Airplane Pilot's As Physicists

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

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 2.5*10^27
*4.5*10^-26 *250 = 5.6*10^4 N = 12,600 lb. 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).


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