[OTownandDown]

What gauge is the aluminum?

Typically we'll spec 24-26 gauge if the client doesn't care about oil canning (i.e. this is cheap, thin, and it'll be a bit wavy as a result). Difficult to fasten, as the sheets are prone to tearing around fasteners during wind loading.

18-20 gauge is really thick (greater cost) but not near as much 'wavyness'.

The math obviously changes as the span of flat sheet metal goes up. These are quite large panels, and it would be very difficult to have dead flatness. Perhaps some sort of sandwich panels with stiffer adhered sheets of back-pan would help. Does anyone have a photo of the composite section of a typical panel?

This is why Ideal Roofing sells sheets of wall/roof panels with small crimped reveals rather than dead-flat sheets. The stiffness is increased, and you remove waviness.