If I change my Edge 605 to kilometers while I'm in Europe, what happens to my existing history and what happens when I change it back to miles when I am back in the US? Also what happens to information uploaded to Garmin Connect or stored in Garmin Training Center?
The device always measures in metric units, and all data is stored in metric. The only thing that you are changing is the presentation. Nothing bad should happen because you change from Statute to Metric or vice-versa.
