The Sentinel-2 tiles, how they work ?

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The Sentinel-2 Level 1C products will be split into tiles. and I have searched a little how the naming convention of Sentinel-2 tiles works. I have found some interesting resources in Sentinel-2 website :

• A User Handbook for Sentinel-2 products (which does not explain the naming convention of the tiles)
• A kml file that provides the footprint of all the tiles, and their name. To  access it, go to Sentinel-2 official portal, and click on « Sentinel-2 Level-1C tiling grid », in the key resources menu on the right.

Here is  what I have guessed :

• The first 2 numbers of a tile name (such as 31TCJ) correspond to the UTM zone. The world is divided in 60 UTM zones of 6 degrees width in longitude, with numbers increasing towards the East. Zone 1 is over the Pacific Ocean.
• Each zone is divided in latitude, by chunks of 8 degrees. This is represented by a letter, which increases from South to North.
• And finally, each chunk is divided in 110 km tiles, with a 10 km overlap, from West to East, 4th Letter, and South to North, 5th Letter. What is not easy to guess is the fact that the forth and fifth letters are not reset for each chunk, but continue to increase when changing zone and chunk, but are reset to A when the counter exceeds Z.

For instance :

• the tile in Toulouse, id 31TCJ. 31 is the UTM zone, T is the latitudinal chunk. C denotes the West-East tile position within the chunk and J the South-North position.
• If you want to see the tile in the East of Toulouse, which includes Castres, it will be 31TDJ.

• If you want to see the tile in the North East of Toulouse, which includes Aurillac, it will be 31TDK.
• If you want to see the tile at the West of Toulouse, which includes the Armagnac region, it will be… 30TYP. 30T because it is a different UTM zone, and YP … because this numbering is not practical  ?
• The tile at the South of that one, for which we processed our first Level 2A products is  30TYN (because the O letter is excluded, to avoid confusion with 0)

Sorry for that, I would like to have a formula which guesses the tile name as a function of the longitude and latitude, but I am not able to figure out one. Has any of you heard of one ? What I am happy with is the fact that tiles overlap by 10km. This ovelap means an increase of 21 % of the data volume, which is already large, but enables to process Level 2A products independently. It is very difficult to detect a cloud shadow when you do not see the corresponding cloud. And on the edge of the tiles, you will have shadows on clouds you do not see. But thanks to the overlap, the shadows will be well detected on the other overlapping tile. A colleague of mine told me this grid was born in the brain of an American solldier (yes, soldiers have brains ). Here is a description, which sadly does not tell how the two last letters were defined. This said, in 1789, during the French revolution, a project to devide French territory in tiles had been set-up by the Sieyes-Thouret comittee. The project was not appproved, but if it had been, I am quite sure that Lamartine would have found much more poetic names than those used for Sentinel-2.