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Re: Physics of Flight

Let me focus on one aspect of Stefan's trolley illustration (see below)
The system is made of three objects. It is located in space, far away
from all big objects (to ignore gravity) and is initially at rest (with
respect to distant stars and galaxies). It consists of a very long rigid
platform with a wall, of a spring cannon, situated away from the
wall, and of a projectile, to be ejected from the cannon at t=0. Each
of the three objects is practically one-dimentional. There is no friction
in this idealization. The three masses are identical.

The projectile is ejected with the speed v and the cannon gains the
same speed in the opposite direction. The platform is still at rest but
the cannon recoils toward the wall. After couple of minutes (hours)
the wall is hit. It is a perfect elastic collision. The cannon stops and
the platform takes its linear momentum. The end result is the
cannon ball at rest and two objects moving away with equal and
opposite speeds. This result is exactly the same as if there were no
cannon (one end of the ejecting spring being attached to the wall.)

You can place as many mass objects (keeping masses identical
as above) as you wish. The final results is the same, the initial
projectile, which was never close to the wall moves as if it were
pushed directly by the wall. Only the number of collisions is
much larger.

I know that this is not a good model for molecules which are
pushed down by the rotating "wings" of a helicopter, or by
the wings of an airplane. Only an analogy. Soaring birds and
gliders, by the way, also push air down. Just repeating a
small part of what Stefan wrote.
Ludwik Kowalski

Stefan Jeglinski wrote:

I think we might be having a problem distinguishing between whether
something happens, as opposed to whether it must happen. Specifically:
(1) Does a hovering vehicle that is employing a reaction engine also
exert some force on the earth? Answer: typically yes. (2) Must it do
so in order to hover? Answer: absolutely not.

It seems from my reading of this thread is that there is not an issue
about air being redirected downward by the wind. The exact mechanism
for this is apparently debated extensively. The real hot topic seems
to be whether a wing can be described as a reaction engine.

To return to my earlier toy model (a guy throwing balls off a
frictionless rolling trolley), it seems to me there are 1:1
correspondences between its features and the argued issues. I am
leaving out precise language here to get the point across; I don't
think I've compromised much, if anything. Also keep in mind that it's
a toy model; take it seriously only for the physics it entails.

1. My guy throws balls off the trolley and propels himself forward.
1. The wing throws air down and propels itself up (lift).

In my example, I also surmised the presence of a rigid wall connected
to the earth.

2. When the ball bounces off the wall, it imparts an additional small
impulse to the earth. My guy actually sees this as an increase in his
speed, since he's in a frictionless trolley and all. If my guy was
throwing the balls hard enough, he could be hitting a wall quite far
away without changing the result. In fact, he might already have
thrown another ball off before the 1st even hits the wall, so that he
doesn't even have direct knowledge that the ball ever hit the wall.
If he instead threw the ball at the escape velocity and missed the
wall, this would be a distinguishably different result w.r.t. his
final speed though, so perhaps he -would- have direct knowledge,
albeit *delayed*.

2. "The air thrown down from a wing can't possibly hit the ground and
cause the same effect." I would argue why not in principle? The air
undergoes so many other collisions that it's effects seems diminished
to an infinite degree, but in fact this is the argument of why a jar
with a fly in it weighs the same on average whether the fly is flying
or not. Even though the air pushed down by the fly seems like it
would be infinitely diminished in it's ability to "hit the bottom of
the jar," it does not appear to be impossible in reality. In fact it
appears to be required behavior, albeit via many many collisions. I
like Brian's description:

If I eject one molecule downwards at high speed, I can expect
it to share with two molecules at lower speed, and so on in
increasing quantities until at appreciable distances beneath,
it will be instrumentally difficult to detect the small pressure
increment over the large area in question.

The idea is that a single molecule's large momentum is ultimately
split among so many masses that no velocity need be large. But see
my postscript.

I don't think that anyone would argue that my trolley guy is not
using an reaction engine as that word has been used in this thread.
From this standpoint, the wing does the same thing (reaction engine)
as per item number one above. OTOH, I think John's argument is that
ultimately, the wing stays up because the air eventually hits the
ground. And indeed that seems to be a consideration. But in the same
way that my guy need not hit the wall with the ball to go, I see this
not as a requirement but only as a consideration (in agreement with
Michael Edmiston I think).

Which means that John would probably agree with me up to the point
N-1 and then claim that step N is unjustified :-) John, help me out
and tell me exactly where I'm going wrong, in your opinion. I have
not doubt that you can come up with a flight analogy that causes my
trolley guy to make a wrong prediction about the mechanism of flight,
as you did in the green cheese post (in fact, my postscript does just
this but not with a flight analogy). But I am unconvinced that it
would speak to the gist; it seems to me that there should be a zeroth
order claim here that cannot be obfuscated by complex flight
examples.

Stefan Jeglinski

Post script. I myself would be careful about my bouncing ball
analogy. It cannot be compared properly to the motion of molecules in
the air (hereafter referred to as wind). The crux is I believe the
difference between elastic and inelastic collision and some (dare I
say it) entropy arguments. IIRC, wind hitting something is generally
an inelastic collision (IOW, none of the momentum doubling behavior
that results from an elastic bounce collision - wind doesn't "bounce"
AFAIK). Even though my trolley guy's ball can bounce off the wall
elastically or splat/stick to it inelastically, it still imparts
momentum to the earth through the wall and is perceived as a speed
increase in the trolley. But a mass of air being thrown downward, say
from 35,000 feet? Even with Brian's fine description, I suspect that
energy loss through inelastic collision, and some kind of entropy
argument that I am not smart enough to present or probably
understand, makes me wonder if the thrown-down air ever actually
affects the ground. I hereby invoke some principal about signal being
lost in the noise and bow out of the discussion because I'm not even
clear on what an inertial frame is anymore. But then there's that fly
in the jar...