Friday, October 22, 2010

Flying with Fillo: a Physics Lesson

Traveling with the Fillo pillow on an airplane, I've noticed something interesting. I'll often fall asleep with it before the flight takes off, and when I wake up (in the air, at altitude), the pillow will be super pressurized and rock hard.

I usually let out a bit of air, and all is well and squishy again. But what is going on here? How pressurized is this pillow getting while I'm flying? This all sounds like a homework problem for a physics class that I once fell asleep in.

It turns out that airplane cabins are pressurized when the plane is flying above 3000 m (9800 ft). Since air is thinner at these high altitudes, planes pump in compressed air to maintain a pressurized environment as close to sea level as possible (As a side note, the reason that they don't maintain exact sea level pressure while flying is that the fuselage is not designed to handle that pressure differential). So for example, at 39,000 ft, the cabin will be pressurized to 6,900 ft (thanks Wikipedia!), which is equivalent to a ambient pressure of 10.9 psi instead of the sea level pressure of 14.7 psi.

If you're a numbers person, follow this line of reasoning. Before the plane takes off, you inflate your pillow to about 1.5 psi. Note that this means your inflated pillow is at 1.5 psi greater than the atmospheric pressure (which most of the time is 14.7 psi, sea level pressure, unless you're flying out of Denver or SLC). As the plane is flying, say at 39,000 ft, the pressure inside the cabin drops to 10.9 psi. This makes the air inside your pillow push out on the fabric walls even harder, since there is less air inside the cabin to push back. So when you're flying, the air in your pillow feels like it is at 5.3 psi instead of the 1.5 psi that you started at, due to the relative pressure difference. When your plane lands, the pressure should go back down to what it originally was.

A free NEMO sticker pack to the first person who can tell me what pressure the pillow is at once the plane is at 39,000 ft when you take off from the Denver airport!



Ian said...

if you accept that for every 1,000 feet you go up the air pressure drops 4%, at the "mile high" airport in Denver (at 5,400 feet) the air pressure is approx. 3.4 psi lower than sea level (being 11.3). Using this formula, the air pressure at 6,900 feet is 10.65. Throughout the flight, the air pressure is dropping .65 psi making the fillo go from 1.5 (you're still inflating it to the same pressure regardless of your relative height) psi to 2.15 psi -- approximately of course! :)

Anonymous said...

Hi Connie,
1.83 atm?

Do I win?

Fun post.

Connie said...

Since the Denver airport is roughly 5400 ft (5,431 ft if you want to be a bit more precise), the ambient air pressure as the plane is sitting on the runway is about 12.2 psi (or 0.83 atm). If we know that the plane is maintained at about 10.9 psi at 39,000 ft, the pillow will now be at 2.8 psi when you're flying at level where you can turn on your electronic devices and take off your seatbelt.

Nice work Ian (as we learned in school, showing your process is always a good thing). The logic is correct, although we had slightly different starting pressures for the Denver airport. Ian, can you send your address to NEMO customer service as I will send you out some stickers?

I'll try to post another fun problem like this soon.