Gentle warning: although shorter than my average post, it contains a higher than usual geek-like content. You have been warned.
About a month ago, as an early celebration of our 40th wedding anniversary, my wife and I went on a trip to Switzerland – by train. Whilst getting around Switzerland by train, cable car and funicular was a complete joy, it has to be admitted that the haul there and back again was a long one. Even for a supporter of train travel it was long. However, even these journeys had their mitigating factors. The slowly changing scenery moving past our window was one, much as it was when we crossed the Canadian Rockies by train some years back, ending up in Vancouver. On the way out we broke our journey in Strasbourg where, apart from a view of the buildings associated with our soon-to-be-former membership of the EU, I was able to indulge in a little glass-spotting …
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| One of the more spectacular stained glass windows to be found in Strasbourg Cathedral. (The original image was elliptical since I had to photograph the high-level round window from the aisle of the church: I have ‘adjusted’ the image to undo the effects of perspective.) |
Conversations with our fellow travellers are a bonus as well, but a physicist’s mind also has a tendency to wander into less populated mental territory. Almost without realising it I found myself converting the displayed speed of one of ours train from the km/hr shown on its display into metres/second (over 85 metres each second!) and thence into miles per hour. That’s around 200 mph, should you wish to know. (In passing, you’ll probably be grateful that I have resisted the temptation to digress into a paragraph or two on measurement units. It will surely come, but perhaps in a future post …) Now, unless we approach the speed of sound, which is about 340 m/s near sea level, the drag due to air friction increases as the square of the speed. As an example, the drag will have increased four-fold as the train accelerated from 100 mph to 200 mph; these numbers underline the importance of streamlined designs and all the engineering behind them. Of course, the frictional drag also depends on the density of the medium through which an object is moving. For instance, the reason a submarine is subject to relatively huge frictional forces is simply because it’s moving through a medium, sea water, which is more than 800 times denser that the air at the surface. Similarly, providing it can still get enough oxygen for its engines to function, a jet is better off flying in the thinner air present at high altitude. In a (very) round-about way, this observation provides the introduction to one of the central topics of this post …
The highlight of our vacation, if you’ll forgive the weak pun, was a journey to Europe’s highest railway station, Jungfrauhoch at an altitude of 3454 m (11,371 ft). It’s a stunning location, as many are in Switzerland, and we were fortunate to get only a little snow, low wind speeds, breaks in the cloud and temperatures not too far below 0°C. Just above Jungfrauhoch – accessible via a lift/elevator I’m glad to say – is the Sphinx Observatory (here) at 3571 m. Although not used in the classic ‘star-gazing’ sense, there are several international ecological/environmental research projects based there (here). These include spectroscopic solar observation as a means of probing the Earth’s atmosphere: in others words, looking carefully at what wavelengths light is ‘filtered out’ of the Sun’s rays as a means of identifying with precision the constituents of this high-altitude air. However, as a chronic asthmatic, and having the left-overs from a recent cold the worst symptoms of which had miraculously abated the day prior to our journey, one of my pre-occupations on the day was breathing. In true geeky style, this served to prompt a simple experiment to illustrate the effects of air pressure.
The highlight of our vacation, if you’ll forgive the weak pun, was a journey to Europe’s highest railway station, Jungfrauhoch at an altitude of 3454 m (11,371 ft). It’s a stunning location, as many are in Switzerland, and we were fortunate to get only a little snow, low wind speeds, breaks in the cloud and temperatures not too far below 0°C. Just above Jungfrauhoch – accessible via a lift/elevator I’m glad to say – is the Sphinx Observatory (here) at 3571 m. Although not used in the classic ‘star-gazing’ sense, there are several international ecological/environmental research projects based there (here). These include spectroscopic solar observation as a means of probing the Earth’s atmosphere: in others words, looking carefully at what wavelengths light is ‘filtered out’ of the Sun’s rays as a means of identifying with precision the constituents of this high-altitude air. However, as a chronic asthmatic, and having the left-overs from a recent cold the worst symptoms of which had miraculously abated the day prior to our journey, one of my pre-occupations on the day was breathing. In true geeky style, this served to prompt a simple experiment to illustrate the effects of air pressure.
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| The Sphinx Observatory; the inset of yours truly not only helps to prove that I was there, but also serves to mask a few unsightly cables. |
The experimental setup was simple: take an empty plastic water bottle and screw it tight shut at high altitude, then simply compare it with an otherwise identical bottle back at ‘base camp’ (aka our hotel room, which happened to be at a more modest 586 m altitude). The image below says it all.
The bottle on the left provides the 586 m reference point, as it were, whilst the bottle on the right – sealed shut at Jungfrauhoch’s 3454 m, and therefore almost 3 km higher – has been partially crushed. The reason is straightforward. At the altitude of our hotel the air pressure was about 94480 Pa (Pascal: equivalent to about 945 mb, or 13.7 psi) but the bottle sealed at Jungfrauhoch started its journey with an air pressure of only 66154 Pa (about 9.6 psi, so only 70% of the lower altitude value). In other words, as the pressure outside the bottle started to increase as we were descending, it simply crushed the bottle, reducing its volume to the point at which outside and inside pressures were in balance again. And where does this ‘pressure’ come from? Well, from the collision of the air molecules with the bottle’s inner and outer surfaces: more collisions per second on the outside surface of the bottle than on the inner surface will result in a net force which will push the sides inwards. Why were there more collisions each second on the bottle’s outside surface as we descended? Simply because the air’s pressure is related to its density: higher pressure means higher density, which in turn means there are more molecules available to collide with the bottle. The density of the air at Jungfrauhoch was about 0.85 kg per cubic metre, but this had risen to about 1.1 kg/cubic metre by the time we had descended to the hotel.
I should add in passing that this effect had been noted by my children during a much earlier holiday, in 1998 in fact. This vacation included a stay in Yosemite National Park, within which the altitude varies between about 1200 and 1500 m. Their observation was, in a sense, the obverse of my simplistic experiment: they noted that an unopened bag of crisps (or potato chips in the local language) had inflated like a balloon. What they were seeing, of course, was the effect of higher pressure inside the bag than outside. The bag was sealed in a factory at low altitude, and was about to be consumed at higher altitude: there were more collisions each second between the air molecules and the inside surface of the bag than were occurring at its outer surface.
Ah, the joys of taking physics on vacation. There’s more from Switzerland however.
I should add in passing that this effect had been noted by my children during a much earlier holiday, in 1998 in fact. This vacation included a stay in Yosemite National Park, within which the altitude varies between about 1200 and 1500 m. Their observation was, in a sense, the obverse of my simplistic experiment: they noted that an unopened bag of crisps (or potato chips in the local language) had inflated like a balloon. What they were seeing, of course, was the effect of higher pressure inside the bag than outside. The bag was sealed in a factory at low altitude, and was about to be consumed at higher altitude: there were more collisions each second between the air molecules and the inside surface of the bag than were occurring at its outer surface.
Ah, the joys of taking physics on vacation. There’s more from Switzerland however.
Part way through our holiday, in the depths of the night, I spotted what I initially thought might be Saturn, which I knew was supposed to be visible at the time. It was low in the sky and near the almost-full moon. The snapshot I took at the time is shown below. Just to be sure, I contacted a local amateur astronomy club via Twitter – so useful to have access to a ‘hive-mind’ on such occasions. I am grateful to @AshfordAstro and to @roger931 for letting me know that I had, in fact, been observing Mars that night. Either way, this is the sort of thing that can, for me at least, boost the spirits through any stretch of broken sleep. It also served to remind me that one of my plans for ‘retirement’ was to invest in a small telescope and to get back into the astronomy that inspired me so much as a young person. I must find the time to do that …
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| This was taken on our very modest compact camera, which was steadied using the window frame in our hotel room. |
