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This is what happens when severe turbulence hits a plane

Passengers on an American Airlines flight between Seoul and Dallas post videos showing the sheer fright during turbulence.

A woman holds up a plate that crashed on her head during the flight. Marc Stanley/NBC Dallas screenshot by Chris Matyszczyk/CNET

Flying is safe, we're always told. Which doesn't mean that it can't be frightening.

Tuesday morning, an American Airlines flight from Seoul, South Korea to Dallas-Fort Worth International Airport encountered unexpected and severe turbulence.

Four passengers and one member of the crew were injured, according to NBC Dallas, but none seriously. Perhaps inevitably, some passengers decided to film the experience and post the results to YouTube.

A video posted by someone called John (now taken down by the user) shows the sheer terror as the plane dropped. Shot in the coach section of the plane, John offered commentary such as "this is the most frightening thing I've ever seen."

He also spoke of how much he loves his family, as if wanting them to perhaps get the message in the event something truly terrible happened. The video also shows people holding hands across the aisle.

There's a certain contrast between this and another video -- this one shot in business class. Posted to NBC Dallas courtesy of lawyer Marc Stanley, it documents some of the damage, such as a plate that apparently crashed on a passenger's head.

The plane was a Boeing 777-200 with 240 passengers and 15 crew. Instead of continuing on to Dallas after the approximately hour-long turbulence, the pilot diverted to Narita airport in Tokyo.

American Airlines did not immediately respond to a request for comment.

In planes of past eras, turbulence could cause a plane to crash. These days, aircraft design makes that much more unlikely.

Airline pilot Patrick Smith, who writes the popular Ask The Pilot blog, has frequently pointed out that what might seem a big drop to passengers could be only 20 feet.

He writes: "For all intents and purposes, a plane cannot be flipped upside-down, thrown into a tailspin, or otherwise flung from the sky by even the mightiest gust or air pocket."

For those who are especially uncomfortable with being in a large metal tube suspended some 37,000 feet in the air, no amount of reassurance is enough. However, Smith cautions: "The level of turbulence required to dislodge an engine or bend a wing spar is something even the most frequent flyer -- or pilot for that matter-- won't experience in a lifetime of traveling."

Still, it's the fear that it could -- even if only theoretically -- happen that makes some passengers fear for their lives. It's still a wonder to some (including me) how those tubes of engineering stay up in the sky.

Updated at 4:58 p.m. PT with the removal of a video, which had been taken down from YouTube by the user, and the addition of the below video from CBS This Morning.