Lift and Angle of Attack

"Dave Daniels" wrote in message
...
[...] Firstly, can the lift acting on an aircraft go negative?

Yes, though a non-symmetrical wing (the most common type) will not have an
exactly reversed lift-to-angle-of-attack profile for negative angles of
attack. That is, negative five degrees of AOA won't produce the same amount
of lift downward as positive five degrees of AOA produces upward. Most
wings are designed to optimize lift in the upward direction and so will get
more lift for the same angle of attack in the positive direction, compared
to the negative direction.

[...] Secondly, does the angle at which an aircraft
is banked affect the angle of attack?

The only thing that affects angle of attack is the airplane's attitude
relative to its path of flight. If I were writing a simulator, I would just
use the velocity vector and the attitude (bank, roll, and pitch angle) to
determine angle of attack. Whether roll angle affects the angle of attack
depends on your definition of "affects" and how exactly you're calculating
angle of attack. But generally speaking, if the flight path is not exactly
aligned with the longitudinal axis of the airplane, the roll angle does
affect the angle of attack, albeit in a small way.

Aerodynamically there's another thing to consider, which is that the force
called lift is directed perpendicular to relative wind. In anything other
than straight and level flight, this means lift is not exactly opposite
gravity. In order to calculate vertical acceleration, the simulator code
will have to break the lift vector into multiple components, one of which
will be the vertical component acting against gravity. Again, roll angle
(among other things) needs to be accounted for to figure out the vertical
component of lift.

[...] Thirdly, induced drag: I have read that this
is inversely proportional to the square of the aircraft's
velocity, but I do not see how this follows from the equations I
have seen. It appears to me that the greater the velocity, the
greater the induced drag. I must be missing something fundamental
here. Can anyone explain it?

For a constant angle of attack, increased airspeed means increased induced
drag. However, it also means increased lift. Induced drag is a by-product
of lift. In normal cruise flight, induced drag actually goes *down* as
airspeed increases, because lift remains constant. The only way to keep
lift constant is to reduce angle of attack as the airspeed increases, and
reducing the angle of attack reduces drag faster than increasing airspeed
increases it.

Pete

In article ,
ArtP wrote:

Keep in mind when working with a program, the programmer frequently
takes shortcuts to produce the desired result. While the AOA may not
change the vertical component of lift will decrease as the bank
increases.

This particular simulator was written during the late 1980s and
early 1990s. The target PC would have been something like a 20Mhz
386 with no floating point instructions then. I do not want to
take anything away from the programmers for an interesting piece
of code, but they were forced to take a lot of shortcuts.

It sounds like you are confusing parasitic drag and induced drag.
Parasitic drag (result of friction) increases as with speed. Induced
drag (result of AOA) decreases with speed (the faster you go the
smaller the AOA required to maintain altitude).

That begins to make more sense. I think that my problem was that
I was assuming that the induced drag decreased with velocity at
any angle of attack or altitude. If the lift is constant, then
higher speeds require a smaller lift coefficient and therefore the
induced drag coefficient is smaller. Am I on the right track here?

Dave Daniels

"Dave Daniels" wrote in message
...
[...] If the lift is constant, then
higher speeds require a smaller lift coefficient and therefore the
induced drag coefficient is smaller. Am I on the right track here?

Yes. It is, in fact, basically what all three respondents to your post
(myself included) said.

In ,
Dave Daniels wrote:

In article ,
ArtP wrote:


snip

It sounds like you are confusing parasitic drag and induced drag.
Parasitic drag (result of friction) increases as with speed. Induced
drag (result of AOA) decreases with speed (the faster you go the
smaller the AOA required to maintain altitude).

That begins to make more sense. I think that my problem was that
I was assuming that the induced drag decreased with velocity at
any angle of attack or altitude. If the lift is constant, then
higher speeds require a smaller lift coefficient and therefore the
induced drag coefficient is smaller. Am I on the right track here?

Dave Daniels

If you'd typed "If the lift is constant, then higher speeds require a smaller
angle of attack and therefore induced drag {quantity of} is smaller", I'd have
agreed with you immediately. I fail to see how coefficients (of anything) can
become smaller, or larger.

Sorry to be pedantic but, as far as I understand it, 'coefficients' are physical
constants. In this case, they are characteristics of a particular airframe.

The parasitic drag coefficient will go in proportion to a combination of frontal
area and total surface area (note that the frontal area presented to the
relative wind will change with variations in angle of attack, following a pitch
control input). The quantity of parasitic drag increases with the cube of the
airspeed, multiplied by this coefficient, mutiplied by the mass per unit time of
air flowing over it. (in kg.m.s-1 aka Watts, if I' m not mistaken)

I was loose with the definition of airspeed there and since we're cubing it, we
need to be more specific. Whilst TAS is fine for dead reckoning navigation
calculations, I think IAS is a better measure of airflow over the wing because
the stalling speed is the same, expressed in IAS, at all altitudes. (And when
that stalling speed converges with the highest achievable forward speed in level
flight, the plane reaches its 'service ceiling'). IAS falls short of TAS by an
increasing margin, as altitude increases and I think the drag should be
calculated on the basis of the lower, IAS value.

As I see it, a given mass of air (density * volume), moving over a wing in unit
time will produce a given quantity of lift, at a specified AoA, whether you
prefer the Bernoulli principle, or the air-deflection theory (or both) for what
generates it. Therefore, at altitude you *can* fly faster and further (in unit
time) but you also *have to* in order to generate enough lift. (You have to fly
through a larger volume of less-dense air for the mass to be the same, which can
only be done by travelling further forward and, if done in unit time, this
obviously means faster).

As mentioned in previous replies, induced drag is the result of the production
of lift which, by not being perpendicular to the wing (as viewed in
cross-section) retards forward motion to some extent. At higher speeds, the
required amount of lift can be achieved at a reduced angle of attack. This
brings the induced drag vector closer to the vertical and the retardation
component of it is thus minimized (it never totally goes away). A useful side
effect of this is that, by presenting a reduced frontal area to the relative
wind (nearly edge-on), the element of the planes parasitic drag, contributed by
the wings, is reduced and higher speeds become more possible. The induced drag
coefficient, however, remains a constant, for that particular aircraft.


One slight complication (for the programmer) is that real wing profiles are not
uniform across the span - the wingtips may present a slightly different AoA to a
particular relative wind than the wing roots. It can be designed that way so
that *part* of a wing will stall at a slightly higher speed than (and thus in
advance of) the section where the control surfaces are. The turbulence of the
stalled portion causes a vibration which the pilot will be able to feel, as a
warning that a full stall is about to occur and give them time to take action.
Conversely, when no stall is occuring, the fractionally higher AoA means the
wing roots generate more lift than the wingtips, so the strongest part of the
wing takes a larger share of the overall load and wing flexing is minimized.

As far as PC simulators are concerned, modelling multi-modal wings like that, or
the fluid dynamics calculations of air over wings is still far too complex, so
they have to treat a plane as a point mass, with moments of inertia (if that's
not a contradiction in terms) and calculate the forces acting on it. Separate
factors for induced drag, surface area drag etc go into the flight model but
these may be empirically determined values which just happen to make the overall
flight model performance feel 'right', across a range of conditions, rather than
having any resemblance to corresponding factors for the real thing.


--�
regards,

Mark

"Mark Cherry" wrote in message
...
Sorry to be pedantic but, as far as I understand it, 'coefficients' are
physical
constants. In this case, they are characteristics of a particular
airframe.

You're not being pedantic. You're just being wrong. A "coefficient" is
simply a number in an equation. It may or may not be a physical constant,
but in the case of lift, it is not. It varies with the angle of attack, as
does the coefficient of drag.

You can break the coefficient of drag down into its component parts, induced
and parasitic (aka "form" or "friction") drag. But even the parasitic
component changes slightly with angle of attack, simply because of the
change in the cross-section of the airframe presented to the relative wind.
As you noted, the parasitic component changes even more when flying in
uncoordinated flight, such as a slip or skid.

[...] Whilst TAS is fine for dead reckoning navigation
calculations

It's not just fine. It's necessary.

[...] (And when
that stalling speed converges with the highest achievable forward speed in
level
flight, the plane reaches its 'service ceiling').

Wrong again. An airplane's "service ceiling" is defined to be the altitude
at which the climb rate is lower than 100 feet per minute. An airplane's
*absolute* ceiling is the altitude at which the airspeeds corresponding to
best rate of climb (Vy) and best angle of climb (Vx) converge, which is the
altitude beyond which the airplane simply cannot climb. The airspeeds Vx
and Vy, the same at absolute altitude, are well above stall speed.

There IS another altitude that is of importance for airplanes that can climb
especially high and which go particularly fast. That is, the point at which
stall speed and the Mach buffet speed converge. At that altitude, going
slower stalls the airplane and going faster results in Mach buffet. Perhaps
that is what you were thinking of.

[...] The induced drag
coefficient, however, remains a constant, for that particular aircraft.

As I mentioned above, no. The induced drag coefficient changes along with
the lift coefficient, and depends not only on the airfoil, but also on the
angle of attack.

[...] The turbulence of the
stalled portion causes a vibration which the pilot will be able to feel,
as a
warning that a full stall is about to occur and give them time to take
action.

One will experience turbulence *prior* to stall even in an airplane with a
constant angle-of-incidence airfoil. The pre-stall buffet is caused by the
airflow separation, which starts to happen before the actual stalling angle
of attack, along with this turbulent airflow striking the horizontal
stabilizer (the latter happens only in aircraft in which the horizontal
stabilizer is in the path of the airflow coming off of the wing, of course).

Pete

In ,
Peter Duniho wrote:

snip

Okay, thanks for those corrections. Looks like I'd started out on a false
premise and, once started, the tendency is to follow-through to the finish. g
Apologies for wasting anyone's time.

I'm familiar with Cd figures quoted for cars - which present a more or less
fixed cross sectional area to the airflow - and the editable drag parameters
within the old flight dynamics editor s/w for Flight Shop created aircraft. Even
if it's not so in reality, it looks as if the sim's flight model treats these
factors as constants. shrug I really should read more but I enjoy simming
far, far too much.


--�
regards,

Mark

In article , Mark Cherry
writes

Sorry to be pedantic but, as far as I understand it, 'coefficients' are physical
constants. In this case, they are characteristics of a particular airframe.

True, they are, but the lift coefficient is a property at a given angle
of attack so they are characteristics of an airframe but only for a
given angle of attack. For small angles of attack then the lift
coefficient depends almost directly on the angle of attack.

The parasitic drag coefficient will go in proportion to a combination of frontal
area and total surface area (note that the frontal area presented to the
relative wind will change with variations in angle of attack, following a pitch
control input). The quantity of parasitic drag increases with the cube of the
airspeed, multiplied by this coefficient, mutiplied by the mass per unit time of
air flowing over it. (in kg.m.s-1 aka Watts, if I' m not mistaken)

Generally speaking parasitic drag depends on the square of the speed.
Power required depends on the cube of the speed.

Drag is a force, measured in Newtons or pounds force. Drag is a force;
watts are power.

The classic drag equation is
D = 0.5*(air density) * (reference area - usually wing area) *(
(velocity)^2) * (drag coefficient)

where velocity is TAS NOT IAS.

You seem to be confusing Power required with the drag force.

But I see Peter Duniho has already posted corrections!
--
-----------------------------------------------------------
David Francis E-Mail reply to
-----------------------------------------------------------

In ,
David wrote:

In article , Mark Cherry
writes

Sorry to be pedantic but, as far as I understand it, 'coefficients'
are physical constants. In this case, they are characteristics of a
particular airframe.

True, they are, but the lift coefficient is a property at a given
angle of attack so they are characteristics of an airframe but only
for a given angle of attack. For small angles of attack then the lift
coefficient depends almost directly on the angle of attack.

The parasitic drag coefficient will go in proportion to a
combination of frontal area and total surface area (note that the
frontal area presented to the relative wind will change with
variations in angle of attack, following a pitch control input). The
quantity of parasitic drag increases with the cube of the airspeed,
multiplied by this coefficient, mutiplied by the mass per unit time
of air flowing over it. (in kg.m.s-1 aka Watts, if I' m not
mistaken)

Generally speaking parasitic drag depends on the square of the speed.
Power required depends on the cube of the speed.

Drag is a force, measured in Newtons or pounds force. Drag is a force;
watts are power.

The classic drag equation is
D = 0.5*(air density) * (reference area - usually wing area) *(
(velocity)^2) * (drag coefficient)

where velocity is TAS NOT IAS.

You seem to be confusing Power required with the drag force.

But I see Peter Duniho has already posted corrections!


Similar thanks go to you. Dunno how that 'cubed' nonsense got in there. Call
it 'brain fade'...
Now let's see how much of this I remember in 6 month's time. ;-)



--
regards,

Mark

Please go to http://airtrafficcontrol.no-ip.org:8080 or
http://private-pilot.no-ip.org:8080 .
There had an answer for aerodynamics. (used for FAA written test)
"Dave Daniels" wrote in message
...
I have some questions about lift and angle of attack that I hope
somebody can answer. First of all, I should say that I am not a
pilot, nor am I an aeronautical engineer and my understanding of
aerodynamics is superficial at best. Heck, even my maths is pretty
ropey. (It reminds me a bit of someone being asked what skills they
brought to a construction job and they replied "I can cut wood,
but not in a straight line".) Anyway, I have been looking at the
source code of a flight simulator and trying to work out what it
does. I have a number of questions. Firstly, can the lift acting
on an aircraft go negative? Instead of the force pushing the
aircraft up, can it push the aircraft down if say, the angle of
attack is negative? Secondly, does the angle at which an aircraft
is banked affect the angle of attack? Trying to figure it out in
my head, I would say 'no' but the program implies otherwise. What
is the answer here? Thirdly, induced drag: I have read that this
is inversely proportional to the square of the aircraft's
velocity, but I do not see how this follows from the equations I
have seen. It appears to me that the greater the velocity, the
greater the induced drag. I must be missing something fundamental
here. Can anyone explain it?

Dave Daniels

Also try http://www.monmouth.com/%7Ejsd/fly/how/htm/how.html

Answers
1. yes
2. bank and AoA are independent
3. depends on whether you fix at level flight or constant angle of
attack

Joan
==
In message , "Sniper@SDU"
writes
Please go to http://airtrafficcontrol.no-ip.org:8080 or
http://private-pilot.no-ip.org:8080 .
There had an answer for aerodynamics. (used for FAA written test)
"Dave Daniels" wrote in message
...
I have some questions about lift and angle of attack that I hope
somebody can answer. First of all, I should say that I am not a
pilot, nor am I an aeronautical engineer and my understanding of
aerodynamics is superficial at best. Heck, even my maths is pretty
ropey. (It reminds me a bit of someone being asked what skills they
brought to a construction job and they replied "I can cut wood,
but not in a straight line".) Anyway, I have been looking at the
source code of a flight simulator and trying to work out what it
does. I have a number of questions. Firstly, can the lift acting
on an aircraft go negative? Instead of the force pushing the
aircraft up, can it push the aircraft down if say, the angle of
attack is negative? Secondly, does the angle at which an aircraft
is banked affect the angle of attack? Trying to figure it out in
my head, I would say 'no' but the program implies otherwise. What
is the answer here? Thirdly, induced drag: I have read that this
is inversely proportional to the square of the aircraft's
velocity, but I do not see how this follows from the equations I
have seen. It appears to me that the greater the velocity, the
greater the induced drag. I must be missing something fundamental
here. Can anyone explain it?

Dave Daniels




--
Joan Walsh