Is it too cold?

The quest to find models and measurements to define thermal comfort

Thermal comfort is defined in the ISO 7730 standard as being “That condition of mind which expresses satisfaction with the thermal environment”. A definition most can agree on, but also a definition which is not easily converted into physical parameters.

Thermal comfort standards use the PMV model to recommend acceptable thermal comfort conditions. The recommendations made by ASHRAE Standard 55 (ASHRAE, 1992). These thermal conditions should ensure that at least 90% of occupants feel thermally satisfied .

The Predicted Mean Vote (PMV) model combines four physical variables (air temperature, air velocity, mean radiant temperature, and relative humidity) and two personal variables (clothing insulation and activity level) into an index that can be used to predict thermal comfort. The index provides a score that corresponds to the ASHRAE thermal sensation scale, and represents the average thermal sensation felt by a large group of people in a space.

ASHRAE Thermal Sensation Scale

-3 — cold

-2 — cool

-1- slightly cool

0-neutral

1-slightly warm

2 — warm

3- hot

Fanger’s PMV Model was developed in the 1970’s from laboratory and climate chamber studies. In these studies, participants were dressed in standardised clothing and completed standardised activities, while exposed to different thermal environments. In some studies the researchers chose the thermal conditions, and participants recorded how hot or cold they felt, using the seven-point ASHRAE thermal sensation scale.

It is based on thermoregulation and heat balance theories. According to these theories, the human body employs physiological processes (e.g. sweating, shivering, regulating blood flow to the skin) in order to maintain a balance between the heat produced by metabolism and the heat lost from the body. In extreme thermal conditions, this regulation is necessary for the body to function properly. In office buildings, it is very unlikely that temperatures associated with serious bodily dysfunction will occur, but thermoregulation is still used to maintain a comfortable heat balance.

Maintaining this heat balance is the first condition for achieving a neutral thermal sensation. However, Fanger (1970) noted that “man’s thermoregulatory system is quite effective and will therefore create heat balance within wide limits of the environmental variables, even if comfort does not exist”.

To be able to predict conditions where thermal neutrality would occur, Fanger (1967) investigated the body’s physiological processes when it is close to neutral. Fanger determined that the only physiological processes influencing heat balance in this context were sweat rate and mean skin temperature, and that these processes were a function of activity level. Fanger (1967) used data from a study by McNall, Jaax, Rohles, Nevins and Springer (1967) to derive a linear relationship between activity level and sweat rate.

College-age participants in this study were exposed to different thermal conditions while wearing standardised clothing, and voted on their thermal sensation, using the ASHRAE scale. The linear relationship was formed from those participants (n=183) who stated that they felt thermally neutral (i.e. voted ‘0’) for a given activity level.

Fanger (1967) also conducted a study using 20 college-age participants, to derive a linear relationship between activity level and mean skin temperature. In this experiment, participants wore standardised clothing and took part in climate chamber tests at four different activity levels (sedentary, low, medium and high). It is important to note that participants were not asked to vote on their thermal sensation in this study. Instead, the experimental conditions used temperatures that had been found to achieve thermal neutrality in McNall et al’s (1967) study. Therefore, although Fanger claimed that the participants were at, or near, thermal neutrality, this assumption was not directly tested. This methodology has lead some to question the formulation of the PMV model.

Fanger (1967) substituted these two linear relationships into heat balance equations, to create a ‘comfort equation’. The comfort equation describes all combinations of the six PMV input variables that result in a neutral thermal sensation. This equation was then validated against studies by Nevins, Rohles, Springer and Feyerherm (1966) and McNall et al (1967), in which college-age participants rated their thermal sensation in response to specified thermal environments. The air temperature where participants were thermally neutral in these studies showed good agreement with the predictions made by the comfort equation.

The comfort equation predicts conditions where occupants will feel thermally neutral. However, for practical applications, it is also important to consider situations where subjects do not feel neutral.

By combining data from Nevins et al (1966), McNall et al (1967) and his own studies, Fanger (1970) used data from 1396 participants to expand the comfort equation. The resulting equation described thermal comfort as the imbalance between the actual heat flow from the body in a given thermal environment and the heat flow required for optimum (i.e. neutral) comfort for a given activity. This expanded equation related thermal conditions to the seven point ASHRAE thermal sensation scale, and became known as the PMV index. Fanger (1970) also developed a related index, called the Predicted Percentage Dissatisfied (PPD). This index is calculated from PMV, and predicts the percentage of people who are likely to be dissatisfied with a given thermal environment.

In the aftermath of his work, Fanger defined a scale of thermal sensation with seven levels (ranging from 3 — hot, to -3 — cold), translating, through it, the 3 degree of discomfort associated with the different combinations of environmental and personal variables tested in climate chambers. Based on the relationship between the thermal sensation experienced by users in a controlled environmental chambers and the thermal balance equation, Fanger calculated the Predicted Mean Vote (PMV) Index predicts the mean comfort response of a larger group of people PMV index through the following expression:

In addition to this index, Fanger proposed another indicator that, based on this one, estimated the Predicted Percentage of Dissatisfied (PPD). The PPD index calculation is done using the following equation:

The PMV and PPD form a Ushaped relationship, where percentage dissatisfied increases for PMV values above and below zero (thermally neutral). The PMV index is mathematically complex to compute, so Fanger (1970) provided lookup tables to help practitioners determine appropriate thermal conditions. Information from these tables, and graphical representations of comfort conditions, is also provided in modern thermal comfort standards (e.g. ASHRAE, 1992: ISO, 1994). In recent years, computer programs have been developed to calculate PMV, and programming code is provided in ISO Standard 7730 (ISO, 1994).

Observing it, we verify that it is not possible to achieve a zero value for the predicted percentage of dissatisfied, because to the index value 0 of the PMV index corresponds a predictable minimum percentage of dissatisfied of 5%.

In other studies, participants controlled the thermal environment themselves, adjusting the temperature until they felt thermally ‘neutral’ (i.e. neither hot nor cold; equivalent to voting ‘0’ on the ASHRAE thermal sensation scale).

P.O. Fanger, Thermal Comfort, McGraw-Hill Book Company 1972.

ISO 7730, Moderate Thermal Environments — Determination of the PMV and PPD indices and specification of the conditions for thermal comfort, 1995.1)

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