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In the March, 2002 Unicom, a reader asked why a flight from Honolulu to Houston went far enough north to pass just south of Los Angeles. The reader, who obviously didn't understand great circles, speculated the flight was routed to avoid Mexican airspace. However, the reply, which explained about great circle routes, was incomplete.
A few years ago, I was transferred to Germany, and the day before our flight I took my kids to a library to show them where we would be flying. I used a globe and string stretched from Chicago to Frankfurt to show the actual shortest path, then showed them in an atlas that the same path appears curved on a flat map. So when they saw us passing near Greenland on the in-flight display, they understood what was happening.
Trying the same trick between Honolulu and Houston yields a surprise. While the great circle does indeed pass just north of the California-Mexico border, it is not all that close to Los Angeles, and continues to cross the US-Mexico border several times.
So it appears the route was indeed a modified great circle, to keep it in US airspace after all.
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