On 16 Oct, 16:17, Le Chaud Lapin wrote:
On Oct 16, 6:31 am, Thomas wrote:



On 9 Oct, 21:08, Le Chaud Lapin wrote:
You may want to check out my web pageshttp://www.physicsmyths.org.uk/bernoulli.htm
andhttp://www.physicsmyths.org.uk/drag.htmfor a closer examination
of the physics behind the aerodynamic lift and drag.

The main point I am making there is that it is physically nonsense to
claim that changing merely the tangential velocity of the air stream
relative to the surface would in any way produce a resultant force (at
least for a non-viscous gas).
What one needs for a pressure change
(and thus a force) on the surface is a change in the numbers and/or
the velocity of the molecules hitting it, i.e. it is only the vertical
component of the velocity that is relevant here. Only this can produce
the lift for an airfoil, either because of the increased number of
collisions on the lower side or the decreased number of collisions on
the upper side (both situations lead to a lift).

I agree, but there are some that seem to think the contrary, as you
know, with the Coanda effect.http://en.wikipedia.org/wiki/Coand%C4%83_effect

What is troubling about many of these theories is that, at the precise
moment where the reader is most alert in anticipation of the meat of
the explanation, the hand-waving begins. In the link above, the clause
entitled Causes, it is written:

"The effect of a spoon apparently attracting a flow of water is caused
by this effect as well, since the flow of water entrains gases to flow
down along the stream, and these gases are then pulled, along with the
flow of water, in towards the spoon, as a result of the pressure
differential. "

Hmmm...."and these gases are then pulled"...

pulled? By what?


The Coanda effect is only due to the viscosity of the gas/fluid and
thus would not appear for a non-viscous gas, but the aerodynamic lift
does (so the Coanda effect can not possibly be an instrumental cause
for the latter).

Based on the simple kinematical model for the change of the molecular
collision rates with the wing surface, one can indeed get a good
estimate for the lift of Boeing 747 for instance:

consider first a plate of a size 1 m^2 moving head-on with a velocity
of 250 m/s in air; air has a number density of about 10^25 molecules/
m^3 (at 10,000 m), so in 1 sec the plate will be hit by 10^25*250 =
2.5*10^27 molecules. If you assume that each molecule has a weight of
4.5*10^-26 kg, this means that the force on the plate is 2*2.5*10^27
*4.5*10^-26 *250 = 5.6*10^4 N = 12,600 lb (the additional factor 2 is
due to the fact that in an elastic collision with the plate, the
momentum change is twice the momentum of the molecule). Of course, the
wing surface is not directly facing into the airstream but only at a
very shallow angle. Let's assume that this angle (the average slope of
the upper wing surface) is about 5 deg; this means that the force
calculated above has to be multiplied by a factor sin(5)*cos(5) to
obtain the lift and by a factor sin^2(5) to obtain the drag force,
which results in about 1,100 lb and 95 lb respectively. Now this would
be for a wing surface of 1m^2; however the total wing area of the
Boeing 747 is 541 m^2 (see http://www.airliners.net/info/stats.main?id=100
), so the forces become about 600,000 lb for the lift and 50,000 lb
for the drag (by the wings). Note that this figure for the lift force
is pretty close to the maximum weight of a 747 (considering the crude
nature of the derivation, in particular the assumption of a 5 deg
angle for the slope of the upper wing surface).

And it should be
obvious that for this to be the case, one must either have the lower
side of the wing facing to a certain degree into the airstream, and/or
the upper side facing to a certain degree opposite to the airstream.
This is why one either needs a certain 'angle of attack' or a
correspondingly shaped airfoil. And it should be obvious that in order
to have an asymmetric force (i.e. a higher upward than downward force)
one needs the surfaces of the airfoil to be orientated in some way
asymmetrical relatively to the airstream. So a perfectly symmetrical
airfoil (front to back) at a zero angle of attack (like I indicated in
Fig.1 on my pagehttp://www.physicsmyths.org.uk/bernoulli.htm) should
not produce any lift as the upward force (from the rear part) is
exactly equal to the downward force (from the front part). All that
would happen is that the wing experiences an anti-clockwise torque.
This is the reason why the rear part of the wing (behind the apex)
must always have a larger surface than the front part. At least I have
yet to see an airfoil where this is not the case and where it can be
used at a zero angle of attack.
(the Bernoulli principle is in direct contradiction to this as it
would also predict a lift for a perfectly symmetric airfoil in this
sense).

I just read both your web pages.

BTW, your explanation of d'Alembert's Paradox and the blow-over-paper-
attached-to-table experiment could both use diagrams. I am trying the
blow over the paper experiment now and I am not sure if I am doing it
as you described. Could you provide a more vivid description so I can
make sure?


Well, the point is that the commonly given example with blowing over
the sheet of paper only works because (due to the orientation of the
paper surface) you are blowing away from the paper. The (on avarage)
initially stationary air molecules will thus be pulled with the air
molecules coming out of your mouth, i.e. away from the paper, which
will thus create a corresponding reduction of the number of molecules
near the paper surface, i.e. a pressure reduction. However, this all
can only happen a) because of the viscosity of the air (the molecules
coming out of your mouth collide with the air molecules, and b)
because you are blowing to a certain degree away from the paper. Would
you blow exactly parallel to the surface of a flat sheet of paper,
nothing would happen at all (it is obvious that if the sheet would
lift up at the 'downstream' end, it would be pushed right back again
into a position where the surface is parallel to the airstream (as
this is the force free equilibrium position)).


So since this effect (llike the Coanda effect) relies on the
viscosity of the air, it has nothing to do with the aerodynamic lift
(which also would occur if the air was completely inviscid).

Thomas