Cathedral ceilings need either a vented (cold-roof) or unvented (hot-roof) assembly, with foam type chosen accordingly. Cincinnati Climate Zone 4A typically uses closed-cell on the underside of the roof deck for unvented hot-roof assemblies; vented cathedrals use open-cell in the rafter cavity with a 1-inch air gap to the roof deck.
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Cathedral ceilings (also called vaulted ceilings) are the upper assembly where the ceiling follows the underside of the roof rather than enclosing a flat attic. Common in 1920s-1940s Tudor revival homes in Hyde Park and Mariemont, in 1980s-2000s great rooms in Mason and West Chester, and in modern homes throughout the metro. Two design approaches, both code-compliant. (1) Vented (cold-roof) assembly: the rafter cavity holds insulation but a 1-inch ventilation gap runs continuously from soffit to ridge above the insulation. Cool outside air flows through the gap, carrying away any moisture that migrates up through the insulation. The roof deck stays cold (matching outdoor temperature), which prevents condensation and ice dams. Insulation typical: open-cell foam at 8-10 inches in the rafter cavity, leaving 1 inch of vent space. Strict-code compliant: requires continuous soffit vents and continuous ridge vent, plus the air gap. (2) Unvented (hot-roof) assembly: the rafter cavity is fully filled with closed-cell foam directly applied to the underside of the roof deck. No ventilation gap. The roof deck stays warm (essentially at indoor temperature), eliminating ice dams. Insulation typical: closed-cell foam at 5-8 inches in the rafter cavity. Requires careful detailing at the eaves and ridge to prevent water infiltration paths. The unvented hot-roof approach is more common in Cincinnati Climate Zone 4A for two reasons. (1) The cathedral geometry usually has narrow rafter depths (2x10 or 2x12) that cannot hold both R-49 of open-cell and a 1-inch vent gap. Closed-cell at 7 inches delivers R-49 in 2x10 framing with room for the structural reveal at the ceiling drywall. (2) Ice damming is a recurring problem on Cincinnati cathedral ceilings in poorly insulated homes; the hot-roof approach eliminates ice damming by design. The trade-off: unvented hot-roof requires roof-deck adhesion that cannot be reversed; future roof replacement projects need careful planning. Vented cold-roof preserves the ability to access the roof deck from above. Cincinnati installer guidance: for cathedral retrofits in homes built before 1990, hot-roof closed-cell is the typical recommendation. For new construction or for homeowners who plan major roof work in the next 10 years, vented cold-roof with open-cell preserves flexibility. The on-site assessment identifies which approach fits the specific home.