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Evgenii Konkin
Evgenii Konkin

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Roof Color Changes Cooling Load by 7 Tons on a 30,000 sq ft Building. Here Is the Math.

#hvac #engineering #energy #building

A dark roof absorbs 94% of solar energy. A white roof absorbs 22%. The difference on a 30,000 sq ft warehouse in Phoenix: 7 tons of cooling load from the roof alone.

Sol-air temperature

The roof does not see outdoor air temperature — it sees sol-air temperature, which includes solar radiation absorbed by the surface:

T_sol-air = T_outdoor + (α × I / h_o) - correction

Where:
  α = solar absorptance (1 - reflectance)
  I = solar irradiance (BTU/hr·ft²)
  h_o = outside surface coefficient (~3.0 BTU/hr·ft²·°F)
  correction ≈ 7°F for horizontal surfaces
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Phoenix design day example 

Outdoor: 110°F
Solar irradiance: 290 BTU/hr·ft²

Dark roof (reflectance 0.06, absorptance 0.94):
  T_sol-air = 110 + (0.94 × 290 / 3.0) - 7 = 194°F

White roof (reflectance 0.78, absorptance 0.22):
  T_sol-air = 110 + (0.22 × 290 / 3.0) - 7 = 124°F

Difference: 70°F before insulation enters the equation
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The dark roof surface reaches 170°F. The white roof stays at 115°F.

Cooling load calculation 

Q_roof = Area × U-value × (T_sol-air - T_indoor)

Roof: 30,000 ft², R-25 (U = 0.04), Indoor: 75°F

Dark roof:
  Q = 30,000 × 0.04 × (194 - 75)
    = 30,000 × 0.04 × 119
    = 142,800 BTU/hr = 11.9 tons

White roof:
  Q = 30,000 × 0.04 × (124 - 75)
    = 30,000 × 0.04 × 49
    = 58,800 BTU/hr = 4.9 tons

Difference: 7.0 tons
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Roof color vs insulation — which matters more? 

Combination              Roof Cooling Load
──────────────────────────────────────────
Dark roof, R-15          19.8 tons
Dark roof, R-25          11.9 tons
Dark roof, R-38           7.8 tons
White roof, R-15          8.2 tons  ← beats dark R-38!
White roof, R-25          4.9 tons
White roof, R-38          3.2 tons
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A white roof at R-15 outperforms a dark roof at R-38. Reflectance is cheaper than insulation for reducing roof cooling load.

Cost comparison 

White TPO vs dark membrane:
  Premium: +$0.30/ft² × 30,000 = $9,000
  Smaller HVAC: -$3,500 (7 tons × $500/ton)
  Annual energy: -$2,800 (7T × 1,200h × 1.2kW/T × $0.11)
  Net cost: $5,500
  Payback: 2.0 years
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Where reflectance matters most 

City           Solar (BTU/hr·ft²)   Reflectance Impact
────────────────────────────────────────────────────────
Phoenix           290               Very high
Las Vegas         280               Very high
Miami             260               High (+ humidity)
Dallas            250               High
Atlanta           230               Moderate
Chicago           210               Moderate
Seattle           180               Low
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In high-solar climates, roof color is the single most cost-effective cooling load reduction.

The rule

When calculating cooling load, never use outdoor air temperature for the roof. Use sol-air temperature — it includes the solar energy the roof absorbs. And the easiest way to reduce sol-air temperature is to change the roof color.

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