You will have trouble getting them to stay up and trouble getting them down. Then if it is windy you'll have the trouble of them blowing in on you unless they are secured to the bottom somehow.

It would make more sense to have some kind of blind that would roll up and down, perhaps bamboo blinds

That's what I'm trying to figure out... how to secure them up at the top and how to secure them to the bottom.

I would forget the canvas and instead plant a tall evergreen hedge the length of the pergola.....maybe box? Or maybe something that flowers with fragrance, like viburum

Hmmm, "heavy pieces of canvas" are going to act like a sail, and your pergola is at risk of getting blown into the next county, and ripped-out of whatever header secures it to the house.

You should be thinking instead "shade cloth" which is loose-woven so that the fabrice doesn't act as a wind-catching sail. Think "tennis court screens" which intend to block the wind for better tennis...

If you get, say, a SHADE47 cloth (from amleo.com) which is grommetted every 2 feet, you secure your cloth permanently at the top and roll-it-up & tie-it-off when not in use. when deployed you should secure it with rubber bungees or some such to take-up some of the natural flex that will occur on windy days.

I like the evergreen hedge idea, it's exactly what I would suggest.

Though, if you don't like that, you might consider adding a lattice section. Covering the space with a large section of lattice would keep with your pergola's theme, allow a lot of light in, but really help break the wind.

we're working on the exact same thing!