Newsgroups: sci.aeronautics
From: drela@mit.edu (Mark Drela)
Subject: Re: Wing Theory
Date: Tue, 7 Apr 1998 03:56:58 GMT

Don Stauffer wrote:

> The real question does remain, why does the air go faster over the top.
> I've got my own explanation, but not sure if folks by it.  But Newton's
> explanation of lift does not explain why air goes faster over top
> either. But we can agree that it does, right?

The higher speed over the top is "explained" by F = ma (Newton's Law),
just like 99.9% of everything else in the universe.


A more detailed explanation might go as follows.
At least this is how I visualize it:

If you orient a stationary airfoil at some angle of attack and set it
into motion, the flow will curl up around the trailing edge, and form
a "starting vortex" just above the trailing edge.  The lower pressure at
the center of this vortex will draw the upper-surface flow aft and thus
accelerate it until the flow no longer tries to curl around the trailing
edge, and the vortex vanishes (is swept downstream to be more precise).
Walla!  Faster upper surface flow!


Now let's say you are cruising along steadily:

If the upper-surface flow slows down slightly because of some disturbance,
the flow will again try to curl around the trailing edge, and the vortex
will re-appear, and will then re-accelerate the upper flow back up to its
equilibrium speed.  Similarly, if the bottom flow slows down accidentally,
a small vortex will curl around to the *bottom* side, and accelerate the
bottom back up.  Hence, the top and bottom velocities stay at whatever
ratio is necessary to keep the trailing edge vortex from appearing.
This equilibrium at the trailing edge is in effect the Kutta condition.


  Mark Drela                          First Law of Aviation:
  MIT Aero & Astro          "Takeoff is optional, landing is compulsory"

Newsgroups: sci.aeronautics
From: drela@athena.mit.edu (Mark Drela)
Subject: Re: How do airplanes fly?
Date: Mon, 13 Apr 1998 05:00:46 GMT

In article <1991Dec5.021651.6548@math.ucla.edu>, barry@arnold.math.ucla.edu
(Barry Merriman) writes:

|> How do planes fly? This thread started on sci.physics, but physicists
|> don't seem to know how flight works. I'm hoping the aero engineers
|> can give a good intuitive explanation.
|>
|> More precisely, here's what I'd like: starting from the
|> wing at rest, show, using obvious forces, how the
|> lift develops, and why the corresponding flow is stable.
|>
|> The explanation should make it intuitively obvious whether
|> such things as surface curvature, angle of attack and
|> sharp trailing edge are necessary for lift.

Whew! That's a toughie.  Here's my shot ...

First, let's dispel some myths.

MYTH #1
"The air over the top of the airfoil has to go farther, so it goes faster
to meet up with the air going under the airfoil at the same time".

This is what Encyclopedia Britannica says.  It is also totally wrong.
In fact, a collection of fluid "globs" lined up in a vertical line
will be anything but vertical once they pass the airfoil.  The
"before & after" picture is crudely indicated below.

  before . . . . . >                     after
    o                                                o
    o                                                o
    o                                               o
    o                                               o
    o          _-----____                   o
    o         c______________       o
    o             airfoil                  o
    o                                        o
    o                                         o
    o                                         o

The deformation in the line is NOT due to the boundary layer!  It looks
like this in inviscid flow.  In fact, if the leading edge is blunt, the
one glob starting out exactly on the stagnation streamline never gets to
the airfoil, let alone past it!  (it's a simple calculus exercise to show
this).  A continuous line of particles therefore never gets "cut" by the
airfoil, but gets stretched out indefinitely.  Clearly, MYTH #1 makes no
sense in this context.


MYTH #2
"The lowered pressure over the top of the wing is _caused_ by
the higher velocity there, in accordance with Bernoulli's Law."

It is misleading to use Bernoulli's Law in a cause-and-effect argument.
I could just as well say that the velocity over the wing is higher because
the air accelerates towards the lower pressure there.  The squabble here
is over semantics more than anything else.  I like to think of Bernoulli's
Law in the following terms:

"In an irrotational, effectively inviscid flow, pressure and velocity
are uniquely related by...  (we all know the actual formula)",

and avoid using it in any kind of physical explanation of flow phenomena.


MYTH #3
"The flow around an airfoil and the lift on it are non-unique"

This is only true in a mathematical oversimplification of reality -- namely
inviscid flow.  In a real viscous fluid, there is only one flow which
satisifies conservation of mass, momentum, and energy everywhere.  Typically,
this "physically correct" (PC ?) flow will satisfy the Kutta condition (smooth
flow-off) at a sharp trailing edge.  If the flow does not come off smoothly,
such as shortly after the start of the wing motion, viscous forces acting at
the sharp trailing edge will cause a vortex to roll off on the upper side,
if the angle of attack is positive.  The lowered pressure at the core of
this vortex will accelerate the upper flow towards it, setting up the
"lifting" flow pattern.

I should add that in some rare instances, several distinct flows may be
possible (e.g. stall hysteresis), but not infinitely many.  Also, the
only possible flow may be oscillatory (e.g. vortex-shedding off a cylinder).
These are mainly curiosities, however.


So to answer your questions...

|> Here's a few ground rules for the discussion:
|>
|> (1) No "explanations" of the form:
|>     air must (for some bogus reason) flow faster over the
|>     top than the bottom, therefore, by conservation of energy,
|>     (= bournoulli's law) there is low pressure on top and net lift.
|>
|>      This is the physicist's argument. The main flaw is that they
|>      _assume_ a lifting flow pattern (fast on top, slow on bottom),
|>      and then invoke conservation of E to verify it is lifting. THis
|>      argument would be reasonable if they could give a valid argument that
|>      the flow pattern would arise at take off, and is also stable
|>      against perturbations. After all, there are other, non-lifting, flows
|>      past airplane wings. The argument would get even better if they would
|>      also scrap bournoulli, and show exactly how the forces acting arise,
|>      so that would could get an intuitive feel for what is going on.

There is one unique flow past a wing (see MYTH 3).  The pressure field
associated with this flow exerts a lift on the wing which depends on the
wing shape, angle of attack, dynamic presure, etc.  To "see" why the
pressure must be lower over the wing, think of the curvatures of the
streamlines above and below an airfoil at an angle of attack, and the
pressure gradients necessary to force the fluid globs in curved paths
(I'm sorry, but you have to rely on at least  F = ma  at some point).


                     .       .
              .                    .
   .    .                - p             .     .
                    _____
                          -----_____

FLOW >>>                 + p
                     .      .
              .                    .
   .    .                                .     .


Note that the streamlines are roughly parallel to the airfoil at the
sharp trailing edge, as required by viscosity.  Clearly, the pressure
over the wing must be decreased, and the pressure under the wing increased
to force the streamlines into this pattern.

I hope this answers some of your questions.



  Mark Drela                          First Law of Aviation:
  MIT Aero & Astro          "Takeoff is optional, landing is compulsory"