My old house has an extension with open beams. It has a A-shape cathedral ceiling. Currently, it does not have any insulation. The rafters are 4x6 and about 3 ft apart for each other rafter beam. Since i m living in southern California. When outside is 95 degree, inside is 105 degree =-(
If i want to get at least R52, does spray foam able to get this result (since i only have 6" height on the beam... do i need to lower the ceiling to create more space for the insulation? Any suggest? How do you do it?

An update. Today it is 90degree outside, my inside now is 77degree. I have not done anything to my exposure roof yet. I only modify few thing in the attic that connect to the extension area. I added radiation barrier on the slope side of the roof 100% cover. Added 80% R30 insulation in the attic, so most of the area will have at least R40+ insulation. I also added two gable fans operates at 85 and 95 degrees. I m happy with the result. If i have not improve the heat gain issue in the attic, i believed today my inside temperature will not be 77, but will be at least 90+. I will keep it updated, so that i hope this blog will help other with a similar situation.