Monday, February 22, 2016

The weight of the sky

As a child I was fascinated by the idea that the Greeks and other ancients perceived the heavens as being solid. The most famous depiction, in the West, is that of Atlas holding up the sky. The Greeks also figured out that the Earth was round, but had an even more sophisticated perception of the geometry of the sky and thought that it was also round. Round and solid. A sphere.

The Farnese Atlas, Roman copy of the 2nd century BC Greek original

Atlas was condemned by Zeus to hold up the sky as punishment for joining Chronos in the god wars. I’m not sure who had been holding it up until that point, nor am I sure how Atlas managed to sustain a sex life subsequently, seeing as he fathered – among others – the Pleiades, the stars of Matariki. Maybe it was during his brief holiday, when Herakles took over his job in exchange for Atlas snatching the apples from the Esperides on his behalf. This is Herakles on the job.

When Atlas came back, he appeared reluctant to relieve the hero of the celestial burden. So Herakles asked him to hold it for a minute while he tied his sandal straps then wandered off, whistling casually. Yes: he wasn’t the brightest fellow in titandom, old Atlas. However, somewhat incongruously, we still name atlases after him in spite of the fact they are mostly maps of the Earth, rather than the sky. That’s because the great Dutch cartographer Mercator put him on the cover. This, from a 1634 edition of the 1607 original.

I remained fascinated about the concept of the weight of air, growing up. Air exerts pressure, this much I knew. And changes in pressure changed the nature of gases and liquids, this I also knew. For instance, when we holidayed in our caravan in the Alps I knew pasta would take longer to cook, because water no longer boiled at 100°C, but at a lower temperature, due to the decrease in pressure. I was also told – but couldn’t quite so readily observe – that there was less oxygen at high altitudes. This seemed counterintuitive as I found it quite easy to go on long mountain hikes, compared to when I had to breathe the miasmic gas of the city.

Pressure is essentially the weight of the atmosphere above our heads, which is 100 km high. That’s how much sky there is above us, up to the so called Kármán line, above which point molecules are so far apart it counts as outer space. All this air is a mix of gases – chiefly nitrogen (78%) and oxygen (21%) – whose molecules aren’t weightless. The whole atmosphere has been estimated to weigh over 5 million billion metric tons, but I find that quite meaningless. Another way to think about it is that we walk around with a column of air as wide as our shoulders above our heads. At sea level, this column exerts a pressure – that is to say, weighs – 14 pounds per square inch, or 10 metric tons per square metre. And if a plane travels directly above you head, for a fraction of a second its weight forms part of the weight of that column of air. We’re all little Atlases, walking around like that.

I took a photo of the sky last month. The beautiful Wellington summer sky, which goes on and on.

One of the things I like about Wellington is that the sky has true depth, unlike the northern Italian sky of my youth, whose encircling Alps kept as if under a lid. I don’t know anything about the physics of why that is, but I can tell the difference: over here I can see the sky and how much of it there is.

Back to our 100 km-tall column of air, occasionally containing passing planes. At 10 metric tons per square metre, even our little portable sky by rights should crush us immediately. But it’s easier to think of the air as operating like a liquid. We stand at the bottom of a sea of sky. And while the pressure is higher at the bottom, as it is in the sea, it’s also all around us, which supports us as we walk, or swim. Archimedes’ law applies in the air as much as in water, in other words. Pressure buoys us at the same time as it weighs on us.

So long as we are talking arbitrarily closed systems, we might also say that portions of clear sky are heavier than equal portions of cloudy sky. Here we must distinguish between cause and effect: bad weather occurs because (pardon the simplification) areas of low pressures relative to areas of high pressure cause air to rise and cool, condensing into water vapour – that’s the cause – whereas weighing a certain volume of clear sky versus the same volume of cloudy sky is a rather crude way of measuring a local effect that may not apply to the entire system. But anyway, I really just want to bring up Amedeo Avogadro, that old looker.

The air is made of gas and in 1811 Avogadro theorised that different gases contain the same number of atoms and molecules per unit of volume given the same atmospheric conditions. Therefore humid air entails the substitution of some of the nitrogen and oxygen in the atmosphere with an equal number of molecules of water vapour, in order to maintain the Avogadro constant, well, constant. And because water weighs less than either nitrogen or oxygen, given the same temperature and pressure a slice of clear sky weighs more than a slice of cloudy sky of equal volume.

Okay, I’m nearly done. Planes. Planes travel typically at 30,000 feet and above because the air is less dense there, so it’s easier to push against it. At the same time, the cabin has to be pressurised because at that altitude there is too little oxygen for people to breathe. If it were pressurised at 1 atmosphere, meaning the pressure at sea level, this high pressure would push against the walls of the plane, which would have to be extremely heavy to withstand it. So on most planes the pressure is kept at the equivalent of 7,000 to 8,000 feet of altitude. That’s the height of my childhood caravan holidays. The new Boeing 787s can afford to increase the cabin pressure (or lower the artificial altitude, if you like) because they are made of carbon and are not subject to metal fatigue.

Finally: temperature. This one has always confused the hell out of me, as the effects of altitude on temperature aren’t linear. They zig and zag. Up to about the height of a Mount Everest and a half, temperature decreases the further up you go. Which is counter-intuitive if you think you’re getting close to the sun, but at those low altitudes most of the heat is reflected by the surface of the Earth. Then from 14,000 to 50,000 metres (that is to say, in the stratosphere), temperature increases with altitude, because sun radiation is the main heater. Then from 50,000 to 90,000 metres you get into the mesosphere, where temperature falls again due to the high concentrations of ozone, which filters sun radiation, and carbon dioxide, which at those altitudes has a complex cooling effect. (Where by complex I mean ‘I don’t really understand it’.) Finally in the last 10 kilometres of atmosphere, up to Kármán line, the temperature rises again due to the unfiltered radiation, but gas molecules are so far apart that it no longer makes a lot of sense to even speak of temperature.

These are some things I learned lately about the sky. I hope they’re not wrong.

In sad news this week, Umberto Eco died. You can read the obituary I wrote for Overland if you like.


Anonymous said...

Some more for Philosopher Joe!

fluid = (gas, liquid)
supercritical fluid = fluid != (gas, liquid)
Bernoulli: f(velocity) + f(depth) + f(pressure) = constant. Another version of energy balance. In low density fluids you are essentially at equal pressure, not so in high density fluids.

Ever seen liquid nitrogen freeze by boiling it?


Anonymous said...

Forgot to add that you are quite right that carbon fibre reinforced composites do not suffer from metal fatigue. They do, however, suffer from composite fatigue if cyclically loaded in a similar manner. The microscopic and atomic level defects that control the fracture of materials exist just as much in polymer matrix composites as they do in crystalline metals and alloys.


Giovanni Tiso said...

A supercritical fluid sounds like something I might be into.