The terms in Equation (1) have units of power per unit area and refer to the surface area of the nude body. The most useful measure of nude body surface area, originally proposed by DuBois and DuBois (1916), is described by

(4)

where

A correction factor f_cl = A_cl/A_D must be applied to the heat transfer terms from the skin (C, R, and E_sk) to account for the actual surface area A_cl of the clothed body. Table 7 presents f_cl values for various clothing ensembles. For a 68 in. tall, 154 lb man, A_D = 19.6 ft². All terms in the basic heat balance equations are expressed per unit DuBois surface area.

Sensible heat exchange from the skin must pass through clothing to the surrounding environment. These paths are treated in series and can be described in terms of heat transfer (1) from the skin surface, through the clothing insulation, to the outer clothing surface, and (2) from the outer clothing surface to the environment.

Both convective C and radiative R heat losses from the outer surface of a clothed body can be expressed in terms of a heat transfer coefficient and the difference between the mean temperature t_cl of the outer surface of the clothed body and the appropriate environmental temperature:

(5)

(6)

where

The coefficients h_c and h_r are both evaluated at the clothing surface. Equations (5) and (6) are commonly combined to describe the total sensible heat exchange by these two mechanisms in terms of an operative temperature t_o and a combined heat transfer coefficient h:

(7)

where

(8)

(9)

Based on Equation (8), operative temperature t_o can be defined as the average of the mean radiant and ambient air temperatures, weighted by their respective heat transfer coefficients.

The actual transport of sensible heat through clothing involves conduction, convection, and radiation. It is usually most convenient to combine these into a single thermal resistance value R_cl, defined by

(10)

where R_cl is the thermal resistance of clothing in ft² · °F · h/Btu.

Because it is often inconvenient to include the clothing surface temperature in calculations, Equations (7) and (10) can be combined to eliminate t_cl:

(11)

where t_o is defined in Equation (8).

Evaporative heat loss E_sk from skin depends on the amount of moisture on the skin and the difference between the water vapor pressure at the skin and in the ambient environment:

(12)

where

Procedures for calculating R_e,cl and h_e are given in the section on Engineering Data and Measurements. Skin wettedness is the ratio of the actual evaporative heat loss E_sk to the maximum possible evaporative heat loss E_max with the same conditions and a completely wet skin (w = 1). Skin wettedness is important in determining evaporative heat loss. Maximum evaporative potential E_max occurs when w = 1.

Evaporative heat loss from the skin is a combination of the evaporation of sweat secreted because of thermoregulatory control mechanisms E_rsw and the natural diffusion of water through the skin E_dif:

(13)

Evaporative heat loss by regulatory sweating is directly proportional to the rate of regulatory sweat generation:

(14)

where

The portion w_rsw of a body that must be wetted to evaporate the regulatory sweat is

(15)

With no regulatory sweating, skin wettedness caused by diffusion is approximately 0.06 for normal conditions. For large values of E_max or long exposures to low humidities, the value may drop to as low as 0.02, because dehydration of the outer skin layers alters its diffusive characteristics. With regulatory sweating, the 0.06 value applies only to the portion of skin not covered with sweat (1 – w_rsw); the diffusion evaporative heat loss is

(16)

These equations can be solved for w, given the maximum evaporative potential E_max and the regulatory sweat generation E_rsw:

(17)

Once skin wettedness is determined, evaporative heat loss from the skin is calculated from Equation (12), or by

(18)

To summarize, the following calculations determine w and E_sk:

Although evaporation from the skin E_sk as described in Equation (12) depends on w, the body does not directly regulate skin wettedness but, rather, regulates sweat rate ṁ_rsw [Equation (14)]. Skin wettedness is then an indirect result of the relative activity of the sweat glands and the evaporative potential of the environment. Skin wettedness of 1.0 is the upper theoretical limit. If the aforementioned calculations yield a wettedness of more than 1.0, then Equation (14) is no longer valid because not all the sweat is evaporated. In this case, E_sk = E_max.

Skin wettedness is strongly correlated with warm discomfort and is also a good measure of thermal stress. Theoretically, skin wettedness can approach 1.0 while the body still maintains thermoregulatory control. In most situations, it is difficult to exceed 0.8 (Berglund and Gonzalez 1977). Azer (1982) recommends 0.5 as a practical upper limit for sustained activity for a healthy, acclimatized person.

During respiration, the body loses both sensible and latent heat by convection and evaporation of heat and water vapor from the respiratory tract to the inhaled air. A significant amount of heat can be associated with respiration because air is inspired at ambient conditions and expired nearly saturated at a temperature only slightly cooler than t_cr.

The total heat and moisture losses through respiration are

(19)

(20)

where

Under normal circumstances, pulmonary ventilation rate is primarily a function of metabolic rate (Fanger 1970):

(21)

where

For typical indoor environments (McCutchan and Taylor 1951), the exhaled temperature and humidity ratio are given in terms of ambient conditions:

(22)

(23)

where ambient t_a and exhaled t_ex air temperatures are in °F. For extreme conditions, such as outdoor winter environments, different relationships may be required (Holmér 1984).

The humidity ratio of ambient air can be expressed in terms of total or barometric pressure p_t and ambient water vapor pressure p_a:

(24)

Respiratory heat loss is often expressed in terms of sensible C_res and latent E_res heat losses. Two approximations are commonly used to simplify Equations (22) and (23) for that purpose. First, because dry respiratory heat loss is relatively small compared to the other terms in the heat balance, an average value for t_ex is determined by evaluating Equation (22) at standard conditions of 68°F, 50% rh, sea level. Second, noting in Equation (23) that there is only a weak dependence on t_a, the second term in Equation (23) and the denominator in Equation (24) are evaluated at standard conditions. Using these approximations and substituting latent heat h_fg and specific heat of air c_p,a at standard conditions, C_res and E_res can be determined by

(25)

(26)

where p_a is expressed in psi and t_a is in °F.

Equations (11) and (12) describe heat loss from skin for clothed people in terms of clothing parameters R_cl, R_e,cl, and f_cl; parameters h and h_e describe outer surface resistances. Other parameters and definitions are also used. Although these alternative parameters and definitions may be confusing, note that information presented in one form can be converted to another form. Table 1 presents common parameters and their qualitative descriptions. Table 2 presents equations showing their relationship to each other. Generally, parameters related to dry or evaporative heat flows are not independent because they both rely, in part, on the same physical processes. The Lewis relation describes the relationship between convective heat transfer and mass transfer coefficients for a surface [see Equation (41) in Chapter 6]. The Lewis relation can be used to relate convective and evaporative heat transfer coefficients defined in Equations (5) and (12) according to

(27)

where LR is the Lewis ratio and, at typical indoor conditions, equals approximately 205°F/psi. The Lewis relation applies to surface convection coefficients. Heat transfer coefficients that include the effects of insulation layers and/or radiation are still coupled, but the relationship may deviate significantly from that for a surface. The i terms in Tables 1 and 2 describe how the actual ratios of these parameters deviate from the ideal Lewis ratio (Oohori et al. 1984; Woodcock 1962).

Table 2 Relationships Between Clothing Parameters

Sensible Heat Flow

Evaporative Heat Flow

Parameters Relating Sensible and Evaporative Heat Flows

Depending on the combination of parameters used, heat transfer from the skin can be calculated using several different formulations (see Tables 2 and 3). If the parameters are used correctly, the end result will be the same regardless of the formulation used.

Total skin heat loss (sensible heat plus evaporative heat) can be calculated from any combination of the equations presented in Table 3. Total skin heat loss is used as a measure of the thermal environment; two combinations of parameters that yield the same total heat loss for a given set of body conditions (t_sk and w) are considered to be approximately equivalent. The fully expanded skin heat loss equation, showing each parameter that must be known or specified, is as follows:

(28)

where t_o is the operative temperature and represents the temperature of a uniform environment (t_a – t̄_r) that transfers dry heat at the same rate as in the actual environment [t_o = (t̄_rh_r + t_ah_c)/(h_c + h_r)]. After rearranging, Equation (28) becomes

(29)

This equation allows evaluation of the trade-off between any two or more parameters under given conditions. If the trade-off between two specific variables (e.g., operative temperature and humidity) is to be examined, then a simplified form of the equation suffices (Fobelets and Gagge 1988):

(30)

Table 3 Skin Heat Loss Equations

Sensible Heat Loss

Evaporative Heat Loss

Equation (30) can be used to define a combined temperature t_com, which reflects the combined effect of operative temperature and humidity for an actual environment:

or

(31)

where p_tcom is a vapor pressure related in some fixed way to t_com and is analogous to p_wb,s for t_wb. The term wi_mLR p_tcom is constant to the extent that i_m is constant, and any combination of t_o and p_a that gives the same t_com results in the same total heat loss.

Figure 2. Constant Skin Heat Loss Line and Its Relationship to t_oh and ET*

Two important environmental indices, humid operative temperature t_oh and effective temperature ET*, can be represented in terms of Equation (31). The humid operative temperature is that temperature which at 100% rh yields the same total heat loss as for the actual environment:

(32)

where p_oh,s is saturated vapor pressure, in psi, at t_oh.

The effective temperature is the temperature at 50% rh that yields the same total heat loss from the skin as for the actual environment:

(33)

where p_ET*, s is saturated vapor pressure, in psi, at ET*.

The psychrometric chart in Figure 2 shows a constant total heat loss line and the relationship between these indices. This line represents only one specific skin wettedness and permeation efficiency index. The relationship between indices depends on these two parameters (see the section on Environmental Indices).

Maximum Capacity. In choosing optimal conditions for comfort and health, the rate of work done during routine physical activities must be known, because metabolic power increases in proportion to exercise intensity. Metabolic rate varies over a wide range, depending on the activity, person, and conditions under which the activity is performed. Table 4 lists typical metabolic rates for an average adult (A_D = 19.6 ft²) for activities performed continuously. The highest power a person can maintain for any continuous period is approximately 50% of the maximal capacity to use oxygen (maximum energy capacity).

A unit used to express the metabolic rate per unit DuBois area is the met, defined as the metabolic rate of a sedentary person (seated, quiet): 1 met = 18.4 Btu/h · ft² = 50 kcal/h · m². A normal, healthy man at age 20 has a maximum capacity of approximately M_act = 12 met, which drops to 7 met at age 70. Maximum rates for women are on average about 30% lower. Long-distance runners and trained athletes have maximum rates as high as 20 met. An average 35-year-old who does not exercise has a maximum rate of about 10 met, and activities with M_act > 5 met are likely to prove exhausting.

Intermittent Activity. Often, people’s activity consists of a mixture of activities or a combination of work/rest periods. A weighted average metabolic rate is generally satisfactory, provided that activities alternate frequently (several times per hour). For example, a person whose activities consist of typing 50% of the time, filing while seated 25% of the time, and walking about 25% of the time would have an average metabolic rate of 0.50 × 20 + 0.25 × 22 + 0.25 × 31 = 23 Btu/h · ft² (see Table 4).

Accuracy. Estimating metabolic rates is difficult. Values given in Table 4 indicate metabolic rates only for the specific activities listed. Some entries give a range and some a single value, depending on the data source. The level of accuracy depends on the value of M_act and how well the activity can be defined. For well-defined activities with M_act < 1.5 met (e.g., reading), Table 4 is sufficiently accurate for most engineering purposes. For values of M_act > 3, where a task is poorly defined or where there are various ways of performing a task (e.g., heavy machine work), the values may be in error by as much as ±50% for a given application. Engineering calculations should thus allow for potential variations.

Measurement. When metabolic rates must be determined more accurately than is possible with tabulated data, physiological measurements with human subjects may be necessary. The rate of metabolic heat produced by the body is most accurately measured by the rate of respiratory oxygen consumption and carbon dioxide production. An empirical equation for metabolic rate is given by Nishi (1981):

(34)

where

The exact value of the respiratory quotient RQ depends on a person’s activity, diet, and physical condition. It can be determined by measuring both carbon dioxide and oxygen in the respiratory airflows, or it can be estimated with reasonable accuracy. A good estimate for the average adult is RQ = 0.83 for light or sedentary activities (M < 1.5 met), increasing proportionately to RQ = 1.0 for extremely heavy exertion (M = 5.0 met). Estimating RQ is generally sufficient for all except precision laboratory measurements because it does not strongly affect the value of the metabolic rate: a 10% error in estimating RQ results in an error of less than 3% in the metabolic rate.

A second, much less accurate, method of estimating metabolic rate physiologically is to measure the heart rate. Table 5 shows the relationship between heart rate and oxygen consumption at different levels of physical exertion for a typical person. Once oxygen consumption is estimated from heart rate information, Equation (34) can be used to estimate the metabolic rate. Other factors that affect heart rate include physical condition, heat, emotional factors, and muscles used. Astrand and Rodahl (1977) show that heart rate is only a very approximate measure of metabolic rate and should not be the only source of information where accuracy is required.

Mechanical Efficiency. In the heat balance equation, the rate W of work accomplished must be in the same units as metabolism M and expressed in terms of A_D in Btu/h · ft². The mechanical work done by the muscles for a given task is often expressed in terms of the body’s mechanical efficiency μ = W/M. It is unusual for μ to be more than 0.05 to 0.10; for most activities, it is close to zero. The maximum value under optimal conditions (e.g., bicycle ergometer) is μ = 0.20 to 0.24 (Nishi 1981). It is common to assume that mechanical work is zero for several reasons: (1) mechanical work produced is small compared to metabolic rate, especially for office activities; (2) estimates for metabolic rates are often inaccurate; and (3) this assumption gives a more conservative estimate when designing air-conditioning equipment for upper comfort and health limits. More accurate calculation of heat generation may require estimating mechanical work produced for activities where it is significant (walking on a grade, climbing a ladder, bicycling, lifting, etc.). In some cases, it is possible to either estimate or measure the mechanical work. For example, a 200 lb person walking up a 5% grade at 4.4 fps (3 mph) would lift a 200 lb weight a height of 0.22 ft every second, for a work rate of 44 ft · lb_f/s, or 204 Btu/h. This rate of mechanical work would then be subtracted from M to determine the net heat generated.

Values for the linearized radiative heat transfer coefficient, convective heat transfer coefficient, and evaporative heat transfer coefficient are required to solve the equations describing heat transfer from the body.

Radiative Heat Transfer Coefficient. The linearized radiative heat transfer coefficient can be calculated by

(35)

where

The ratio A_r/A_D is 0.70 for a sitting person and 0.73 for a standing person (Fanger 1967). Emissivity ε is close to unity (typically 0.95), unless special reflective materials are used or high-temperature sources are involved. It is not always possible to solve Equation (35) explicitly for h_r , because t_cl may also be unknown. Some form of iteration may be necessary if a precise solution is required. Fortunately, h_r is nearly constant for typical indoor temperatures, and a value of 0.83 Btu/h ·ft² · °F suffices for most calculations. If emissivity is significantly less than unity, adjust the value by

(36)

where ε represents the area-weighted average emissivity for the clothing/body surface.

Convective Heat Transfer Coefficient. Heat transfer by convection is usually caused by air movement within the living space or by body movements. Equations for estimating h_c under various conditions are presented in Table 6. Where two conditions apply (e.g., walking in moving air), a reasonable estimate can be obtained by taking the larger of the two values for h_c. Limits have been given to all equations. If no limits were given in the source, reasonable limits have been estimated. Be careful using these values for seated and reclining persons. The heat transfer coefficients may be accurate, but the effective heat transfer area may be substantially reduced through body contact with a padded chair or bed.

Quantitative values of h_c are important, not only in estimating convection loss, but in evaluating (1) operative temperature t_o, (2) clothing parameters I_t and i_m, and (3) rational effective temperatures t_oh and ET*. All heat transfer coefficients in Table 6 were evaluated at or near 14.7 psia. These coefficients should be corrected as follows for atmospheric pressure:

(37)

where

The combined coefficient h is the sum of h_r and h_c, described in Equation (35) and Table 6, respectively. The coefficient h governs exchange by radiation and convection from the exposed body surface to the surrounding environment.

Evaporative Heat Transfer Coefficient. The evaporative heat transfer coefficient h_e for the outer air layer of a nude or clothed person can be estimated from the convective heat transfer coefficient using the Lewis relation given in Equation (27). If the atmospheric pressure is significantly different from the reference value (14.7 psia), the correction to the value obtained from Equation (27) is

(38)

where h_ec is the corrected evaporative heat transfer coefficient in Btu/h · ft² · °F.

Thermal Insulation. The most accurate ways to determine clothing insulation are (1) measurements on heated mannikins (McCullough and Jones 1984; Olesen and Nielsen 1983) and (2) measurements on active subjects (Nishi et al. 1975). For most routine engineering work, estimates based on tables and equations in this section are sufficient. Thermal mannikins can measure the sensible heat loss from “skin” (C + R) in a given environment. Equation (11) can then be used to evaluate R_cl if environmental conditions are well defined and f_cl is measured. Evaluation of clothing insulation on subjects requires measurement of t_sk, t_cl, and t_o. Clothing thermal efficiency is calculated by

(39)

The intrinsic clothing insulation can then be calculated from mannikin measurements, provided f_cl is measured and conditions are sufficiently well defined to determine h accurately:

(40)

where q is heat loss from the mannikin in Btu/h · ft².

Clothing insulation value may be expressed in clo units. To avoid confusion, the symbol I is used with the clo unit instead of the symbol R. The relationship between the two is

(41)

or 1.0 clo is equivalent to 0.88 ft² · °F · h/Btu.

Because clothing insulation cannot be measured for most routine engineering applications, tables of measured values for various clothing ensembles can be used to select an ensemble comparable to the one(s) in question. Table 7 gives values for typical indoor clothing ensembles. More detailed tables are presented by McCullough and Jones (1984) and Olesen and Nielsen (1983). Accuracies for I_cl on the order of ±20% are typical if good matches between ensembles are found. Values of thermal insulation and clothing area factors for clothing ensembles typical of the Arabian Gulf region may be found in Al-ajmi et al. (2008).

ASHRAE research project RP-1504 (Havenith et al. 2015) produced a database of static total and intrinsic clothing thermal insulation values and vapor permeability indices for non-Western ensembles. The report presents tabulated data for more than 40 ensembles from India, Pakistan, Indonesia, Kuwait, Nigeria, Ghana, and China. Table 8 gives values for a selection of these ensembles. Local regional thermal insulation values for the ensembles were also measured, together with data on the effects of air velocity, posture, and walking on the total thermal insulation values.

When a premeasured ensemble cannot be found to match the one in question, estimate the ensemble insulation from the insulation of individual garments. Table 9 lists common individual garments. The insulation of an ensemble is estimated from the individual values using a summation formula (McCullough and Jones 1984):

(42)

where I_clu,i is the effective insulation of garment i, and I_cl, as before, is the insulation for the entire ensemble. A simpler and nearly as accurate summation formula is (Olesen 1985)

(43)

Either Equation (42) or (43) gives acceptable accuracy for typical indoor clothing. The main source of inaccuracy is in determining the appropriate values for individual garments. Overall accuracies are on the order of ±25% if the tables are used carefully. If it is important to include a specific garment not included in Table 8, its insulation can be estimated by (McCullough and Jones 1984)

(44)

where

Values in Table 7 may be adjusted by information in Table 9 and a summation formula. Using this method, values of I_clu,i for the selected items in Table 9 are then added to or subtracted from the ensemble value of I_cl in Table 7.

When a person is sitting, the chair generally has the effect of increasing clothing insulation by up to 0.15 clo, depending on the contact area A_ch between the chair and body (McCullough et al. 1994). A string webbed or beach chair has little or no contact area, and the insulation actually decreases by about 0.1 clo, likely because of compression of the clothing in the contact area. In contrast, a cushioned executive chair has a large contact area that can increase the intrinsic clothing insulation by 0.15 clo. For other chairs, the increase in intrinsic insulation ΔI_cl can be estimated from

(45)

where A_ch is in ft².

For example, a desk chair with a body contact area of 2.9 ft² has a ΔI_cl of 0.1 clo. This amount should be added to the intrinsic insulation of the standing clothing ensemble to obtain the insulation of the ensemble when sitting in the desk chair.

Although sitting increases clothing insulation, walking decreases it (McCullough and Hong 1994), as does air movement (Havenith and Nilsson 2004). The change in clothing insulation ΔI_cl can be estimated from the standing intrinsic insulation I_cl of the ensemble and the walking speed (Walkspeed) in steps per minute:

(46)

For example, the clothing insulation of a person wearing a winter business suit with a standing intrinsic insulation of 1 clo would decrease by 0.52 clo when the person walks at 90 steps per minute (about 2.3 mph). Thus, when the person is walking, the intrinsic insulation of the ensemble would be 0.48 clo.

A correction for both walking and air speed for a person in normal or light clothing (0.6 clo < I_cl < 1.4 clo, or 1.2 clo < I_T < 2.0 clo, respectively) is given by Havenith and Nilsson (2004) and Havenith et al. (2012) as

(47)

where

Permeation Efficiency. Permeation efficiency data for some clothing ensembles are presented in terms of i_cl and i_m in Table 7. Values of i_m can be used to calculate R_e,t using the relationships in Table 2. Ensembles worn indoors generally fall in the range 0.3 < i_m < 0.5. Assuming i_m = 0.4 is reasonably accurate (McCullough et al. 1989) and may be used if a good match to ensembles in Table 7 cannot be made. The value of i_m or R_e,t may be substituted directly into equations for body heat loss calculations (see Table 3). However, i_m for a given clothing ensemble is a function of the environment as well as the clothing properties. Unless i_m is evaluated at conditions very similar to the intended application, it is more rigorous to use i_cl to describe the permeation efficiency of the clothing. The value of i_cl is not as sensitive to environmental conditions; thus, given data are more accurate over a wider range of air velocity and radiant and air temperature combinations for i_cl than for i_m. Relationships in Table 2 can be used to determine R_e,cl from i_cl, and R_e,cl can then be used for body heat loss calculations (see Table 3). McCullough et al. (1989) found an average value of i_cl = 0.34 for common indoor clothing; this value can be used when other data are not available.

Measuring i_m or i_cl may be necessary if unusual clothing (e.g., impermeable or metallized) and/or extreme environments (e.g., high radiant temperatures, high air velocities) are to be addressed. There are three different methods for measuring the permeation efficiency of clothing: (1) using a wet mannikin to measure the effect of sweat evaporation on heat loss (McCullough 1986), (2) using permeation efficiency measurements on component fabrics as well as dry mannikin measurements (Umbach 1980), and (3) using measurements from sweating subjects (Holmer 1984; Nishi et al. 1975). For an overview, please see ISO Standard 9920.

Clothing Surface Area. Many clothing heat transfer calculations require that clothing area factor f_cl be known. The most reliable approach is to measure it using photographic methods (Olesen et al. 1982). Other than actual measurements, the best method is to use previously tabulated data for similar clothing ensembles. Table 7 is adequate for most indoor clothing ensembles. No good method of estimating f_cl for an ensemble from other information is available, although a rough estimate can be made by (McCullough and Jones 1984)

(48)

The total evaporative heat loss (latent heat) from the body through both respiratory and skin losses, E_sk + E_res, can be measured directly from the body’s rate of mass loss as observed by a sensitive scale:

(49)

where

When using Equation (49), adjustments should be made for any food or drink consumed, body effluents (e.g., wastes), and metabolic weight losses. Metabolism contributes slightly to weight loss primarily because the oxygen absorbed during respiration is converted to heavier CO₂ and exhaled. It can be calculated by

(50)

where

Thermal environment parameters that must be measured or otherwise quantified to obtain accurate estimates of human thermal response are divided into two groups: those that can be measured directly and those calculated from other measurements.

Directly Measured Parameters. Seven psychrometric parameters used to describe the thermal environment are (1) air temperature t_a, (2) wet-bulb temperature t_wb, (3) dew-point temperature t_dp, (4) water vapor pressure p_a, (5) total atmospheric pressure p_t, (6) relative humidity (rh), and (7) humidity ratio W_a. These parameters are discussed in detail in Chapter 1, and methods for measuring them are discussed in Chapter 36. Two other important parameters include air velocity V and mean radiant temperature t̄_r. Air velocity measurements are also discussed in Chapter 36. The radiant temperature is the temperature of an exposed surface in the environment. The temperatures of individual surfaces are usually combined into a mean radiant temperature  . Finally, globe temperature t_g, which can also be measured directly, is a good approximation of the operative temperature t_o and is also used with other measurements to calculate the mean radiant temperature.

Calculated Parameters. The mean radiant temperature is a key variable in thermal calculations for the human body. It is the uniform temperature of an imaginary enclosure in which radiant heat transfer from the human body equals the radiant heat transfer in the actual nonuniform enclosure. Measurements of the globe temperature, air temperature, and air velocity can be combined to estimate the mean radiant temperature (see Chapter 36). Accuracy of determined this way varies considerably, depending on the type of environment and accuracy of the individual measurements. Because the mean radiant temperature is defined with respect to the human body, the shape of the sensor is also a factor. The spherical shape of the globe thermometer gives a reasonable approximation of a seated person; an ellipsoid sensor gives a better approximation of the shape of a human, both upright and seated.

Mean radiant temperature can also be calculated from the measured temperature of surrounding walls and surfaces and their positions with respect to the person. Most building materials have a high emittance ε, so all surfaces in the room can be assumed to be black. The following equation is then used:

(51)

where

Because the sum of the angle factors is unity, the fourth power of mean radiant temperature equals the mean value of the surrounding surface temperatures to the fourth power, weighted by the respective angle factors. In general, angle factors are difficult to determine, although Figures 3A and 3B may be used to estimate them for rectangular surfaces. The angle factor normally depends on the position and orientation of the person (Fanger 1982).

Figure 3. Mean Value of Angle Factor Between Seated Person and Horizontal or Vertical Rectangle when Person Is Rotated Around Vertical Axis (Fanger 1982)

If relatively small temperature differences exist between the surfaces of the enclosure, Equation (51) can be simplified to a linear form:

(52)

Equation (52) always gives a slightly lower mean radiant temperature than Equation (51), but the difference is small. If, for example, half the surroundings (F_p– N = 0.5) has a temperature 10°F higher than the other half, the difference between the calculated mean radiant temperatures [according to Equations (51) and (52)] is only 0.4°F. If, however, this difference is 200°F, the mean radiant temperature calculated by Equation (52) is 20°F too low.

Mean radiant temperature may also be calculated from the plane radiant temperature t_p r in six directions (up, down, right, left, front, back) and for the projected area factors of a person in the same six directions. For a standing person, the mean radiant temperature may be estimated as

(53)

For a seated person,

(54)

The plane radiant temperature t_pr , introduced by Korsgaard (1949), is the uniform temperature of an enclosure in which the incident radiant flux on one side of a small plane element is the same as that in the actual environment. The plane radiant temperature describes thermal radiation in one direction, and its value thus depends on the direction. In comparison, mean radiant temperature describes the thermal radiation for the human body from all directions. The plane radiant temperature can be calculated using Equations (50) and (51) with the same limitations. Area factors are determined from Figure 4.

Figure 4. Analytical Formulas for Calculating Angle Factor for Small Plane Element

The radiant temperature asymmetry Δt_pr is the difference between the plane radiant temperature of the opposite sides of a small plane element. This parameter describes the asymmetry of the radiant environment and is especially important in comfort conditions. Because it is defined with respect to a plane element, its value depends on the plane’s orientation, which may be specified in some situations (e.g., floor to ceiling asymmetry) and not in others. If direction is not specified, the radiant asymmetry should be for the orientation that gives the maximum value.

Unsolicited thermal complaints can increase a building’s operation and maintenance (O&M) cost by requiring unscheduled maintenance to correct the problem.

Figure 6. Air Speed to Offset Temperatures Above Warm-Temperature Boundaries of Figure 5

Figure 7. Predicted Rate of Unsolicited Thermal Operating Complaints

Federspiel (1998) analyzed complaint data from 690 commercial buildings with a total of 23,500 occupants. The most common kind of unsolicited complaint was of temperature extremes. Complaints were rarely because of individual differences in preferred temperature, because 96.5% of the complaints occurred at temperatures less than 70°F or greater than 75°F; most complaints were caused by HVAC faults or poor control performance.

The hourly complaint rate per zone area of being too hot (ν_h) or too cold (ν_l) can be predicted from the HVAC system’s operating parameters, specifically the mean space temperature (μ_T), standard deviation of the space temperature (σ_T), and the standard deviation of the rate of change in space temperature (, ):

(57)

(58)

where the subscripts H, L, and B refer to too hot, too cold, and building (Federspiel 2001).

The building maintenance and space temperature records of six commercial buildings in Minneapolis, Seattle, and San Francisco were analyzed for the values of the H and L model parameters (Federspiel et al. 2003) of Table 11. Complaint  rates predicted by the model for these building parameters are graphed in Figure 7. Arrival complaints occur when the temperature exceeds either the hot or cold complaint level when occupants arrive in the morning. Operating complaints occur during the occupied period when the temperature crosses above the hot complaint level or below the cold complaint level. Arriving occupants generally have a higher metabolic power because of recent activity (e.g., walking).

Complaint prediction models can be used to determine the minimum discomfort temperature (MDT) setting that minimizes the occurrences of thermal complaints for a building with known or measured HVAC system  parameters σ_TB and σ_TB. Similarly, complaint models can be used with building energy models and service call costs to determine the minimum cost temperature (MCT) where the operating costs are minimized. For example, the summer MDT and MCT in Sacramento, California, are 73 and 77°F for a commercial building at design conditions with σ_TB = 0.6°F and σ_TB = 1°F. For these conditions, temperatures below 73°F increase both cold complaints and energy costs, and those above 77°F increase hot complaints and costs. Thus, the economically logical acceptable temperature range for this building is 73 to 77°F for minimum operating cost and discomfort (Federspiel et al. 2003).

Asymmetric or nonuniform thermal radiation in a space may be caused by cold windows, uninsulated walls, cold products, cold or warm machinery, or improperly sized heating panels on the wall or ceiling. In residential buildings, offices, restaurants, etc., the most common causes are cold windows or improperly sized or installed ceiling heating panels. At industrial workplaces, the reasons include cold or warm products, cold or warm equipment, etc.

Recommendations in ISO Standard 7730 and ASHRAE Standard 55 are based primarily on studies reported by Fanger et al. (1980). These standards include guidelines regarding the radiant temperature asymmetry from an overhead warm surface (heated ceiling) and a vertical cold surface (cold window). Among the studies conducted on the influence of asymmetric thermal radiation are those by Fanger and Langkilde (1975), McIntyre (1974, 1976), McIntyre and Griffiths (1975), McNall and Biddison (1970), and Olesen et al. (1972). These studies all used seated subjects, who were always in thermal neutrality and exposed only to the discomfort resulting from excessive asymmetry.

Figure 9. Percentage of People Expressing Discomfort Caused by Asymmetric Radiation

The subjects gave their reactions on their comfort sensation, and a relationship between the radiant temperature asymmetry and the number of subjects feeling dissatisfied was established (Figure 9). Radiant asymmetry, as defined in the section on Environmental Parameters, is the difference in radiant temperature of the environment on opposite sides of the person. More precisely, radiant asymmetry is the difference in radiant temperatures seen by a small flat element looking in opposite directions.

Figure 9 shows that people are more sensitive to asymmetry caused by an overhead warm surface than by a vertical cold surface. The influence of an overhead cold surface or a vertical warm surface is much less. These data are particularly important when using radiant panels to provide comfort in spaces with large cold surfaces or cold windows.

Loveday et al. (1998) used a series of controlled climate chamber studies to establish the design conditions required for thermal comfort for sedentary subjects conducting office work in combined chilled-ceiling and displacement ventilation environments. As part of this study, Hodder et al. (1998) found that the vertical radiant temperature asymmetry for the typical range of ceiling temperatures (71.6 to 54.5°F) encountered in practice in these combination environments had no effect on the overall thermal comfort of the seated occupants, and that existing guidance regarding toleration of radiant asymmetry in these environments remains valid.

Other studies of clothed persons in neutral environments found thermal acceptability unaffected by radiant temperature asymmetries of 18°F or less (Berglund and Fobelets 1987) and comfort unaffected by asymmetries of 36°F or less (McIntyre and Griffiths 1975).

Draft is an undesired local cooling of the human body caused by air movement. This is a serious problem, not only in many ventilated buildings but also in automobiles, trains, and aircraft. Draft has been identified as one of the most annoying factors in offices. When people sense draft, they often demand higher air temperatures in the room or that ventilation systems be stopped.

Fanger and Christensen (1986) aimed to establish the percentage of the population feeling draft when exposed to a given mean velocity. Figure 10 shows the percentage of subjects who felt draft on the head region (the dissatisfied) as a function of mean air velocity at the neck. The head region comprises head, neck, shoulders, and back. Air temperature significantly influenced the percentage of dissatisfied. There was no significant difference between responses of men and women. The data in Figure 10 apply only to persons wearing normal indoor clothing and performing light, mainly sedentary work. Persons with higher activity levels are not as sensitive to draft (Jones et al. 1986).

Figure 10. Percentage of People Dissatisfied as Function of Mean Air Velocity

A study of the effect of air velocity over the whole body found thermal acceptability unaffected in neutral environments by air speeds of 50 fpm or less (Berglund and Fobelets 1987). This study also found no interaction between air speed and radiant temperature asymmetry on subjective responses. Thus, acceptability changes and the percent dissatisfied because of draft and radiant asymmetry are independent and additive.

Fanger et al. (1989) investigated the effect of turbulence intensity on sensation of draft. Turbulence intensity significantly affects draft sensation, as predicted by the following model. This model can be used to quantify draft risk in spaces and to develop air distribution systems with a low draft risk.

(59)

where PD is percent dissatisfied and Tu is the turbulence intensity (in percent) defined by

(60)

For V < 9.8 fpm, insert V = 9.8, and for PD > 100%, insert PD = 100%. V_sd is the standard deviation of the velocity measured with an omnidirectional anemometer having a 0.2 s time constant.

The model extends the Fanger and Christensen (1986) draft chart model to include turbulence intensity. In this study, Tu decreases when V increases. Thus, the effects of V for the experimental data to which the model is fitted are 68 < t_a < 79°F, 10 < V < 100 fpm, and 0 < T_u < 70%. Figure 11 gives more precisely the curves that result from intersections between planes of constant T_u and the surfaces of PD = 15%.

At thermal conditions above neutrality, air movement can be beneficial for thermal comfort. Arens et al. (2009) found people prefer more air movement under some conditions in office spaces. Applications of this include ceiling fans and personal environmental control systems in offices and transportation systems.

In most buildings, air temperature normally increases with height above the floor. If the gradient is sufficiently large, local warm discomfort can occur at the head and/or cold discomfort can occur at the feet, although the body as a whole is thermally neutral. Among the few studies of vertical air temperature differences and the influence of thermal comfort reported are Eriksson (1975), McNair (1973), McNair and Fishman (1974), and Olesen et al. (1979). Subjects were seated in a climatic chamber and individually exposed to different air temperature differences between head and ankles (Olesen et al. 1979). During the tests, the subjects were in thermal neutrality because they were allowed to change the temperature level in the test room whenever they desired; the vertical temperature difference, however, was kept unchanged. Subjects gave subjective reactions to their thermal sensation; Figure 12 shows the percentage of dissatisfied as a function of the vertical air temperature difference between head (43 in. above the floor) and ankles (4 in. above the floor).

Figure 11. Draft Conditions Dissatisfying 15% of Population (PD = 15%)

Figure 12. Percentage of Seated People Dissatisfied as Function of Air Temperature Difference Between Head and Ankles

A head-level air temperature lower than that at ankle level is not as critical for occupants. Eriksson (1975) indicated that subjects could tolerate much greater differences if the head were cooler. This observation is verified in experiments with asymmetric thermal radiation from a cooled ceiling (Fanger et al. 1985).

Because of direct contact between the feet and the floor, local discomfort of the feet can often be caused by a too-high or too-low floor temperature. Also, floor temperature significantly influences a room’s mean radiant temperature. Floor temperature is greatly affected by building construction (e.g., insulation of the floor, above a basement, directly on the ground, above another room, use of floor heating, floors in radiant-heated areas). If a floor is too cold and the occupants feel cold discomfort in their feet, a common reaction is to increase the temperature level in the room; in the heating season, this also increases energy consumption. A radiant system, which radiates heat from the floor, can also prevent discomfort from cold floors.

The most extensive studies of the influence of floor temperature on foot comfort were performed by Olesen (1977a, 1977b), who, based on his own experiments and reanalysis of data from Nevins and Feyerherm (1967), Nevins and Flinner (1958), and Nevins et al. (1964), found that flooring material is important for people with bare feet (e.g., in swimming halls, gymnasiums, dressing rooms, bathrooms, bedrooms). Ranges for some typical floor materials are as follows:

To save energy, insulating flooring materials (cork, wood, carpets), radiant heated floors, or floor heating systems can be used to eliminate the desire for higher ambient temperatures caused by cold feet. These recommendations should also be followed in schools, where children often play directly on the floor.

For people wearing normal indoor footwear, flooring material is insignificant. Olesen (1977b) found an optimal temperature of 77°F for sedentary and 73.5°F for standing or walking persons. At the optimal temperature, 6% of occupants felt warm or cold discomfort in the feet. Figure 13 shows the relationship between floor temperature and percent dissatisfied, combining data from experiments with seated and standing subjects. In all experiments, subjects were in thermal neutrality; thus, the percentage of dissatisfied is only related to discomfort caused by cold or warm feet. No significant difference in preferred floor temperature was found between females and males.

Figure 13. Percentage of People Dissatisfied as Function of Floor Temperature

Fanger (1973) determined the preferred ambient temperature for each of a group of subjects under identical conditions on four different days. Because the standard deviation was only 1.0°F, Fanger concluded that comfort conditions for an individual can be reproduced and vary only slightly from day to day.

Because metabolism decreases slightly with age, many have stated that comfort conditions based on experiments with young and healthy subjects cannot be used for other age groups. Fanger (1982), Fanger and Langkilde (1975), Langkilde (1979), Nevins et al. (1966), and Rohles and Johnson (1972) conducted comfort studies in Denmark and the United States on different age groups (mean ages 21 to 84). The studies revealed that the thermal environments preferred by older people do not differ from those preferred by younger people. The lower metabolism in older people is compensated for by a lower evaporative loss. Collins and Hoinville (1980) confirmed these results.

The fact that young and old people prefer the same thermal environment does not necessarily mean that they are equally sensitive to cold or heat. In practice, the ambient temperature level in the homes of older people is often higher than that for younger people. This may be explained by the lower activity level of elderly people, who are normally sedentary for a greater part of the day.

Many believe that people can acclimatize themselves by exposure to hot or cold surroundings, so that they prefer other thermal environments. Fanger (1982) conducted experiments involving subjects from the United States, Denmark, and tropical countries. The latter group was tested in Copenhagen immediately after their arrival by plane from the tropics, where they had lived all their lives. Other experiments were conducted for two groups exposed to cold daily. One group comprised subjects who had been doing sedentary work in cold surroundings (in the meat-packing industry) for 8 h daily for at least 1 year. The other group consisted of winter swimmers who bathed in the sea daily.

Only slight differences in preferred ambient temperature and physiological parameters in the comfort conditions were reported for the various groups. These results indicate that people cannot adapt to preferring warmer or colder environments, and therefore the same comfort conditions can likely be applied throughout the world. However, in determining the preferred ambient temperature from the comfort equations, a clo-value corresponding to local clothing habits should be used, such as those given in Table 8 and in Havenith et al. (2015). A comparison of field comfort studies from different parts of the world shows significant differences in clothing habits depending on, among other things, outdoor climate (Nicol and Humphreys 1972). According to these results, adaptation has little influence on preferred ambient temperature. In uncomfortable warm or cold environments, however, adaptation often has an influence. People used to working and living in warm climates can more easily accept and maintain a higher work performance in hot environments than people from colder climates.

Fanger (1982), Fanger and Langkilde (1975), and Nevins et al. (1966) used equal numbers of male and female subjects, so comfort conditions for the two sexes can be compared. The experiments show that men and women prefer almost the same thermal environments. Women’s skin temperature and evaporative loss are slightly lower than those for men, and this balances the somewhat lower metabolism of women. The reason that women often prefer higher ambient temperatures than men may be partly explained by the lighter clothing often worn by women.

Because people cannot adapt to prefer warmer or colder environments, it follows that there is no difference between comfort conditions in winter and in summer. McNall et al. (1968) confirmed this in an investigation where results of winter and summer experiments showed no difference. On the other hand, it is reasonable to expect comfort conditions to alter during the day because internal body temperature has a daily rhythm, with a maximum late in the afternoon, and a minimum early in the morning.

In determining the preferred ambient temperature for each of 16 subjects both in the morning and in the evening, Fanger et al. (1974) and Ostberg and McNicholl (1973) observed no difference. Furthermore, Fanger et al. (1973) found only small fluctuations in preferred ambient temperature during a simulated 8 h workday (sedentary work). There is a slight tendency to prefer somewhat warmer surroundings before lunch, but none of the fluctuations are significant.

Fanger (1982) related comfort data to physiological variables. At a given level of metabolic activity M, and when the body is not far from thermal neutrality, mean skin temperature t_sk and sweat rate E_rsw are the only physiological parameters influencing heat balance. However, heat balance alone is not sufficient to establish thermal comfort. In the wide range of environmental conditions where heat balance can be obtained, only a narrow range provides thermal comfort. The following linear regression equations, based on data from Rohles and Nevins (1971), indicate values of t_sk and E_rsw that provide thermal comfort:

(61)

(62)

At higher activity levels, sweat loss increases and mean skin temperature decreases, both of which increase heat loss from the body core to the environment. These two empirical relationships link the physiological and heat flow equations and thermal comfort perceptions. By substituting these values into Equation (11) for C + R, and into Equations (17) and (18) for E_sk, Equation (1) (the energy balance equation) can be used to determine combinations of the six environmental and personal parameters that optimize comfort for steady-state conditions.

Fanger (1982) reduced these relationships to a single equation, which assumed all sweat generated is evaporated, eliminating clothing permeation efficiency i_cl as a factor in the equation. This assumption is valid for normal indoor clothing worn in typical indoor environments with low or moderate activity levels. At higher activity levels (M_act > 3 met), where a significant amount of sweating occurs even at optimum comfort conditions, this assumption may limit accuracy. The reduced equation is slightly different from the heat transfer equations developed here. The radiant heat exchange is expressed in terms of the Stefan-Boltzmann law (instead of using h_r), and diffusion of water vapor through the skin is expressed as a diffusivity coefficient and a linear approximation for saturated vapor pressure evaluated at t_sk. The combination of environmental and personal variables that produces a neutral sensation may be expressed as follows:

(63)

where

(64)

The values of h_c and f_cl can be estimated from tables and equations given in the section on Engineering Data and Measurements. Fanger used the following relationships:

(65)

(66)

Figures 14 and 15 show examples of how Equation (63) can be used.

Equation (63) is expanded to include a range of thermal sensations by using a predicted mean vote (PMV) index. The PMV index predicts the mean response of a large group of people according to the ASHRAE thermal sensation scale. Fanger (1970) related PMV to the imbalance between actual heat flow from the body in a given environment and the heat flow required for optimum comfort at the specified activity by the following equation:

(67)

where L is the thermal load on the body, defined as the difference between internal heat production and heat loss to the actual environment for a person hypothetically kept at comfort values of t_sk and E_rsw at the actual activity level. Thermal load L is then the difference between the left and right sides of Equation (63) calculated for the actual values of the environmental conditions. As part of this calculation, clothing temperature t_cl is found by iteration as   

(68)

Figure 14. Air Velocities and Operative Temperatures at 50% rh Necessary for Comfort (PMV = 0) of Persons in Summer Clothing at Various Levels of Activity

Figure 15. Air Temperatures and Mean Radiant Temperatures Necessary for Comfort (PMV = 0) of Sedentary Persons in Summer Clothing at 50% rh

After estimating the PMV with Equation (67) or another method, the predicted percent dissatisfied (PPD) with a condition can also be estimated. Fanger (1982) related the PPD to the PMV as follows:

(69)

where dissatisfied is defined as anybody not voting –1, +1, or 0. This relationship is shown in Figure 16. A PPD of 10% corresponds to the PMV range of ±0.5, and even with PMV = 0, about 5% of the people are dissatisfied.

The PMV-PPD model is widely used and accepted for design and field assessment of comfort conditions. ISO Standard 7730 includes a short computer listing that facilitates computing PMV and PPD for a wide range of parameters.

The PMV model is useful only for predicting steady-state comfort responses. The two-node model can be used to predict physiological responses or responses to transient situations, at least for low and moderate activity levels in cool to very hot environments (Gagge et al. 1971a, 1986). This model is a simplification of thermoregulatory models developed by Stolwijk and Hardy (1966). The simple, lumped parameter model considers a human as two concentric thermal compartments that represent the skin and the core of the body.

Figure 16. Predicted Percentage of Dissatisfied (PPD) as Function of Predicted Mean Vote (PMV)

The skin compartment simulates the epidermis and dermis and is about 1/16 in. thick. Its mass, which is about 10% of the total body, depends on the amount of blood flowing through it for thermoregulation. Compartment temperature is assumed to be uniform so that the only temperature gradients are between compartments. In a cold environment, blood flow to the extremities may be reduced to conserve the heat of vital organs, resulting in axial temperature gradients in the arms, legs, hands, and feet. Heavy exercise with certain muscle groups or asymmetric environmental conditions may also cause nonuniform compartment temperatures and limit the model’s accuracy.

All the heat is assumed to be generated in the core compartment. In the cold, shivering and muscle tension may generate additional metabolic heat. This increase is related to skin and core temperature depressions from their set point values, or

(70)

where BF is percentage body fat and the temperature difference terms are set to zero if they become negative (Tikusis and Giesbrecht 1999).

The core loses energy when the muscles do work on the surroundings. Heat is also lost from the core through respiration. The rate of respiratory heat loss depends on sensible and latent changes in respired air and the ventilation rate as in Equations (19) and (20).

In addition, heat is conducted passively from the core to the skin. This is modeled as a massless thermal conductor (K = 0.93 Btu/h · ft² · °F). A controllable heat loss path from the core consists of pumping variable amounts of warm blood to the skin for cooling. This peripheral blood flow Q_bl in L/h · ft² depends on skin and core temperature deviations from their respective set points:

(71)

The temperature terms can only be > 0. If the deviation is negative, the term is set to zero. For average persons, the coefficients BFN, c_dil, and S_tr are 0.585, 2.57, and 0.28. Further, skin blood flow Q_bl is limited to a maximum of 8.4 L/h · ft². A very fit and well-trained athlete could expect to have c_dil = 9.

Dry (sensible) heat loss q_dry from the skin flows through the clothing by conduction and then by parallel paths to the air and surrounding surfaces. Evaporative heat follows a similar path, flowing through the clothing and through the air boundary layer. Maximum evaporation E_max occurs if the skin is completely covered with sweat. The actual evaporation rate E_sw depends on the size w of the sweat film:

(72)

where w is E_rsw/E_max.

The rate of regulatory sweating E_rsw (rate at which water is brought to the surface of the skin in Btu/h · ft²) can be predicted by skin and core temperature deviations from their set points:

(73)

where t_b = (1 – α_sk) t_cr + α_skt_sk and is the mean body temperature, t_bset = 97.68°F, and c_sw = 20.43 Btu/h · ft² · °F. The temperature deviation terms are set to zero when negative. The fraction of the total body mass considered to be thermally in the skin compartment is α_sk:

(74)

Regulatory sweating Q_rsw in the model is limited to 0.1 L/h · ft² or 200 Btu/h · ft². E_rsw evaporates from the skin, but if E_rsw is greater than E_max , the excess drips off.

An energy balance on the core yields

(75)

and for the skin,

(76)

where c_cr, c_sk , and c_p,bl are specific heats of core, skin, and blood (0.83, 0.83, and 1.0 Btu/lb · °F, respectively), and SkBF is ρ_blQ_bl, where ρ_bl is density of blood (2.34 lb/L).

Equations (75) and (76) can be rearranged in terms of dt_sk/dθ and dt_cr/dθ and numerically integrated with small time steps (10 to 60 s) from initial conditions or previous values to find t_cr and t_sk at any time.

After calculating values of t_sk, t_cr, and w, the model uses empirical expressions to predict thermal sensation (TSENS) and thermal discomfort (DISC). These indices are based on 11-point numerical scales, where positive values represent the warm side of neutral sensation or comfort, and negative values represent the cool side. TSENS is based on the same scale as PMV, but with extra terms for ±4 (very hot/cold) and ±5 (intolerably hot/cold). Recognizing the same positive/negative convention for warm/cold discomfort, DISC is defined as

TSENS is defined in terms of deviations of mean body temperature t_b from cold and hot set points representing the lower and upper limits for the zone of evaporative regulation: t_b,c and t_b,h, respectively. The values of these set points depend on the net rate of internal heat production and are calculated by

(77)

(78)

TSENS is then determined by

(79)

where η_ev is the evaporative efficiency (assumed to be 0.85).

DISC is numerically equal to TSENS when t_b is below its cold set point t_b,c and it is related to skin wettedness when body temperature is regulated by sweating:

(80)

where E_{rsw , req} is calculated as in Fanger’s model, using Equation (62).

Unlike the two-node model, which represents the body as one cylinder with two nodes of core and skin, multisegment models divide the body into more segments (e.g., head, chest, hands, feet) and more tissue layers (e.g., core, muscle, fat, skin). They are intended to predict thermal physiology and thermal comfort in nonuniform [e.g., offices with displacement ventilation or underfloor air, radiant-cooled ceiling/floors, or natural and mixed-mode ventilation; personal environmental control (PEC) systems] and transient (e.g., occupants moving between different environments in offices, quick-responding PECs, automobiles) environments. Major multisegment physiological models include Fiala (1998), Fiala et al. (2003), Gordon (1974), Huizenga et al. (2001), Kraning and Gonzalez (1997), Smith (1991), Stolwijk (1971), Tanabe et al. (2002), Werner and Webb (1993), and Wissler (1964, 1985, 1988). These models mostly use finite-difference or finite-element methods, and include active thermoregulatory control in addition to passive heat transfer. They predict skin temperature for several local body segments, and central core temperature. They also predict other physiological parameters, such as segment sweat rate and skin wettedness, shivering, and cardiac blood flow.

Comfort is independently predicted from the output of physiological models. One comfort model, based on a review of literature addressing human sensation testing, uses an average of local skin temperatures and its time derivative to predict whole-body thermal sensation under stable and transient environments (Fiala 1998; Fiala et al. 2003). Another model uses the heat storage rate of the skin or core to predict whole-body thermal sensation under stable and transient environments (Wang 1994; Wang and Peterson 1992). The Berkeley comfort model predicts thermal sensation and comfort for each segment as well as for the whole body, using local skin temperatures, core temperature, and their time derivatives (Zhang 2003; Zhang et al. 2010a, 2010b, 2010c).

The equivalent homogeneous temperature (EHT) approach uses segmented electrical manikin measurements to determine the equivalent uniform environment for each body part (Nilsson 2007; Wyon et al. 1989). From these, comfortable environmental temperature ranges have been defined for each of the body segments. The EHT can determine comfort under nonuniform environments that are at steady state.

Adaptive models do not actually predict comfort responses but rather the almost constant conditions under which people are likely to be comfortable in buildings. In general, people naturally adapt and may also make various adjustments to themselves and their surroundings to reduce discomfort and physiological strain. It has been observed that, through adaptive actions, an acceptable degree of comfort in residences and offices is possible over a range of air temperatures from about 63 to 88°F (Humphreys and Nicol 1998).

Adaptive adjustments are typically conscious actions such as altering clothing, posture, activity schedules or levels, rate of working, diet, ventilation, air movement, and local temperature. They may also include unconscious longer-term changes to physiological set points and gains for control of shivering, skin blood flow, and sweating, as well as adjustments to body fluid levels and salt loss. However, only limited documentation and information on such changes is available.

An important driving force behind the adaptive process is the pattern of outdoor weather conditions and exposure to them. This is the principal input to adaptive models, which predict likely comfort temperatures t_c or ranges of t_c from monthly mean outdoor temperatures t_out. Humphreys and Nicol’s (1998) model is based on data from a wide range of buildings, climates, and cultures:

(81)

Adaptive models are useful to guide design and energy decisions, and to specify building temperature set points throughout the year. An ASHRAE-sponsored study (de Dear and Brager 1998) on adaptive models compiled an extensive database from field studies to study, develop, and test adaptive models. For climates and buildings where cooling and central heating are not required, the study suggests the following model:

(82)

where t_oc is the operative comfort temperature. The adaptive model boundary temperatures for 90% thermal acceptability are approximately t_oc+ 4.5°F and t_oc – 4°F according to ASHRAE Standard 55-2013.

In general, the value of using an adaptive model to specify set points or guide temperature control strategies is likely to increase with the freedom that occupants are given to adapt (e.g., by having flexible working hours, locations, or dress codes).

The Two-Node Model section shows that comfort and thermal sensation are not necessarily the same variable, especially for a person in the zone of evaporative thermal regulation. Figures 17 and 18 show this difference for the standard combination of met-clo-air movement used in the standard effective temperature ET*. Figure 17 demonstrates that practically all basic physiological variables predicted by the two-node model are functions of ambient temperature and are relatively independent of vapor pressure. All exceptions occur at relative humidities above 80% and as the isotherms reach the ET* = 107°F line, where regulation by evaporation fails. Figure 18 shows that lines of constant ET* and wettedness are functions of both ambient temperature and vapor pressure. Thus, human thermal responses are divided into two classes: those in Figure 17, which respond only to heat stress from the environment, and those in Figure 18, which respond to both heat stress from the environment and the resultant heat strain (Stolwijk et al. 1968).

For warm environments, any index with isotherms parallel to skin temperature is a reliable index of thermal sensation alone, and not of discomfort caused by increased humidity. Indices with isotherms parallel to ET* are reliable indicators of discomfort or dissatisfaction with thermal environments. For a fixed exposure time to cold, lines of constant t_sk, ET*, and t_o are essentially identical, and cold sensation is no different from cold discomfort. For a state of comfort with sedentary or light activity, lines of constant t_sk and ET* coincide. Thus, comfort and thermal sensations coincide in this region as well. The upper and lower temperature limits for comfort at these levels can be specified either by thermal sensation (Fanger 1982) or by ET*, as is done in ASHRAE Standard 55, because lines of constant comfort and lines of co0nstant thermal sensation should be identical.

Figure 17. Effect of Environmental Conditions on Physiological Variables

Figure 18. Effect of Thermal Environment on Discomfort

Effective temperature ET* is probably the most common environmental index, and has the widest range of application. It combines temperature and humidity into a single index, so two environments with the same ET* should evoke the same thermal response even though they have different temperatures and humidities, as long as they have the same air velocities.

The original empirical effective temperature was developed by Houghten and Yaglou (1923). Gagge et al. (1971a, 1971b) defined a new effective temperature using a rational approach. Defined mathematically in Equation (33), this is the temperature of an environment at 50% rh that results in the same total heat loss E_sk from the skin as in the actual environment.

Because the index is defined in terms of operative temperature t_o, it combines the effects of three parameters (t_r, t_a, and p_a) into a single index. Skin wettedness w and the permeability index i_m must be specified and are constant for a given ET* line for a particular situation. The two-node model is used to determine skin wettedness in the zone of evaporative regulation. At the upper limit of regulation, w approaches 1.0; at the lower limit, w approaches 0.06. Skin wettedness equals one of these values when the body is outside the zone of evaporative regulation. Because the slope of a constant ET* line depends on skin wettedness and clothing moisture permeability, effective temperature for a given temperature and humidity may depend on the person’s clothing and activity. This difference is shown in Figure 19. At low skin wettedness, air humidity has little influence, and lines of constant ET* are nearly vertical. As skin wettedness increases because of activity and/or heat stress, the lines become more horizontal and the influence of humidity is much more pronounced. The ASHRAE comfort envelope shown in Figure 5 is described in terms of ET*.

Because ET* depends on clothing and activity, it is not possible to generate a universal ET* chart. A standard set of conditions representative of typical indoor applications is used to define a standard effective temperature SET*, defined as the equivalent air temperature of an isothermal environment at 50% rh in which a subject, wearing clothing standardized for the activity concerned, has the same heat stress (skin temperature t_sk) and thermoregulatory strain (skin wettedness w) as in the actual environment.

The humid operative temperature t_oh is the temperature of a uniform environment at 100% rh in which a person loses the same total amount of heat from the skin as in the actual environment. This index is defined mathematically in Equation (32). It is analogous to ET*, except that it is defined at 100% rh and 0% rh rather than at 50% rh. Figures 2 and 19 indicate that lines of constant ET* are also lines of constant t_oh. However, the values of these two indices differ for a given environment.

Originally proposed by Belding and Hatch (1955), this rational index is the ratio of total evaporative heat loss E_sk required for thermal equilibrium (the sum of metabolism plus dry heat load) to maximum evaporative heat loss E_max possible for the environment, multiplied by 100, for steady-state conditions (S_sk and S_cr are zero) and with t_sk held constant at 95°F. The ratio E_sk/E_max equals skin wettedness w [Equation (18)]. When heat stress index (HSI) > 100, body heating occurs; when HSI < 0, body cooling occurs. Belding and Hatch (1955) limited E_max to 220 Btu/h · ft², which corresponds to a sweat rate of approximately 0.21 lb/h · ft². When t_sk is constant, loci of constant HSI coincide with lines of constant ET* on a psychrometric chart. Other indices based on wettedness have the same applications (Belding 1970; Gonzalez et al. 1978; ISO Standard 7933) but differ in their treatment of E_max and the effect of clothing. Table 12 describes physiological factors associated with HSI values.

Figure 19. Effective Temperature ET* and Skin Wettedness w [Adapted from Gonzalez et al. (1978) and Nishi et al. (1975)]

Skin wettedness w is the ratio of observed skin sweating E_sk to the E_max of the environment as defined by t_sk, t_a, humidity, air movement, and clothing in Equation (12). Except for the factor of 100, it is essentially the same as HSI. Skin wettedness is more closely related to the sense of discomfort or unpleasantness than to temperature sensation (Gagge et al. 1969a, 1969b; Gonzalez et al. 1978).

The WBGT is an environmental heat stress index that combines dry-bulb temperature t_db, a naturally ventilated (not aspirated) wet-bulb temperature t_nwb, and black globe temperature t_g, according to the relation (Dukes-Dobos and Henschel 1971, 1973)

(83)

This form of the equation is usually used where solar radiation is present. The naturally ventilated wet-bulb thermometer is left exposed to sunlight, but the air temperature t_a sensor is shaded. In enclosed environments, Equation (83) is simplified by dropping the t_a term and using a 0.3 weighting factor for t_g.

The black globe thermometer responds to air temperature, mean radiant temperature, and air movement, whereas the naturally ventilated wet-bulb thermometer responds to air humidity, air movement, radiant temperature, and air temperature. Thus, WBGT is a function of all four environmental factors affecting human environmental heat stress.

The WBGT index is widely used for estimating the heat stress potential of industrial environments (Davis 1976). In the United States, the National Institute of Occupational Safety and Health (NIOSH) developed criteria for a heat-stress-limiting standard (NIOSH 1986). ISO Standard 7243 also uses the WBGT. Figure 20 summarizes permissible heat exposure limits, expressed as working time per hour, for a fit individual, as specified for various WBGT levels. Values apply for normal permeable clothing (0.6 clo) and must be adjusted for heavy or partly vapor-permeable clothing. For example, the U.S. Air Force (USAF) recommended adjusting the measured WBGT upwards by 10°F for personnel wearing chemical protective clothing or body armor. This type of clothing increases resistance to sweat evaporation about threefold (higher if it is totally impermeable), requiring an adjustment in WBGT level to compensate for reduced evaporative cooling at the skin.

Several mathematical models are available for predicting WBGT from environmental factors: air temperature, psychrometric wet-bulb temperature, mean radiant temperature, and air motion (Azer and Hsu 1977; Sullivan and Gorton 1976).

Figure 20. Recommended Heat Stress Exposure Limits for Heat Acclimatized Workers [Adapted from NIOSH (1986)]

The WGT, introduced by Botsford (1971), is a simpler approach to measuring environmental heat stress than the WBGT. The measurement is made with a wetted globe thermometer called a Botsball, which consists of a 2.5 in. black copper sphere covered with a fitted wet black mesh fabric, into which the sensor of a dial thermometer is inserted. A polished stem attached to the sphere supports the thermometer and contains a water reservoir for keeping the sphere covering wet. This instrument is suspended by the stem at the site to be measured.

Onkaram et al. (1980) showed that WBGT can be predicted with reasonable accuracy from WGT for temperate to warm environments with medium to high humidities. With air temperatures between 68 and 95°F, dew points from 45 to 77°F (relative humidities above 30%), and wind speeds of 15 mph or less, the experimental regression equation (r = 0.98) in °F for an outdoor environment is

(84)

This equation should not be used outside the experimental range given because data from hot/dry desert environments show differences between WBGT and WGT that are too large (10°F and above) to be adjusted by Equation (84) (Matthew et al. 1986). At very low humidity and high wind, WGT approaches the psychrometric wet-bulb temperature, which is greatly depressed below t_a. However, in the WBGT, t_nwb accounts for only 70% of the index value, with the remaining 30% at or above t_a.

The wind chill index (WCI) is an empirical index developed from cooling measurements obtained in Antarctica on a cylindrical flask partly filled with water (Siple and Passel 1945). The index describes the rate of heat loss from the cylinder by radiation and convection for a surface temperature of 91.4°F, as a function of ambient temperature and wind velocity. As originally proposed,

(85)

where V and t_a are in mph and °F, respectively, and WCI units are kcal/(h · m²). Multiply WCI by 0.368 to convert to Btu/h · ft². The 91.4°F surface temperature was chosen to be representative of the mean skin temperature of a resting human in comfortable surroundings.

Some valid objections have been raised about this formulation. Cooling rate data from which it was derived were measured on a 2.24 in. diameter plastic cylinder, making it unlikely that WCI would be an accurate measure of heat loss from exposed flesh, which has different characteristics from plastic (curvature, roughness, and radiation exchange properties) and is invariably below 91.4°F in a cold environment. Moreover, values given by the equation peak at 56 mph, then decrease with increasing velocity.

Nevertheless, for velocities below 50 mph, this index reliably expresses combined effects of temperature and wind on subjective discomfort. For example, if the calculated WCI is less than 1400 and actual air temperature is above 14°F, there is little risk of frostbite during brief exposures (1 h or less), even for bare skin. However, at a WCI of 2000 or more, the probability is high that exposed flesh will begin to freeze in 1 min or less unless measures are taken to shield exposed skin (such as a fur ruff to break up wind around the face).

Rather than using the WCI to express the severity of a cold environment, meteorologists use an index derived from the WCI called the equivalent wind chill temperature t_eq, wc. This is the ambient temperature that would produce, in a calm wind (defined for this application as 4 mph), the same WCI as the actual combination of air temperature and wind velocity:

(86)

where t_eq,wc is in °F (and frequently referred to as a wind chill factor), thus distinguishing it from WCI, which is given either as a cooling rate or as a plain number with no units. For velocities less than 4 mph, Equation (86) does not apply, and the wind chill temperature is equal to the air temperature.

Equation (86) does not imply cooling to below ambient temperature, but recognizes that, because of wind, the cooling rate is increased as though it were occurring at the lower equivalent wind chill temperature. Wind accelerates the rate of heat loss, so that the skin surface cools more quickly toward the ambient temperature. Table 13 shows a typical wind chill chart, expressed in equivalent wind chill temperature.

Optical and thermal properties of skin must be considered in studies of the effects of infrared radiation in (1) producing changes in skin temperature and skin blood flow, and (2) evoking sensations of temperature and comfort (Hardy 1961). Although the body can be considered to have the properties of water, thermal sensation and heat transfer with the environment require a study of the skin and its interaction with visible and infrared radiation.

Figure 21. Variation in Skin Reflection and Absorptivity for Blackbody Heat Sources

Figure 21 shows how skin reflectance and absorptance vary for a blackbody heat source at the temperature (in °R) indicated. These curves show that darkly pigmented skin is heated more by direct radiation from a high-intensity heater at 4500°R than is lightly pigmented skin. With low-temperature, low-intensity heating equipment used for total area heating, there is minimal, if any, difference. Also, in practice, clothing minimizes differences.

Changes in skin temperature caused by high-intensity infrared radiation depend on the thermal conductivity, density, and specific heat of living skin (Lipkin and Hardy 1954). Modeling skin heating with the heat transfer theory yields a parabolic relation between exposure time and skin temperature rise for nonpenetrating radiation:

(87)

where

Figure 22. Comparing Thermal Inertia of Fat, Bone, Moist Muscle, and Excised Skin to That of Leather and Water

Product kρ c_p is the physiologically important quantity that determines temperature elevation of skin or other tissue on exposure to nonpenetrating radiation. Fatty tissue, because of its relatively low specific heat, is heated more rapidly than moist skin or bone. Experimentally, kρ c_p values can be determined by plotting Δt² against 1.13J ² θ (Figure 22). The relationship is linear, and the slopes are inversely proportional to the kρ c_p of the specimen. Comparing leather and water with body tissues suggests that thermal inertia values depend largely on tissue water content.

Living tissues do not conform strictly to this simple mathematical formula. Figure 23 compares excised skin with living skin with normal blood flow, and skin with blood flow occluded. For short exposure times, the kρ c_p of normal skin is the same as that in which blood flow has been stopped; excised skin heats more rapidly because of unavoidable dehydration that occurs postmortem. However, with longer exposure to thermal radiation, vasodilation increases blood flow, cooling the skin. For the first 20 s of irradiation, skin with normally constricted blood vessels has a kρ c_p value one-fourth that for skin with fully dilated vessels.

Skin temperature is the best single index of thermal comfort. The most rapid changes in skin temperature occur during the first 60 s of exposure to infrared radiation. During this initial period, thermal sensation and the heating rate of the skin vary with the quality of infrared radiation (color temperature in °R). Because radiant heat from a gas-fired heater is absorbed at the skin surface, the same unit level of absorbed radiation during the first 60 s of exposure can cause an even warmer initial sensation than penetrating solar radiation. Skin heating curves tend to level off after a 60 s exposure (Figure 23), which means that a relative balance is quickly created between heat absorbed, heat flow to the skin surface, and heat loss to the ambient environment. Therefore, the effects of radiant heating on thermal comfort should be examined for conditions approaching thermal equilibrium.

Figure 23. Thermal Inertias of Excised, Bloodless, and Normal Living Skin

Stolwijk and Hardy (1966) described an unclothed subject’s response for a 2 h exposure to temperatures of 41 to 95°F. Nevins et al. (1966) showed a relation between ambient temperatures and thermal comfort of clothed, resting subjects. For any given uniform environmental temperature, both initial physiological response and degree of comfort can be determined for a subject at rest.

Physiological implications for radiant heating can be defined by two environmental temperatures: (1) mean radiant temperature t_r and (2) ambient air temperature t_a. For this discussion on radiant heat, assume that (1) relative humidity is less than 50%, and (2) air movement is low and constant, with an equivalent convection coefficient of 0.51 Btu/h · ft² · °F.

The equilibrium equation, describing heat exchange between skin surface at mean temperature t_sk and the radiant environment, is given in Equation (28), and can be transformed to give (see Table 2)

(88)

where M′ is the net heat production (M – W) less respiratory losses.

By algebraic transformation, Equation (88) can be rewritten as

(89)

where ERF = h_r( – t_a) is the effective radiant field and represents the additional radiant exchange with the body when ≠ t_a.

The last term in Equation (89) describes heat exchange with an environment uniformly heated to temperature t_a. The term h_r, evaluated in Equation (35), is also a function of posture, for which factor A_r /A_D can vary from 0.67 for crouching to 0.73 for standing. For preliminary analysis, a useful value for h_r is 0.83 Btu/h · ft² · °F, which corresponds to a normally clothed (at 75°F) sedentary subject. Ambient air movement affects h_c, which appears only in the right-hand term of Equation (89).

Although the linear radiation coefficient h_r is used in Equations (88) and (89), the same definition of ERF follows if the fourth power radiation law is used. By this law, assuming emissivity of the body surface is unity, the ERF term in Equation (89) is

(90)

where σ is the Stefan-Boltzmann constant, 0.1712 × 10⁻⁸ Btu/h ·  ft² · °R⁴.

Because t̄_r equals the radiation of several surfaces at different temperatures (T₁, T₂, . . . , T_j),

(91)

where

ERF is the sum of the fields caused by each surface T_j [e.g., T₁ may be an infrared beam heater; T₂, a heated floor; T₃, a warm ceiling; T₄, a cold plate glass window (T₄ < T_a); etc.]. Only surfaces with T_j differing from T_a contribute to the ERF.

The comfort equation for radiant heat (Gagge et al. 1967a, 1967b) follows from definition of ERF and Equation (8):

(92)

Thus, operative temperature for comfort is the temperature of the ambient air plus a temperature increment ERF/h, a ratio that measures the effectiveness of the incident radiant heating on occupants. Higher air movement (which increases the value of h or h_c) reduces the effectiveness of radiant heating systems. Clothing lowers t_o for comfort and for thermal neutrality.

Values for ERF and h must be determined to apply the comfort equation for radiant heating. Table 3 may be used to estimate h. One method of determining ERF is to calculate it directly from radiometric data that give (1) radiation emission spectrum of the source, (2) concentration of the beam, (3) radiation from the floor, ceiling, and windows, and (4) corresponding angle factors involved. This analytical approach is described in Chapter 54 of the 2019 ASHRAE Handbook—HVAC Applications.

For direct measurement, a black globe, 6 in. in diameter, can measure the radiant field ERF for comfort, by the following relation:

(93)

where t_g is uncorrected globe temperature in °F and V is air movement in fpm. The average value of A_r/A_D is 0.7. For a black globe, ERF must be multiplied by α for the exposed clothing/skin surface. For a subject with 0.6 to 1.0 clo, t_o for comfort should agree numerically with t_a for comfort in Figure 5. When t_o replaces t_a in Figure 5, humidity is measured in vapor pressure rather than relative humidity, which refers only to air temperature.

Other methods may be used to measure ERF. The most accurate is by physiological means. In Equation (89), when M, t_sk – t_a, and the associated transfer coefficients are experimentally held constant,

(94)

The variation in evaporative heat loss E (rate of weight loss) caused by changing the wattage of two T-3 infrared lamps is a measure in absolute terms of the radiant heat received by the body.

A third method uses a directional radiometer to measure ERF directly. For example, radiation absorbed at the body surface (in Btu/h · ft²) is

(95)

where irradiance J can be measured by a directional (Hardy-type) radiometer, α is the surface absorptance effective for the source used, and A_i is the projection area of the body normal to the directional irradiance. Equation (95) can be used to calculate ERF only for the simplest geometrical arrangements. For a human subject lying supine and irradiated uniformly from above, A_i/A_D is 0.3. Figure 21 shows variance of α for human skin with blackbody temperature (in °R) of the radiating source. When irradiance J is uneven and coming from many directions, as is usually the case, the previous physiological method can be used to obtain an effective A_i/A_D from the observed ΔE and Δ(α J ).

Because of the large interpersonal variability in thermal requirements, some occupants in any uniformly conditioned environment will be too warm at the same time as others are too cool. The ASHRAE 80% acceptability criterion reflects this physiological constraint. Only environments that respond to individual preferences are capable of thermally satisfying all occupants (Bauman et al. 1998). Such occupant-specific microenvironments may be conditioned with low energy input because their aggregate volume is smaller than the total space volume, and because heating or cooling the occupants themselves may be more energy efficient than space conditioning. Such designs require attention to the thermal sensitivities of different parts of the human body and to the physical properties of its microenvironment.

In warm conditions, the comfort of the head and hands dictates a person’s overall discomfort; in cool conditions, the feet and hands dictate overall discomfort (Arens et al. 2006; Zhang 2003). Keeping the feet and hands warm is necessary to prevent discomfort from vasoconstriction in the limbs. However in warm conditions, the hands and wrists are important heat dissipaters, and cooling them is important. Arens et al. (2006) and Zhang (2003) suggest that a personal environmental control (PEC) system, also called task-ambient conditioning (TAC) or personal ventilation (PV) systems, that focuses directly on these body parts may offer an energy-efficient means for improving comfort in office environments.

PEC fan systems using either recirculated room air or outdoor air can provide comfort and improve perceived air quality (Amai et al. 2007; Arens et al. 2008, 2011; Dygert and Dang 2011; Melikov 2003; Russo and Khalifa 2011; Sekhar et al. 2005; Tham and Willem 2004; Yang et al. 2009, 2010; Zhang et al. 2010d). Air quality can also be improved, because fan flows above 60 fpm disrupt the body’s thermal plume that carries pollutants upward to the breathing zone (Arens et al. 2008, 2011).

Using air movement for cooling has constraints. Strong airflow directed at the eyes might cause dry-eye discomfort and should be avoided (Melikov et al. 2011). However, a large percentage of office occupants in neutral and warm conditions prefer an increase in available air movement (Arens et al. 2009). A recent study of hemoglobin levels showed that air movement also reduces fatigue (Nishihara and Tanabe 2011; Tanabe and Nishihara 2004).

Foot heating is usually done by radiant heating or through contact with a heated surface. Efficiency of these systems depends greatly on confining the heating to the body surfaces without too much loss to the surrounding air.

Hands and wrists may both be heated and cooled by contact with conductive surfaces. Wrist cooling may not require actively cooled surfaces, because the skin is almost always at a higher temperature than surfaces in a normal environment.

Some researchers suggest that a PEC system can be part of an energy-saving strategy (Hoyt et al. 2009; Zhang et al. 2011) by keeping occupants comfortable while allowing the surrounding spaces to be less conditioned (Figure 24). The success of this strategy also depends on the length of time occupants are away from the PEC zone. Once steady state is reached, the change of sensations when moving from a comfortable environment to one less comfortable is much slower than the change on returning to comfortable conditions (Zhang et al. 2010a). For example, 10-min excursions climbing stairs were judged comfortable throughout, despite an 82°F stairwell temperature, whereas 15-min excursions climbing stairs became uncomfortable; occupants judged their status comfortable/acceptable within 30 s of returning to the PEC zone.

Tolerance limits to high temperature vary with the ability to (1) sense temperature, (2) lose heat by regulatory sweating, and (3) move heat from the body core by blood flow to the skin surface, where cooling is the most effective. many interrelating processes are involved in heat stress (Figure 25).

Skin surface temperatures of 113°F trigger pain receptors in the skin; direct contact with metal at this temperature is painful. However, because thermal insulation of the air layer around the skin is high, much higher dry-air temperatures can be tolerated (e.g., 185°F for brief periods in a sauna). For lightly clothed subjects at rest, tolerance times of nearly 50 min have been reported at 180°F db; 33 min at 200°F; 26 min at 220°F; and 24 min at 240°F. In each case, dew points were lower than 86°F. Short exposures to these extremely hot environments are tolerable because of cooling by sweat evaporation. However, when ambient vapor pressure approaches 0.87 psi (97°F dp, typically found on sweating skin), tolerance is drastically reduced. Temperatures of 122°F can be intolerable if the dew-point temperature is greater than 77°F, and both deep body temperature and heart rate rise within minutes (Gonzalez et al. 1978).

The rate at which and length of time a body can sweat are limited. The maximum rate of sweating for an average man is about 4 lb/h. If all this sweat evaporates from the skin surface under conditions of low humidity and air movement, maximum cooling is about 214 Btu/h · °F. However, because sweat rolls off the skin surface without evaporative cooling or is absorbed by or evaporated within clothing, a more typical cooling limit is 6 met (10 Btu/h · ft²), representing approximately 2.2 lb/h of sweating for the average man.

Figure 24. Recommended Temperature Set Points for HVAC with PEC Systems and Energy Savings from Extending HVAC Temperature Set Points [Based on Hoyt et al. (2009) and Zhang et al. (2011)]

Thermal equilibrium is maintained by dissipation of resting heat production (1 met) plus any radiant and convective load. If the environment does not limit heat loss from the body during heavy activity, decreasing skin temperature compensates for the core temperature rise. Therefore, mean body temperature is maintained, although the gradient from core to skin is increased. Blood flow through the skin is reduced, but muscle blood flow necessary for exercise is preserved. The upper limit of skin blood flow is about 200 lb/h (Burton and Bazett 1936).

Body heat storage of 318 Btu (or a rise in t_b of 2.5°F) for an average-sized man represents an average voluntary tolerance limit. Continuing work beyond this limit increases the risk of heat exhaustion. Collapse can occur at about 635 Btu of storage (5°F rise); few individuals can tolerate heat storage of 872 Btu (6.8°F above normal).

The cardiovascular system affects tolerance limits. In normal, healthy subjects exposed to extreme heat, heart rate and cardiac output increase in an attempt to maintain blood pressure and supply of blood to the brain. At a heart rate of about 180 bpm, the short time between contractions prevents adequate blood supply to the heart chambers. As heart rate continues to increase, cardiac output drops, causing inadequate convective blood exchange with the skin and, perhaps more important, inadequate blood supply to the brain. Victims of this heat exhaustion faint or black out. Accelerated heart rate can also result from inadequate venous return to the heart caused by blood pooling in the skin and lower extremities. In this case, cardiac output is limited because not enough blood is available to refill the heart between beats. This occurs most frequently when an overheated individual, having worked hard in the heat, suddenly stops working. The muscles no longer massage the blood back past the valves in the veins toward the heart. Dehydration compounds the problem by reducing fluid volume in the vascular system.

If core temperature t_cr increases above 106°F, critical hypothalamic proteins can be damaged, resulting in inappropriate vasoconstriction, cessation of sweating, increased heat production by shivering, or some combination of these. Heat stroke damage is frequently irreversible and carries a high risk of death.

Another problem, hyperventilation, occurs mainly in hot/wet conditions, when too much CO₂ is washed from the blood. This can lead to tingling sensations, skin numbness, and vasoconstriction in the brain with occasional loss of consciousness.

Figure 25. Schematic Design of Heat Stress and Heat Disorders [Modified by Buskirk (1960) from scale diagram by Belding (1967) and Leithead and Lind (1964)]

Because a rise in heart rate or rectal temperature is essentially linear with ambient vapor pressure above a dew point of 77°F, these two changes can measure severe heat stress. Although individual heart rate and rectal temperature responses to mild heat stress vary, severe heat stress saturates physiological regulating systems, producing uniform increases in heart rate and rectal temperature. In contrast, sweat production measures stress under milder conditions but becomes less useful under more severe stress. The maximal sweat rate compatible with body cooling varies with (1) degree of heat acclimatization, (2) duration of sweating, and (3) whether the sweat evaporates or merely saturates the skin and drips off. Total sweat rates over 4.4 lb/h can occur in short exposures, but about 2.2 lb/h is an average maximum sustainable level for an acclimatized man.

Figure 26 shows the decline in heart rate, rectal temperature, and skin temperature when exercising subjects are exposed to 104°F over a period of days. Acclimatization can be achieved by working in the heat for 100 min each day: 30% improvement occurs after the first day, 50% after 3 days, and 95% after 6 or 7 days. Increased sweat secretion while working in the heat can be induced by rest. Although reducing salt intake during the first few days in the heat can conserve sodium, heat cramps may result. Working regularly in the heat improves cardiovascular efficiency, sweat secretion, and sodium conservation. Once induced, heat acclimatization can be maintained by as little as one workout a week in the heat; otherwise, it diminishes slowly over a 2- to 3-week period and disappears.

Human performance in extreme cold ultimately depends on maintaining thermal balance. Subjective discomfort is reported by a 154 lb man with 19.4 ft² of body surface area when a heat debt of about 100 Btu is incurred. A heat debt of about 600 Btu is acutely uncomfortable; this represents a drop of approximately 4.7°F (or about 7% of total heat content) in mean body temperature.

This loss can occur during 1 to 2 h of sedentary activity outdoors. A sleeping individual will wake after losing about 300 Btu, decreasing mean skin temperature by about 5.5°F and deep body temperature by about 1°F. A drop in deep body temperature (e.g., rectal temperature) below 95°F threatens a loss of body temperature regulation, and 82.4°F is considered critical for survival, despite recorded survival from a deep body temperature of 64.4°F.

Figure 26. Acclimatization to Heat Resulting from Daily Exposure of Five Subjects to Extremely Hot Room (Robinson et al. 1943)

Activity level also affects human performance. Subjective sensations reported by sedentary subjects at a mean skin temperature of 92°F are comfortable; at 88°F, uncomfortably cold; at 86°F, shivering cold; and at 84°F, extremely cold. The critical subjective tolerance limit (without numbing) for mean skin temperature appears to be about 77°F. However, during moderate to heavy activity, subjects reported the same skin temperatures as comfortable. Although mean skin temperature is significant, the temperature of the extremities is more frequently the critical factor for comfort in the cold. Consistent with this, one of the first responses to cold exposure is vasoconstriction, which reduces circulatory heat input to the hands and feet. A hand-skin temperature of 68°F causes a report of uncomfortably cold; 59°F, extremely cold; and 41°F, painful. Identical verbal responses for the foot surface occur at approximately 2.7 to 3.5°F warmer temperatures.

An ambient temperature of −30°F is the lower limit for useful outdoor activity, even with adequate insulative clothing. At −60°F, almost all outdoor effort becomes exceedingly difficult; even with appropriate protective equipment, only limited exposure is possible. Reported exposures of 30 min at −103°F have occurred in the Antarctic without injury.

In response to extreme heat loss, maximal heat production becomes very important. When the less-efficient vasoconstriction cannot prevent body heat loss, shivering is an automatic, more efficient defense against cold. This can be triggered by low deep body temperature, low skin temperature, rapid change of skin temperature, or some combination of all three. Shivering is usually preceded by an imperceptible increase in muscle tension and by noticeable gooseflesh produced by muscle contraction in the skin. It begins slowly in small muscle groups, initially increasing total heat production by 1.5 to 2 times resting levels. As body cooling increases, the reaction spreads to additional body segments. Ultimately violent, whole-body shivering causes maximum heat production of about 6 times resting levels, rendering the individual totally ineffective.

Given sufficient cold exposure, the body undergoes changes that indicate cold acclimatization. These physiological changes include (1) endocrine changes (e.g., sensitivity to norepinephrine), causing nonshivering heat production by metabolism of free fatty acids released from adipose tissue; (2) improved circulatory heat flow to skin, causing an overall sensation of greater comfort; and (3) improved circulatory heat flow to the extremities, reducing the risk of injury and allowing activities at what ordinarily would be severely uncomfortable temperatures in the extremities. Generally, these physiological changes are minor and are induced only by repeated extreme exposures. Nonphysiological factors, including training, experience, and selection of adequate protective clothing, are more useful and may be safer than dependence on physiological changes.

Food energy intake requirements for adequately clothed subjects in extreme cold are only slightly greater than those for subjects living and working in temperate climates. This greater requirement results from added work caused by (1) carrying the weight of heavy clothing (energy cost for heavy protective footwear may be six times that of an equivalent weight on the torso); and (2) the inefficiency of walking in snow, snowshoeing, or skiing, which can increase energy cost up to 300%.

To achieve proper protection in low temperatures, a person must either maintain high metabolic heat production by activity or reduce heat loss by controlling the body’s microclimate with clothing. Other protective measures include spot radiant heating, showers of hot air for work at a fixed site, and warm-air-ventilated or electrically heated clothing. Extremities (e.g., fingers and toes) are at greater risk than the torso because, as thin cylinders, they are particularly susceptible to heat loss and difficult to insulate without increasing the surface for heat loss. Vasoconstriction can reduce circulatory heat input to extremities by over 90%.

Although there is no ideal insulating material for protective clothing, radiation-reflective materials are promising. Insulation is primarily a function of clothing thickness; the thickness of trapped air, rather than fibers used, determines insulation effectiveness.

Protection for the respiratory tract seems unnecessary in healthy individuals, even at −50°F. However, asthmatics or individuals with mild cardiovascular problems may benefit from a face mask that warms inspired air. Masks are unnecessary for protecting the face because heat to facial skin is not reduced by local vasoconstriction, as it is for hands. If wind chill is great, there is always a risk of cold injury caused by freezing of exposed skin. Using properly designed torso clothing, such as a parka with a fur-lined hood to minimize wind penetration to the face, and 35 Btu/h of auxiliary heat to each hand and foot, inactive people can tolerate −67°F with a 10 mph wind for more than 6 h. As long as the skin temperature of fingers remains above 60°F, manual dexterity can be maintained and useful work performed without difficulty.