This is slightly off-topic, but I saw another opportunity for education. Warren, you still have the floor, by all means continue...
I took a gander over at Cap'n Bob's forum earlier tonight. They don't seem to like me much. But among their comments was the following, referring to an
earlier post of mine:
Cap'n Bob said:
"Compressibility!" he claims...
Ok students, what happens when you compress air? It gets more dense and pressure increases, right? What happens as you get lower in altitude, air gets more dense and pressure increases.. right?
So, if the altimeter was erroneous due to "compressibility", it would be reading LOWER than actual altitude! Meaning, the 187 MSL calculated above, is actually reading lower than the actual altitude of the aircraft, according to Mackey's theory.
Source
The problem is a lack of vocabulary. What I wrote was "compressibility," which Cap'n Bob thinks means "compression." This is not the case.
Compressibility is another way to describe the effects of transonic or supersonic flow. When air flows at low speeds, well below the speed of sound, it is effectively incompressible. But note the key word "flow." If you put air that isn't moving at all in a cylinder and compress it, you will find that it compresses. But you cannot compress air just by blowing it around at subsonic speeds. This is because the air automatically equalizes its pressure, and it does so at the speed of sound.
So if it's flowing much slower than the speed of sound, you will never find any appreciable difference in its static pressure, and it is thus, for all intents and purposes, incompressible. This kind of flow can be treated through equations based on simple conservation of mass and energy, like the Bernoulli formula, and the assumption that the static pressure and the density are effectively constant.
When air approaches the speed of sound, however, "compressibility" sets in. What it means is that under the right conditions, we can no longer assume density is constant, and thus neither can we assume static pressure is constant. Applied to an aircraft, this can happen even at aircraft speeds below Mach 1 -- hence there is no clean distinction between subsonic and supersonic when aircraft are involved. We call this overlap the "transonic" regime. But why does it happen?
Why is because the aircraft shape accelerates the flow. If the aircraft is traveling at the
critical Mach number, which can be as low as about 0.6, this means that at some point, probably flowing over the wings, the airflow is accelerated to the point that it becomes supersonic. When that happens, we can no longer treat the air as constant pressure, or constant density.
In supersonic flow over an aircraft, a shock wave will form, in this case a particularly weak one. This shock wave defines a discontinuity in the flow. As you follow a little chunk of air, it will start subsonic, speed up gradually, speed up continuously, and when it encounters the shock it
suddenly changes speed, direction, density, pressure, temperature, everything.
But does the pressure increase, as Cap'n Bob insists?
It might, but it might not. All that "compressibility" means is that the pressure is not constant. It does not mean that the pressure must always be equal or greater than ambient pressure. It can also be much less.
In fact, it is
commonly much less. One of the best known and most easily visible effects of compressibility is a vapor cone, which is defined mathematically by the
Prandtl-Glauert Singularity. If you've ever been to an airshow and seen high performance aircraft maneuvering steeply, you've probably seen this -- and it happens at subsonic speeds.
What's happening is that, under maneuver, the airflow is briefly accelerated to sonic speed, and a weak shock forms, attached to the wings. The air gets compressed and heats up in the shock, losing a bit of heat to the boundary layer and so on. But the airfoil isn't done yet. It next
decompresses the air, and so doing also reduces the temperature, since there's no heat entering or leaving the fluid. If it decompresses the air enough, this causes water to condense, forming the cloud.
The cloud is proof positive that transonic flow, and compressibility, can actually lower the pressure of air passing over the aircraft.
So, what effect compressibility has on the static probe feeding our altimeter depends crucially on where the probe is and what the airflow looks like over the aircraft. At transonic speed, which AA 77 was according to the new data, the pressure altimeter could see an artificially high static pressure (viz. an artificially low altitude reading), or an artificially low one (with the opposite effect). Cap'n Bob claims it could only see a higher pressure, but he's wrong, which is somewhat inexcusable for a pilot to misunderstand.
I don't know enough about the aircraft or the precise flow to guess whether it would go up or down. Could even be both if buffeting or detached flow sets in at the port location. One would probably have to test this to be sure, and I am reasonably certain that no Boeing 757 in history has flown this fast, this low, and lived to tell the tale. Hence, all I know for sure is that it makes the reading relatively unreliable.
Fortunately, the Radar Altimeter doesn't care about compressibility, so this is the preferred measurement in this case, as I said before. Provided Warren's extraction is correct -- and I see no reason to doubt it at this point -- this instrument shows a steady descent to a reported altitude of
four feet, followed by silence. This is rather remarkable behavior unless one concludes, as the evidence leads us, that the aircraft crashed shortly afterward.
Hope that was useful. When you see "compressiblity," don't equate this with compression. There's no container at work here. What you should think instead is "supersonic flow" and "pressure can go up or down." Subsonic problems can be solved with equations based on conservation of mass, but supersonic problems are much more concerned with temperature.
ETA: And in other news, Cap'n Bob has already griped about this post... wow. Too bad I didn't have my stopwatch handy.