4. Thermal adaptation
4.1 Introduction
Although most people today spend more than 90% of their time indoors (living, working, travelling), humans are, from an evolutionary point of view, “outdoor animals” (Baker, 2004). The first humanoids lived outside, without clothing and without a hut. By seeking shelter in caves and under trees, sitting in the sun to warm up and later in time making clothes and creating campfires, humans adapted to weather conditions and climatic variations. Three and a half million years later, just before the Industrial Revolution, our ancestors still lived outside most of the day. They worked the land, sowed, harvested, irrigated, drained, fished, hunted, cut trees, built huts, houses, and they did it all largely outdoors. People had extensive knowledge of temperature, wind, clouds and rain. In many places in the world, architecture was developed that took the local climate into account to make the indoor climate in homes and other buildings as comfortable as possible. Examples include windcatchers in ancient Persia that bring airflow inside the building to provide cooling, patios in southern Spain, located between tall buildings for shade and with lots of greenery that lowers the temperature through evaporation. In other areas, thick clay walls were used to buffer heat in combination with small windows. In tropical humid regions, houses were built with huge overhanging roofs for shade and open walls to allow wind flowing through the building. There are wonderful examples of this “vernacular architecture”, although regrettably the principles have largely been forgotten or are not applied. Fortunately, nowadays we begin to see applications of these building methods again, combined with modern building materials.
From the Industrial Revolution to the present, a negligible moment on the evolutionary time scale, people have increasingly worked and lived indoors. Until the middle of the last century, there was often a close relationship between indoor and outdoor climates. People were used to indoor temperatures of 10°C or even lower in severe winters, and in summer it was sometimes warmer inside than outside. With the invention of air conditioning at the beginning of the twentieth century and through increasingly better building techniques, it became possible to make the indoor climate virtually independent of the outdoor climate. All over the world, in the most diverse climates, the same kind of buildings with an identical indoor climate appeared. In recent years, however, research has increasingly shown that people actually feel more comfortable and healthier in an indoor climate that to some extent naturally varies with the outdoor climate. This is most likely due to the fact that we as a species have been used to these variations for tens of thousands of years. But what exactly does this adaptation mean? People in buildings have various options for adapting to the thermal environment. A distinction can be made here between behavioural, physiological and psychological adaptation, with interaction between the first and third form of adaptation.
4.2 Behavioural adaptation
Satisfaction with the indoor climate is strongly influenced by the possibilities users have to influence the factors that determine their feelings of warmth and to adjust them to their wishes (Figure 2.8). The most important of these are increasing or decreasing air speed and air temperature by opening or closing windows or doors or using a ceiling or table fan and adjusting clothing insulation by changing clothes. Other behavioural adaptations include seeking the warmth of the sun or finding shade, doing more or less exercise (higher or lower metabolic heat production), drinking hot or cold drinks and sitting in a warmer or cooler place within the building.
In naturally ventilated, free running and hybrid buildings, which in most cases have openable windows, the users can vary the air velocity and temperature by controlling the windows. In air-conditioned buildings with a closed façade, this possibility is either non-existent or very limited9. The RP-884 study shows that in naturally ventilated buildings the relationship between measured air velocity and indoor temperature is stronger than in air-conditioned buildings. In naturally ventilated buildings, 53% of the variance10 in air velocities measured at the workplace is explained by differences in the indoor temperature. In air-conditioned buildings this is only 34%. In naturally ventilated buildings, users are therefore more active in controlling their heat balance by varying the air speed than in air-conditioned buildings. It also appears that in naturally ventilated buildings the relationship between clothing insulation and indoor temperature is stronger than in air-conditioned buildings. In naturally ventilated buildings, 66% of the variance in clothing insulation is explained by differences in indoor temperature. In air-conditioned buildings this is only 18%. The occupants are more active in controlling their heat balance by varying the clothing insulation than in air-conditioned buildings. The difference is even greater than for air velocity. People naturally have the ability to adapt to changing temperatures through behaviour, which keeps them comfortable. In a conditioned environment, where the climate system is designed to manage the temperature, the occupants often do not need to and cannot do anything for their thermal comfort and behavioural adaptation is, as it were, discouraged. In psychology, this is called learned helplessness (Carlsen, 2010).
4.3 Physiological adaptation
As explained in paragraph 2.2, the core temperature of the human body must be kept at around 37°C. When the core temperature is in danger of deviating from this, involuntary physiological reactions follow (Figure 2.8). The most important of these are vasoconstriction and shivering when the temperature is too low and vasodilation and sweating when the temperature is too high (vasoconstriction and vasodilation occur before behavioural adaptation). People who spend long periods of time in an air-conditioned environment lose some of the body's physiological ability to adapt adequately to temperature changes, especially higher temperatures. This was shown in a laboratory study comparing two groups of subjects (Yu et al., 2012). One group consisted of persons who spent more than 10 hours per day during the previous summer in an air-conditioned environment (usually the work environment), hereafter referred to as the AC group. The other group consisted of persons who spent less than 2 hours per day during the previous summer in an air-conditioned environment, hereafter referred to as the NV (naturally ventilated) group. The individuals in both groups were subjected to heat shock by moving them from a room with a temperature of 26°C to a room with a temperature of 36°C. Thermal sensation was also asked. At the moderate temperature, both groups reported the same thermal sensation and comfort level. But at the high temperature, the AC group felt warmer and less comfortable than the NV group. To explain this, several physiological measurements were taken that are indicative of how the body responds to heat shock, including skin temperature and sweat volume. The blood level of heat shock protein 70 (HSP70) was also measured. This protein has a protective function against heat stress. It appeared that each of these parameters partly explained why the NV group felt more comfortable and less warm at higher temperatures:
At the moderate temperature, the NV group had a higher skin temperature than the AC group. During exposure to the high temperature, the skin temperature of both the NV group and the AC group increased, but the skin temperature for the NV group remained higher than that of the AC group. This indicates a better physiological adaptation of the NV group to the high temperature.
At the higher temperature, the NV group were sweating more than the AC group, which meant that more body heat was being transferred to the environment by sweat evaporation in the NV group. This also indicates a better physiological adaptation of the NV group to the higher temperature.
Heat shock exposure had no effect on HSP70 levels in either group. But at both temperatures, the HSP70 levels of the NV group were about one and a half times higher than those of the AC group.
4.4 Psychological adaptation
Although behavioural and physiological adaptation bring the body heat balance closer to a neutral heat balance, it does not always bring it completely to neutral. Nevertheless, building users can still feel comfortable. This is possible because, based on past experience, they have expectations of higher and lower temperatures occurring in certain situations. RP-884 shows that the spread of acceptable temperatures is largely related to the distribution of measured temperatures in each individual building. This indicates that when users expect a greater range of temperatures based on past experience, they also find a greater range of temperatures acceptable. Conversely, if due to previous experience, users expect a constant temperature, the range of temperatures considered acceptable is narrowed accordingly. It is important to note that getting used to a wider range only works if the range is related to the external temperature in a way that the occupants can understand, as is the case in free running, non-cooled buildings. If the indoor temperatures are not related to the outdoor temperatures, but are caused by random variations in the operation of the air-conditioning system, the acceptability of temperature variations decreases. Expectations thus depend on the type of building. If occupants have experiences of both naturally ventilated and air-conditioned buildings, they will also expect and accept higher temperatures in summer in naturally ventilated buildings. Wagner et al. (2006) show how sophisticated the expectations of occupants are. It turns out that occupants of naturally ventilated buildings accept higher temperatures in the afternoon than in the morning in summer (Figure 4.1). A temperature of 25.5 °C in the morning is still experienced as somewhat warm by most occupants, while in the afternoon the same temperature is experienced as just right. This is because occupants expect higher temperatures in the afternoon than in the morning.
The importance of user expectations is further underlined by the fact that in semi-outdoor environments, for example a covered outdoor terrace or an indoor space that is open to the outdoors, people accept a much wider range of ambient temperatures than in indoor environments (Nakano & Tanabe, 2003a). They are also more active in adjusting their clothing (Nakano & Tanabe, 2003b). Although users in semi-outdoor environments can influence the insulating value of their clothing and perhaps have some influence on air velocity and radiation temperature by sitting in a different position, their influence on air temperature is almost negligible. The greater tolerance is therefore largely due to the adjusted expectation of users in semi-outdoor environments combined with the adjustment of their clothing.
4.5 The interaction between behavioural and psychological adaptation
Indoor environmental quality is important for overall building user satisfaction and thermal comfort is the most important indoor environmental factor, but thermal comfort is experienced differently in different types of buildings. Research into marketing strategies distinguishes between basic factors, bonus factors and proportional factors. Basic factors are factors which consumers take for granted and which are therefore minimum requirements. For these factors, the fulfilment of extra-high requirements does not lead to a higher degree of satisfaction with the product as a whole, but when the minimum requirements are not met, this will lead to dissatisfaction. Thus, the negative effect on overall satisfaction of a poor performance of a basic factor is greater than the positive effect of an extra good performance. Bonus factors are properties that are not expected by consumers. Not meeting these characteristics will not lead to dissatisfaction with the product as a whole. However, if one or more bonus factors are met, user satisfaction with the product will increase. So the positive effect on overall satisfaction of a good performance of a bonus factor is greater than the negative effect of a poor performance of that bonus factor. With proportional factors, the effect on consumer satisfaction is proportionally distributed. When these factors perform well, consumers are satisfied with the product as a whole; when they perform poorly, consumers are dissatisfied (Figure 4.2).
The applicability of this classification to the indoor environment was investigated by Kim & de Dear (2012). They used a dataset in which the ratings of individual indoor environment factors and the rating of the indoor environment as a whole were available for users of various office buildings. It was also known whether the buildings were air-conditioned, naturally ventilated or mixed mode (mixed mode is defined in this study as air-conditioned buildings with windows that can be opened, as also used in the analyses of RP-884). The study shows that thermal comfort is a basic factor in air-conditioned buildings, a proportional factor in mixed-mode buildings and a bonus factor in naturally ventilated buildings.
Acceptable thermal comfort is a minimum requirement for people in air-conditioned buildings. They do not notice the indoor climate if it meets their expectations. If the thermal comfort in these buildings does not meet expectations, this has a negative impact on overall satisfaction with the indoor environment. In naturally ventilated buildings, expectations are not as high. Thermal discomfort does not lead to a negative rating of the indoor environment as a whole. But if the thermal indoor climate is perceived as good, this contributes to a positive appreciation of the indoor environment as a whole. In mixed-mode buildings, thermal comfort leads to a higher rating of the indoor environment as a whole and thermal discomfort to a lower rating. The fact that thermal comfort is a bonus factor in naturally ventilated buildings is due to the combination of the influence that users have on the thermal indoor climate, making them feel co-responsible for their own thermal comfort, and the understanding that in naturally ventilated buildings the indoor temperature varies with the outdoor temperature. Furthermore, occupants in naturally ventilated buildings appear to pay more attention to local weather conditions. This affects their expectations, allowing them to anticipate indoor temperatures to a certain extent and make adjustments accordingly. In air-conditioned buildings, occupants have less influence on air temperature and air velocity than in naturally ventilated buildings. Moreover, they have largely lost the ability to control their heat balance by adjusting their clothing insulation (Carlsen, 2010). They also pay less attention to local weather conditions. Based on experiences with the current building, or with air-conditioned buildings in the past, they expect the building to provide a comfortable temperature. They do not feel responsible for their own thermal comfort. Therefore, in air-conditioned buildings, thermal comfort is a basic factor.
Interestingly, the study by Kim & de Dear found that noise levels is a basic factor in air-conditioned buildings and a bonus factor in naturally ventilated buildings. This factor has different meanings in air-conditioned and naturally ventilated buildings. In general, there are three types of noise sources in an office space:
Noise from outside, in naturally ventilated buildings this is mainly determined by traffic noise and how far the windows are opened;
Noise from the air handling and ventilation system;
Noise from colleagues and office equipment.
In air-conditioned buildings, the closed façade means that noise from outside will not determine the noise level, unless the sound insulation of the façade is inadequate or the noise level is very high. There will be noise from the air handling system, depending on the way the air is supplied. In fully air-conditioned buildings with an open plan layout, there will often be noise from colleagues in adjacent desks. The noise of the air handling system, where the degree of nuisance depends on the noise level, cannot be influenced by the occupants. If the noise is perceived as annoying for a long period, it can also lead to symptoms such as headaches, fatigue and loss of concentration. The annoyance caused by the noise of colleagues and office equipment in the room in question is not determined by the noise level (Nemecek, 1980). Annoyance is more severe the greater the intelligibility and informational content, and the lesser the localisability, predictability and perceived necessity. These matters cannot be influenced by users either. Annoyance caused by noise from colleagues and office equipment can also lead to symptoms such as headaches, fatigue and loss of concentration (Cohen & Weinstein, 1982). It is therefore understandable that noise is a basic factor in air-conditioned buildings. If noise is experienced as a nuisance, it also leads to symptoms that negatively influence the quantity and quality of work (Vroon et al., 1990). The perceived quality of the indoor environment as a whole will also decline.
In naturally ventilated buildings, noise is usually mainly from outside when windows are open and the noise level depends on the position of the windows. Noise caused by the air-conditioning system is rare in passively conditioned buildings. Also, because such buildings are usually designed as smaller office spaces or room offices, noise from colleagues and office equipment is less likely to be a problem. Naturally ventilated buildings offer the occupants optimum possibilities for balancing the positive and negative effects of opening windows. At one moment, people will open the window (further) to obtain more cooling. They will then accept the higher noise level from outside, which is quite possible because they feel responsible for it and because dissatisfaction with the noise level does not lead to dissatisfaction with the indoor environment as a whole. Noise is a bonus factor in this type of building. At other times, for example when extra concentration is needed for a certain period of time, you can close the window (or set it to a very small aperture, if possible). If it gets a bit warmer as a result, people will accept that too, because thermal comfort is also a bonus factor. The decision is also your own decision. A good compromise between thermal comfort and noise level can also be found by adjusting the open window to an intermediate position. This also emphasises the importance of being able to set windows to different positions.
The importance of adaptive options and how to use them is often not recognised. This is especially true for high performance buildings that incorporate passive building strategies, which require the active involvement of the occupants, which is typical for achieving energy saving and occupant comfort targets. A study in 8 high performance buildings in de U.S. found that there was a significant difference between those who had received effective training and those who had not (Day & Gunderson, 2015). Those who indicated they had received effective training were significantly more satisfied with their office environment than those who had not received training. Moreover, people who did not understand how to operate their controls can, in a sense, be equated with people who did not have access to building controls at all.
4.6 Alliesthesia
The word alliesthesia originates in Greek (allios=altered; esthsia=feeling) and describes that certain sensory stimuli can induce a pleasant or unpleasant feeling, depending on a person's internal state. Although over a long period of time a neutral thermal sensation is often experienced as most comfortable for the body as a whole, localised cooling or warming of the body over a short period of time can be very pleasant. For example, when the body's core temperature, which, as mentioned, must remain constant as much as possible for physiological processes to function properly, becomes lower than the setpoint, warming of a peripheral part of the body will bring the core temperature closer to the setpoint and this will be experienced as pleasant. This pleasurable experience also occurs when the core temperature exceeds the setpoint and a peripheral part of the body is cooled. This is called positive alliesthesia, which can also be called thermal delight. But when a part of the body cools down or warms up and the difference between the core temperature and the setpoint therefore increases, it will be experienced as unpleasant. This is called negative alliesthesia. Alliesthesia does not only occur when experiencing temperature, but also, for example, when experiencing thirst. The body needs a certain level of water. When this is too low, for example due to not drinking enough or because the kidneys produce too much urine, the body sends signals to the brain that evoke a feeling of thirst and the desire to drink something. When something is consumed, even if it is only a glass of water, it evokes a feeling of pleasure. It is similar with temperature. If someone is feeling cold after a cold winter walk, it can be particularly pleasant to sit down by an open fire, even if the heat exposure is so great that we would experience it as too hot under normal circumstances. The feeling of thermal discomfort is reduced by overcompensation, because it returns the core temperature to the set point faster. Another example we all know: during a very hot day, a cool breeze on your face is experienced as very pleasant, because it brings the core temperature back towards setpoint. Another example to illustrate that it can also be about small peripheral parts of the body: if you are cold, a cup of hot drink in your hands leads to thermal pleasure; if you are warm, a can of cold drink in your hands or briefly on your forehead leads to thermal pleasure.
Thermal pleasure can even be enhanced when different thermal factors have an opposite effect at the same time. Visitors to a restaurant, for example, often prefer the terrace or a semi-outdoor environment to sitting indoors, even if the indoor environment better meets the indoor climate requirements. Apparently, people find it, to a certain extent, more pleasant to feel solar radiation and wind at the same time. In such situations, people unconsciously seek to stimulate the senses. This is also shown in a study conducted in a restaurant with a normal air-conditioned indoor environment and a semi-outdoor environment without air conditioning with a glass roof and an open connection to the outdoors (Shimoda et al., 2003). The reasons given by respondents who chose the semi-outdoor environment included: openness (32%), fresh air (12%), sunlight (8%), lack of air conditioning (7%) and wind (5%). The research by Nakano and Tanabe (2003b) and Shimoda et al. (2003) shows that more than 80% of the occupants of a semi-outdoor environment chose this of their own free choice. It is also striking that Nakano and Tanabe (2003a) show that people spend much less time in a semi-outdoor environment than in an indoor environment. Nakano and Tanabe (2003b) indicate that the time spent in a semi-outdoor environment is usually no more than one hour. People usually only need such conditions for a short period of time. Apparently, a neutral thermal sensation and positive alliesthesia are complementary; if the core temperature is at or close to the setpoint, people prefer a thermal neutral sensation, if the core temperature deviates too much from the setpoint they look for forms of positive alliesthesia. Positive alliesthesia is only possible if the occupant of the space has sufficient possibilities to adapt the thermal environment, for example, to (temporarily) open a window or change its position, to (temporarily) set a table fan to an extra high setting, or to (partially) raise an outdoor sunshade in order to feel more solar radiation. The regular occurrence of positive alliesthesia in addition to a generally neutral thermal sensation leads to thermal delight and increased satisfaction with the indoor thermal environment. The absence of positive alliesthesia, as in the case of a temperature controlled within narrow limits, is experienced as thermal boredom (de Dear, 2009, 2010, 2011).
4.7 The strict temperature limits paradox
In air-conditioned buildings, what one might call the strict temperature limits paradox occurs. The narrower the limits within which the indoor temperature is maintained, the more the occupants lose the ability to keep themselves comfortable through their own behaviour, especially adapting their clothing insulation, and the more their bodies lose the ability to physiologically adapt to higher temperatures. If, as is inevitable in these buildings with more complex systems, occasional deviations from the set temperature occur that are not related to the outside temperature, this will lead to discomfort and dissatisfaction. This is supported by Li et al. (2019) who conclude from their research results that “Occupants becoming accustomed to, or even demanding, tighter temperature tolerances might explain why tight temperature ranges do not necessarily improve thermal comfort”. The likelihood of these occasional deviations is higher when the robustness (see Chapter 5) of the building and its installations is low, as is often the case when complex HVAC technology is employed to keep the temperature within narrow limit limits. The narrow temperature limits paradox also involves the fact that a temperature that is controlled within narrow limits and where possibilities for influencing the temperature are limited can lead to thermal boredom. This can result in dissatisfaction with the indoor thermal environment, which will be expressed as “too hot”, “too cold” or “varying temperatures”, while this is not reflected in temperature measurements. A related explanation that goes one step further is the following: Vroon et al. (1990) describes a phenomenon from general psychology: sensory deprivation. When test subjects are placed in a situation with as little sensory stimulation as possible, by laying them in a lukewarm bath in a room without light or sound, they eventually start to hallucinate. By analogy, Vroon et al. (1990) hypothesised that a thermally very stable environment, in which insufficient sensory stimuli are perceived, leads to the experience of high, low or changing temperatures that are not actually there, ultimately resulting in discomfort.
It is still the standard view among some designers that varying temperatures, such as those found in naturally ventilated buildings, place an undesirable burden on users and are not comfortable or even healthy. In air-conditioned buildings, controlling the temperature within narrow limits removes this burden, leading to greater comfort and health, so the reasoning goes. However, the reverse appears to be true: the temperature differences that occur in a well-designed naturally ventilated building are a healthy burden for the organism, while the tightly controlled temperature in air-conditioned buildings is an unhealthy underload for the organism.
4.8 Adaptation and air movement
In the adaptive thermal comfort models, the effect of air velocity on thermal comfort is not explicitly visible, whereas this parameter can have an influence under certain conditions. Air velocity can have a cooling effect in warm conditions, but can be experienced as an annoying draught in a cool environment. Influencing the air velocity is an important possibility in the adaptation process between occupant and building. Field studies show that twice as many building users would prefer more air movement than less air movement (Toftum, 2003; Zhang et al., 2007). Influencing air velocities is a means of achieving a thermally acceptable situation and also contributes to improving perceived air quality (Melikov, 2012). Building users look for opportunities to influence air velocities by, for example, opening windows or using fans (ceiling, table or standing).
Initially, research into air velocities was carried out in climate chambers and focused on the influence of mechanical ventilation on the sensation of draught. One of the first studies took place in a climate chamber, where subjects were exposed for two and a half hours to fluctuating air speeds from a mechanical ventilation system (Fanger, 1986). The turbulence of the air speed was characterised by the turbulence intensity, defined as the standard deviation (spread) of the air speed divided by the mean air speed. In a follow-up study, a model was developed that predicts the percentage of dissatisfied as a function of air temperature, Mean air speed and turbulence intensity (Fanger et.al., 1988). Figure 4.3 shows this relationship (Brüel & Kjær, 1988). This became the basis of the draught-risk model, which was incorporated into the EN-ISO 7730 (2005) and ASHRAE-55 (2017) standards.
However, air velocities coming from open windows or ventilation grilles are experienced differently from air velocities coming from a ventilation system, because the air turbulences are different in character. In naturally ventilated and mixed-mode buildings, air velocities are generally higher than in air-conditioned buildings, especially in conditions with temperatures above 26°C. Figure 4.4 illustrates this, as it shows a stronger relationship between air temperature and air velocity in naturally ventilated buildings (Parkinson, de Dear & Brager, 2020).
When a person is in a warm or cold environment, it is not the “temperature” that is felt, but we notice a change in the nerve endings in our skin, the thermoreceptors. The combined effect of air and radiant temperature and air speed on our skin sends signals to our brain (Zang, 2003). Hot and cold environments are felt differently because the skin contains separate heat and cold receptors (de Dear, 2010). Air speed changes with a frequency between 0.2 Hz and 1.0 Hz have a strong cooling effect, with frequencies between 0.3 and 0.5 Hz being perceived as an unpleasant draught (Madsen, 1984; Huang et al., 2012).
Because air movements originating from windows, facade grilles or fans are different in character from air movement caused by a ventilation system, it is also informative to study air velocities in the frequency domain (Djamila, 2014). For this purpose, the power spectral density (PSD) is determined, which indicates how the energy of the air velocity is distributed in relation to the frequency of fluctuations caused by eddies in a turbulent air flow (Quang, 2006). Natural air currents have more energy in the low frequencies and are perceived as more pleasant. Air currents caused by a ventilation system have more energy in the high frequencies and this is perceived as more unpleasant. To visualise the differences in characteristics between airflows, the β-value is used, which is the slope of the logarithmic power density spectrum E(f). The higher the β-value, the greater the power in the low frequencies, and the larger the eddies that are characteristic of natural airflow. Figure 4.5 gives examples of β-values of natural and mechanical airflows, showing that natural airflows have a higher β-value than mechanical ones. Airflows with higher β-values are perceived as more pleasant and the optimum range is around 1.40 to 1.80, values that are mainly found with natural airflows. This supports the findings that people prefer natural airflows to airflows from mechanical ventilation systems (Kang et al., 2013).
If ceiling fans or tabletop fans are used in warm conditions, an air velocity of approximately 0.6m/s is optimal if the control of the fan is shared by several people and an air velocity up to approximately 0.8m/s is acceptable if the fan is operated individually (Zhai et al., 2017; Cândido et al., 2010). At air velocities higher than approximately 0.9m/s, there is a risk of paper lying on desks being blown away. EN 16798-1 (2019) also permits increased air velocities, if these can be controlled by building users. Figure 4.6 shows that an air speed of, for example, 0.8m/s corresponds to an increase in comfort temperature of approximately 2.8°C. Or in other words, with a good fan it feels as if the temperature is about 2.8°C lower.
9 Some fully air-conditioned buildings have some form of operable windows. This is often done to meet the wishes of the client or occupants, but the design is sometimes insufficiently well thought-out to be able to speak of effective openable windows.
10 The variance is a measure of variability. The explained variance
(R2) indicates the extent to which one variable influences the other and varies between 0% (no
influence at all) and 100% (complete correlation). The explained variance is equal to the square of the correlation (r) between the variables. The correlation is a measure of the relationship between two variables and ranges from 1.0 (complete
correlation) via 0.0 (no correlation at all) to -1.0 (complete opposite correlation). Because the correlation has a value between +1.0 and -1.0, the numerical value of the explained variance is always lower than that of the correlation. Looking
only at the correlation can lead to an instinctive overestimation of the relationship. For example, a correlation of 0.30 may seem substantial, but the explained variance is no higher than 9%. Correlations must be above about 0.50 to arrive at a
substantial explained variance. Examples:
When r=0.50, R2=25%;
When r=0.70, R2=49%.