We did an energy audit on this home in Waterville, Maine. Their heating bill was $11,200 a year. Mostly the cause was all the cathedral ceilings. Almost every room has cathedrals to the roof. And the rooms were 9 to 12 feet tall. It’s easy to figure the problem, a 2×10 rafter can only hold 8″ of fiberglass and if it’s installed poorly, as this was, they may only have an R value of around 20 at best. This home was four times leakier than the BPI standard.
In this situation about all you can do is dense pack the rafters from the ridge. Fill them up solid with insulation and increase the R value and stop all the air leaks. Also, most of the doors were worn out and needed new weather stripping, or to be replaced.