"Larry Dighera" wrote in message
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As an example of the limited increase in ground speed provided by a
quartering tailwind, let's take the case of a 30 knot wind from
135-degrees. The table indicates an increase of +21 knots can be
expected, but that +21 knot increase in forward velocity must be used
to overcome a 21 knot crosswind to track the desired course line,
which results in a net 0 knot increase in ground speed.

Your math is off again.

It is true that a quarting 45-degree aft tailwind results in equal
components parallel to and perpendicular to your course. However, that does
not mean that you "use up" all of the tailwind component to compensate for
the crosswind component.

In order to find out the true effect of any winds aloft on your groundspeed,
you need to look at not only the wind speed and direction, but the
aircraft's speed as well. The faster the aircraft or the slower the wind,
the less correction is actually required in order to compensate for the
crosswind.

Furthermore, just as a wind of only 30 knots gets to push you sideways by 21
knots at the same time that it pushes you forward at 21 knots, an airplane
gets to use a significant portion of its forward speed to compensate for a
crosswind without sacrificing much of that forward speed for "progress made
good".

So it appears
to me, that only those winds within 45-degrees of directly aft (or a
90-degree arc) will actually result in a real increase in ground
speed.

You still aren't looking at it correctly. Taking your example, an airplane
traveling at 100 knots will require a 12 degree heading change to compensate
for the 21 knot crosswind. In doing so, the theoretical tailwind component
of 21 knots will be reduced to 19 knots, a loss of only 2 knots due to the
crab. Nearly all of the tailwind contributes to forward movement along the
desired course.

Or stated differently, the probability of encountering a
tailwind sufficient to increase ground speed is 1 in 4; only 25% of
the time wind will result in a net increase in ground speed.

Do you agree with that?

No, I do not. It takes a fairly strong, nearly-direct-crosswind "tailwind"
to result in zero or negative contribution to groundspeed by that tailwind.
In the vast majority of cases, the aircraft has plenty of speed relative to
the wind to allow a relatively minor crab to fully compensate for the
crosswind, while still gaining some advantage from the tailwind.

Assuming equal distribution of wind directions and speeds, the percentage of
those directions and speeds that results in a positive contribution to
groundspeed is much closer to 50% than to 0%. It's certainly less than 50%,
but not by a whole heck of a lot (I haven't done any sort of calculation,
but I'm confident it's safely past the 40% mark).

No disrespect intended, but I'd suggest you could use a little practical
time with your wind angles. If you have an E6B or wind correction angle
calculator of any sort, this won't take long and should be relatively easy.
Use some sample values of interest (the various examples posted to this
thread would probably be interesting and useful) and see what you get.

Pete