Alan Baker wrote:
In article . com,
wrote:
Jose wrote:
The hovering spacecraft has zero horizontal and vertical momentum.
It has weight, directed downwards. The engine accelerates
mass downward producing an upward force equal in magnitude
and opposite in direction to the weight of the spacecraft. This
imparts an acceleration to the spacecraft equal in magnitude and
opposite in direction from the local acceleration due to gravity.
The flying wing has some horizontal momentum which is secondary here,
How much?
and zero vertical momentum.
It also has weight, directed downwards. The wing accelerates
mass downward (mass it finds in the air molecules) producing
an upward force equal in magnitude and opposite in direction to
the weight of the wing (and its presumably attached aircraft. It does
so by finding air in front of it, flinging it downwards and forwards
(which causes the air in front to try to get out of the way by rising).
In the steady state, one can measure high pressure below and low
pressure above, but this is just the macroscopic manifestation of the
greater number of molecular collisions below, and the lesser number of
collisions above. That's what pressure is - we have both agreed on this.
The greater number of collisions below
imparts an acceleration to the aircraft equal in magnitude and
opposite in direction from the local acceleration due to gravity.
I agree that lift is a force, exerted on the aircraft by the air,
which in steady level flight is equal in magnitude and opposite
in direction to the weight of the aircraft. Energy is 'pumped'
into the air by the plane. There is no need for a net momentum
exchange between the airplane and the air in order for
energy to be exchanged or for forces to be applied.
Indeed, in those last two paragraphs above, you make
no mention of momentum.
BTW, I was wrong to invoke conservation of momentum.
Momentum is conserved in elastic collisions, like the
collision between a cue ball and the eight ball. Momentum
is not conserved in inelastic collisions, like the collision
between a cue ball and a nerf ball.
You are incorrect. Momentum is *always* conserved.
How is momentum conserved when a cue ball hits a nerf ball?
Roll the airplane into a 90 degree bank. The weight is
now orthogonal to the lift. As teh airplane falls, it
banks even though there is no Earth 'under' the
belly. Why?
Because the wings are exerting a force on the air and the air
consequently experiences a change in momentum.
Yes, both the airplane and the air experience a net change in
momentum when the aircraft climbs, descends, or banks.
In level flight at constant speed the aircraft has constant horzontal
and zero vertical momentum.
The air exerts a force on the wings. In level flight, this force is
countered by an equal and opposite force exerted on the aircraft by the
gravitational attraction of the earth. Without that countering force,
the aircraft would accelerate upward. That's what an unbalanced force
*does*.
Yes, no question about weight being balanced by lift.
But the wings also exert a force on the air (Newton, remember: for every
force there is an equal and opposite, etc., etc.). That force is not
countered by *anything*. Hence, the air is accelerated downward; a
continuous stream of air receives an constant change in momentum.
If the air has a net increase in downward momentum, how is
momentum conserved.
F = ma; that's the way we normally see it presented. This equation
relates force, mass and acceleration. It assumes a constant force acting
on a constant mass will produce a constant acceleration, and the mass
will start moving faster and faster.
But there is an equally valid presentation of that equation; one which
is more useful for examining what happens with an aircraft moving
through the air:
F = md/t^2; force is equal to mass, times distance, divided by the time
squared. If you keep velocity and time squared together, you get
acceleration of course, but there's no rule that says you have to. In
fact, the rules of equations say exactly the opposite: that an equation
is equally valid regardless of the way you group multiplications and
divisions.
So:
F = m/t * v/t; the force is equal to the rate of mass per unit time,
multiplied by the distance per unit time.
What that says is that if you change the velocity of a given mass flow
(air) by a given velocity, then you will get a given force.
Yes, Force is the time rate of change of momentum.
In other words, an aircraft passing through the air will cause a portion
of that air to be disturbed downward. Because the aircraft is moving
forward a constant speed, it imparts a downward velocity to certain mass
of air each unit of time.
The air starts moving downward with a certain velocity.
I don't deny that downflow occurs. The pont is that downflow is a
consequence of lift, not the cause of lift, and it is balanced by
upflow, (albeit a more diffuse flow) otherwise the upper atmosphere
would run out of air.
Once you understand this, you understand why induced drag is less at
hight speeds than low. Go twice as fast, and you encounter twice as much
air in any unit time, and thus only need to impart a velocity to it that
is half as much. But because the kinetic energy involved is proportional
to mass and proportional to the *square* of velocity. Twice as much mass
doubles its contribution to energy lost, but half the velocity
*quarters* its contribution; giving an overall kinetic energy lost to
induced drag of half as much when going twice as fast.
Interesting.
--
FF