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I read an anecdote about someone who took playing cards onto an airplane. In the pressurised cabin, the cards had a significant bend that was not so pronounced at ground level.

This got me thinking about how a bent sheet would behave under pressure. At first I thought it would have no effect because the pressure is equal on all sides. However I started to wonder if the elastic forces would compete with the air pressure, causing a maximum amount of bend in a vacuum which would decrease with increasing pressure.

Does the air pressure affect the amount of 'bend' in something?

(Although humidity may have to do with bending the cardboard in the anecdote, I'm more interested in the physics of how pressure affects a bent sheet.)

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Pressure should have no effect on the bending or flexure of paper, because air can move fairly easily into and out of pieces of paper- but the humidity effect is HUGE.

This is because the cellulose microfibers that make up paper have a great affinity for water, and they expand significantly when they are exposed to humidity in the air.

The affinity effect is big enough that a common way to dry out the interior of a car that has gotten wet is to stuff the whole inside of the car with wadded-up newsprint and park it in the sun with the windows closed, and at the end of the day to open it up, discard the (moist) paper, and repeat the process until the car is dried out.

The swelling effect is so big that inexpensive dial hygrometers have a strip of thick paper coiled up like a spiral watch spring inside them, which has a thin layer of aluminum foil bonded to one side. the outside end of the coil is fixed in position, and when the paper absorbs humidity from the ambient air, the coil tries to unwind as the paper expands- but the aluminum doesn't. The inside end of the coil is attached to an indicator needle which rotates with humidity changes and is calibrated to show % humidity on a scale.

The air conditioning cycle inside a plane will make the humidity inside the plane different from the ambient outside, which will make a box of playing cards swell or shrink when taken into the plane and opened up. Since the playing cards are faced with a significant layer of mineral filler or laminated with plastic on one side, they will curl one way or the other as the humidity changes.

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