Challenges
How it is checked
The same physics as How an arch stands. The vault is a pointed or round arch of stone blocks that can push but never pull: it stands if a line of thrust fits inside it. Its push goes into the walls, and with flying buttresses on to the buttresses. Each stands while the push on its base lands inside it. Inside the middle third the whole base presses down; outside it, a joint opens; outside the base, it tips.
The storm
Height costs more than stone. A gale with gusts of about 40 m/s (145 km/h) presses on the roof and the clerestory, about 1 kN on every square metre, and the roof hands it to the walls on the lee side. That is what the upper tier of flyers at Amiens is for. The push grows with the height of everything above the aisle roofs.
What is simplified
Everything not chosen here follows Amiens' proportions: the arcade, the triforium and the aisles scale with the height of the walls. A transept needs one aisle, for now. Every bay is the same, the forces are per metre of the nave, and the collapse in 3D is drawn, not computed. Crushing, settlement, mortar and the slenderness of tall piers are not modeled.