Thermal comfort is highly subjective. Not only is it subject to personal preference and acclimatisation, but internal and external temperature sensing is integrated such that the overall sensation may be pleasing or displeasing depending on whether the resulting effect is towards or away from the restoration of deep body temperature. A cold sensation will be pleasing when the body is overheated, but unpleasant when the core is already cold. At the same time, the temperature of the skin is by no means uniform. As well as variations caused by vasoregulation there are variations in different parts of the body which reflect the differences in vasculation and subcutaneous fat. The wearing of clothes also has a marked effect on the level and distribution of skin temperature.

Thus, sensation from any particular part of the skin will depend on time, location and clothing, as well as the temperature of the surroundings.

### Environmental Factors

For the purposes of building design, comfort is defined negatively as the absence of any form of thermal stress. True comfort conditions will therefore require only minimal activation of any of the regulatory systems described above. It has been shown that bodily heat loss/gain is interdependently related to the following four environmental factors:

- Dry Bulb Temperature (DBT),
- Mean Radiant Temperature (MRT),
- Relative Humidity (RH) and
- Air Movement (Vel).

### Physiological Factors

In addition to environmental factors, there are two physiological factors that affect a person's thermal comfort, each of which vary between individuals and the activities to be performed within any particular space.

- Metabolic Rate (Met) and
- Clothing Level (Clo)

### Comfort Prediction

The prediction of comfort requires a mathematical model of the relationship between one or more climatic factors and the resulting comfort sensation that would be experienced by someone. As humans are often not the most logical or reliable of test subjects, such a relationship is difficult to discern experimentally. Thus, most models are based on survey data of large numbers of people under many different conditions.

The main aim of comfort models is to provide a single index that encompases all the relevant conditions - such that two situations with different conditions, but with the same index, would result in a very similar comfort sensation. There have been a number of indexes proposed with varying degrees of complexity and appropriateness. These vary from simple linear equations relating an indoor comfort temperature to the outdoor dry bulb temperature, to complex algorithms that attempt to compute the influence of all the environmental and physiological factor described above. The most complex are not always the most accurate and the simplest are not always the easiest to use.

Of this range of models, only three are considered here: the simple **Thermal Neutrality** model, the **Adaptive** model and the more complex **Predicted Mean Vote**.

### Thermal Neutrality

Thermal Neutrality (* Tn*) refers to the air temperature at which, on average, a large sample of people would feel neither hot nor cold. This temperature is affected by both the average annual climate and seasonal fluctuations within it. Experiments have found that

*correlates well with the outdoor average dry bulb temperature, such that the relationship can be given by:*

**Tn**Tn = 17.6 + 0.31 Tave

As everyone's response to the environment is not the same, an allowance can be made by specifying a temperature range within which 'most' people would be comfortable. The width of this comfort zone is taken to be Ã‚Â±2K about the thermal neutrality temperature if the annual average temperature is used, or Ã‚Â±1.75 if the mean monthly average is used instead. The following graph shows the relationship between a rolling mean monthly average outdoor temperature (from *d-15* to *d+15*) and the thermal neutrality comfort band.

### Adaptive Comfort

Adaptive comfort models add a little more human behaviour to the mix. They assume that, if changes occur in the thermal environment to produce discomfort, then people will generally change their behaviour and act in a way that will restore their comfort. Such actions could include taking off clothing, reducing activity levels or even opening a window. The main effect of such models is to increase the range of conditions that designers can consider as comfortable, especially in naturally ventilated buildings where the occupants have a greater degree of control over their thermal environment.

BEHAVIOUR | EFFECT | OFFSET |
---|---|---|

Jumper/Jacket on or off | Changes Clo by ± 0.35 | ± 2.2K |

Tight fit/Loose fit clothing | Changes Clo by ± 0.26 | ± 1.7K |

Collar and tie on or off | Changes Clo by ± 0.13 | ± 0.8K |

Office chair type | Changes Clo by ± 0.05 | ± 0.3K |

Seated or walking around | Varies Met by ± 0.4 | ± 3.4K |

Stress level | Varies Met by ± 0.3 | ± 2.6K |

Vigour of activity | Varies Met by ± 0.1 | ± 0.9K |

Different postures | Varies Met by ± 10% | ± 0.9K |

Consume cold drink | Varies Met by -0.12 | + 0.9K |

Consume hot drink/food | Varies Met by +0.12 | - 0.9K |

Operate desk fan | Varies Vel by +2.0m/s | + 2.8K |

Operate ceiling fan | Varies Vel by +1.0m/s | + 2.2K |

Open window | Varies Vel by +0.5m/s | + 1.1K |

As they depend on human behaviour so much, adaptive models are usually based on extensive surveys of thermal comfort and indoor/outdoor conditions. This research clearly shows that providing people with the means to control their local environment greatly increases the percentage of satisfied occupants and makes them more forgiving of occasional periods of poor performance. Humphreys & Nicol (1998) give equations for calculating the indoor comfort temperature from outdoor monthly mean temperature as follows.

Free Running Building:

Tc = 11.9 + 0.534 Tave

Heated or Cooled Building:

Tc = 23.9 + 0.295(Tave-22) exp([-(Tave-22)/33.941]²)

Unknown system (an average of all buildings):

Tc = 24.2 + 0.43(Tave-22) exp(-[(Tave-22)/28.284]²)

The following graphs show these relationships using a rolling mean monthly average outdoor temperature (from *d-15* to *d+15*). As you can see, the different formula can give
quite different values so their appropriate application is advised. Of course I'm hoping to deftly sidestep the important question *so just what is their appropriate application*. However if you have to ask, my advice would be to use the free running method for any building in which the occupants can directly control their own local environment, with fans, lights and operable windows. The heated and cooled formula is more applicable to fully thermostatically controlled air-conditioned buildings. Having said that, in the preparation of my own consulting reports I tend to use the average of all buildings formula.

**Select Comfort Algorithm:** :: Adaptive - Free Running :: Adaptive - Heated/Cooled ::
Adaptive - Average :: of All :: Thermal Neutrality

### The Auliciems Model

Auliciems built somewhat on these adaptive models for Australian conditions. However, the adaptive comfort equation he developed is a function of both mean outdoor dry bulb temperature and the average indoor temperature (Ti). In most design situations, the indoor temperature will not be known. However this can be useful in the analysis of existing buildings or the determination of comfort from internal hourly temperature predictions. The Auliciems equation is given as:

Tc = 9.22 + 0.48 Ti + 0.14 Tave

### Predicted Mean Vote

The Predicted Mean Vote (PMV) refers to a thermal scale that runs from Cold (-3) to Hot (+3), originally developed by Fanger and later adopted as an ISO standard. The original data was collected by subjecting a large number of people (reputedly many thousands of Isreali soldiers) to different conditions within a climate chamber and having them select a position on the scale the best described their comfort sensation. A mathematical model of the relationship between all the environmental and physiological factors considered was then derived from the data. It wasn't actually as simple as that, as the fundamentals of the equation are actually based on a physical analysis of the thermal exchanges and then modified slightly to fit the data, however it's a fair summary. If you want to look at the predicted mean vote in action, download PsychoTool and have a play. For those who wish to know all the gory detail please read on.

From the PMV, the Predicted Percentage of Dissatisfied people (PPD) can be determined. As PMV moves away from neutral (PMV = 0) in either direction, PPD increases. The maximum number of people dissatisfied with their comfort conditions is 100% and, as you can never please all of the people all of the time, the minimum number even in what would be considered perfectly comfortable conditions is 5%.

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The PMV equation for thermal comfort is a steady-state model. It is an empirical equation for predicting the average vote of a large number of people on a 7 point scale (-3 to +3) of thermal comfort. The equation uses the steady state heat balance of the human body and develops a link between the thermal comfort vote and the degree of stress or load on the body (e.g sweating, vasoconstriction, vasodilation) caused by any deviation from perfect balance. The greater the load, the more the comfort vote will deviate from zero.

The partial derivative of the load function is estimated by exposing enough people to enough different conditions to fit a curve. PMV is arguably the most widely used thermal comfort index today. The ISO (International Standards Organization) Standard 7730 (ISO 1984), "Moderate Thermal Environments - Determination of the PMV and PPD Indices and Specification of the Conditions for Thermal Comfort," uses limits on PMV as an explicit definition of the comfort zone.

The PMV equation only applies to humans exposed for a long period to constant conditions at a constant metabolic rate. Conservation of energy leads to the following heat balance equation:

H - Ed - Esw- Ere - L = R + C

Where:
**H** = internal heat production,
**Ed** = heat loss due to water vapor diffusion through the skin,
**Esw** = heat loss due to sweating,
**Ere** = latent heat lossdue to respiration,
**L** = dry respiration heat loss,
**R** = heat loss by radiation from the surface of a clothed body,
**C** = *heat loss by convection from the surface of a clothed body*

The equation is expanded by substituting each component with a function derivable from basic physics. All of the functions have measurable values with the exception of clothing surface temperature and the convective heat transfer coefficient which are functions of each other. To solve the equation, an initial value of clothing temperature is estimated, the convective heat transfer coefficient is then computed, and a new clothing temperature calculated etc. This is continued by iteration until both are known to a satisfactory degree. If the body is assumed not to be in thermal balance, the heat equation can be re-written as:

L = H - Ed - Esw - Ere - R - C

Where:
**L** is the thermal load on the body.

Define thermal strain or sensation **Y** as some unknown function of **L** and metabolic rate. Holding all variables constant except air temperature and metabolic rate, we use mean votes from climate chamber experiments to write **Y** as function of air temperature for several activity levels. Then substituting **L** for air temperature, determined from the heat balance equation above, evaluate the partial derivative of **Y** with respect to **L** at **Y**=0 and plot the points versus metabolic rate. An exponential curve is fit to the points and integrated with respect to **L**. **L** is simply renamed "PMV" and we have (in simplified form):

PMV = exp(Met) * L

PMV is "scaled" to predict thermal sensation votes on a seven point scale (hot 3, warm 2, slightly warm 1, neutral 0, slightly cool -1, cool -2, cold -3) by virtue of the fact that for each physical condition, **Y** is the mean vote of all subjects exposed to that condition. The major limitation of the PMV model is the explicit constraint of skin temperature and evaporative heat loss to values for comfort and 'neutral' sensation at a given activity level.

### Related Links

- INNOVA Thermal Comfort booklet
- http://www.innova.dk/books/thermal/thermal.htm

- Web-Based Comfort Calculator
- http://atmos.es.mq.edu.au/~rdedear/pmv/

- Oseland, N.
- Adaptive Thermal Comfort Models, BRE, Building Services Journal, Dec 1998.

- Humphreys, M., Nicol, J.,
- Understanding the Adaptive Approach to Thermal Comfort, ASHRAE Trans., 1998.