# Thermal Comfort Fundamentals ## Table of Contents - [[#Overview]] - [[#Definition of Thermal Comfort]] - [[#The Six Factors]] - [[#Heat Balance of the Human Body]] - [[#Fanger's PMV-PPD Model]] - [[#Predicted Mean Vote Scale]] - [[#Predicted Percentage Dissatisfied]] - [[#Comfort Zone]] - [[#Operative Temperature]] - [[#Local Thermal Discomfort]] - [[#ASHRAE Standard 55]] - [[#ISO 7730]] - [[#Measurement and Assessment]] - [[#Design Implications]] - [[#Key References and Standards]] --- ## Overview Thermal comfort is a central concern in architectural design, directly affecting occupant satisfaction, health, productivity, and energy consumption. Designing for thermal comfort requires understanding the physiological, psychological, and environmental factors that determine how people perceive their thermal environment. This article covers the foundational Fanger PMV/PPD model and associated standards. The complementary adaptive comfort approach, which is particularly relevant to naturally ventilated buildings, is treated in [[Adaptive Comfort Model]]. For the graphical representation of comfort conditions, see [[Psychrometric Chart for Design]]. For integration with building services, see [[HVAC Fundamentals for Architects]]. --- ## Definition of Thermal Comfort ASHRAE Standard 55 defines thermal comfort as: > "That condition of mind which expresses satisfaction with the thermal environment." This definition recognises that thermal comfort is **subjective** -- it depends on individual perception, not solely on measurable physical quantities. Nevertheless, statistical models allow the architect to design environments that satisfy the majority of occupants. --- ## The Six Factors Thermal comfort depends on the interaction of six variables -- four environmental and two personal: ### Environmental Factors | Factor | Symbol | Unit | Typical Measurement | |--------|--------|------|-------------------| | Air temperature | T_a | degC | Thermometer, thermocouple | | Mean radiant temperature | T_r | degC | Globe thermometer | | Air velocity | V_a | m/s | Hot-wire anemometer | | Relative humidity | RH | % | Hygrometer, psychrometer | ### Personal Factors | Factor | Symbol | Unit | Description | |--------|--------|------|------------| | Metabolic rate | M | met (1 met = 58.2 W/m2) | Heat generated by the body based on activity level | | Clothing insulation | I_cl | clo (1 clo = 0.155 m2K/W) | Thermal resistance of clothing ensemble | ### Typical Values **Metabolic rate:** | Activity | Rate (met) | |----------|-----------| | Sleeping | 0.7 | | Seated, relaxed | 1.0 | | Sedentary office work | 1.2 | | Standing, light work | 1.6 | | Walking (4 km/h) | 2.0 | | Heavy manual work | 3.0-4.0 | **Clothing insulation:** | Ensemble | Insulation (clo) | |----------|-----------------| | Shorts, short-sleeve shirt | 0.3-0.4 | | Trousers, long-sleeve shirt | 0.6-0.7 | | Business suit | 1.0 | | Heavy winter clothing | 1.5-2.0 | --- ## Heat Balance of the Human Body The human body maintains core temperature at approximately 37 degC through a balance of heat production and heat loss: **M - W = Q_conv + Q_rad + Q_evap + Q_resp + Q_cond + S** Where: - M = metabolic rate - W = external mechanical work (usually small) - Q_conv = convective heat loss (depends on T_a, V_a) - Q_rad = radiative heat loss (depends on T_r) - Q_evap = evaporative heat loss (depends on RH, V_a) - Q_resp = respiratory heat loss - Q_cond = conductive heat loss (usually negligible) - S = body heat storage (positive = warming, negative = cooling; comfort requires S approximately equal to 0) Thermal comfort exists when S approaches zero without requiring significant thermoregulatory effort (sweating or shivering). --- ## Fanger's PMV-PPD Model Professor P. Ole Fanger (1970, Technical University of Denmark) developed the Predicted Mean Vote (PMV) model based on extensive climate chamber experiments with over 1,300 subjects. ### Basis The model calculates the thermal load on the body -- the difference between internal heat production and heat loss to the environment -- for a person in thermal steady state. This load is then correlated to a subjective thermal sensation vote. ### Assumptions - Steady-state conditions (not transient or rapidly changing) - Uniform thermal environment (no significant asymmetries) - Sedentary to moderate activity levels (0.8-4.0 met) - Mechanically conditioned environments (air-conditioned buildings) - Occupants assumed to be passive (cannot adapt clothing or environment freely) ### Calculation The PMV equation is complex and is typically computed using software or lookup tables. The key inputs are all six comfort factors. The full equation is given in ISO 7730 Annex D. --- ## Predicted Mean Vote Scale PMV predicts the mean thermal sensation of a large group of people on the ASHRAE seven-point scale: | PMV Value | Sensation | |-----------|-----------| | +3 | Hot | | +2 | Warm | | +1 | Slightly warm | | 0 | Neutral | | -1 | Slightly cool | | -2 | Cool | | -3 | Cold | ### Design Target For general comfort, the target is: **-0.5 < PMV < +0.5** This corresponds to the range where most occupants feel thermally neutral or only slightly warm/cool. --- ## Predicted Percentage Dissatisfied PPD is derived from PMV and represents the predicted percentage of occupants who would find the thermal environment unacceptable: **PPD = 100 - 95 x exp(-0.03353 x PMV^4 - 0.2179 x PMV^2)** ### Key PPD Values | PMV | PPD (%) | |-----|---------| | 0 | 5 | | +/- 0.5 | 10 | | +/- 1.0 | 26 | | +/- 2.0 | 77 | **Important:** Even at PMV = 0 (perfect thermal neutrality), the minimum PPD is **5%** -- it is impossible to satisfy everyone. The practical design target of PPD < 10% corresponds to PMV between -0.5 and +0.5. --- ## Comfort Zone The comfort zone defines the range of environmental conditions where PMV/PPD criteria are satisfied. On a psychrometric chart (see [[Psychrometric Chart for Design]]), the comfort zone is typically bounded by: ### ASHRAE 55 Comfort Zone (PMV-based, for 0.5 clo and 1.0-1.2 met) - **Operative temperature:** approximately 23-26 degC (summer, 0.5 clo) - **Operative temperature:** approximately 20-24 degC (winter, 1.0 clo) - **Relative humidity:** 30-60% (no strict upper limit in ASHRAE 55, but 65% often used) - **Air speed:** < 0.2 m/s (default; elevated air speed extends the upper limit) ### Elevated Air Speed ASHRAE 55 allows the upper operative temperature limit to be increased when air speed is elevated, provided occupants have personal control: | Air Speed (m/s) | Approximate Upper Limit Increase (degC) | |------------------|----------------------------------------| | 0.3 | +1.2 | | 0.6 | +1.8 | | 0.9 | +2.2 | | 1.2 | +2.5 | This provision is critical for naturally ventilated and ceiling-fan-assisted buildings. --- ## Operative Temperature Operative temperature (T_op) combines air temperature and mean radiant temperature into a single index that better represents the thermal stimulus experienced by the body: **T_op = (h_r x T_r + h_c x T_a) / (h_r + h_c)** For typical indoor conditions with low air speed (< 0.2 m/s): **T_op approximately equals (T_a + T_r) / 2** Operative temperature is the primary index used in ASHRAE 55 and ISO 7730 for defining comfort zones. ### Design Significance - In well-insulated buildings, T_a and T_r are similar, so T_op approaches T_a - In poorly insulated buildings or near large glazed areas, T_r may differ significantly from T_a - A cold window (T_r low) or a sunlit wall (T_r high) creates radiant asymmetry that affects comfort even when T_a is controlled --- ## Local Thermal Discomfort Even when whole-body PMV is within the comfort range, local thermal discomfort can cause dissatisfaction. ### Sources and Limits (ISO 7730 Category B) | Source | Criterion | |--------|----------| | Radiant temperature asymmetry (warm ceiling) | < 5 degC | | Radiant temperature asymmetry (cold wall/window) | < 10 degC | | Radiant temperature asymmetry (cold ceiling) | < 14 degC | | Radiant temperature asymmetry (warm wall) | < 23 degC | | Vertical air temperature difference (head to ankle) | < 3 degC | | Floor surface temperature | 19-29 degC | | Draught rate (DR < 20%) | V_a < 0.2 m/s at T_a = 20 degC | ### Practical Implications - Large single-glazed windows cause cold radiant asymmetry in winter -- specify low-U glazing or position radiators beneath windows - Underfloor heating must maintain surface temperature within 19-29 degC range - Ceiling-mounted chilled beams or radiant panels must limit warm ceiling asymmetry - Air supply diffusers must minimise draught in the occupied zone (especially at neck level for seated occupants) --- ## ASHRAE Standard 55 *Thermal Environmental Conditions for Human Occupancy* (current edition: ASHRAE 55-2020) ### Scope - Defines comfort criteria for mechanically conditioned and naturally ventilated buildings - Includes both the PMV/PPD method and the adaptive comfort model - Specifies requirements for elevated air speed, local discomfort, temperature cycles, and ramps ### Compliance Methods 1. **Graphic comfort zone method** -- plot operative temperature vs humidity on the comfort chart 2. **Analytical comfort zone method** -- calculate PMV/PPD using the six factors 3. **Adaptive model** -- for naturally conditioned spaces (see [[Adaptive Comfort Model]]) 4. **Elevated air speed method** -- extends upper temperature limit with increased air movement --- ## ISO 7730 *Ergonomics of the Thermal Environment -- Analytical Determination of Thermal Comfort Using PMV and PPD* (current edition: ISO 7730:2005) ### Categories ISO 7730 defines three comfort categories: | Category | PMV Range | PPD (%) | Application | |----------|-----------|---------|------------| | A | -0.2 to +0.2 | < 6 | High expectation (special facilities) | | B | -0.5 to +0.5 | < 10 | Normal expectation (standard offices) | | C | -0.7 to +0.7 | < 15 | Acceptable (some compromise) | Category B is the standard design target for most commercial buildings. --- ## Measurement and Assessment ### Instruments | Parameter | Instrument | Placement | |-----------|-----------|-----------| | Air temperature | Shielded thermocouple or thermistor | At head and ankle height (seated: 0.1 m and 1.1 m) | | Mean radiant temperature | Black globe thermometer (150 mm) | At body centre height | | Air velocity | Omnidirectional hot-wire anemometer | At ankle, waist, and head height | | Humidity | Capacitive or psychrometric sensor | At body centre height | ### Post-Occupancy Evaluation Measured physical conditions should be supplemented by occupant satisfaction surveys. The BUS (Building Use Studies) methodology and CBE (Center for the Built Environment, Berkeley) survey are widely used tools for assessing thermal comfort in practice. --- ## Design Implications ### For the Architect 1. **Envelope quality** determines radiant conditions: insulation, glazing U-value, and solar control directly affect T_r 2. **Window design** affects both air velocity (ventilation) and radiant asymmetry 3. **Exposed thermal mass** moderates temperature swings and radiant peaks 4. **Floor finishes** affect floor surface temperature comfort 5. **Ceiling height and air distribution** affect vertical temperature stratification 6. **Occupant control** (operable windows, blinds, personal fans) significantly improves perceived comfort even without changing measured conditions ### Common Design Errors - Specifying air temperature setpoints without considering mean radiant temperature - Ignoring radiant asymmetry from large glazed areas - Over-reliance on PMV/PPD in naturally ventilated buildings (use adaptive model instead) - Failing to account for clothing variation between seasons - Designing for average conditions rather than the range of conditions experienced --- ## Key References and Standards - Fanger, P.O. (1970). *Thermal Comfort: Analysis and Applications in Environmental Engineering* - ASHRAE Standard 55-2020. *Thermal Environmental Conditions for Human Occupancy* - ISO 7730:2005. *Ergonomics of the Thermal Environment* - CIBSE Guide A -- Environmental Design (comfort criteria) - EN 16798-1:2019 -- Indoor environmental input parameters - Auliciems, A. and Szokolay, S. (2007). *Thermal Comfort* (PLEA Note 3) - Nicol, F., Humphreys, M., and Roaf, S. (2012). *Adaptive Thermal Comfort* --- #environment #comfort