Thursday 22 January 2015

Solar Impulse Route Calculations

Given that the Solar Impulse team published their round-the-world route overview yesterday, I thought it would be interesting to perform some basic navigation calculations based on that.

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

Follow the Sun

Sunlight is, of course,  the key to Solar Impulses's success. You can use the SunDial function within Really-Simple-Moving-Map to see just how much sunlight Solar Impulse can expect at each point along the route.

For example, here's the Sun track for the starting point in Abu Dhabi, computed for the day I'm writing this post (22 Jan 2015). 


This challenge represents an extremely impressive combination of engineering, technical, and human achievement. Very best of luck to the Solar Impulse team. I look forward to following their progress in the coming weeks, and hope they manage to break that next set of world-records in their sights.


...and talking of record-breaking, whilst warming-up in Abu Dhabi, I recommend they try the Formula Rossa roller-coaster, the fastest in the world...had a go at New Year. Breath-taking.