Thermal Comfort: PMV/PPD Analysis and ASHRAE Standards

Overview

Thermal comfort quantifies human thermal sensation under specified environmental and personal conditions. The analytical framework combines heat transfer physics with empirical data from controlled human subject studies.

Heat Balance Equation

Human thermal comfort requires zero net heat storage:

Where:

• $M$ = metabolic rate (W/m²)
• $W$ = external work (typically 0 for sedentary)
• $Q_{sk}$ = skin heat loss (W/m²)
• $Q_{res}$ = respiratory heat loss (W/m²)
• $Q_{evap}$ = evaporative heat loss (W/m²)

Skin Heat Loss

Convection and radiation from skin surface:

Where:

• $h_c$ = convective heat transfer coefficient (W/m²·K)
• $h_r$ = radiative heat transfer coefficient (W/m²·K)
• $A_{cl}$ = clothed body surface area (m²)
• $t_{cl}$ = clothing surface temperature (°C)
• $t_a$ = air temperature (°C)
• $\bar{t}_r$ = mean radiant temperature (°C)

Respiratory Heat Loss

Where:

• $p_a$ = water vapor pressure (kPa)
• First term: sensible heat loss
• Second term: latent heat loss

PMV Model

Predicted Mean Vote (PMV) predicts thermal sensation on a 7-point scale:

PMV Calculation

The PMV equation (Fanger’s model):

Where $L$ = thermal load on body:

Clothing Surface Temperature

Iterative solution required:

Where:

• $I_{cl}$ = clothing insulation (m²·K/W or clo)
• $f_{cl}$ = clothing area factor

PPD Model

Predicted Percentage Dissatisfied (PPD) relates to PMV:

graph LR
    A[-3 PMV
100% PPD] --> B[0 PMV
5% PPD]
    B --> C[+3 PMV
100% PPD]
    B -.->|Optimal| B
    style B fill:#4f4,stroke:#333
    style A fill:#f44,stroke:#333
    style C fill:#f44,stroke:#333

  

Key Finding: Even at PMV = 0 (neutral), PPD = 5%

• Individual differences in thermal preference
• Minimum achievable dissatisfaction

Input Parameters

Metabolic Rate

Body surface area (DuBois equation):

Where:

• $m$ = body mass (kg)
• $h$ = height (m)
• $A_D$ = surface area (m²)

Clothing Insulation

Conversion: 1 clo = 0.155 m²·K/W

ASHRAE 55 Compliance

Acceptable Thermal Environment

For PMV/PPD Method:

• $-0.5 \le PMV \le +0.5$ (PPD < 10%)
• Category II: $-0.7 \le PMV \le +0.7$ (PPD < 15%)

Graphical Comfort Zone

For typical indoor clothing (0.5-1.0 clo) and activity (1.0-1.3 met):

graph TD
    A[Winter: 20-23.5°C] --> C[Comfort Zone]
    B[Summer: 23-26°C] --> C
    C --> D[RH: 30-60%]
    C --> E[Air Velocity < 0.2 m/s]
    style C fill:#4f4,stroke:#333

  

Operative Temperature

The temperature that combines air and radiant effects:

For low air velocities ($v < 0.2$ m/s):

Local Discomfort

Draft Rating

Percentage of people bothered by draft:

Where:

• $v$ = local air velocity (m/s)
• $Tu$ = turbulence intensity (%)

Limit: DR < 15% for comfort

Vertical Air Temperature Difference

Between ankle (0.1 m) and head (1.1 m):

Limit: $\Delta t_{vertical} < 3°C$

Floor Surface Temperature

Acceptable range for bare feet or light footwear:

Limit: 19°C < $t_{floor}$ < 29°C

Radiant Asymmetry

Warm ceiling / cool wall asymmetry:

Limit: $\Delta t_r < 5°C$ (warm ceiling)

Adaptive Comfort Model

For naturally ventilated buildings, occupants adapt to outdoor conditions:

Where:

• $t_{comf}$ = comfort temperature (°C)
• $t_{rm(out)}$ = running mean outdoor temperature (°C)

Running mean calculation:

80% Acceptability Limits: $t_{comf} \pm 3.5°C$

graph LR
    A[Outdoor Temp
Rising] --> B[Adaptive Model
Higher Setpoint]
    A --> C[PMV Model
Fixed Setpoint]
    B -.->|Energy Savings| D[20-30%]
    style B fill:#4f4,stroke:#333
    style C fill:#f99,stroke:#333

  

Practical Application

Design Workflow

1. Specify Design Conditions:

   • Activity level (met)
   • Clothing insulation (clo)
   • Acceptable PMV range

2. Calculate Required Environment:

   • Solve PMV equation for $t_a$ and $\bar{t}_r$
   • Check local discomfort criteria
   • Verify humidity constraints

3. System Design:

   • Size HVAC to maintain calculated conditions
   • Control strategy for operative temperature
   • Prevent drafts and stratification

Example Calculation

Given:

• Activity: Office work (1.2 met = 70 W/m²)
• Clothing: Business suit (1.0 clo = 0.155 m²K/W)
• Target: PMV = 0
• Relative humidity: 50%
• Air velocity: 0.1 m/s

Find: Required air temperature if $\bar{t}_r = t_a$

Solution: Using iterative PMV solver:

At this condition: PPD = 5%

Seasonal Adjustment

Winter:

• Clothing: 1.0 clo
• Comfort range: 20-23.5°C

Summer:

• Clothing: 0.5 clo
• Comfort range: 23-26°C

Energy Saving: 3°C setpoint difference reduces HVAC energy by 15-25%

Advanced Considerations

Individual Control

Personal comfort systems (PCS) improve satisfaction:

• Desk fans
• Task lighting with radiant component
• Localized heating/cooling

Impact: Can extend acceptable temperature range by ±2.5°C

Transient Conditions

Dynamic thermal comfort models account for:

• Thermal history
• Rate of temperature change
• Intermittent occupancy

Guideline: Temperature ramp rate < 0.5°C/hour

Humidity Effects

While not direct PMV input, humidity affects:

• Evaporative heat loss
• Perceived air quality
• Mold/condensation risk

Recommended Range: 30% < RH < 60%

Measurement and Verification

Required Sensors

• Air temperature: ±0.5°C accuracy
• Globe temperature: For radiant measurement
• Air velocity: ±0.05 m/s (anemometer)
• Humidity: ±5% RH

Operative Temperature Measurement

Using black globe thermometer:

Where $t_g$ = globe temperature (°C)

Conclusion

Thermal comfort analysis provides quantitative design targets for HVAC systems. The PMV/PPD model, validated across diverse populations and climates, predicts thermal sensation from measurable environmental and personal parameters.

Key design principles:

• Target PMV between -0.5 and +0.5 for 90% satisfaction
• Control operative temperature, not just air temperature
• Address local discomfort factors (draft, asymmetry, stratification)
• Consider adaptive opportunities in naturally ventilated spaces

Proper application of thermal comfort standards balances occupant satisfaction with energy efficiency, supporting both human productivity and sustainability goals.

Technical content by Evgeniy Gantman, HVAC Research Engineer