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I recently had a trip to Italy from LAX on Lufthansa. On the way back the plane's great circle trajectory took it over Canada and eventually through California on what to me was an odd path. Instead of intersecting the LAX landing pattern east of LA, the plane went over Thousand Oaks, reached Malibu (north west of the airport), took a left, went east for a while, then did a 180 turn to begin its approach.

What is the reason for this path? Why not head south towards San Bernadino, then turn right (west)?

The flight planning computer decided that route had the shortest time on that day. The arrival you described is the standard route for arrivals from the north, northwest and most Hawaii flights, it is called the SADDE 6 arrival.

http://flightaware.com/resources/airpor ... /SADDE+SIX