Why is it not possible to refine the process that is being used by
Dick Johnson by using the gadgets that are available.
That would refine the data acquisition and would make the
resolution much finer. The work load is very high during the process.
Dick invited me to a test flight from 12000ft and not much useable
data was obtained from my only attempt. It sure takes practice.
One certainly has to chew gum, use a stop watch, make notes of time,
speed and temperature and flap settings, maintain speeds, change
speed and stabilize it.
This every 500ft, At the same time Fly a big circle around the airport,
so you have a place to land when finished. I may have left things out.
What electronic aids could be used that would help in this matter?
Udo
"Richard Brisbourne" wrote in message
...
Robert Ehrlich wrote:
After this discussion we are far from the original question, i.e.
can we infer anything about the polar of a glider just from GPS
fligth logs of this glider?
The obvious answer several people gave was: no because the airmass
movement is unknown.
Well, as a former mathematician, I would say this is just what the
name says: an unknown. Would we be able to determine it?
The problem is this is not a single unknown, it is an infinity of them.
And despite the fact that each track log point gives 3 equations, this
would not be sufficient for determining an infinite number of unknown.
Even when considering the finite number of unknowns consisting of the
3 components of the airmass speed at each point of the log, we have
more unknowns than equation since we have also the unknown polar we
want to determine.
So is there a solution?
We can do for other unknowns just what we do with the polar data,
which are also an infinity of unknowns: reduce their number by
assuming a simple model depending of a small number of unknowns, this
is usually done for the polar by assuming a quadratic approximation
depending only on 3 parameters.
In the same way we can assume that the horizontal components of
the wind are constant on the flight area at a given altitude, and
that the evolution with altitude could be carcterized with a few
parameter, e.g. wind speed at 3 given altitudes and polynomial
interpolation between them.
For the vertical component of airmass movement, we can assume that
the pilot is following some speed-to-fly rule caracterized by
a MC setting and the 3 parameters of the glider polar that was
used for making the MC ring or programming the flight computer.
Even these values may be considered as unknowns.
So we have now a small number of unknowns and a comparatively
large number of equations from the flight log, plus the few
ones from the physics relating position to speed, airspeed and
wind to ground speed, sink to height, sink to airspeed according
to the speed to fly rule and so on. Our system is no more undetermined
but overdetermined, probably there is no exact solution, but there
are methods for determining a most likely solution, i.e. values
for the unknowns that minimize the way the equations are not
satisfied (least square method or others).
As I am only a *former* mathematician, I will not go further
in this way, maybe somebody who is a real mathematician will
complete the job, or somebody who is teaching maths will
propose that as a project for students, this is the lazy method
I would have used when I was myself teaching :-)
Yeah- but would you believe the answer when you got it?
Not to mention another unknown- airflow separation during pull-ups and
pushovers, and effect of varying g-forces.
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