Many of us have experienced the ear pain that can sometimes accompany flying in an airplane. I personally have taken a six-hour flight with dual ear infections and am no stranger to just how unpleasant this can be. But even with a basic understanding of why this occurs, it was only on my most recent flight that I gained a real appreciation of the pressures my ear drums were dealing with.

When I fly, I typically make sure that I bring my own heavy-duty water bottle and fill it up at the airport – doing my tiny part to reduce the amount of waste created by passengers. But a delay left me boarding my most recent flight with that bottle still empty.  I ended up with a new, thin plastic water bottle and, as it turned out, a fun visualization of the ideal gas law. Though the actual equation is PV=nRT, my teenaged self liked to call it “pivnert,” and that is the name that came to mind when I was flying last week.

I had finished drinking my water about halfway through the flight and fell asleep. When I woke up, the bottle I had sealed and left in my lap had already begun changing shape. The plane had started to descend. I looked to my travel companion and held up the bottle smiling and said, “Look! Pivnert!” Thankfully my travel companion was an engineer and simply said “Nice!” instead of “What is wrong with you?” or “What did you call me?”

Bottle just starting to deform.

So what am I talking about?

With any container, the pressure of the gas (P) contained within it depends on the interaction of the volume (V), amount of gas in the space (n), and the temperature (T).

  • If the volume of the container doesn’t change, it would make sense that there would be a greater pressure when there is more air in the container as compared to less.
  • If the volume of the container AND the amount of gas in the container is the same, then increasing the temperature will increase the energy with which the atoms move around and collide with the side of the container. Driving up the temperature would make the pressure go up as well.
  • Depending on the temperature scale you are using  and the units of energy you want, you will need to include something that tells you how much energy you get from a gas at a given temperature (R)

Or, in other words:

(Note that this is an ideal gas law, and assumes that the molecules do not naturally repel or attract each other and are small enough not to have their volume matter compared to the volume of the space overall. For the purposes of our unsophisticated bottle example, we can assume this is the case).

As we continued on our way down the bottle became increasingly deformed, occasionally letting out a crackle as the plastic gave way. The bottle had been at equal pressure with the airplane cabin when I closed it at ~35,000 feet. As the plane descended and the pressure in the cabin started to go back up, the bottle had no mechanism for correcting and began to suffer – much like my ears.

Bottle becoming increasingly deformed as we descend (from top left to lower right).

Our middle ears also contain pockets of air that are typically the same pressure as the air outside of our bodies. When the pressure in our environment changes, we are able to equalize it by allowing air to flow through the Eustachian tube in and out from the back of our nose (like slowly opening the cap of the bottle). This is most commonly done by swallowing or yawning. But when we change elevations quickly (like during takeoff and landing) or the airflow through our Eustachian tube gets restricted (like when you have a cold or inflammation), our swallowing and yawning cannot make up the difference quickly enough and we start to feel the pain caused by this imbalance.

I was shocked at just how much the bottle deformed as we descended. There was a serious enough change in pressure for the bottle to squash nearly flat where the plastic was the thinnest. The temperature was basically constant, the amount of gas in the bottle could not really change, and the pressure outside of the bottle was increasing. The only thing left to give way was the volume.

I tried to imagine my ear drums dealing with the change in pressure that was deforming the bottle. It just seemed like too much. I thought that perhaps I had somehow squashed the bottle in my sleep. Not all of that deformation could have happened from landing. I became convinced that I was somehow documenting more than just the change in pressure, so I waited until we landed and had my feet on solid ground. And then I opened the bottle.

(What is missing from this video is me giggling to myself and saying “pivnert” afterwards.)

That sound and that cracking was the bottle getting to regain its original volume as the pressure equalized. No squashing, no cheating - the flight had actually deformed the bottle that much. I was amazed at how effective or bodies are at accommodating that kind of change in pressure, and also appreciative of why it hurts to badly when our system is not able to work as efficiently as it should.

Next time, I plan to take a balloon.