Economic (Least-Cost) Insulation Thickness
The insulation tiles size to a surface temperature or a heat-loss budget; none asks what thickness costs LEAST. Energy falls as 1/R while insulation cost rises linearly, so the total has a single minimum with a closed form: t = k(sqrt(C/(k x price x CRF)) - R0). A 250 F line running 8,000 h/yr wants 4.12 in, cutting heat loss 96.8% and paying back in 0.21 years. Deliberately THINNER than a surface-temperature or condensation limit - those are separate tiles and they win where they apply.
Formula and source
Annual energy $ = dT/(R0 + t/k) x hours x $/MMBtu / (1e6 x efficiency); annual capital $ = price_per_in_sf x t x CRF with CRF = i/(1-(1+i)^-n); the minimum of the sum is t_opt = k(sqrt(C/(k x price x CRF)) - R0), C = dT x hours x $/MMBtu / (1e6 x efficiency).
Economic-thickness (least-life-cost) analysis built from the standard conduction relation and a capital recovery factor - closed form, no table reproduced.
Audience
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