Google duct booster fans or axial duct fans.

Thank you for the suggestions.

(1) unfortunately ceiling fans (probably would need two) don't go with the room in terms of the beams, views etc.

(2) I'll google duct booster fans or axial duct fans, a specific suggestion for a quiet one much appreciated!

" hot air near ceiling that naturally rises in winter "

Hot air rises in the summertime too.

That's a large room. To move enough air through a duct, you're going to need several large openings top and bottom, a large duct and a powerful fan.

Anything can be done but a large ceiling fan or two would be a much better (and likely quieter) solution.

Thanks for the input. One fan would look OK in that room and we may do that. Also, It's a barn style house so there's a cupola and that will be the highest point. The cupola is operable so we can open it in summer to vent air. We can have registers within the cupola, so in winter the idea is to suck air back down towards the floor. There's room to hide ducting so the real issue is how big a blower we'd need to suck air down and if we can find a quiet one.

What is your purpose? What problem are you trying to solve?

If energy/money savings, my guess is that the electricity needed to run the blowers will cost considerably more than any benefit from energy savings. All you'll do is create a loop of air.

Vaulted ceilings are quite energy inefficient and make rooms feel uncomfortable (less cozy, not human scale, etc.). There's a reason that you rarely see them outside of U.S. suburbs.

I've been dealing with this in various houses since the 80s. My final solution was to buy a small Vornado fan, place it in a corner or behind a piece of furniture, aim it up (straight up if possible), turn it on low, and leave it alone. You have to turn it off to clean the blades about every 3 months. You don't need anything else. The warm air will circulate in less than a minute. I like the Vornado brand fan for many reasons, but it was the first one to run continuously longer than a week without making noise. 34 years. That's how long I've had Vornado fans running in my house.

Thanks, many good suggestions.

I like the Vornado idea, I have small fans like that and they move considerable air and are quiet.

I think there will be a considerably greater temperature difference than a few degrees.

You haven't given the dimensions of the open area but think of the size of a medium to large size ceiling fan. Think of the size of the cone of moving air it produces, imagine how large a squirrel cage fan and how large ducts would be needed to move a comparable amount of air. And think about how much noise that will make. And how hard it will blow out along the floor.

Ceiling fans are often seen in rooms with vaulted ceilings, even in commercial structures. There must be a reason why.

Just read a blog about BluBox thermal fan - great idea and US cottage industry. Can be bought on heatstick.com

Make sure you have covered angled vents (kind of like this https://www.amazon.com/Ventilaider-Deflector-Low-Profile-Non-Adjustable-Sidewalls/dp/B09CZL59WZ/ref=asc_df_B09CZL59WZ/?tag=hyprod-20&linkCode=df0&hvadid=532423223930&hvpos=&hvnetw=g&hvrand=16860139863354245117&hvpone=&hvptwo=&hvqmt=&hvdev=m&hvdvcmdl=&hvlocint=&hvlocphy=9016908&hvtargid=pla-1485715464394&psc=1) where it shoots the air across the floor instead of straight up in the air. It mixes with the cold air as it casually rises. The air will rise any ways, but you also want to have atleast and 1/8th to a 1/4 of an inch thick glass windows, and then tungsten oxide or pure silicon dioxide for storm windows, they're very strong, they can be thin and still very strong but they will cloud or freeze. You can also roll mylar plastic and glue it on the walls and plaster over it and then paint and it wont let any heat out, or in. If you don't want thick windows mylar works too well lol. Sometimes they don't suck fresh air in through the furnace and they try and recirculate it through the furnace to minimize heat loss or rise in the gas or electric bill. But less oxygen in the house lowers the furnace's flame's burning efficiency. And then no pollutants will get pushed out through the pressure relief vents. If there's no pressure relief vents it can be hard to open the main doors.

In some other really large houses and I would just leave the furnace running because of having suction fans on for smoking or because of methane, carbon dioxide build up, other pollutants. And it would cool the house down and the furnace would stay on I almost just put a little heater on a vent sucking air in and a suction fan sucking air and smoke out. Smoking sucks if you cant light and take a few puffs where ever you're standing. But air purifiers do get rid of smoke.

You may need air flow restrictors on your vents so that it allows pressure to build up in the duct at the vent and shoot the air down the longer ducts to the vents that are further from the plenum (place above or below the furnace where all the ducts intersect).

Measure all the ducts from the plenum to the vent, and add the length together. Divide each duct's length into the total of all the duct's length's from the plenum. Say the total is 100 feet, one duct is 45 feet, one is 25 feet, one is 20 feet, and one is 10 feet. The shortest duct needs the most resistance to cause a pressure build up 10 ÷100 is .10 so it's 10%, subtract 10% from 100% you get 90%. You want 90% restriction on the vent. Say the vent is 40 square inches or you might want to put the restrictor on the duct. The duct is 20 square inches you want to only let 90 percent of that air through so you want to block it. You would only want 2 square inches or circular inches in total size of the hole or many holes if you want to drill a bunch of small ones in a metal, wood, or plastic plate. And you do this calculation for each duct and then you put the thermometer for the thermostat in the coldest part of the house. The furnace will run longer but it will be evenly heated, if you have hot spots or cold spots you may want to add more vents, You could do the same type of calculation if you want to add multiple vents to one duct.

HVAC systems can get very sophisticated especially if we start trying to monitor humidity, pressure, drafts, oxygen levels, pollutants, and stuff like that. Furnaces almost became like computers, but there's a lot of methods or a different kind of engineering that isn't mechanical, or electrical. It's also possible to heat the duct without burning anything by having two magnets close together or moving back and forth. One of my old furnaces wasn't electrical or gas. I used two air hydraulic lifts (like the car lifts in garages) to spin something, one goes up and pushes the other one down and then it goes back up and pushes the other one down and it just keeps going on and on forever, unless it's switched off. Nothing was electronic besides tvs, computers, and telephones. Even light bulbs were just heated crystals and we didn't mind wicks being burned regularly, it was just the oil that sucked, it started as whale oil, but eventually they started using petroleum and everyone almost died of cancer. I use to make records out of pure carbon, I was standing by a pile of carbon from burning wood and some one yelled something to me and then I would hear the same thing again a little quieter, and I said why do you yell it at me and then say it again quietly really close by. He said I didn't and I said whatever. Eventually I fell down and I heard myself fall and complain. Record players werent electric at first anyways and they winded themselves back up and you just had to switch the rolls. They kind of forced this whole electricity everything thing on us, but electricity was more simple, but everything became motors, timers, belts, sensors and then eventually microchips, instead of gears and pulleys, and all these other methods.