My home is 2000 sq. ft., story and 1/2, cathedral ceiling in living room and dining room.
Forced air on main floor. Baseboard heat upstairs. I have two ceiling fans in the living room and dining room. These are on all the time. They have a 6 ft pipe extension from the ceiling, to help to move air. There is a balcony open to the living room on the second floor.
Hi Margaret, I am not an HVAC guy but the logical thing would be to find a way to extend your forced air system to the second floor. The best bet would be to call in some pros and let them design the system. You will probably end up with some boxed in ductwork and bulkheads but you will get AC where you want it.
The other alternative would be to look at ductless split systems. They can be configured for most situations.
If you are serious about it, put your requirements in the "post your project" section so you can get some local contractors to have a look.
Good luck with It!
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