thcrozier, you meant speed of sound, of course
Both denoted by
c
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So, how
might the CVR record the sound of a tail explosion via microphones in the nose?
To begin, I suggest that the investigators will probably be able to distinguish a microphone signal from a signal resulting from mechanical disturbance of the recorder and its wiring. (In electronic engineering, the generic term for this second category of signal is "microphonics".) To begin, the microphones probably have a well-characterized response to sound impulses which is quite slow in electronic terms. A microphonic signal resulting from a violent impact is likely to have a much steeper rise time.
Ordinary sound would take about 0.1 seconds to travel the length of the A321 pressure vessel.
From a high explosive, the pressure front would travel some part of the distance as a shock wave (supersonically) ... potentially at more than 10 times the speed of sound. Depending on how far the shock wave can propagate, the travel time might be substantially reduced.
To the extent that sound is conducted through the structure of the fuselage, it could reach the cockpit in 0.01 seconds, or even less.
So, if the CVR can survive as long as a tenth of second, or even less than that, it could be able to capture the sound of an explosion taking place quite near to it.
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How long, then, might the CVR survive?
A high explosive shock wave can travel so quickly (possibly 20 times the speed of sound), that for the purposes of this disaster it is reasonable to estimate the travel time (from the point of explosion to the solid objects between that point and the CVR) as zero.
But in the path between a galley-area explosion and the CVR, there are several layers of material, including the structure of the galley itself, linings, insulation, and the pressure bulkhead.
The shock wave can get around these objects to the extent that gas-leakage paths exist, or are opened by the shock wave itself. However, the wave reaching the CVR probably didn't stop its functioning. It is a very hardened unit, and the intensity of the pressure wave was necessarily dissipated to some degree by the time it reached the CVR.
Most likely, what stopped the CVR was direct mechanical impact by parts of the airplane on the CVR itself, or its cabling.
Considering one possible sequence:
- the blast wave (by a perhaps circuitous path) reaches the pressure bulkhead
- concurrently, overpressure both deforms & breaks the galley structure, and propels the pieces rearward like a piston
- in response to overpressure, and perhaps also the impact of objects that have become projectiles, the bulkhead deforms, first elastically and then plastically
- deformation of the pressure bulkhead exceeds its structural capacity, opening a rupture
- from this point, continued failure of the bulkhead is progressive ... the blast overpressure may already be dissipating, but cabin pressure is exerting about half a ton per square foot on the now compromised bulkhead
- static pressure and the dynamic forces from egress of cabin air peel open the initial crack(s)
- bulkhead material, or other pieces from the aircraft that have become projectiles, strike the CVR and/or its wiring
Certainly, the actual sequence could have been a lot different from that. It would depend on which is the fastest route through the points of least resistance.
Although all these hypothetical events happen very fast, none of them are instantaneous. They all take time, and to some extent they are sequential (that is, one event does not begin until a preceding event has progressed to some extent).
I think it is plausible, and even probable, that whichever object hammered the CVR or its cabling could have taken a tenth of second to get there.
The blast wave can travel 20000 feet per second, but the solid object that killed the CVR may have been travelling more like 100 feet per second. Whatever speed it was going, it had to be accelerated to that velocity: it didn't reach it instantaneously.