Re: Heat/Air Problem
While your proportional ratios may be logical unfortunately this may not be the case in practical terms. The issue has to do more with the required amount of cubic feet per minute air flow ( CFM ) needed to supply the size of the room. Also the amount of CFM of returm air flow to properly circulate the air maintaining a balanced flow.The size and distance the ducting is a big factor for proper flow.
Unfortunately many times problems with air flow isn't as simple as playing with dampers. For example ... if a 5 inch duct has a capacity of 300 cfm and thinking that closing a damper somewhere downstream will increase the flow ..... well it can't provide any more than it can physically handle .... in other words if that duct is rated at 300 cfm max. you can't expect it to provide 400 cfm.
If the lower level family room is lower than the level of the furnace .... that space will be cooler during the heating season. It's more difficult to move heated air downward since it wants to naturally rise. The opposite happens during the cooling season.... cold air wants to naturally settle downward so it's easier to move this air down.
Personally I don't believe in using booster fans since this indicates a problem with the overall delivery system.
There could be problems with improper duct sizes and/or length , leaks , too many restrictions , not enough or poor orientation of return air ducting , not enough CFM supply from the blower, etc..
Sounds as though you would benifit having an HVAC contractor evaluate things first hand.
Just a thought.
"" an ounce of perception -- a pound of obscure "