Backwash Causes Lift?

Tina wrote:
Still waiting for the conservation of momentum derivation. My husband,
also trained as an engineer, casually remarked he didn't think you
could get from Newton's First Law to the that confirms my memory,
but we are both willing to have that belief rebutted.

You can't get conservation of momentum from F = m*a (or vice versa) since
the latter is not a statement about anything being conserved. But you can
get "For every force there is an equal opposite force" from conservation
of momentum, and vice versa, with a small number of assumptions. You can
use derivatives to derive one way and integration to derive the other.
Here are several conservation laws that share a common derivation,
starting with:

Center of Mass is Conserved
---------------------------
Center of mass of a closed system of particles of mass m1, m2, m3, ... mn
must remain fixed for all time, which with a suitable selection of
coordinate origins may be stated mathematically as:

(a) m1*x1 + m2*x2 + m3*x3 + ... = 0
m1*y1 + m2*y2 + m3*y3 + ... = 0
m1*z1 + m2*z2 + m3*z3 + ... = 0

Note that this doesn't say that, for example, x1 can't vary with time. It
only says that if it does then m1, m2, m3, x2 or x3 or other masses or
positions must somehow change so the left hand side still remains zero.

Momentum is Conserved
---------------------
If position with respect to time is continuous (no discontinuities; e.g.
no jumps) then we can take the time derivative of the above, yielding:

(b) m1*dx1/dt + m2*dx2/dt + m3*dx3/dt + ... = 0
(And so on for the other coordinate axis.)

This is of course just the conservation of momentum equations because
dx1/dt = Vx1, a velocity. Note that d(m1*x1)/dt would have been more
appropriate if the mass of particles varies with time.

Force is Conserved
------------------
Given the continuity assumption above, then we can keep taking time
derivatives of the above, yielding the next conservation statement:

(c) m1*d^2(x1)/dt^2 + m2*d^2(x2)/dt^2 + m3*d^2(x3)/dt^2 + ... = 0
(And so on for the other coordinate axis.)

This is of course just the old equal and opposite action statement in
mathematical form because d^2(x1)/dt^2 = ax1, an acceleration.

So if one claims any _one_ of the above conservation laws exists then the
other two appear to follow with only a small set of (presumably
reasonable) assumptions.

Of course, but the specific statement I wanted made clear had to do
with getting conservation of momentum from Newton's relationship
between force, mass, and acceleration. The OP claimed to be an
engineer, he was suggesting something I thought was unlikely and you
demonstrated that nicely.

Tina wrote:
Of course, but the specific statement I wanted made clear had to do
with getting conservation of momentum from Newton's relationship
between force, mass, and acceleration. The OP claimed to be an
engineer, he was suggesting something I thought was unlikely and you
demonstrated that nicely.

Didn't he say he was an electronics engineer? Unless he's doing work on
electromechanical devices I can see how one can get rusty on dynamics.

I'm not sure questions regarding lift belong in a piloting group anyway.
Fluid dynamics is a particularly difficult subject because it is easy to
overlook things, such as: if a wing accelerates air downward, then
according to conservation of momentum some other mass must be accelerated
upward.

Jim, I guess it depends on the institution and the intellegence of the
student. My husband graduated even longer ago than I did with degrees
in electronics, but he was well trained in mechanics as well. It may
be the newer schools don't offer as broad a base in classical
mechanics and physics.

What is especially interesting is that theories are offered that do
not predict observations very well. I skydived a few times, and my
sensation was that my arched body (the negative of a classic airfoil)
was being supported by a pillow of air, not being drawn up into a
partial vacuum. In fact if memory serves I don't remember the jump
suits of others bellowing in the back either.

And if one holds one's hand out of a car window, the psudo lift
provided by air deflecting from the surface facing the wind does not
seem to come from something at the trailing edge -- in fact one can
put one's wrist in the trailing position and still feel the same
impact -- delta momentum - forces.

For a theory to be accepted it has to predict observations. Trailing
edge downwash and some other things written here don't seem to do
that. But it is fun. Shall we talk about flying a kind of roll with
having the pilot experience exactly 1 G into the seat during the
sequence? That is about as much fun as talking about an airplane take
off from a belt sander, or taking off into a 70 KT headwind, turning
downwind and not falling out of the sky.




On Oct 4, 7:48 pm, Jim Logajan wrote:
Tina wrote:
Of course, but the specific statement I wanted made clear had to do
with getting conservation of momentum from Newton's relationship
between force, mass, and acceleration. The OP claimed to be an
engineer, he was suggesting something I thought was unlikely and you
demonstrated that nicely.

Didn't he say he was an electronics engineer? Unless he's doing work on
electromechanical devices I can see how one can get rusty on dynamics.

I'm not sure questions regarding lift belong in a piloting group anyway.
Fluid dynamics is a particularly difficult subject because it is easy to
overlook things, such as: if a wing accelerates air downward, then
according to conservation of momentum some other mass must be accelerated
upward.

Tony writes:

For a theory to be accepted it has to predict observations. Trailing
edge downwash and some other things written here don't seem to do
that.

Actually, downwash can be directly observed in appropriate atmospheric
conditions. There are pictures on the Web that illustrate this.

Remember, in order to accelerate something upward, something else must be
accelerated downward.

When you hold your hand out the window of a car at an angle, and you feel it
being raised, where does the energy to raise your hand come from?

"Jim Logajan" wrote

Didn't he say he was an electronics engineer? Unless he's doing work on
electromechanical devices I can see how one can get rusty on dynamics.

Jim, this is MX reborn. Give it up.
--
Jim in NC