Cooling Load Calculations

Building Specifications

Location: Jacksonville, FL

Facility type: electronic casino

Conditioned floor area: 2,420 sf

Design occupant load: 59 persons

Heat gain from the building envelope, lighting, electrical equipment, and occupants determines the HVAC system’s cooling load

Design Conditions

Infiltration rate: 1–2 ACH (air changes per hour, typical range)

Breathing zone:

• Between 3″ and 72″ above finished floor (AFF)

• At least 24″ from walls or air supply openings/equipment

Indoor relative humidity (per ASHRAE & ACCA):

• Recommended comfort: 30%–60% RH

• Cooling design: ~50% RH (40–60%)

• Heating design: ~30% RH (often 30–40%)

• Note: <20% RH may cause dryness/discomfort; >60% RH may promote mold and IAQ issues

Indoor design temperature (heating, DB):

• 70°F per ACCA Manual J

• 68˚F–72°F per ASHRAE 55 / Fundamentals (commonly 72°F)

Indoor design temperature (cooling, DB):

• 75˚F per ACCA Manual J

• 72˚F–76˚F per ASHRAE 55 / Fundamentals

Outdoor design dry-bulb temperature: 92.8˚F (1% cooling), 28.6˚F (99.6% heating) per ASHRAE Climatic Data

∆T (cooling) = Tₒ – Tᵢ = 92.8°F – 75°F = 17.8°F

Heat Gain

Basic formula: Q_dot (cooling) = U × A × ∆T

More accurate method: use Cooling Load Temperature Difference (CLTD) instead of ΔT

CLTD (°F) selected for light construction and a 95°F outdoor design dry-bulb (DB) temperature

Note: Even with CLTD, a ~15% error may still occur

Rough Estimation

Cooling load ≈ 0.25 to 0.35 tons per 100 sf of conditioned floor area

Q = 2,420 ft² × 0.30 tons / 100 sf = 7.26 tons

Outdoor air requirement ≈ 15%–25% of supply air

Roof Heat Gain

A = 2,420 ft² with 3 ft attic air space

R-values: 1.79 (½" acoustical ceiling tile), 30 (9¼" R-19 insulation)

Overall U-value = 1 / R_total = 0.03 Btu/h·ft²·°F

Q_roof (cooling): U × A × CLTD = 0.03 × 2,420 × 28 = 2,033 Btuh

Doors Heat Gain

(2) insulated 1-¾″ metal doors, east wall

A_door: 80″ × 36″ × 2 = 40 ft²

Q_doors (cooling) = 0.40 × 40 × 16 = 256 Btuh

Concrete Slab Heat Transfer

Thickness = 4" (0.333 ft)

∆T = 5°F

A_face = 2,420 sf

A_exposed_edges = 0.333 ft × (41 ft × 2) = 27.3 sf

U_face = 0.05 Btu/h·ft²·°F

U_edge = 0.81 Btu/h·ft²·°F

Q_slab = [(0.05 × 2,420) + (0.81 × 27.3)] × 5 = 716 Btuh

East Wall Heat Gain

A_wall_gross = 128″ (10.67 ft) × 41 ft = 437 sf 

A_wall_net = gross wall area (437 sf) – windows (80 sf) – doors (40 sf) = 317 sf

R-values (wall assembly):

• Outside air film (7.5 mph wind): 0.33

• Concrete block (lightweight, 12" CMU): 2.04–2.56

• Plywood (¾″): 1.08

• Gypsum board (½″): 2.22

• Inside air film (vertical): 0.68–0.69

Q_E_wall = U_total × A_wall_net × CLTD = 0.15 × 317 × 16 = 761 Btuh

West Wall Heat Gain

The wall assembly matches the east wall, with a 1″ stucco finish (R = 4.76)

Total wall area = 82 sf + 36 sf = 118 sf

• Wall above windows = 24″ × 41 sf = 82 sf

• Wall between windows: 16.5″ × 104″ × 3 = 36 sf

Q_W_wall = 0.09 × 118 × 16 = 170 Btuh

Windows Solar Heat Gain

Concepts & Factors

• Solar radiation through glazing significantly affects space heat gain, especially during peak sun hours (~ 3–5 hrs/day).

Equations

• Q_fes = (A_s × SHGF + A_sh × SHGF_sh) × SC

• Q_fs = Q_fes × CLF (accounts for time lag, space load)

Parameters

• A_s = Unshaded glass area = [1 – (SL / window width)] × A_tot

• A_sh = Shaded glass area = A_tot – A_s

• SHGF = Solar Heat Gain Factor (Btu/hr·ft²), based on latitude (32°N) and hottest month (June)

• SHGF_sh = Shaded SHGF, adjusted for orientation and month

• SC = Shading Coefficient (depends on glass and shading device)

• SL = Shade Line = SLF × shadow width from overhang

• SCL (Solar Cooling Load) = SHGF × CLF

• CLF = Cooling Load Factor (accounts for time lag effect)

• GLF = Glass Load Factor = SCL × SC

Glass Area

• Area of door (aluminum frame single-pane glass) = 72” x 104” = 52 sf

• Area of (6) windows = 66” x 104” = 48 sf

• Total glass area = 52′ + (48′ x 6) = 340 sf

Method 1 (less accurate)

U = 1.27 Btu/hr-sf-°F

Q_windows = 1.27 x 16 x 340 = 6,910 btuh 

Method 2 (more accurate)

• Overhang width = 101″ → SL = 0.8 × 101 = 81″

• A_s = [1 – (81/104)] × 340 = 75 ft²

• A_sh = 340 – 75 = 265 ft²

• SHGF = 1,169 Btu/ft²·day ÷ 8 hrs = 146 Btuh·ft²

• SHGF_sh = 142 W/m² × 0.0929 × 3.41 = 45 Btuh·ft²

• SC (shading coefficient): 1.0 (no shade), 0.50 (blinds or translucent roller shades), 0.25 (white shades)

Q_windows = (75 × 146 + 265 × 45) × 0.50 = 11,438 Btuh (with shades)

Lighting Heat Gain

Method 1 (less accurate)

Common Space Type: Computer Room

Lighting Power Density (LPD): 0.94 (from 2021 ASHRAE Handbook Fundamentals, Table 2 Lighting Power Densities Using Space-by-Space Method)

Q = 3.412 × 0.94 W/sf × 2,420 sf = 7,762 Btuh

Method 2 (more accurate)

Equation

Q = 3.412 × W × BF × CLF

Parameters

• 3.412 = conversion factor from watts to Btuh

• W = lighting power in watts

• BF = Ballast Factor (accounts for heat loss in fluorescent lamp ballasts)

• CLF = cooling load factor (accounts for heat storage in lighting fixtures, typical value = 1.0)

Lighting Fixtures

• (25) 4′ × 2′ fixtures, each with (4) U-bend T12 lamps (48″ length), Ballast Factor: 0.92

• (6) 2′ × 2′ fixtures, each with (2) T12 lamps (24″ length), Ballast Factor: 0.94

• Lamp Power: 32 W

Q_lighting = 3.412 × [(25 × 4 × 32 × 0.92 × 1.0) + (6 × 2 × 32 × 0.94 × 1.0)] = 11,277 btuh

Occupant Heat Gain

Equations

• Sensible heat: Q_s = qs x n x CLF

• Latent heat: Q_l = ql x n

Parameters

• Activity type: office work

• Activity level: moderate

• Sensible heat gain per person (qs): 250 btuh

• Latent heat gain per person (ql): 200 btuh

• Number of occupants (n): 59

• Diversity factor: 0.9

• CLF (capacity of space to absorb and store heat): 0.91 – 1.0

Q_occupants_undiversified = (qs + ql) x n = 450 btuh/person x 59 = 26,550 btuh

Q_occupants_diversified = 26,550 x 0.9 = 23,895 btuh

Equipment Heat Gain

Power Consumption

• Computers: (59) with 21″ monitors, 130 W each (continuous)

• Computer: (1) with 15″ monitor, 110 W (continuous)

• Televisions: (2) 50″ (Westinghouse), 151.3 kWh/yr each

• Refrigerator: (1) 15 ft³, 510 Btuh

• Laser printer: (1) 240 Btuh

• Coffee maker: (1) 2,590 Btuh

• (1) 8-head soda machine: 2,185 Btuh

• Other office equipment: 25% of nameplate power

Q_computers_21″ = 3.412 × (59 × 130 W) = 26,170 Btuh

Q_computer_15″ = 3.412 × 110 W = 375 Btuh

Q_televisions = 2 × 151.3 kWh/yr × 0.3895 (Btuh per kWh/yr) = 118 Btuh

Q_equip_undiversified = 32,188 Btuh

Q_equip_diversified = 32,188 × 0.7 = 22,532 Btuh

Total Load (roof + doors + slab + walls + windows + lighting + occupants + equipment):
Q_total = 2,033 + 256 + 716 + 761 + 170 + 11,438 + 11,277 + 23,895 + 22,532 = 73,078 Btuh

Ventilation Air

Parameters 

(Ventilation Rates obtained from ASHRAE 62.1, Table 6.2.2 - Outdoor Air Requirements)

• Occupancy category: Casino (Gaming Area) per ASHRAE 62.1

• Rp (per person): 15 CFM/person

• Ra (per area): 0.06 CFM/ft²

• Pz (occupant load): 59 persons

• Az (conditioned floor area) = 2,420 ft2

• Ez (distribution effectiveness): 1.00

Equations

• Ventilation rate in the breathing zone outdoor air: Vbz_dot = Rp × Pz × Ra × Az

• Zone outdoor airflow: Voz_dot = Vbz_dot / Ez

• Voz_dot = (5 × 59 + 0.06 × 2,420) / 1.0 = 440.2 cfm

• Design ventilation rate = 445 cfm (rounded up to the nearest 5 cfm)

Sensible Cooling of Ventilation Air

Sensible heat (h_s) = 1.08 × Voz_dot × ∆T = 1.08 x 440.2 ft3/min x 17.8°F = 8,462 btuh

• Reference: https://engineeringtoolbox.com/cooling-heating-equations-d_747.html

• Load on the coil due to leakage in the return air duct and the return air fan is assumed negligible

Latent Cooling of Ventilation Air

Latent heat (h_l) = 4,840 × Voz_dot × dw_lb

• Humidity ratio difference (dw_lb) = 0.0206 lb water/dry air

• Mean coincident wet-bulb temperature (T_wb) = 25.4°C = 77.7°F

• Latent heat (h_l) = 4,840 x 440 ft3/min x 0.0206 = 43,870 btuh

Total Cooling Load

Total heat (sensible + latent): h_t = h_s + h_l = 8,462 + 43,870 = 52,332 btuh

Q_t = Q_l+s_r + h_t = 73,078 + 52,332 = 125,410 btuh / 12,000 = 10.5 tons

Alternative Method

Total heat (h_t) = 4.5 x Voz_dot x dh

• Enthalpy difference (dh) = h_o - h_i

• h_o = 45.5 (using psychrometric chart at T_db = 92.8˚F and dw_lb = 0.0206)

• h_i = 28 (using psychrometric chart at T_db = 75˚F and RH = 50%)

h_t = 4.5 x 440.2 x (45.5 - 28) = 34,666 btuh

Q_t = Q_l+s_r + h_t = 73,078 + 34,666 = 107,744 btuh / 12,000 = 9.0 tons