Oh yes I have seen those tents take off - most exciting around horses and cattle hahahaha!I have one of mine run a span of 10' wide (20' long) and it works well. That said, 16' is a long run and it most likely will sag some in the middle. Could you run a couple of 16' (or maybe 18') 2X4s from the barn to the fence? Depending on the length, certainly one on each end of the tarp....but maybe one in the middle, too? (I am hesitant about one in the middle, as a breeze will cause it to rub and possibly wear). You could probably start with one shade tarp 10;X16', with a 2x4 at each end, and see how it works for you. If you like it, put up one additional 2x4 and run a second tarp. That would end up giving you a 20X16 shaded space, be more manageable for you, and help limit the sag. Mine do just fine with strong winds and heavy rains so far - they are porous enough. Just don't let leaves build up on it and then get a heavy rain storm. Mine is under a pine and near some maples - I just take a BLUNT stick or shovel and push up/shake the tarp from underneath and most of the detritus shakes/falls off.
While this would give them protection from the rain and sun, It will also catch the wind something fierce and try to take off on you!
I could run a 2x18' from barn to fence no problem, there would be no issue with load as the tarp isn't that heavy. I have no trees nearby, it would only be stupid horses tearing it down. I would also need to take into account the gateways.
But yes a couple of them would work great.
I can't put anything on the south side of the barn as that is an open paddock side - the fence is 50' from the barn

OK so I will need to check into this - most interesting - wish my mum hadn't given away the RV shades - they would have been great on the NW hen house side..... Maybe my uncle doesn't want them... ?