Thermal comfort is the condition of mind that expresses satisfaction with the thermal environment and is assessed by subjective evaluation (ANSI/ASHRAE Standard 55). Maintaining this standard of thermal comfort for occupants of buildings or other enclosures is one of the important goals of HVAC (heating, ventilation, and air conditioning) design engineers.
Thermal neutrality is maintained when the heat generated by human metabolism is allowed to dissipate, thus maintaining thermal equilibrium with the surroundings. The main factors that influence thermal comfort are those that determine heat gain and loss, namely metabolic rate, clothing insulation, air temperature, mean radiant temperature, air speed and relative humidity. Psychological parameters such as individual expectations also affect thermal comfort.
The Predicted Mean Vote (PMV) model stands among the most recognized thermal comfort models. It was developed using principles of heat balance and experimental data collected in a controlled climate chamber under steady state conditions. The adaptive model, on the other hand, was developed based on hundreds of field studies with the idea that occupants dynamically interact with their environment. Occupants control their thermal environment by means of clothing, operable windows, fans, personal heaters, and sun shades. 
The PMV model can be applied to air conditioned buildings, while the adaptive model can be generally applied only to buildings where no mechanical systems have been installed. There is no consensus about which comfort model should be applied for buildings that are partially air conditioned spatially or temporally.
- 1 Significance of thermal comfort
- 2 Factors influencing thermal comfort
- 3 Thermal comfort models
- 4 Adaptation
- 5 Effects of natural ventilation on thermal comfort
- 6 Thermal sensitivity of individuals
- 7 Sex differences
- 8 Thermal comfort in different regions
- 9 Thermal stress
- 10 Thermal comfort of livestock
- 11 Research
- 12 Thermal comfort for patients and hospital staff
- 13 See also
- 14 References
- 15 Further reading
Significance of thermal comfort
Satisfaction with the thermal environment is important for its own sake and because it influences productivity and health. Office workers who are satisfied with their thermal environment are more productive. Thermal discomfort has also been known to lead to sick building syndrome symptoms. The combination of high temperature and high relative humidity serves to reduce thermal comfort and indoor air quality.
Although a single static temperature can be comfortable, thermal delight, alliesthesia is usually caused by varying thermal sensations. Adaptive models of thermal comfort allow flexibility in designing naturally ventilated buildings that have more varying indoor conditions. Such buildings may save energy and have the potential to create more satisfied occupants.
Factors influencing thermal comfort
Since there are large variations from person to person in terms of physiological and psychological satisfaction, it is hard to find an optimal temperature for everyone in a given space. Laboratory and field data have been collected to define conditions that will be found comfortable for a specified percentage of occupants.
There are six primary factors that directly affect thermal comfort that can be grouped in two categories: personal factors - because they are characteristics of the occupants - and environmental factors - which are conditions of the thermal environment. The former are metabolic rate and clothing level, the latter are air temperature, mean radiant temperature, air speed and humidity. Even if all these factors may vary with time, standards usually refer to a steady state to study thermal comfort, just allowing limited temperature variations.
People have different metabolic rates that can fluctuate due to activity level and environmental conditions. The ASHRAE 55-2010 Standard defines metabolic rate as the level of transformation of chemical energy into heat and mechanical work by metabolic activities within an organism, usually expressed in terms of unit area of the total body surface. Metabolic rate is expressed in met units, which are defined as follows:
1 met = 58.2 W/m² (18.4 Btu/h·ft²), which is equal to the energy produced per unit surface area of an average person seated at rest. The surface area of an average person is 1.8 m² (19 ft²).
ASHRAE Standard 55 provides a table of met rates for a variety of activities. Some common values are 0.7 met for sleeping, 1.0 met for a seated and quiet position, 1.2-1.4 met for light activities standing, 2.0 met or more for activities that involve movement, walking, lifting heavy loads or operating machinery. For intermittent activity, the Standard states that is permissible to use a time-weighted average metabolic rate if individuals are performing activities that vary over a period of one hour or less. For longer periods, different metabolic rates must be considered.
According to ASHRAE Handbook of Fundamentals, estimating metabolic rates is complex, and for levels above 2 or 3 met – especially if there are various ways of performing such activities – the accuracy is low. Therefore, the Standard is not applicable for activities with an average level higher than 2 met. Met values can also be determined more accurately than the tabulated ones, using an empirical equation that takes into account the rate of respiratory oxygen consumption and carbon dioxide production. Another physiological yet less accurate method is related to the heart rate, since there is a relationship between the latter and oxygen production.
The Compendium of Physical Activities is used by physicians to record physical activities. It has a different definition of met that is the ratio of the metabolic rate of the activity in question to a resting metabolic rate. As the formulation of the concept is different from the one that ASHRAE uses, these met values cannot be used directly in PMV calculations, but it opens up a new way of quantifying physical activities.
Food and drink habits may have an influence on metabolic rates, which indirectly influences thermal preferences. These effects may change depending on food and drink intake. Body shape is another factor that affects thermal comfort. Heat dissipation depends on body surface area. A tall and skinny person has a larger surface-to-volume ratio, can dissipate heat more easily, and can tolerate higher temperatures more than a person with a rounded body shape.
The amount of thermal insulation worn by a person has a substantial impact on thermal comfort, because it influences the heat loss and consequently the thermal balance. Layers of insulating clothing prevent heat loss and can either help keep a person warm or lead to overheating. Generally, the thicker the garment is, the greater insulating ability it has. Depending on the type of material the clothing is made out of, air movement and relative humidity can decrease the insulating ability of the material.
1 clo is equal to 0.155 m²·K/W (0.88 °F·ft²·h/Btu). This corresponds to trousers, a long sleeved shirt, and a jacket. Clothing insulation values for other common ensembles or single garments can be found in ASHRAE 55.
The air temperature is the average temperature of the air surrounding the occupant, with respect to location and time. According to ASHRAE 55 standard, the spatial average takes into account the ankle, waist and head levels, which vary for seated or standing occupants. The temporal average is based on three-minutes intervals with at least 18 equally spaced points in time. Air temperature is measured with a dry-bulb thermometer and for this reason it is also known as dry-bulb temperature.
Mean radiant temperature
The radiant temperature is related to the amount of radiant heat transferred from a surface, and it depends on the material’s ability to absorb or emit heat, or its emissivity. The mean radiant temperature, depends on the temperatures and emissivities of the surrounding surfaces as well as the view factor, or the amount of the surface that is “seen” by the object. So the mean radiant temperature experienced by a person in a room with the sunlight streaming in varies based on how much of her body is in the sun.
Operative temperature attempts to combine the effects of air and mean radiant temperatures into one metric. It is often approximated as the average of the air dry-bulb temperature and of the mean radiant temperature at the given place in a room. In buildings with low thermal mass, the operative temperature is sometimes considered to be simply the air temperature.
Air speed is defined as the rate of air movement at a point, without regard to direction. According to ASHRAE Standard 55, it is the average speed of the air to which the body is exposed, with respect to location and time. The temporal average is the same as the air temperature, while the spatial average is based on the assumption that the body is exposed to a uniform air speed, according to the SET thermo-physiological model. However, some spaces might provide strongly nonuniform air velocity fields and consequent skin heat losses that cannot be considered uniform. Therefore, the designer shall decide the proper averaging, especially including air speeds incident on unclothed body parts, that have greater cooling effect and potential for local discomfort.
Relative humidity is the ratio of the amount of water vapor in the air to the amount of water vapor that the air could hold at the specific temperature and pressure. While the human body has sensors within the skin that are fairly efficient at feeling heat and cold, relative humidity (RH) is detected indirectly. Sweating is an effective heat loss mechanism that relies on evaporation from the skin. However at high RH, the air has close to the maximum water vapor that it can hold, so evaporation, and therefore heat loss, is decreased. On the other hand, very dry environments (RH < 20-30%) are also uncomfortable because of their effect on the mucous membranes. The recommended level of indoor humidity is in the range of 30-60% in air conditioned buildings, but new standards such as the adaptive model allow lower and higher humidities, depending on the other factors involved in thermal comfort.
A way to measure the amount of relative humidity in the air is to use a system of dry-bulb and wet-bulb thermometers. While the former measures the temperature with no regard to moisture - such in weather reports - the latter has a small wet cloth wrapped around the bulb at its base, so the measurement takes into account water evaporation in the air. The wet-bulb reading will thus always be at least slightly lower than the dry bulb one. The difference between these two temperatures can be used to calculate the relative humidity: the larger the temperature difference between the two thermometers, the lower the level of relative humidity.
The wetness of skin in different areas also affects perceived thermal comfort. Humidity can increase wetness on different areas of the body, leading to a perception of discomfort. This is usually localized in different parts of the body, and local thermal comfort limits for skin wettedness differ by locations of the body. The extremities are much more sensitive to thermal discomfort from wetness than the trunk of the body. Although local thermal discomfort can be caused from wetness, the thermal comfort of the whole body will not be affected by the wetness of certain parts.
Recently, the effects of low relative humidity and high air velocity were tested on humans after bathing. Researchers found that low relative humidity engendered thermal discomfort as well as the sensation of dryness and itching. It is recommended to keep relative humidity levels higher in a bathroom than other rooms in the house for optimal conditions.
Thermal comfort models
When discussing thermal comfort, there are two main different models that can be used: the static model (PMV/PPD) and the adaptive model.
Static comfort model: PMV/PPD
The PMV/PPD model was developed by P. O. Fanger using heat balance equations and empirical studies about skin temperature to define comfort. Standard thermal comfort surveys ask subjects about their thermal sensation on a seven point scale from cold (-3) to hot (+3). Fanger’s equations are used to calculate the Predicted Mean Vote (PMV) of a large group of subjects for a particular combination of air temperature, mean radiant temperature, relative humidity, air speed, metabolic rate, and clothing insulation. Zero is the ideal value, representing thermal neutrality, and the comfort zone is defined by the combinations of the six parameters for which the PMV is within the recommended limits (-0.5<PMV<+0.5). Although predicting the thermal sensation of a population is an important step in determining what conditions are comfortable, it is more useful to consider whether or not people will be satisfied. Fanger developed another equation to relate the PMV to the Predicted Percentage Dissatisfied (PPD). This relation was based on studies that surveyed subjects in a chamber where the indoor conditions can be precisely controlled.
This method treats all occupants the same and disregards location and adaptation to the thermal environment. It basically states that the indoor temperature should not change as the seasons do. Rather, there should be one set temperature year-round. This is taking a more passive stand that humans do not have to adapt to different temperatures since it will always be constant.
ASHRAE Standard 55-2010 uses the PMV model to set the requirements for indoor thermal conditions. It requires that at least 80% of the occupants be satisfied.
The CBE Thermal Comfort Tool for ASHRAE 55 allows users to input the six comfort parameters to determine whether a certain combination complies with ASHRAE 55. The results are displayed on a psychrometric or a temperature-relative humidity chart and indicate the ranges of temperature and relative humidity that will be comfortable with the given the values input for the remaining four parameters.
Elevated air speed method
ASHRAE 55 2013 accounts for air speeds above 0.2 m/s separately than the baseline model. Because air movement can provide direct cooling to people, particularly if they are not wearing too much clothing, higher temperatures can be more comfortable than the PMV model predicts. Air speeds up to 0.8 m/s are allowed without local control, and 1.2 m/s is possible with local control. This elevated air movement increases the maximum temperature for an office space in the summer to 30°C from 27.5°C.
Local thermal discomfort
Although thermal comfort is usually discussed for the body as a whole, thermal dissatisfaction may also occur just for a particular part of the body, due to local sources of unwanted heating, cooling or air movement. According to the ASHRAE 55-2010 standard, there are four main causes of thermal discomfort to be considered. A section of the standard specifies the requirements for these factors, that apply to a lightly clothed person engaged in near sedentary physical activity. This is because people with higher metabolic rates and/or more clothing insulation are less thermally sensitive, and consequently have less risk of thermal discomfort.
Radiant temperature asymmetry
Large differences in the thermal radiation of the surfaces surrounding a person may cause local discomfort or reduce acceptance of the thermal conditions. ASHRAE Standard 55 sets limits on the allowable temperature differences between various surfaces. Because people are more sensitive to some asymmetries than others, for example that of a warm ceiling vs. that of hot and cold vertical surfaces, the limits depend on which surfaces are involved. The ceiling is not allowed to be more than 5 °C (9.0 °F) warmer, whereas a wall may be up to 23 °C (41 °F) warmer than the other surfaces.
While air movement can be pleasant and provide comfort in some circumstances, it is sometimes unwanted and causes discomfort. This unwanted air movement is called draft and is most prevalent when the thermal sensation of the whole body is cool. People are most likely to feel a draft on uncovered body parts such as their head, neck, shoulders, ankles, feet, and legs, but the sensation also depends on the air speed, air temperature, activity, and clothing.
Vertical air temperature difference
Thermal stratification that results in the air temperature at the head level being higher than at the ankle level may cause thermal discomfort. ASHRAE Standard 55 recommends that the difference not be greater than 3°C (5.4°F). 
Floor surface temperature
Floors that are too warm or too cool may cause discomfort. ASHRAE 55 recommends that floor temperatures stay in the range of 19–29 °C (66–84 °F) in spaces where occupants will be wearing lightweight shoes.
Adaptive comfort model
The adaptive model is based on the idea that outdoor climate influences indoor comfort because humans can adapt to different temperatures during different times of the year. The adaptive hypothesis predicts that contextual factors, such as having access to environmental controls, and past thermal history influence building occupants' thermal expectations and preferences. Numerous researchers have conducted field studies worldwide in which they survey building occupants about their thermal comfort while taking simultaneous environmental measurements. Analyzing a database of results from 160 of these buildings revealed that occupants of naturally ventilated buildings accept and even prefer a wider range of temperatures than their counterparts in sealed, air conditioned buildings because their preferred temperature depends on outdoor conditions. These results were incorporated in the ASHRAE 55-2004 standard as the adaptive comfort model. The adaptive chart relates indoor comfort temperature to prevailing outdoor temperature and defines zones of 80% and 90% satisfaction.
The ASHRAE-55 2010 Standard has introduced the prevailing mean outdoor temperature as the input variable for the adaptive model. It is based on the arithmetic average of the mean daily outdoor temperatures over no fewer than 7 and no more than 30 sequential days prior to the day in question. It can also be calculated by weighting the temperatures with different coefficients, assigning increasing importance to the most recent temperatures. In case this weighting is used, there is no need to respect the upper limit for the subsequent days. In order to apply the adaptive model, there should be no mechanical cooling system for the space, occupants should be engaged in sedentary activities with metabolic rates of 1-1.3 met, and a prevailing mean temperature greater than 10 °C (50 °F) and less than 33.5 °C (92.3 °F).
This model applies especially to occupant-controlled, natural conditioned spaces, where the outdoor climate can actually affect the indoor conditions and so the comfort zone. In fact, studies by de Dear and Brager showed that occupants in naturally ventilated buildings were tolerant of a wider range of temperatures. This is due to both behavioral and physiological adjustments, since there are different types of adaptive processes. ASHRAE Standard 55-2010 states that differences in recent thermal experiences, changes in clothing, availability of control options and shifts in occupant expectations can change people thermal responses.
There are basically three categories of thermal adaptation, namely Behavioral, Physiological and Psychological. The latter, that refers to an altered thermal perception and reaction due to past experiences and expectations, is an important factor in explaining the difference between field observations and PMV predictions (based on the static model) in naturally ventilated buildings. In these buildings the relationship with the outdoor temperatures is twice as strong as predicted.
Adaptive models of thermal comfort are implemented in other standards such as European EN 15251 and ISO 7730 standard. While the exact derivation methods and results are slightly different from the ASHRAE 55 adaptive standard, they are substantially the same. A larger difference is in applicability. The ASHRAE adaptive standard only applies to buildings without mechanical cooling installed, while EN15251 can be applied to mixed-mode buildings provided the system is not running.
The body has several thermal adjustment mechanisms to survive in drastic temperature environments. In a cold environment the body utilizes vasoconstriction; which reduces blood flow to the skin, skin temperature and heat dissipation. In a warm environment, vasodilation will increase blood flow to the skin, heat transport, and skin temperature and heat dissipation. If there is an imbalance despite the vasomotor adjustments listed above, in a warm environment sweat production will start and provide evaporative cooling. If this is insufficient, hyperthermia will set in, body temperature may reach 40 °C (104 °F) and heat stroke may occur. In a cold environment shivering will start, involuntarily forcing the muscles to work and increasing the heat production by up to a factor of 10. If equilibrium is not restored, hypothermia will set in, which can be fatal. Long term adjustments to extreme temperatures of a few days to six months may result in cardiovascular and endocrine adjustments. A hot climate may create increased blood volume, improving the effectiveness of vasodilation, enhanced performance of the sweat mechanism, and the readjustment of thermal preferences. In cold or underheated conditions, vasoconstriction can become permanent resulting in decreased blood volume, and increased body metabolic rate.
In naturally ventilated buildings occupants take numerous actions to keep themselves comfortable when the indoor conditions drift towards discomfort. Operating windows and fans, adjusting blinds/shades, changing clothing, consuming food and drinks are some of the common adaptive strategies. Amongst these adjusting windows is the most common. Those occupants who take these sorts of actions tend to feel cooler at warmer temperatures than those who do not.
These behavioral actions significantly influence energy simulation inputs, and researchers are developing behavior models to improve the accuracy of simulation results. For example, there are many window opening models that have been developed till date but there is no consensus over the factors that trigger window opening.
Effects of natural ventilation on thermal comfort
Many buildings use a HVAC (heating ventilation air conditioning) unit to control their thermal environment. Other buildings are naturally ventilated and do not rely on such mechanical systems to provide thermal comfort. Depending on the climate, this can drastically reduce energy consumption. It is sometimes seen as a risk, though, since indoor temperatures can be too extreme if the building is poorly designed. Properly designed naturally ventilated buildings keep indoor conditions within the range where opening windows and using fans in the summer and wearing extra clothing in the winter can keep people thermal comfortable.
Thermal sensitivity of individuals
The thermal sensitivity of an individual is quantified by the descriptor FS, which takes on higher values for individuals with lower tolerance to non-ideal thermal conditions. This group includes pregnant women, the disabled, as well as individuals whose age is below fourteen or above sixty, which is considered the adult range. Existing literature provides consistent evidence that sensitivity to hot and cold surfaces declines with age. There is also some evidence of a gradual reduction in the effectiveness of the body in thermoregulation after the age of sixty. This is mainly due to a more sluggish response of the counteraction mechanisms in lower part of the body that are used to maintain the core temperature of the body at ideal values.
Situational factors include the health, psychological, sociological and vocational activities of the persons.
While thermal comfort preferences between sexes seems to be small, there are some differences. Studies have found men report discomfort due to rises in temperature much earlier than women. Men also estimate higher levels of their sensation of discomfort than women. One recent study tested men and women in the same cotton clothing, performing mental jobs while using a dial vote to report their thermal comfort to the changing temperature. Many times, females will prefer higher temperatures. But while females were more sensitive to temperatures, males tend to be more sensitive to relative humidity levels.
An extensive field study was carried out in naturally ventilated residential buildings in Kota Kinabalu, Sabah, Malaysia. This investigation explored the gender thermal sensitivity to the indoor environment in non air-conditioned residential buildings. Multiple hierarchical regression for categorical moderator was selected for data analysis; the result showed that females were slightly more sensitive than males to the indoor air temperatures. Whereas, under thermal neutrality; it was found that males and females have similar thermal sensation.
Thermal comfort in different regions
In different areas of the world, thermal comfort needs may vary based on climate. In China there are hot humid summers and cold winters causing a need for efficient thermal comfort. Energy conservation in relation to thermal comfort has become a large issue in China in the last several decades due to rapid economic and population growth. Researchers are now looking into ways to heat and cool buildings in China for lower costs and also with less harm to the environment.
In tropical areas of Brazil, urbanization is causing a phenomenon called urban heat islands (UHI). These are urban areas, which have risen over the thermal comfort limits due to a large influx of people and only drop within the comfortable range during the rainy season. Urban Heat Islands can occur over any urban city or built up area with the correct conditions. Urban Heat Islands are caused by urban areas with few trees and vegetation to block solar radiation or carry out evapotranspiration, many structures with a large proportion of roofs and sidewalks with low reflectivity that absorb heat, high amounts of ground-level carbon dioxide pollution that retains heat released by surfaces, great amounts of heat generated by air conditioning systems of densely packed buildings and large amount of automobile traffic generating heat from engines and exhaust.
In the hot humid region of Saudi Arabia, the issue of thermal comfort has been important in mosques where Muslims go to pray. They are very large open buildings which are used only intermittently (very busy for the noon prayer on Fridays) making it hard to ventilate them properly. The large size requires a large amount of ventilation but this requires a lot of energy since the buildings are used only for short periods of time. Some mosques have the issue of being too cold from their HVAC systems running for too long and others remain too hot. The stack effect also comes into play due to their large size and creates a large layer of hot air above the people in the mosque. New designs have placed the ventilation systems lower in the buildings to provide more temperature control at ground level. Also new monitoring steps are being taken to improve the efficiency.
The concept of thermal comfort is closely related to thermal stress. This attempts to predict the impact of solar radiation, air movement, and humidity for military personnel undergoing training exercises or athletes during competitive events. Values are expressed as the Wet Bulb Globe Temperature or Discomfort Index. Generally, humans do not perform well under thermal stress. People’s performances under thermal stress is about 11% lower than their performance at normal thermal conditions. Also, human performance in relation to thermal stress varies greatly by the type of task you are completing. Some of the physiological effects of thermal heat stress include increased blood flow to the skin, sweating, and increased ventilation.
Thermal comfort of livestock
Although thermal comfort of humans is the main focus of thermal comfort studies, the needs of livestock must be met as well for better living and production. The Department of Animal Production in Italy produced a study on ewes, which tested rumen function and diet digestibility of ewes chronically exposed to a hot environment. These two bodily functions were reduced by the hot temperatures offering insight that thermal comfort levels are important to livestock productivity.
The factors affecting thermal comfort were explored experimentally in the 1970s. Many of these studies led to the development and refinement of ASHRAE Standard 55 and were performed at Kansas State University by Ole Fanger and others. Perceived comfort was found to be a complex interaction of these variables. It was found that the majority of individuals would be satisfied by an ideal set of values. As the range of values deviated progressively from the ideal, fewer and fewer people were satisfied. This observation could be expressed statistically as the % of individual who expressed satisfaction by comfort conditions and the predicted mean vote (PMV). This approach was challenged by the adaptive comfort model developed from the ASHRAE 884 project which revealed that occupants were comfortable in a broader range of temperature.
This research is applied to create Building Energy Simulation (BES) programs for residential buildings. Residential buildings in particular can vary much more in thermal comfort than public and commercial buildings. This is due to their smaller size, the variations in clothing worn, and different uses of each room. The main rooms of concern are bathrooms and bedrooms. Bathrooms need to be at a temperature comfortable for a human with or without clothing. Bedrooms are of importance because they need to accommodate different levels of clothing and also different metabolic rates of people asleep or awake. Discomfort hours is a common metric used to evaluate the thermal performance of a space.
Thermal comfort research in clothing is currently being done by the military. New air-ventilated garments are being researched to improve evaporative cooling in military settings. Some models are being created and tested based on the amount of cooling they provide.
In the last twenty years, researchers have also developed advanced thermal comfort models that divide the human body into many segments, and predict local thermal discomfort by considering heat balance. This has opened up a new arena of thermal comfort modeling that aims at heating/cooling selected body parts.
Thermal comfort for patients and hospital staff
Whenever the studies referenced tried to discuss the thermal conditions for different groups of occupants in one room, the studies ended up simply presenting comparisons of thermal comfort satisfaction based on the subjective studies. No study tried to reconcile the different thermal comfort requirements of different types of occupants who compulsorily must stay in one room. Therefore, it looks to be necessary to investigate the different thermal conditions required by different groups of occupants in hospitals to reconcile their different requirements in this concept. To reconcile the differences in the required thermal comfort conditions it is recommended to test the possibility of using different ranges of local radiant temperature in one room via a suitable mechanical system.
Although different researches are undertaken on thermal comfort for patients in hospitals, it is also necessary to study the effects of thermal comfort conditions on the quality and the quantity of healing for patients in hospitals. There are also original researches that show the link between thermal comfort for staff and their levels of productivity, but no studies have been produced individually in hospitals in this field. Therefore, researches for coverage and methods individually for this subject are recommended. Also research in terms of cooling and heating delivery systems for patients with low levels of immune system protection such as HIV patients, burned patients, etc. are recommended. There are important areas, which still need to be focused on including thermal comfort for staff and its relation with their productivity, using different heating system to prevent hypothermia in the patient and to improve the thermal comfort for hospital staff simultaneously.
Finally, the interaction between people, systems and architectural design in hospitals is a field in which require further work needed to improve the knowledge of how to design buildings and systems to reconcile many conflicting factors for the people occupying these buildings.
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