Pardon me for jumping in. Initially, I also thought the PF
screwed up. Though following the discussion and matching the
background of physics to these items, I more or less changed
my mind. The general suggestion is: PF should have initiated
a pitch&power approach. It very well could be he did, with this
as a result.
I did write these articles the last 3-4 weeks, though didn't post,
given my lack of time to keep up with the current thread. Some
of the subjects have been touched in recent posts, though I
keep my writing included, to take care for a complete line of view.
I neither did have time to match all of the raised items with
the actual AF447 figures. Maybe somebody wants to do this.
My apologies about this.
In the, up to now 5 threads, some physics came along. Physics, which are
sometimes so far off, that conclusions drawn on that are totally off. As such I
do give some thoughts how to approach those items.
1. Usage of TAS to calculate Kinetic Energie exchange for height.
====================================
- Since Kinetic Energy is non linear in speed, it's not an option
to consider the change in TAS a suitable parameter for change in
Kinetic Energy. For a zero speed based start to calculate the speed
of a dropping item as function of it's height, that's ok.
Since the Kinetic Energy is the SQR of the speed, the Kinetic
Energy of different perpendicular axis are independent.
- For general exchange of speed into another direction or height
(Potential Energy), the actual inertial speed has to be used,
so at least the ground speed and not TAS. I would even say, groundspeed
corrected with the earths' rotational speed (roughly 1800 m/s). Due
to lack of time, I didn't have the time to think this through for
100%, though I do expect this to be relevant.
This can be understood from the following thought-experiments:
= Assume the windspeed suddenly becomes zero. Will the effective
Kinetic Energy of the airplane change ? Nop.
(The airplane will show reactions after the change, though that's because
the force-field does change).
= Assume with the airplain flies with constant speed, the earth rotation
is suddenly stopped (that would give a mess on the ground, though it's
only a thought experiment). Would the effective Kinetic Energy of
the airplane change ? Nop. When an airplane lifts off, the airplane
starts with a speed related to the ground plus a TAS to generate
sufficient lift to lift off.
- So the Kinetic Energy will be 0.5 * M * SQR (| TAS + WINDSPEED + Vrotation |).
Of course everything in 3D vector calculations. M is the airplane mass. The
bars "| |" represent the calculation of the length of a vector.
- To get an impression how much the effect is. The example assumes
for ease of calculation, all vectors have the same direction. In general,
this is not the real situation:
Kinetic Energy presumed to be "released" from an object bleeding of a 250 m/s TAS back to zero:
0.5 * M * 62500 = 31750 M
Kinetic Energy released from an object bleeding of (TAS) 250 + (Windspeed) 50 +
(V-earth-rotation) 1800 m/s to a TAS of zero (with the same wind/earth-rotational speed):
0.5 * M * 4410000 - 0.5 * M * 4202500 = 103750 * M
So when doing the Ekin calculations properly, around 3 times more Energy
becomes available for height gain. Note: Speeds only intended for example
purposes, these aren't the actual AF447 figures.
Usage of TAS to calculate the energy exchange gave a "suitable" fit
for the AF447 case. Why is the difference so big ? I'll get to that a
little further in this article.
Only vertical speed vs. high, the normal Energy constant formula can be used.
2. Effect FL38 turn on TAS and as such on Stall warning reactivation.
=======================================
Nobody mentioned the potential effect of the 180+ degree turn at FL38 on
the return of the stall warning. Such a turn would have a significant
effect on the experienced windspeed and as such on the TAS.
Once at FL38, the airplanes' Inertial Kinetic Energy would be
reasonable constant during the time it takes for the turn. The TAS
however changes a lot. Depending on the wind direction, up to
twice the windspeed.
Maybe somebody might want to match this aspect with the actual AF447 data.
3. The presumed HS stalled status on the way down.
=====================================
Once the airplane got a reasonable downward vertical speed component,
I don't think the AF447 HS is stalled at all (on the contrary, has super-lift),
Why: Typical aspect with a stall is: release of the boundary layer over
the airfoil AND a sudden increase of the speed vector component opposite
of the intended lift force. On the main wings, both components do influence
each other increase both values after initial upset, significantly.
A situation, with an AoA getting higher than the main wing can handle, starts
very fast.
Now to the HS: The intended "lift" for the A330 HS is downward. The speed vector
of the AF447 HS on it's path down to earth, is also downward. The pressure gradient
is actually pushing the air towards the airfoil. So no reason
at all for boundary separation. More the contrary: Because the downward speed vector
"pushes" the airflow on the airfoil, the tendency to boundary separation will be less.
Another aspect relevant in this, is: The HS airfoil does have to curved surfaces,
bottom side a lot, the upper side just little bit. So both sides of the HS generate
lift, where the downward lift force is significantly higher.
Now back to the AF447 HS on it's downward trajectory. The downward speed
is so high that the upper side of the HS airfoil will have (nearly) complete boundary
layer separation, so the upper airfoil surface is completely stalled. The net effect
is an even greater downward lift vector on the HS.
Or so to say: Because of the huge HS downward lift force, the normally nose heavy
airplane doesn't topple over to a nose down situation.
Because of the high downward HS lift, this airfoil is (together with the VS) perfectly
able to stabilize the aircraft on it's way down and prevent a spin or even a roll.
The above can also be argued from the opposite side. The BEA has reported
the airplane went down in a stable state. This can only be reached when a
configuration with airfoils with sufficient "lift" are present. Since the main wings
are definitely stalled, the stable factor must come from the HS/VS span.
Another reasoning from the other side: The A330 is layed out nose heavy
and with stalled main wings the residual main wing lift vector has moved
aft. Despite that, the aircraft didn't topple over it's nose down. So there MUST
be a force to compensate this nose down tendency. This can only be the
downward lift force of the HS.
4. The correlation between Stall (-warning) and AoA
=====================================
This item has been raised, including the statement, a stall (-warning)
is only a function of AoA. On first glance, this is true. However,
there are more aspects very important for this AF447 situation.
For a buzzer type C152+ stall warning device, the warning goes
of when the AoA approaches the max actual value for that
particular configuration of the aircraft. The buzzer "measures"
the actual critical value itself.
For the stall warning principle on the AF447, the AoA is measured
to calculate the Stall situation based on several assumed aerodynamic
values of the airplane and it's surroundings. As long as these assumptions
are valid, the stall warning is calculated properly. If these base
properties do change, the stall warning calculation fails. I also do
expect these stall warning calculations taking into account aspects
as temperature, actual air pressure, configuration and maybe also the actual speed,
simply because with decreasing air pressure, the stall AoA decreases.
Further in this article why this assumption is important for the AF447 situation.
Pure from the physics, I also do expect this stall warning calculation
to be non-linear, though this is not relevant for this article.
The implications of the above, is that, in case the aerodynamics is
different as expected, the airplane can be stalled, without the
stall warning being triggered.
5. Icing type, super cooled water vs huge "clouds" of ice-xtals.
=======================================
Given the pitot tubes are by far the hottest parts of the airplanes'
outside surface (ok, ok, the engines are hotter), the pitot tubes
did clog up completely and there is no reference at all about icing build
up at the outside of the airplane, it's pretty likely the pitots did
absorb a lot of ice-xtals and not super cooled water freezing up
in the pitots. If the AF447 would have encountered super cooled
water, there would have been a lot of ice accumulated on the airframe.
So much, the windshield would have been covered and probably the aerodynamic
properties of the airplane would have been effected significantly. I
did not see any evidence for this.
Another reason to assume, AF447 went into a cloud of ice-xtals, is
the simpel fact that the air temperature at FL350 is around -55 C and
the lowest possible temperature of super cooled water is around -40 C.
Another reason to assume this is an ice-xtals case, is the mention of the huge
amount of noise in the cockpit. A serious indication the pointy end
got bombarded by ice-xtals.
So in summary the AF447 went into a huge and pretty dense cloud of ice-xtals.
6. Effect of ice-xtal on wing stall.
====================================
The first approximation of ice-xtal polluted air, would be to consider
this type of air as "thick" air. And thicker air gives more lift, so
an increase of lift.
However, there is, pure from the physics, probably another effect. Having
a rough airfoil surface, the boundary layer gets disturbed and lets go
much easier with reduced lift as a consequence.
In the AF447 situation, there is not reason to assume, the wings did get
rough. However, the air is polluted with a huge amount of tiny but solid
and dense particles. So much, that from a pure physics side of the matter,
the boundary layer gets disturbed. And a disturbed boundary layer loosens
up. Simply resulting in slightly reduced lift. A wild guess would be
some 5% maybe 10% maybe even 20% reduction in lift.
Why did AF447 not drop out of the air because of this ?
For these speeds, another aspect might become relevant: The floating
of the wings over the polluted air. However the float based
lifting force is significantly lower then the Airfoil shape based Lift.
And not only significantly lower lifting force, though also creating
significantly more drag, also because of the higher angle of incident
required to get that lifting force. Let me call this aspect a "float-stall".
Some more thought-work in progress about:
- THS run away as result of main wing stall after minimal disturbance.
- Double control loop with run away inside loop.
Just let me know if you guys are interested in this.
And yes, every now and then, physics shows unexpected
behavior, so strange, it's difficult to belief......
Again, my apologies for the rough edges in this writing, I
simply do not have the time to polish this up.