The wingspan of the one-seater plane, known as the Si2, is slightly bigger than that of a jumbo jet, but its weight is around that of a family car.
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From Muscat, it will make 12 stops on an epic journey spread over five months, with a total flight time of around 25 days.
It will cross the Arabian Sea to India before heading on to Myanmar, China, Hawaii and New York.
Landings are also earmarked for the midwestern United States and either southern Europe or North Africa, depending on weather conditions.
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The longest single leg will see a lone pilot fly non-stop for five days and nights across the Pacific Ocean between Nanjing, China and Hawaii, a distance of 8,500 kilometers (5,270 miles).
Borschberg and Piccard will alternate stints flying the plane, which can hold only one person, with the aircraft able to fly on autopilot during rest breaks.