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Re: misconceptions: 2D model of 3D flight

At 12:04 AM 8/14/99 -0700, William Beaty wrote:

Ah, you've cut to the central point in the Newton/Bernoulli lifting-force
controversy.

There is no such thing as a Newton/Bernoulli controversy. Bernoulli's
principle is consistent with, and is indeed a consequence of, Newton's laws.

How can any aircraft remain suspended above the ground (or
remain in level flight)?

It can either push upon the earth, or it can employ action/reaction in the
way a rocket does. A helium balloon pushes indirectly upon the earth. So
does an aircraft in "ground effect" flight.

So does *everything*. Gravity is a force between the earth and the
aircraft; the only way to counteract it is a force (indirect or otherwise)
between earth and aircraft. The only question is how indirect it is going
to be.

But when an aircraft is far from the earth, its only option is to employ
action-reaction to produce a net downwards acceleration of massive gasses.

Again, you unnecessarily narrow the statement. At *any* altitude, if the
wheels are not touching the ground, the airplane supports itself by yanking
air downwards.

In other words, the air within the wake-vortex pair behind an aircraft has
been given a net downwards motion and this acts like a "rocket exhaust."

No.

WHen far from the earth, this is the "pure thrust" on which the aircraft
rides.

That is a significant abuse of the word "thrust" which is defined to be the
force produced by the engine. In an ordinary airplane, thrust is
essentially horizontal and I was quite correct in my earlier note to say
"pure thrust" does not support the weight of the airplane. Indeed when the
thrust is zero, the airplane becomes a glider and continues to support its
weight using the lift produced by the wings.

The wings of an airplane do not simply create a spinning pair of
wake-vorticies, they also project those vorticies downwards.

It is not the downward motion of the vortices that lifts the airplane. It
is the downward motion of the *air*. Two airplanes with equal vortices can
produce greatly different amounts of lift. For homework, explain how.

Once we accept all of the above, it becomes obvious that helicopters are
very much like conventional airplanes in that they both ride ENTIRELY upon
thrust.

But we don't accept significant parts of the above. Airplanes in normal
flight are more like gliders (which have no thrust at all) than they are
like hovering helicopters (which depend on huge amounts of thrust).

I've seen many arguments over the years which focus upon the circulation
surrounding a 2D airfoil. One facet of this has not been examined here:
if the circulation extends to a great distance around an airfoil, then it
necessarily interacts with the ground. As a result, a 2D simulation
depicts ground-effect flight, not the normal high-altitude flight of a
real-world aircraft.

True, a 2D wing is always in ground effect.

In ground-effect flight there is need for any
"exhaust" flung downwards.

Actually, the lift in ground effect is very similar to the lift out of
ground effect. That's why people find 2D simulations useful.

It is the *induced drag* that is profoundly affected by ground effect.
Note that induced drag is negligible for an airplane in normal cruising
flight, which is another part of the reason why people find 2D simulations
useful.

In a 3D aircraft the
circulation pattern which surrounds various parts of the wing cancels at a
distance from the aircraft.

It never entirely cancels. Remember, sooner or later the momentum must be
transferred to the ground, or we have violated Newton's first law somewhere.

The circulation cannot reach the ground.

Do you have any experimental or theoretical evidence to support this
statement? And did you perhaps mean vorticity instead of circulation?
There is no such thing as circulation at a point, only circulation around a
loop.

A
3D aircraft is fundamentally different than a stack of 2D airfoil
simulations.

I wouldn't say "fundamentally" different, not at all. It is different in
details, but the details are not important for normal cruising flight.

Another problem with the 2D models: in two dimensions the net upwash MUST
equal the net downwash. In other words, in two dimensions the streamlines
around the airfoil form circles. In a 2D-world there can be no trailing
vortex. A 2D-world lacks the degrees of freedom required to create a
downwards "exhaust". If we follow a parcel of air, we will see it
accelerated upwards as the airfoil approaches, then accelerated downwards
as it passes the airfoil, then accelerated upwards once more. There has
been no *net* force applied to the parcel of air.

This last statement ("no net force") gets the physics diametrically wrong.
Both upwash and downwash contribute to lift. If you want to consider them
separately, the upwash comes up and is stopped by the wing (transferring
net upward momentum to the wing) whereas the downwash is started on its
downward motion by the wing (again imparting net upward momentum to the
wing). Come on, folks, this is basic bouncing-ball physics. Let's get it
right.

In three dimensions things are different

No, in 3D this part of the story is not different.

It might profit students to learn first how a 3D wing works, and only
later to examine the strange world of "flatland aerodynamics."

No way. Flatland aerodynamics is not *that* strange. Beginning students
don't know or want to know about induced drag. Later, when people start
asking about induced drag, it is easy to patch up the 2D model to include it.

If we concentrate too much on 2D simulations, we will come to believe that
real-world airplanes should be able to fly forever,

In fact finite real-world airplanes achieve remarkably high lift-to-drag
ratios, 40:1 or higher, so neglecting drag doesn't seem so terrible. And I
don't think it would be the first time that a physics class neglected a
small amount of friction in order to simplify the presentation. Or are you
such a purist that you force your students to deal with the friction of the
pulleys and the mass of the strings when beginning their analysis of
mechanical advantage?

that pressure-differences are the central concept,

It is one of the central concepts.

that action-reaction is
unimportant and there is zero net deflection of air by the wing,

Net deflection? It depends on the length-scale.
a) If you look right next to a 2D wing, the air most certainly is
deflected. This is what most students want to see, and the 2D model gets
it right, so the conversation should stop there.
b) At an intermediate length scale, there is a question as to where the
upwash comes from and how much there should be. The 2D model is slightly
(not categorically) different from the 3D model at this scale.
c) At the longest length scales, there must be zero net deflection,
because air is conserved. There must be a closed cycle. Again, the 2D
model gets this right. So what are you complaining about?!???!!

and that
the wake-vortex pair which trails behind the aircraft has little to do
with the generation of the lifting force.

Well, in 2D the question of trailing vortices never comes up, but as I said
before, it is easy to patch up the 2D model to handle the 3D case by
invoking the mathematical theorem that says vortex lines cannot have loose
ends.