Here is the interior of the main cathedral at Alcobaca; as I said, at least 30m high.  The perfection of the alignment and shaping of the support pillars is astonishing given the time of construction.

This type of picture also shows off two of its main purposes: To glorify God (and the King) and to overwhelm the population to help keep them in line. 

Imagine being a peasant living in one room of waddle and dauber construction with the pigs and chickens, bathing once a year, eating potatoes and rarely bits of meat.  Then, on special days, walking into such a place where the “rich and educated” breathed fire and brimstone at you from the altar; of course you did what you were told.