Re: [Phys-l] Curious toy

[John Denker <jsd@av8n.com>]

Roger Haar wrote:

> 	The first web site on which I saw  a picture of this toy and two 
> sentences describing it, used a flat-topped dowel, but had a link site 
> in my original post.  The quick and dirty test unit which I made, also 
> had a flat topped dowel.  The dowel pops out just fine.  The only thing 
> that I have thought of, but have not tried is getting a tighter fit 
> between the dowel and the hole.

I have been corresponding with Stefano Oss at the University of Trento
(unitn.it).  He has been doing some simple experiments on closely-related
topics.  Here is a picture:
  http://www.av8n.com/physics/img48/oss-fig2.jpg

The scale is attached to the disk-shaped plate in the middle of the
larger rectangle-shaped plate.  When you shoot a jet of air over the
plate, lift is observed.  This apparatus was intended to minimize
funny edge effects at the edge of the disk.

I am a long way from understanding what's going on, but I think we are
making good progress.  Here are my latest thoughts:

Please refer to
  http://www.av8n.com/physics/img48/jet-lift.png

In scenario #1, there is some chance the Coanda effect will occur at point
A, where the jet hits the curved part of the fixed plate.  (By Coanda effect
I mean curvature-enhanced turbulent mixing.)  Air above the jet will get
mixed into the jet.  See below for more discussion of mixing.

Therefore scenario #2 may be a useful refinement, because it has less potential
for creating confusion.  (The Coanda effect is a notorious source of confusion.)
Note that the plate is flat and starts well behind the opening of the nozzle.

There will still be mixing, even without Coanda.  The mixing will probably not
be as powerful as what you get with the Coanda effect, but it will still occur.
Air from left and right of the jet (points B and C in the diagram) will get
mixed into the jet, and air from above also.

By the way, I suggest making the nozzles out of thin-walled tubing, so that
they can be placed right next to the surface.  This minimizes the chance that
air from /below/ the nozzle will get mixed into the jet.

Mixing is significant for the following reason:  suppose we start out with a
parcel of air with momentum p1 and energy .5 p1^2 / m1.  We mix that with a
parcel initially having momentum zero and energy zero.  Afterwards we have a
larger parcel having momentum p2 and macroscopic kinetic energy .5 p2^2 / m2.
We know p2=p1 by conservation of momentum.  Hence the macroscopic kinetic
energy is less, because of the larger mass in the denominator.  The rest of
the initial energy must have been converted to spinning eddies, and will
eventually be dissipated as heat.

This is relevant because I suspect the eddies are involved in producing the
observed lift.

There's probably a reasonably-simple way of analyzing this situation quantitatively,
but I haven't been able to think of it yet.  Bernoulli-type arguments are not
going to be anywhere near sufficient.

As a further refinement, consider scenario #3.  There are now /three/ nozzles.
At first glance, one might think that if one nozzle produces some lift, three
nozzles would produce even more lift ... but if mixing and eddies are involved,
this setup should produce /less/ lift, because it produces more nearly laminar
flow over the measuring area.

=========

Stefano wrote:

> > The point, as you suggest, is "where does the required momentum come from?".

Yes.  We won't understand what's going on until we can answer that question.

As a related point:  The pressure gradient can be related to streamline curvature,
even in situations where Bernoulli-type arguments cannot easily be applied.
Lift means there must be concave-downward streamlines somewhere.  We won't be
anywhere close to understanding what's going on until we have identified the
concave-downward streamlines.
  http://www.av8n.com/how/htm/airfoils.html#sec-p-versus-v

=============

Also keep in mind that if you have two air masses, meeting at a planar
boundary, sliding past each other, neither one has lower pressure.  This
should be obvious by symmetry and by Galilean relativity.

This tells us that there are many scenarios where air moving uniformly over
such a plate does not produce any lift.

This leads to the conclusion that it cannot simply be the general motion
of the air over the plate that produces the lift;  there must be something
special about the geometry of the jet, and the nonuniformity of the motion.