To start with, taking the proposed route overview, choosing relevant airports, filling in the blanks ("Kansas City airport" for "mid USA", and "Marbella airport" for "South Europe, North Africa"), gives the following approximate route in Google Maps, Really-Simple-Moving-Map, and SkyVector.
Distance and Time calculations
The total flight distance is 18,814 nautical miles, with a nominal (zero wind) total flight time of 27.5 days to be flown in sections over a few months from late-February/early-March 2015, to late-July/early-August, 2015. The following table summarises the distance along each leg in the route (assuming great circles), and the time taken to fly each leg assuming an airspeed of 35 mph (30.4 knots, 55.6 kph), derived from Solar Impulse 2's performance (which I simply found on the internet, as the published average ground-speed: is there perhaps a more accurate indicated airspeed I could use ?). Times are given for zero-wind, 10 knot tailwind, and 10 knot headwind, respectively. This gives an idea of the (significant) effect of (moderate) wind on the performance, given the relatively low airspeed compared with conventional powered aircraft. A wind-speed of 10 knots at the cruising altitude of 5,500 feet would be considered as not atypical.
Of particular note (highlighted in the table) is the longest leg of 4408 nm, across the Pacific from Nanjing (China) to Hawaii. Nominally (in zero wind), this would take 6 days, or 9 days in a 10 knot headwind, or 4 days 13 hours in a 10 knot tailwind. Many of the other legs also exceed one day, so the solar cells will need to be able to charge the batteries as well as keep the aircraft flying during the day, and the batteries will need to provide sufficient power to keep flying through the night, multiple times in the mission.
|Leg||Distance (nautical miles)||Time (zero wind)||Time (10kt tailwind)||Time (10kt headwind)|
|1. Abu Dhabi (UAE) to Muscat (Oman)||206||6h:47m||5h:6m||10h:6m|
|2. Muscat to Ahmenebad (India)||791||1d:2hr:1m||19h:35m||1d:14h:47m|
|3. Ahmenebad to Varanasi (India)||578||19h:1m||14h:18m||1d:4h:20m|
|4. Varanasi to Mandalay (Burma)||757||1d:0h:54m||18h:44m||1d:13h:7m|
|5. Mandalay to Chongqing (China)||717||23h:35m||17h:45m||1d:11h:9m|
|6. Chongqing to Nanjing (China)||659||21h:41m||16h:19m||1d:8h:18m|
|7. Nanjing to Hawaii (US)||4408||6d:1h:0m||4d:13h:7m||9d:0h:5m|
|8. Hawaii to Phoenix (US)||2532||3d:11h:17m||2d:14h:40m||5d:4hr:7m|
|9. Phoenix to Kansas City (US)||905||1d:5hr:46m||22h:21m||1d:20h:22m|
|10. Kansas City to New York City (US)||964||1d:7h:43m||23h:52m||1d:23h:15m|
|11. New York City to Marbella (Spain)||3155||4d:7h:47m||3d:6h:6m||6d:10h:39m|
|12. Marbella to Abu Dhabi||3121||4d:6h:40m||3d:5h:15m||6d:9h:0m|