Anxiety fills your mind with worst-case scenarios. Counteract irrational fears by running through a list of facts. Review airline crash statistics, and look up how many people have died on commercial airplanes in the past 50 years.
It sounds strange, but you might also find it soothing to read about situations where airplanes lost an engine and still landed safely. Every time you come across a statistic or story that makes you feel better, add it to the notes app on your phone. That way, you can pull it up whenever you feel panic rising during a flight.
