Interested to get some feedback on this - we have a 12' D x 16' W patio with a 16.5' high cathedral ceiling. There's currently a 48" Kohler fan up with a 6' down rod that really doesn't do much to move any air out there even before we hit this stagnant heat wave a couple of weeks ago.

I'm not really looking to break the bank on this with a Big A$$ Fan or equivalent and local lighting company recommended a CraftMade model which I don't know a lot about other than seems to have decent reviews online.

Currently looking at a 72" in terms of sizing with a 6' down rod.

Main goal is to just help get some air moving out there on summer days/evenings.

Edit: meant to notate that the back patio faces the northeast so any natural southern breeze is blocked by the house.

Hope you get an expert to tweak properly your new fan size/brand.
EZ to agree with 72-inch light.ctr rec. and Google images suggest it will also have twice the blades mofing air down. Don't know the brand, so check on warranties & returns since reviews you read seem good.

TMI follows
We usually design rear porches to be oriented so the breezes coming from "South" can "wash" the length of the porch which also means no wall nor greenery inhibiting this. Some rural porches actually clear a breeze path. All moot if you are suburban, all houses in a row with fences.

Floor sitting box fans are on sale now. A miniture version of what oil rigs use that also chop up bugs bothering you. Even a superior box fan or two ala Pelonis might do.

Some have used extension cords and mounted several 12-16" Vornado/equal fans high on porch rear wall,
some have even rigged in an all-fans-on switch. (Honeywell fans ala Walmart might also do on a tight budget)

Swamp fans are making a comeback, even in the coastal humid areas
saw some on sale ... Tractor Supply?

I can vouch for Craftmade. Assemble/hang one compared to anything you get at Home Depot and you'll see the difference. They feel better engineered.

They aren't cheap but not BigAFan expensive either.

I can say that across several fans on our last 2 patios, including a craftmade, the BifAFan was worth the splurge compared to the others. I replaced another not cheap fan last year with a Big. I forget the other brand but it was large and well rated outdoors.

All of that said - if you can mount 2 fans on opposite ends of the patio that would help and probably still be cheaper than a Big. Big does have decent sales, you just can't pick and choose your finish - you choose from whatever they put on sale.

I've been happy with the Minka-Aire fan we put on our patio about 4 years ago. It was reasonably priced and has held up well. Moves a lot of air, they have them up to I think 84". Got ours off Amazon and hung it myself.