The Impossibility of Flying Heavy Aircraft Without Training

David CL Francis wrote:
On Fri, 3 Mar 2006 at 05:30:06 in message
.com,
wrote:

Newton had three laws of motion, you're ignoring the first.
Is there a net change inmomentum of the fan? If not,
how can there be a net change of momentum of the air?

I am ignoring nothing. The above statement is wrong. You agree below
that energy is put into the air. In the case of a fan that energy goes
into increasing the velocity of the air. The rate of change of momentum
(mass flow times velocity increase) produces forces that increase the
momentum of the air. Energy changes momentum. Momentum destroyed turns
back into energy.

Well I'm sorry to see that I an not the only one who was confused
on this issue. In Newtonian dynamics, energy is always conserved,
mass is always conserved, and momentum is always conserved.

When the momentum of a body changes, then energy is converted
from one form to another, but the momentum of a body can only
change by being transferred to another body. Momentum,
like energy and mass, is never destroyed.

I'm not fond of 'unit analysis' but consider that the units of energy
and the units of momentum when reduced to fundamental units,
are different. Conversion between the two is impossible.


This argument is hung up on the idea that the air returns to a steady
state eventually - which it does! But not quite back to where it was
because of losses Nevertheless energy is lost and replaced by the
engines of the aircraft.

Yes, the airplane puts energy into the air. But in the closed system
that consists of the airplane and the atmosphere, or the fan and
the air in the room, momentum is conserved, just as mass and
energy are.


... Air moving through the
fan in one direction is offset by air moving around the fan
in the other direction.

The air slows down and looses energy and momentum far away from the
aircraft - so what? Any small drop in pressure at the fan also reaches
back and develops flow some way in front of the fan. For lift purposes
it does not matter much. The air may or may not make its way back to the
inlet again, some of it will.

If only some of it does, then mass is not conserved. ALL of it,
or rather an equivalent amount of displaced mass makes it
back to the inlet of the fan. In order to make it back, it has
velocity. for a rather slow fan in a rather small room the velocity
through the fan may be ten times the average velocity of the
air moving around the fan in the opposite direction. That's
OK, but conservation of momentum requires that ten times
the mass be moving in that opposite direction at one tenth the
'fan' velocity and a moments consideration should convince you
that this also conserves mass.

In te case of the aircraft, the fan is moving through the air so that
when the air (or rather an equivalent displaced mass of air) returns
to the inlet, the inlet has move on.


In open air the volume of air moving around the fan is larger,
but moving at a lower speed than the air moving through the
fan so that the momenta of the flow in either direction is equal
magnitude and opposite in direction to the flow in the other
direction.

Except for losses that occur due to friction and eddies that float away
to dissipate themselves elsewhere.

No. The turbulance dissipates energy, (that is to say it converts to
heat) not momentum.

Momentum is always conserved.

--

FF