Heat Load Calculations

Building Specifications
Location: Jacksonville, FL
Type of facility: electronic casino
Area: 2,420 sf
Occupants: 59

Design Conditions
Infiltration loss: typical range of 1 – 2 ACH (air changes per hour)
Outdoor air requirement: 15 – 25% of ventilation air
Breathing zone: 3″ – 72″ height from the floor and 24″ distance from the walls or AC equipment
Relative Humidity: 30% heating (30% – 40%), 50% cooling (40% – 60%); in general 30% – 35% (< 20% or > 60% is problematic)
Inside heating design temperature: 70˚F per ACCA Manual J and 72˚F per NEC (68˚F – 72˚F)
Inside cooling design temperature: 75˚F (72˚F – 76˚F)
Outdoor dry-bulb temperature (T_o): 92.8˚F (1% cooling), 28.6˚F (99.6% heating)
∆T = T_o – T_i = 92.8˚F – 75˚F = 17.8˚F
ASHRAE Climatic Design Conditions

Cooling Load
To calculate the cooling load, the formula commonly used is Q_dot = U x A x ∆T.
However, a more accurate approach is to use the Cooling Load Temperature Difference (CLTD) instead of ∆T.
It’s important to note that it may still result in approximately a 15% error margin.

Rough estimation
Cooling load of 20 btuh per sf of building area
Q = 2,420 sf x 20 btuh x (1 ton / 12,000 btuh) = 4.0 tons
Minimum ventilation design standard: 20 cfm/person with a reheat system

Roof
Area (A) = 2,420 sq ft with 3′ attic air space
R-value (R) = 1.79 (1/2” acoustical ceiling tile), 30 (9-1/4” R-19 insulation)
Overall U-value (U) = 1/R_tot = 0.03
CLTD = 28 (L- light construction and 95˚F)
Q_roof = 0.03 x 2,420 x 28 = 2,130 btuh

Doors
Qty (2) 1-¾” insulated metal doors in the east wall
A = 80” x 36” = 20 sf
U = 0.40 (Btu/hr-sf-°F)
CLTD = 16 (light construction and 95˚F)
Q_doors = U x A x #_doors x CLTD = 0.40 x 20 x 2 x 16 = 1,220 btuh

Concrete Slab
4” thick slab = 0.333’
∆T = 5˚F
Slab edge of N and S walls have zero heat transfer
A_slab_face = 2,420 sf
A_ slab_edge = 0.333’ x (41’ x 2) = 27.33 sf
U_slab_face = 0.05
U_ slab_edge = 0.81
Q_slab = (0.05 x 2,420 + 0.81 x 27.33) x 5 = 715 btuh

Exterior Walls
Zero heat transfer from N and S facing walls

East wall
Height = 128”, Length = 41’
Area of east wall: 128’ x 41” = 200 sf
A_wall = (12’ x 200’) – A_windows – A_E_door = 2,400 – 80 – 60 = 2,260 sf
Construction materials: 12” concrete block, ¾” plywood, ½” sheetrock, 1″ stucco
R-values:
Outside wind: 0.33 (for 7.5 mph wind)
Inside vertical air film: 0.68 – 0.69
Stucco: 4.76 (1”)
Light-weight (LW) block: 2.04 – 2.56 (12″)
Plywood: 1.08 (3/4”)
Sheetrock: 2.22 (1/2”)
U_tot = 0.09
CLTD = 16 (light construction and 95˚F)
Q_E_wall = 0.09 x 2,260 x 16 = 3,255 btuh

West wall
Area of west wall: 24” (wall above window) x 41’ + 16.5” x 104” x 3 (wall between windows) = 82 + 36 = 118 sf
Q_W_wall = 0.09 x 118 x 16 = 170 btuh

Q_wall_tot = 3,255 + 170 = 3,425 btuh

Windows
Solar radiation passing through glass affects the heat gain of a space
Peak sun per day: 3 – 5 hours
Q_fes = (A_s x SHGF + A_sh x SHGF_sh) x SC
Q_fs = Q_fes x CLF (space cooling load)
A_s (Unshaded Area of Window Glass) = 1 – (SL/window width) x A_tot
A_sh (Shaded Area of Window Glass) = A_tot – A_s
SHGF (Solar Heat Gain Factor), Btu/hr-ft2, using a latitude of 32˚N and the month of June
SHGF_sh (Shaded Solar Heat Gain Factor) accounts for shading due to orientation (East/West) and the month of May
SC = Shading Coefficient
SLF = Shade Line factor
SL (Shade Line) = SLF x shadow width beneath the edge of the overhang
SCL (Solar Cooling Load) = SHGF x CLF, where CLF takes into account the time lag
GLF (Glass Load Factor) = SCL x SC
Number of windows: 6
Area of (aluminum frame single-pane glass) door = 72” x 104” = 52 sf
Area of window = 66” x 104” = 48 sf
Area_tot = 52′ + (48′ x 6) = 340 sf
U = 1.27 Btu/hr-sf-°F
CLTD = 16 (light construction and 95˚F)
Q_windows = 1.27 x 16 x 340 = 6,910 btuh (less accurate)

Width of the overhang = 101”
SLF = 0.8
SL = 0.8 x 101” = 81”
A_s = (1 – (81/104) x 340) = 75 sf
A_sh = 340 – 75 = 265 sf
SHGF = 1,169 Btu/sf-day / 8 hours = 146
SHGF_sh = 142 W/m2 x 0.0929 m2/sf x 3.41 Btu/h-W = 45
SC = 0.50 (blinds or translucent roller shades for single-pane windows), 0.25 (white shades), 1.0 (no shades
Q_windows = (75 x 146 + 265 x 45) x 0.50 = 11,440 btuh (more accurate)

Lighting
Q = 3.412 x W x BF x CLF
3.412 = a conversion factor from watts to btuh
W = watts, which represents the lighting capacity
BF = Ballast Factor, accounting for heat loss in the ballasts of fluorescent lights
CLF = Cooling Load Factor (heat storage in the lighting fixtures)
(25) fixtures measuring 4’X2’ each, with (4) T12 lamps (48” length) per fixture, consuming 32 W per bulb, with a BF = 0.92
(6) fixtures measuring 2’X2’ each, with (2) u-shaped T12 lamps (24″ length) per fixture, consuming 32 W per bulb, with a BF = 0.94
CLF of 1.0 (typical value)
Q_lighting = 3.412 x [(25 x 4 x 32 W x 0.92 x 1.0) + (6 x 2 x 32W x 0.94 x 1.0)] = 11,270 btuh

Occupants
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 people (n): 59
CLF (capacity of space to absorb and store heat): 0.91 – 1.0
Q_s = qs x n x CLF
Q_l = ql x n
Q_occupants_undiversified = (qs + ql) x n = 450 btuh-person x 59 people = 26,550 btuh
Q_occupants_diversified = 26,550 x 0.9 = 23,895 btuh

Equipment
(59) computers with 21” monitors consuming 130 W continuously
(1) computer with 15″ monitor consuming 110 W continuously
(2) 50” televisions (Westinghouse) consuming 151.3 kWh/yr
(1) refrigerator (15 ft3) consuming 510 btuh
(1) laser printer consuming 240 btuh
(1) coffee maker consuming 2,590 btuh
(1) 8 head soda machine consuming 2,185 btuh
Other office equipment accounts for 25% of the nameplate power
Q = 3.41 x (59 computers x 130 W) = 26,150 btuh
Q = 3.41 x (1 computer x 110 W) = 375 btuh
Q = 2 x 151.3 kWh/yr x 0.3895 [(btuh) / (kWh/yr)] = 120 btuh
Q_equipment_undiversified = 32,170 btuh
Q_equipment_diversified = 32,170 x 0.7 = 22,520 btuh

Q_l+s_r = 9,800 + 2,130 + 1,220 + 715 + 3,425 + 11,440 + 11,270 + 23,895 + 22,520 = 86,415 btuh

Ventilation Air
Ventilation rate per person (Rp): 5 cfm/person
Number of people (Pz): 59
Ventilation rate per sf (Ra): 0.06 cfm/ft2
Floor area (Az): 2,420 ft2
Distribution effectiveness (Ez): 1.00
Ventilation rate in the breathing zone outdoor air: V_bz_dot = Rp x Pz x Ra x Az
Zone outdoor airflow: Voz_dot = V_bz_dot / Ez
Voz = (5 x 59 + 0.06 x 2,420) / 1.0 = 440 cfm

Sensible Cooling of Ventilation Air
Sensible heat (h_s) = 1.08 x V_oz x ∆T = 1.08 x 440 ft3/min x 17.8 = 8,460 btuh
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 negligible

Latent Cooling of Ventilation Air
Latent heat (h_l) = 4,840 x V_oz x 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 heat (sensible + latent): h_t = h_s + h_l = 8,460 + 43,870 = 52,330 btuh

Total Cooling Load
(Q_t) = Q_l+s_r + h_t = 86,415 + 52,330 = 138,745 btuh / 12,000 = 11.6 tons

Alternative Method
Total heat (h_t) = 4.5 x V_oz 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 x (45.5 – 28) = 34,650 btuh
Q_t = Q_l+s_r + h_t = 86,415 + 34,650 = 121,065 btuh / 12,000 = 10.1 tons