Headwinds, always

"Larry Dighera" wrote in message
...
[...]
The point I'm making is, that of the 360 degrees available for winds
to intersect the intended course, only about 15% are able to result in
a net ground speed increase.

This is from memory, so I'm sure someone will correct me with a more
detailed analysis.

Of course.

It depends on the strength of the wind.

For example, if you are flying 100 knots, a 20 knot wind from 10 degrees aft
of a direct crosswind gives you a 1.5 knot boost in speed, but a 40 knot
wind from the same direction slows you by 1.1 knots.

The stronger the wind, the more directly behind you it can be and still slow
you down.

That said, your statement that only 15% of the available degrees result in a
true tailwind is plainly false. That would be an arc of only 7.5% degrees
to either direction of straight aft of your heading, when in fact modest
wind speeds even only slight aft of your heading result in a net increase in
groundspeed. And it ignores the fact that it's not simply the direction of
the wind, but also the speed.

It's true that more than 50% of all wind directions and speeds result in a
headwind, but it's only *slightly* more than 50%. Certainly not nearly
enough to explain the original poster's experience.

Pete

On Mon, 6 Jun 2005 10:58:57 -0700, "Peter Duniho"
wrote in
::

"Larry Dighera" wrote in message
.. .
[...]
The point I'm making is, that of the 360 degrees available for winds
to intersect the intended course, only about 15% are able to result in
a net ground speed increase.

This is from memory, so I'm sure someone will correct me with a more
detailed analysis.

Of course.

It depends on the strength of the wind.

For example, if you are flying 100 knots, a 20 knot wind from 10 degrees aft
of a direct crosswind gives you a 1.5 knot boost in speed, but a 40 knot
wind from the same direction slows you by 1.1 knots.

The stronger the wind, the more directly behind you it can be and still slow
you down.

That said, your statement that only 15% of the available degrees result in a
true tailwind is plainly false. That would be an arc of only 7.5% degrees
to either direction of straight aft of your heading, when in fact modest
wind speeds even only slight aft of your heading result in a net increase in
groundspeed. And it ignores the fact that it's not simply the direction of
the wind, but also the speed.

It's true that more than 50% of all wind directions and speeds result in a
headwind, but it's only *slightly* more than 50%. Certainly not nearly
enough to explain the original poster's experience.

Pete


Around 1998 or so, The High Ground column in Plant & Pilot contained
an article titled Estimating Surface Winds. It provided five
paragraphs each dealing with a different aspect of winds, and four
figures. Figure C is titled Estimating Tailwind Component. It shows
wind from astern (0 degrees), 30 degrees off the tail, 60 degrees off
the tail, and wind from off one wing tip (90 degrees). Here are the
captions of each:

0 Degrees: Estimate tailwind component at full wind velocity.

30 Degrees: Estimate tailwind component at full wind velocity.

60 Degrees: Estimate tailwind component at three-quarter wind
velocity

90 Degrees: Estimate tail wind component at one-half wind
velocity.

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.


Here is the text of the article:

ESTIMATING SURFACE WINDS

An awareness of the surface wind is all-important to successful
mountain arrivals and departures. A few rules of thumb are
useful.

1 Estimating Headwind Component. If the wind sock is swinging
within 30 degrees of your runway's alignment, consider the
headwind component at three- fourth the wind velocity.
(Mountain winds are seldom steady; a direction and velocity one
moment may change the next.( Allow one-half the wind's velocity
as your component when the sock swings 30 to 60 degrees off the
runway. And, when the sock's angle to the runway exceeds 60
degrees, count the headwind zero.

2 Estimating Crosswind Component. If the wind lies within 30
degrees of runway alignment, estimate your crosswind component at
one-half the wind's velocity. Estimate your component at
three-fourths the wind's velocity if the wind crosses your runway
at 30 to 60 degrees. If the wind angle exceeds 60 degrees,
estimate your crosswind component to equal the velocity.

3 Estimating Tailwind component. If the wind is blowing within
30 degrees of your tail, consider the wind's full strength as your
tailwind component. A wind 30 to 60 degrees of the tail calls for an
estimated component of three-fourths the wind's velocity. Estimate
your component at one-half the velocity if the wind angle exceeds 60
degrees.

4 Estimating wind velocity. Most wind socks used at small airports
are designed to stiffen at 15 knots. Estimate lesser velocities by
the sock's angle of droop. A sock drooping at a 45-degree angle, for
example, shows a velocity of seven or eight knots.

5 Estimating Wind Correction Angle. Knowing at the outset the
approximate wind correction needed on final approach or initial
climbout is helpful. At typical light plane liftoff or approach
speeds of 55 to 65 knots, correct one degree for each knot of
crosswind component. Thus, an approximate 10-degree correction should
keep you on track when lifting off or landing into a 10-knot crosswind
component.

"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.

But when dealing with mountain flying, and in particular landing on a short
runway, assuming a tailwind component for a 90 degree crosswind is
conservative approach. That is, a 90 degree crosswind clearly doesn't add
half the wind speed to your groundspeed, but the crosswind does create other
effects that could result in a lengthening of the room required to land,
roughly equivalent to a similar increase in groundspeed.

Note that while a tailwind is estimated at full strength, when coming from
within a 30 degree angle, a headwind is estimated only a 3/4 strength, even
when coming from the same angle (in the other direction, of course).

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.

Hope that helps.

Pete

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?

"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