Headwinds, always

Peter Duniho wrote:

"Larry Dighera" wrote in message
news
[...]
So I appears that my recollection was faulty. But it seems counter
intuitive, that a 90-degree crosswind contributes half its velocity to
a tailwind component.


That's because you need to take into account the application of that
particular resource. Applying that sort of thinking to cruise flight IS
counter-intuitive, because it's not correct in that context.

It's not even literally correct in the context of the article you quoted,
but nevertheless the article you quoted has useful information in it.
First, it's a discussion of landing, not cruising. Second, it's a
collection of rules of thumb, not a precise analysis of reality.

It is easy to show that mathematically, a 90 degree crosswind results in no
tailwind component. Without a correction, it results in no headwind
component as well.

I'd like you to show that since it is easy. And a crosswind is relative
to your track, not your heading. OK, now show us the math! :-)

Matt

"Matt Whiting" wrote in message
...
It is easy to show that mathematically, a 90 degree crosswind results in
no tailwind component. Without a correction, it results in no headwind
component as well.

I'd like you to show that since it is easy.

Including crab, a 90 degree crosswind creates a groundspeed of cos(T) * true
airspeed, where T is the crab angle. cos(T) is always less than or equal to
1, so your groundspeed is always less than or equal to your true airspeed,
and so there is no POSITIVE tailwind component (if my inclusion of the word
"POSITIVE" here makes a difference to your previous post, then you're just
being intentionally obtuse, as my meaning was perfectly clear: a 90 degree
crosswind never increases your groundspeed, no matter how strong).

And a crosswind is relative to your track, not your heading.

A crosswind is relative to whatever you define it to me relative to. If you
don't care about where you are going (as is sometimes the case), a 90 degree
crosswind doesn't affect your speed in the direction of your heading at all
(though it does, obviously, affect your speed along your ground track).

OK, now show us the math! :-)

Done.

Pete

Peter Duniho wrote:
"Matt Whiting" wrote in message
...

It is easy to show that mathematically, a 90 degree crosswind results in
no tailwind component. Without a correction, it results in no headwind
component as well.

I'd like you to show that since it is easy.


Including crab, a 90 degree crosswind creates a groundspeed of cos(T) * true
airspeed, where T is the crab angle. cos(T) is always less than or equal to
1, so your groundspeed is always less than or equal to your true airspeed,
and so there is no POSITIVE tailwind component (if my inclusion of the word
"POSITIVE" here makes a difference to your previous post, then you're just
being intentionally obtuse, as my meaning was perfectly clear: a 90 degree
crosswind never increases your groundspeed, no matter how strong).

My question was about the headwind component, and I read it too quickly
and didn't catch the "without a correction" comment which I assume you
meant to discount the crab angle. Yes, a 90 crosswind will not add a
tailwind component, but it will add a headwind component due to the crab
angle required to stay on track.


Matt

"Matt Whiting" wrote in message
...
[...] Yes, a 90 crosswind will not add a tailwind component, but it will
add a headwind component due to the crab angle required to stay on track.

I've basically said so two posts in a row (not to mention in other posts).
Your point escapes me.

On Tue, 7 Jun 2005 11:19:29 -0700, "Peter Duniho"
wrote in
::

[...]

I believe that is the true nature of the article you've quoted: to provide
rules of thumb that offer safe guidance to pilots landing in constrained
areas, especially when the landing area is defined not by prevailing winds
but by terrain restrictions, preventing the pilot from taking best advantage
of the current winds. Where the winds increase the landing distance, they
are assumed to be greater than actual, and where the winds might shorten the
landing distance, they are assumed to be lesser than actual. In neither
case do the estimates provide any assistance in judging the effects of winds
aloft during cruise flight.

Yes. I can see now, that you're right about the article's
inappropriateness in this discussion due to it's intentional bias
toward conservatism. It only serves to further confuse the issue.

Instead, let's look at a Crosswind Correction Table (I hope the
formatting works in your browser):
http://www.auf.asn.au/navigation/wind.html

Table 1: Wind components
Headwind component [for ground speed]
Crosswind component [for WCA]

Wind Speed Wind Speed
WA | 5 10 15 20 25 30 | 5 10 15 20 25 30
----+--------------------------+--------------------
0° | -5 -10 -15 -20 -25 -30 | 0 0 0 0 0 0
15° | -5 -10 -15 -20 -25 -30 | 1 2 4 5 6 7
30° | -4 -9 -13 -17 -21 -25 | 2 5 7 10 12 15
45° | -3 -7 -10 -14 -17 -21 | 3 7 10 14 17 21
60° | -2 -5 -7 -10 -13 -15 | 4 9 13 17 21 25
75° | -1 -2 -4 -5 -6 -7 | 5 10 15 20 25 30
90° | 0 0 0 0 0 0 | 5 10 15 20 25 30
105°| +1 +2 +4 +5 +6 +7 | 5 10 15 20 25 30
120°| +2 +5 +7 +10 +13 +15 | 4 9 13 17 21 25
135°| +3 +7 +10 +14 +17 +21 | 3 7 10 14 17 21
150°| +4 +9 +13 +17 +21 +25 | 2 5 7 10 12 15
165°| +5 +10 +15 +20 +25 +30 | 1 2 4 5 6 7
180°| +5 +10 +15 +20 +25 +30 | 0 0 0 0 0 0
----+--------------------------+--------------------
| 5 10 15 20 25 30 | 5 10 15 20 25 30

ground speed* = TAS + value shown. WCA = value shown / TAS × 60


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. 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. 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?

Why [don't tailwinds exist]? Ginsberg's Theorem, which paraphrases the
three fundementals of thermodynamics. may be a clue.

First Law - You can't win
Second Law - You can't even break even
Third Law - You can't get out of the game

.... and the three great philosophies of the world are based on the
negation of one of these laws:

Capitalism is based on the idea that you can win.
Communism is based on the idea that you can break even. And
Mysticism is based on the idea that you can get out of the game.

Jose
--
The price of freedom is... well... freedom.
for Email, make the obvious change in the address.

"Larry Dighera" wrote in message
...
[...]
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