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30th Aug 2010, 23:18
mm43

Join Date: Jun 2009
Location: NNW of Antipodes
Age: 80
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AF447 - The Numbers

Let's put some numbers on it - revisited.

The following is a rehash of Post #467 and has had the forces in both vectors doubled. The horizontal velocity represents that proposed by Machinbird in Post #468, and the vertical velocity comes very close to what the Cabin Vertical Speed advisory portrays if it happened in real-time, i.e. activation, transmission, receipt handshake and then end of flight.

18240 ft/min = 304 ft/sec, and 100KTS = 168.88 ft/sec, resulting = 347.76 ft/sec or 106 meters/sec.

The mechanics of determining the time over which the acceleration was reduced to zero is not easily calculated due to the cylindrical shape of the fuselage, plus the area of the main wings and elevators come into play. On top of this, the aircraft is initially buoyant, and the forces canceled out will reciprocate as buoyancy moments. If the aircraft impacted terra firma, the time taken to dissipate the impact moments would be about 100 milliseconds and the structural damage would be extreme. In the case we are dealing with, the shape and area of the fuselage combined with the large area of the wing will provide a dampening effect and probably the time to accelerate to zero is around 250 milliseconds, with half the remaining velocity being absorbed each 50 milliseconds.

Density of air at sea level and 25°C is around 1.185 kg/m3, whereas sea water is 1,025 kg/m3 or 865 times denser than air. Not quite solid, but at the velocities we are talking about, its close to it. On top of that we have an aircraft weighing in at about 210 tonnes, but the total volume is about 1260m^3, and that is potentially the water that could be displaced during impact. The moment at impact will be around 210,000kg x 106m/sec = 22,260,000 m kg/s, and that either has to be dissipated by the aircraft or transmitted into the water. Water does not compress, therefore the energy gets turned into a wave with amplitude and length, e.g. the stone in the pond principle.

Looking at the force vectors drawn through the V/S, it can been seen that there would definitely be compression on the forward end of the V/S, and a combination of compression on the aft end caused by the THS forcing framing upwards, later reverting to tension at the aft clevis as the canceling of the forward moment caused the V/S to rotate off in that direction and to port. All these forces will have created their own local tsunami and the effects of that will most likely take a minute to oscillate down to the background sea and swell conditions. HN39's link to a sketch in Post #1345 deals with likely forces the V/S attachments suffered and could easily be adjusted to represent the scenario discussed here.

Likely points of fracture through the fuselage have been marked, and discussion around the items recovered may help determine if there was another fracture near the aft pressure bulkhead (I think not).

However, the initial parting of the waves will result in a violent return of the water, and the wing spar section will pop to the surface, and fractures already formed at its fore and aft ends will be flexed in the opposite direction, causing complete separation of the fuselage ends. Water will invade those ruptured spaces, eventually permeating through linings etc.. and buoyancy will be lost.

The potentially large volume of the aircraft is the reason I believe that the time to arrest the impact forces was close to 250 milliseconds. What little we know of the pathology reports tends to describe spinal and pelvic injuries that point to terminal velocities similar to those represented above. Deformation of the galley sides, toilet doors etc.. was on the narrow sides from bottom to top. In fact the deformation was mostly near the bottom and relatively small in length, which could imply that the "g" forces were high and of a very short duration. Longitudinal distortion to objects recovered was relatively small, possibly indicative of the greater absorption of energy available in that plane.

Finally, even though the BEA was careful not to mention anything specific regarding the forward velocity at impact, they did draw attention to the high vertical speed, i.e "... the airplane had likely struck the surface of the water in a straight line, with a high rate [of] vertical acceleration".

mm43

Last edited by mm43; 10th Apr 2011 at 03:30. Reason: replaced "volumetric area" and "force" with correct names. Thanks PBL.