Theater Air Conditioning Systems & Equipment Selection

System Architecture Selection

Theater air conditioning systems face competing requirements: high sensible cooling loads from occupants and equipment, strict acoustic criteria (NC 25-30), and highly variable occupancy schedules requiring rapid pull-down capability.

Rooftop Units Versus Central Plants

Rooftop packaged units dominate theater applications for several physical and economic reasons:

• Thermal mass elimination: Direct outdoor air access eliminates the thermal mass of chilled water piping, enabling faster temperature response during pre-cooling
• Refrigerant circuit efficiency: Direct expansion refrigeration delivers coefficient of performance (COP) values of 3.0-3.5 at design conditions, compared to 2.5-3.0 for chiller-based systems when accounting for pumping and tower losses
• Acoustic isolation: Equipment vibration remains outside the building envelope, reducing structure-borne noise transmission

Central chilled water plants provide advantages for large multiplex facilities (8+ screens):

The diversity factor advantage becomes significant for facilities exceeding 40,000 cfm total airflow, where central systems benefit from statistical averaging of peak loads across multiple auditoriums.

Packaged Versus Split Systems

Packaged rooftop units place all refrigeration components in a single enclosure, while split systems separate the condensing unit from the air handler.

The heat rejection rate at the condenser follows:

$$Q_{\text{rej}} = Q_{\text{evap}} + W_{\text{comp}} = Q_{\text{evap}} \left(1 + \frac{1}{\text{COP}}\right)$$

For a theater auditorium with 30 tons (360,000 Btu/hr) cooling load at COP = 3.0:

$$Q_{\text{rej}} = 360{,}000 \times \left(1 + \frac{1}{3.0}\right) = 480{,}000 \text{ Btu/hr}$$

Packaged configuration advantages:

• Factory-assembled refrigerant piping eliminates field brazing and leak potential
• Single-point responsibility for performance verification
• Reduced installation labor (40-60% versus split systems)
• Integrated economizer dampers and controls

Split system applications:

• Indoor air handler placement reduces duct run lengths when rooftop space is constrained
• Separation of heat rejection allows condenser placement at grade level for maintenance access
• Multiple air handlers per condensing unit in small facilities (2-4 screens)

Low-Velocity Air Distribution

Acoustic criteria drive air distribution design. The relationship between duct velocity and regenerated noise follows:

$$\text{PWL} = 10 \log_{10}(V^6)$$

where PWL is sound power level and V is velocity. Reducing velocity from 2,000 fpm to 1,200 fpm decreases sound power by 14 dB—critical for achieving NC 25-30 targets.

Supply Air Design Parameters

flowchart TD
    A[Cooling Load Calculation] --> B[Determine Supply Airflow]
    B --> C{Select Distribution Strategy}
    C --> D[Overhead Low-Velocity]
    C --> E[Displacement Ventilation]
    C --> F[Underfloor Air Distribution]
    D --> G[Diffuser Selection NC ≤ 25]
    E --> G
    F --> G
    G --> H[Duct Sizing: V ≤ 1200 fpm]
    H --> I[Sound Attenuator Specification]

The supply air temperature rise due to duct heat gain becomes significant in low-velocity systems:

$$\Delta T = \frac{Q_{\text{gain}}}{.{m} c_p} = \frac{UA(T_{\text{ambient}} - T_{\text{supply}})}{.{m} c_p}$$

For 100 feet of uninsulated sheet metal duct carrying 10,000 cfm at 55°F in a 95°F plenum space:

• U-value ≈ 0.90 Btu/hr·ft²·°F (bare metal)
• Surface area ≈ 340 ft² (48-inch diameter duct)
• Heat gain = 0.90 × 340 × (95 - 55) = 12,240 Btu/hr
• Air mass flow = 10,000 × 0.075 × 60 = 45,000 lb/hr
• Temperature rise = 12,240 / (45,000 × 0.24) = 1.1°F

This 2% temperature increase requires R-6 insulation or routing through conditioned space to maintain setpoint accuracy.

Return Air Path Configuration

Ducted returns prevent cross-talk between adjacent auditoriums. The transmission loss requirement follows:

$$\text{TL} = \text{SWL}{\text{source}} - \text{NC}{\text{target}} - 10\log_{10}(A/A_0)$$

where A is the room absorption and $A_0$ = 1 ft². For two 400-seat auditoriums with SWL = 85 dB at low frequencies and NC 30 target, the required partition TL exceeds 50 dB at 125 Hz—achievable only with fully ducted returns or massive plenum barriers.

Pre-Cooling Strategies

Theater occupancy transitions from near-zero to design capacity in 15-30 minutes during show start times. The space thermal mass provides beneficial capacitance:

$$Q_{\text{stored}} = (mc_p){\text{air}}(T_1 - T_2) + (mc_p){\text{surfaces}}(T_1 - T_2)$$

Pre-Cooling Calculation Example

400-seat auditorium with 15,000 ft³ volume and 12,000 ft² interior surface area (concrete, gypsum):

Air thermal mass: $$Q_{\text{air}} = 15{,}000 \times 0.075 \times 0.24 \times (78 - 72) = 1{,}620 \text{ Btu}$$

Surface thermal mass (1-inch effective depth): $$Q_{\text{surface}} = 12{,}000 \times \frac{1}{12} \times 144 \times 0.20 \times (78 - 72) = 172{,}800 \text{ Btu}$$

Total stored cooling = 174,420 Btu. This thermal capacitance allows setpoint drift to 78°F during unoccupied periods, then 2-hour pre-cooling at 1.5× design capacity recovers to 72°F before audience arrival while storing 48 tons of cooling in the building mass.

Pre-Cooling Control Sequence

sequenceDiagram
    participant BMS as Building Management System
    participant RTU as Rooftop Unit
    participant Space as Auditorium
    participant Schedule as Show Schedule

    Schedule->>BMS: Show start time T-120 min
    BMS->>RTU: Enable pre-cooling mode
    RTU->>Space: Supply air 52°F at 125% airflow
    Space->>BMS: Temperature feedback

    alt Temperature < 72°F at T-30 min
        BMS->>RTU: Reduce to occupied mode
    else Temperature ≥ 72°F at T-30 min
        BMS->>RTU: Maintain pre-cooling mode
        Note over BMS,RTU: Override to prevent warm start
    end

    Schedule->>BMS: Show start time T-0
    BMS->>RTU: Full occupied mode 100% OA

Energy implications: Pre-cooling reduces peak equipment size requirements by 20-30% through thermal mass utilization. The integrated cooling energy remains constant (first law of thermodynamics), but power demand shifts to off-peak periods when outdoor temperatures are 8-12°F lower, improving refrigeration efficiency by 15-25%.

System Component Integration

Economizer operation: Outdoor air economizing provides free cooling when $T_{\text{oa}} < T_{\text{return}} - 2°F$. Given typical theater return air temperatures of 75-78°F and 100% outdoor air requirements during occupied periods, economizer sequences function only during pre-cooling and post-occupancy purge cycles.

Energy recovery: Run-around glycol loops or enthalpy wheels recover 50-70% of exhaust energy. The effectiveness-NTU relationship:

$$\epsilon = \frac{1 - e^{-NTU(1-C^)}}{1 - C^ e^{-NTU(1-C^*)}}$$

For balanced airflows ($C^* = 1$), effectiveness approaches 0.50 at NTU = 1.0, requiring heat exchanger surface area of approximately 2.5 ft² per cfm for practical installations.

Variable air volume versus constant volume: VAV systems reduce energy during partial occupancy but compromise ventilation effectiveness. ASHRAE 62.1 requires ventilation rates based on peak occupancy (7.5 cfm/person + 0.06 cfm/ft²), making VAV turndown limited to post-occupancy periods only.

Conclusion

Theater air conditioning system selection balances acoustic performance, rapid load response, and energy efficiency. Rooftop packaged units dominate through simplicity and first cost advantages, while low-velocity distribution remains non-negotiable for acoustic compliance. Pre-cooling strategies exploit building thermal mass to reduce equipment sizing and shift energy consumption to favorable outdoor conditions, demonstrating the practical application of thermodynamic storage principles.