Why is the lower Saucer deck concave?

[Q'OrnamentalDeqor]

Wide saucers allow roomy decks, and less of a side target

Just wait until Klingons, Romulans, Borg, and the Dreaded Dustmites of Deneb Decem figure out there's a third axis to fiddle with...

 

[Relayer1]

The lower outside edge produced by the concave shaoe acts as a drainage run off for when the inerial dampers fail.