMER: I have
absolutely no "inside" information on the algorithms used in the SN10!

Aircraft heading (direction the nose is pointing) and airspeed together
define a velocity vector that can be drawn as an arrow on a piece of paper,
the angle of the arrow representing the direction and the length of the
arrow representing airspeed. Starting at the tip of this arrow we can add a
second arrow representing wind speed and direction. If we now draw a third
arrow that closes the triangle (from the start of the first arrow to the end
of the second) this arrow represents the aircraft track (direction of travel
over the ground) and ground speed, this being the classical "wind triangle"
well known to pilots. Note that defining any two of the vectors of a wind
triangle automatically defines the third, this vector (like all vectors)
being defined by its magnitude and direction.

The above describes the graphical addition of two vectors.We can also do
vector addition (or subtraction) mathematically, instead of plotting arrows
on paper. The key point here is that the six quantities involved, aircraft
heading, aircraft airspeed, wind direction, wind speed, ground track and
ground speed define three vectors that are related mathematically by a
single (vector) equation:

In the case of a sailplane with an SN10 that has input from a GPS, we have
three knowns, namely true airspeed (the SN10 can compute this from pitot
pressure, static pressure, altitude and temperature), groundspeed and track
(the last two come from the GPS). There are three unknowns, aircraft
heading, wind direction and windspeed. Basically, multiple unknowns can be
calculated by setting up and solving simultaneous equations. There are well
known mathematical and computer algorithms for doing this.

If we make the assumption that the wind direction and speed are constant (at
least in the short term, and within a given altitude band) and if (in the
same short term) the sailplane flies on two distinct headings and / or
airspeeds within that altitude band, we have two different sets of "known"
values to insert into the vector equation. We can treat the resulting
equations as simultaneous equations and solve for the above-mentioned
unknowns. For the best result, the headings and /or airspeeds should be as
different as possible. Theoretically, we can get a unique solution as long
as the headings and / or airspeeds are not absolutely identical, but in the
real world, it appears that (at least sometimes) we need significantly
different headings to get a reliable result. Bear in mind that the even if
the windspeed and direction are indeed constant, the three "known" values
are not known with absolute precision and computers always introduce
round-off errors, some of which can get to be significant in these types of
calculations. Remember too, mathematically-speaking we are cheating. The
"known" values that are plugged into "simultaneous" equations should really
be values that are measured simultaneously! In this case, they are not, they
are values derived at different times and places, the main effect of which
is to make it more likely that the initial assumption of constant wind speed
and wind direction is not quite correct.

If we continue to fly in the same altitude band, with new headings/
airspeeds, we can get new and different input values that can be plugged in
and solved for new values of windspeed and direction. For the reasons stated
above, these results will not be all the same. If the results are clustered
closely together, we can have a high confidence in them. If the values are
all over the place, we can still display a value for the user (pilot), e.g.,
by averaging a number of results, but we will have a low confidence in the
displayed values. (Note: the SN10 does indeed display a confidence value for
each calculated wind speed and direction).

Advantages over windspeed and direction calculated from circle drift:
there's the obvious one that you don't have to circle to get a result.
Additionally, a circling sailplane pilot will often be moving his circle to
get better centered, and such shifts adversely affect the wind calculation.
And anyway, who ever flies perfect circles?

Disadvantages? In practice, the method does seem to require significant
heading changes and sometimes (e.g. some ridge flying, straight line cruises
between thermals, some wave flights) these are just not available. I have
flown with an SN10 for several years and sometimes found it necessary to
make one or more deliberate heading changes to get a calculated wind that
makes sense. If an accurate aircraft heading sensor were added to the SN10,
thus completely defining two of the vectors in the "wind triangle", this
would not be necessary. One lives in hope...

Ray Roberts





wrote in message
oups.com...
Well, I could explain but then I'd have to kill you ;-)
I'm really not sure what algorithms other software
currently uses, but my understanding is that we
have a big advantage by using ASI as well as GPS.
Happy Holidays and Best Regards, Dave

MaD wrote:
My experience is that the wind calculation of the SN10 is extremely
reliable and accurate. I reckon WP is as good as any other device
calculating based on circling drift only, like the LX20 for example. I
often compare SN10 and LX20 values and normally the SN10 is far better.
I'm sure Dave N. can explain why.

Marcel