Load Calculation Methods

Accurate cooling load calculations form the foundation of HVAC system design. Several methods exist, ranging from simplified manual procedures to comprehensive computer-based analyses. Understanding each method’s capabilities and limitations guides appropriate selection.

Evolution of Calculation Methods

Historical Development

Load calculation methods have evolved to address the complexity of transient heat transfer:

1. Steady-State Methods: Early simplistic approach (now obsolete)
2. TETD/TA (1967): Total equivalent temperature differential
3. TFM (1972): Transfer function method
4. CLTD/CLF (1979): Cooling load temperature differential
5. RTS (2001): Radiant time series
6. Heat Balance (2001): Fundamental physics-based approach

Heat Balance Method (HBM)

Fundamental Approach

The heat balance method applies fundamental heat transfer principles directly, solving simultaneous energy balance equations for all surfaces and the room air.

Surface Heat Balance: $$q’’{conv,i} + q’’{SW,i} + q’’{LW,i} + q’’{cond,i} = 0$$

Where:

• $q’’_{conv}$ = convective heat flux
• $q’’_{SW}$ = absorbed short-wave radiation
• $q’’_{LW}$ = long-wave radiation exchange
• $q’’_{cond}$ = conduction heat flux

Air Heat Balance: $$\sum_{surfaces} h_c A_s (T_s - T_{air}) + Q_{internal} + Q_{infiltration} + Q_{system} = 0$$

Advantages

• Accuracy: Most physically rigorous approach
• Flexibility: Handles any construction or geometry
• Fenestration: Detailed solar and optical analysis
• No pre-calculation: Works with any building type

Limitations

• Computational intensity: Requires software
• Input requirements: Detailed building data needed
• Expertise: Understanding of method required for interpretation

Radiant Time Series (RTS) Method

Concept

RTS simplifies the heat balance approach using pre-calculated response factors to convert radiant heat gains to cooling loads.

Total Cooling Load: $$Q_{cooling}(t) = Q_{convective}(t) + \sum_{\theta=0}^{23} r_\theta \cdot Q_{radiant}(t-\theta)$$

Where:

• $r_\theta$ = radiant time factor at hour θ
• $Q_{radiant}(t-\theta)$ = radiant heat gain θ hours ago

Radiant Time Factors

RTFs distribute radiant heat gain over time based on zone thermal characteristics:

Conduction Time Series

CTS factors account for thermal mass effects in opaque construction:

$$q_{wall}(t) = \sum_{\theta=0}^{23} c_\theta \cdot (T_{sol-air}(t-\theta) - T_{room})$$

Applications

• Manual calculations (simplified)
• Spreadsheet implementations
• Educational purposes
• Quick design estimates

Transfer Function Method (TFM)

Mathematical Basis

TFM uses z-transform coefficients to relate current heat gains to current and past loads:

$$Q(t) = \sum_{n=0}^{N} v_n \cdot q(t-n\Delta) - \sum_{m=1}^{M} w_m \cdot Q(t-m\Delta)$$

Where:

• $v_n$ = response coefficients for heat input
• $w_m$ = response coefficients for previous loads
• $q$ = heat gain
• $Q$ = cooling load

Wall and Roof Conduction

Conduction transfer functions (CTFs) characterize thermal response:

$$q’’i(t) = \sum{n=0}^{N} X_n T_{o,t-n} - \sum_{n=0}^{N} Y_n T_{i,t-n} + \sum_{n=1}^{N} \Phi_n q’’_{i,t-n}$$

Zone Response

Room transfer functions convert instantaneous heat gains to cooling loads accounting for thermal storage effects.

CLTD/CLF Method (Simplified)

Cooling Load Temperature Differential (CLTD)

CLTD values combine outdoor-indoor temperature difference with thermal mass effects:

$$Q_{wall/roof} = U \times A \times CLTD_{corrected}$$

CLTD Correction: $$CLTD_{corrected} = CLTD + (78 - T_i) + (T_m - 85)$$

Where:

• $T_i$ = indoor design temperature
• $T_m$ = mean outdoor temperature

Cooling Load Factors (CLF)

CLF values convert instantaneous solar and internal gains to cooling loads:

$$Q_{solar} = SHGC \times A \times SC \times CLF$$

$$Q_{lighting} = W_{lighting} \times F_u \times F_s \times CLF$$

Limitations

• Based on specific construction types
• Limited applicability to modern buildings
• Pre-calculated values may not match actual construction
• Superseded by RTS method

Method Comparison

Software Implementation

Energy Modeling Programs

• EnergyPlus: Heat balance method
• DOE-2: Transfer function method
• HAP, Trace 700: Various methods
• ASHRAE Load Calc: RTS method

Input Requirements

1. Building geometry: Dimensions, orientations
2. Construction: Wall/roof/floor assemblies
3. Fenestration: Window properties, shading
4. Internal loads: Lighting, equipment, occupants
5. Weather data: Design conditions or TMY
6. Schedules: Hourly operating profiles

Practical Guidelines

Method Selection

Use Heat Balance/Software:

• Complex buildings
• Unusual constructions
• Energy analysis required
• High accuracy needed

Use RTS:

• Manual calculations
• Standard commercial buildings
• Quick design iterations
• Educational purposes

Avoid CLTD/CLF:

• Obsolete method
• Use only if specifically required

Safety Factors

After calculating loads:

• System sizing typically includes 10-15% safety factor
• Accounts for uncertainties in assumptions
• Provides future capacity margin
• Do not compound multiple safety factors

Selecting the appropriate load calculation method balances accuracy requirements against available data and computational resources, ensuring reliable HVAC system sizing for each project’s unique circumstances.