Who does flight plans?

Recently, Jose posted:

Mathematically, an "angle" by itself *is* a scalar, and I'm not
arguing otherwise. I'm saying that "Angle Of Attack" requires
direction to have meaning. Without direction, there is no AOA.
[...]

Well, OK. Then, how do you determine the AOA when the aircraft is
parked? If the component of direction is inseparable from the
definition of AOA, how can it be a scalar?

[...]

When you say:

I'm saying that "Angle Of Attack" requires direction to have
meaning.

all you're really saying is that you don't have an angle of attack if
you don't have the requisite components (a relative wind, and a
chord).

I'm not sure that I follow your analogies, here, Jose. But, it may be a
good idea for you to look up the definition of "scalar". It *can not*
include a directional component. Conversely, AOA can not exist without
one.

Neil

Neil Gould wrote:

But, it may be a
good idea for you to look up the definition of "scalar". It *can not*
include a directional component. Conversely, AOA can not exist without
one.

Angle of attack does not "include a directional component". It is just an angle,
which is a scalar quantity.

You have evidently looked up the dictionary definition of scalar, and you read
it, but you didn't understand it.

Dave

"Neil Gould" wrote
Mathematically, an "angle" by itself *is* a scalar, and I'm not arguing
otherwise. I'm saying that "Angle Of Attack" requires direction to have
meaning. Without direction, there is no AOA.

Neil, give us an example of AOA having a "direction".

Well, OK. Then, how do you determine the AOA when the aircraft is parked?

When parked with no wind, there is no relative wind and therefore NO AOA.

Bob Moore

Recently, Bob Moore posted:

"Neil Gould" wrote
Mathematically, an "angle" by itself *is* a scalar, and I'm not
arguing otherwise. I'm saying that "Angle Of Attack" requires
direction to have meaning. Without direction, there is no AOA.

Neil, give us an example of AOA having a "direction".

Well, OK. Then, how do you determine the AOA when the aircraft is
parked?

When parked with no wind, there is no relative wind and therefore NO
AOA.

Stated another way, AOA doesn't exist *without* a directional component.

Neil

Recently, Dave Butler posted:

Neil Gould wrote:

But, it may be a
good idea for you to look up the definition of "scalar". It *can not*
include a directional component. Conversely, AOA can not exist
without one.

Angle of attack does not "include a directional component". It is
just an angle, which is a scalar quantity.

If what you think is true, then it is possible to determine the AOA when
the aircraft is parked. Do so, and I'll revise my thinking. The wonderful
thing about this level of mathematics is that it is not ambiguous. If any
usage results in a violation of the definition, then the usage is wrong,
period.

Neil

I'm not sure that I follow your analogies, here, Jose.

The analogy is merely that you can use one kind of quantity to derive
another kind of quantity. You can use eggs to derive cake, you can use
"time of day" to derive "time", you can use length to derive area, and
you can use vectors to derive scalars.

The simplest example, I suppose, is a ratio. Fifteen kilograms is THREE
times as much as five kilograms. Fifteen inches is THREE times as much
as five inches. The "three" in both cases is the same - it is a pure
scalar quantity. It is the same "three" as the number of fingers on my
hand that are surrounded by other fingers and the number of days in a
long weekend.

Fifteen kilograms is =not= three times as much as five inches. The
units are important when =deriving= the result, but once the result is
correctly derived, it has its own units (or lack of them).

Similarly, two vectors can intersect at an angle. The angle is not a
vector, it is a scalar. As an aside, two vectors (of the same units)
can also define an area; that area is not a vector, it is a scalar (with
units of square fubars, where "fubars" are the unit both vectors are
measured in).

A vector has magnitude and direction. AOA has no direction in and of
itself. To see this, imagine a wing chord which is inclined three
degrees (the leading edge higher) from some reference plane (say, the
fuselage), and a relative wind which is blowing up from ahead and
underneath at an angle of eighteen degrees to that same fuselage, at
seventy knots. This is typical of an approach in a light aircraft.

What is the angle of attack? To be a scalar, it would have just
magnitude (which could include an algebraic sign). To be a vector, it
would have to have magnitude AND direction.

In this case, the angle of attack is twenty-one degrees. It is the
difference between the two angles given (with reference to the same
fuselage). There is no "direction" to this angle (except perhaps an
algebraic sign). So it is not a vector.

One source of confusion arises because in other contexts angles are also
used to define direction, for example wind velocity is a vector whose
angle is a direction component, not a magnigude component. For example,
"zero three zero at ten knots" is a vector, where the magnitude part is
ten knots, and the direction part is 30 degrees East of North. However,
if you put a weight on an old fashioned butcher scale, the pointer moves
through some angle. That angle does =not= represent a direction, it is
a magnitude only, and thus a scalar (related to the weight of the meat
put in the pan). And if you weigh two cuts of meat, note the angles of
the pointer for each weighing, and subtract those angles, the result is
also an angle - a magnitude with no direction component. This is a scalar.

So, depending on context, angles can be magnitudes =or= directions, but
not both at once.

Jose
--
"Never trust anything that can think for itself, if you can't see where
it keeps its brain."
(chapter 10 of book 3 - Harry Potter).
for Email, make the obvious change in the address.

Neil Gould wrote:

If what you think is true, then it is possible to determine the AOA when
the aircraft is parked. Do so, and I'll revise my thinking. The wonderful
thing about this level of mathematics is that it is not ambiguous. If any
usage results in a violation of the definition, then the usage is wrong,
period.

I don't give a flip whether you revise your thinking or not. Your loss.

"Neil Gould" wrote
Stated another way, AOA doesn't exist *without* a directional component.

Directions are measured in reference to "somewhere", Up, Down,
North, South, etc. What is the reference for measuring AOA?

Bob Moore

Recently, Dave Butler posted:

Neil Gould wrote:

If what you think is true, then it is possible to determine the AOA
when the aircraft is parked. Do so, and I'll revise my thinking. The
wonderful thing about this level of mathematics is that it is not
ambiguous. If any usage results in a violation of the definition,
then the usage is wrong, period.

I don't give a flip whether you revise your thinking or not. Your
loss.

Not really.

Have a nice weekend, and fly safely.

Neil

Recently, Jose posted:
[...]
A vector has magnitude and direction. AOA has no direction in and of
itself.

[...]
What is the angle of attack? To be a scalar, it would have just
magnitude (which could include an algebraic sign). To be a vector, it
would have to have magnitude AND direction.

However, it is valid for a vector to have a magnitude of zero. It is NOT
valid for a scalar to have a directional component, and it is meaningless
to have an AOA with no directional component and magnitude (e.g. parked
aircraft have no AOA). Ergo, to have an AOA, you *must* also have velocity
(magnitude) and direction.

[...]
In this case, the angle of attack is twenty-one degrees. It is the
difference between the two angles given (with reference to the same
fuselage).

The two aspects of the AOA is referenced to the wing chord and relative
wind, not the fuselage.

There is no "direction" to this angle (except perhaps an
algebraic sign). So it is not a vector.

I'd say that it is often "OK" to PRESUME the directional components and
IGNORE their value if they are unimportant to usages where only the angle
is needed. But, that's quite a different situation than calling AOA
something it can't be by definition.

[...]
So, depending on context, angles can be magnitudes =or= directions,
but not both at once.

We're not talking about generic "angles", but an "Angle Of Attack", i.e.,
a specific usage which is defined by and inseparable from the components
of motion (aka relative wind). Without those components, AOA doesn't
exist.

Neil