N. London (Moscow)

An Attempt to Establish the Equivalence of Radiation and Convective Heat on the Basis of the Thermal Sensations They Produce¹

From the Department of Industrial Hygiene, Institute of Labor Protection (Director: T. I. Dmitrishen; Head of Department: Z. I. Izraelson)

Establishing standards for the meteorological conditions in hot workshops is extremely difficult in the absence of integrated indices characterizing those conditions, specifically air temperature and radiation. This creates a need to develop a scale of equivalent effective temperatures. For this purpose, as well as for heating and ventilation calculations, it is first necessary to establish the equivalent relationship between the thermal effects of radiant heat and air temperature.

The aim of the present study was to establish this relationship for certain typical cases of practical importance.

¹ The study was conducted with the participation of O. V. Milovanova.

We compared five combinations of air temperature (from 11 to 16°) and radiation (from 0 to 1.3 g-cal/cm² per minute) on the basis of thermal sensation and objective hygienic indicators.

In two dark experimental chambers, each subject was exposed in turn for 60–70 minutes to a meteorological environment that was predominantly convective in one case and predominantly radiative in the other. Both subjective and objective physiological indicators were systematically measured.

Air temperature was measured with paired thermometers and Assmann instruments. Radiation intensity was determined with a Kalitin actinometer; at low intensities, a paired thermometer was used, together with a paired katathermometer as a check. The subjects’ skin and body temperatures (in both irradiated and unirradiated regions), pulse rate, and thermal sensations were recorded. Seven grades of thermal sensation were distinguished: “comfortable,” “pleasantly warm,” “pleasantly cool,” “cool,” “warm,” “cold,” and “hot.” Conditions were considered equivalent in thermal sensation when the ratings either coincided completely or differed by less than one grade within the five grades excluding “cold” and “hot.”

Skin and wall temperatures were determined mainly with a thermoelectric apparatus. In the chamber where convective environments were produced, this apparatus consisted of 4 copper–constantan elements; in the chamber where predominantly radiative environments were produced, it consisted of 11. The elements were connected in turn by a switch to a mirror galvanometer.

The thermocouples used to measure air temperature in the layers of clothing consisted of celluloid rings, with constantan and copper wires (0.1 mm in diameter) stretched across their diameters. The junction was at the center of the ring. To measure the surface temperature of clothing, perforated disks 12 mm in diameter were used, with the thermocouple wire attached to them. Experience showed that wall surface temperature is best measured with simple, unsupported wires secured by strips of adhesive plaster. The wires lie against the surface for a length equal to 250 wire diameters (approximately 5–6 cm). This ensures accurate measurements.

The radiation source was a 500 W, 120 V resistance heater with a reflector. Radiation intensity was measured three times at each of three points, both before and after the experiment: at shoulder level, at the middle of the back (at the lower edge of the shoulder blades), and at seat level.

The experiments were conducted on four subjects aged 17 to 36. One had worked as a baker for five years; the others were students who had not worked in hot workshops.

The subjects’ clothing consisted of a gray cotton shirt worn next to the skin, trousers, socks, and low leather shoes. In a small proportion of the experiments, the subjects also wore an undershirt. During the experiment, the subject remained seated and performed light work (reading a newspaper or a popular book).

Under continuous bilateral irradiation in the range from 0.34 to 0.86 g-cal/cm² per minute, the thermal effect of 0.1 g-cal/cm² per minute is equivalent to a change of 1.8° in the temperature of the air and walls.¹

Conditions equivalent in thermal sensation were characterized in the experiments by similar, but not entirely identical, objective indicators. In particular, radiative environments produced a lower skin temperature on the forehead than on other parts of the body, and a somewhat increased pulse rate. This is explained by the fact that the forehead was not irradiated and, under the radiative conditions, was exposed to colder air than under the convective conditions. The rise in body temperature and increase in pulse rate suggest that the amount of compensatory heat supplied by radiation to produce an equivalent thermal sensation exceeds that required to maintain the same thermal balance of the body (resulting in greater heat accumulation).

Under continuous three-sided irradiation of the torso (back and sides) in the range from 0.35 to 0.9 g-cal, the thermal effect of 0.1 g-cal

¹ For lack of space, all summaries of the experimental results, tables, and graphs of equivalent sensations have been omitted.

…of thermal radiation is equivalent, in terms of thermal sensation, to a change of 2.8° in the temperature of the air and walls.

In this case, too, irradiation produced a lower skin temperature on the forehead than on other parts of the body, as well as an increased pulse rate.

In the third series of experiments, alternate irradiation of the back and sides was tested. Every 3–5 minutes, the subject changed position relative to the radiation source, turning first the back and then a side toward it. Here it proved possible to raise the upper limit of radiation intensity at which an equivalent could be obtained to 1.3 g-cal.

At temperatures below 14°, however, the legs had to be insulated; otherwise, the subject experienced a mixed thermal sensation, making it impossible to establish an equivalent.

Within the range of 0.3 to 1.3 g-cal, the thermal effect of 0.1 g-cal of radiation proved equivalent to a change of 0.65° in the temperature of the walls and air. In other words, the thermal sensation remains unchanged if the ratio between changes in air temperature, expressed in degrees, and irradiation, expressed in tenths of a g-cal, equals 0.65.

Objective physiological measures, as well as the temperature of the clothing and the area beneath it, yield higher readings under predominantly radiative conditions than under predominantly convective conditions.

Thus, all three series of experiments indicate that thermal-sensation equivalents underestimate the heat load due to radiation.

At the low air temperature that prevented an equivalent from being established without insulating the legs, preventing the legs from cooling led to a perceptible increase in the equivalent (0.8° instead of 0.65°). It follows that workers wearing gaiters and exposed to prolonged irradiation can feel quite comfortable at low temperatures, provided that the degree of air heating and the irradiation correspond to the equivalents given above.

As the foregoing shows, the first two series of experiments were conducted with continuous irradiation of the same surface of the body. In the third series, the back, one side, and then the other side were successively exposed to continuous irradiation. A comparison of the equivalents obtained in the third series with those found in the preceding two series shows that periodically shifting the radiation flux from one part of the body surface to another substantially reduces the thermal-sensation equivalent.

In the first two series of experiments, we assumed that the air temperature in both chambers differed only insignificantly from the wall temperature. This assumption is justified only for the chamber in which most of the convective conditions were produced, which was surrounded on all sides by heated rooms. The chamber in which the radiative conditions were produced, however, has one wall exposed to the outdoors. Here the walls may be cooled below or heated above the air temperature. Indeed, in the third series of experiments the wall temperature was in most cases 0.5 to 3.3° higher than the air temperature, apparently because some of the radiation fell on the walls. When convective conditions are produced in this chamber, on the other hand, the walls are generally cooler than the air by 0.5–2.4°, depending on the outdoor temperature and the method of heating the air. Apparently,

The explanation must be sought in the fact that the walls warm up more slowly than the air.

It was then necessary to take into account the relative importance of the air and the walls for thermal sensation.

According to American experiments, thermal sensation may be taken to remain unchanged if the ratio of the changes in air temperature and enclosure temperature lies between 1.1 and 1.25. On this basis, we assumed that air and walls have equal effects on thermal sensation and calculated the equivalent using the arithmetic mean of their temperatures.

For the third series of experiments, this resulted in a 10% reduction in the equivalent compared with the value calculated on the basis of air temperature alone.

For the first and second series, the necessary corrections for wall temperature are smaller, since one wall warmed up less than the others; this partly compensated for any possible increase in the heating of the latter.

The fourth series of experiments was conducted with irradiation from all sides. In one of the chambers, a panel of incandescent lamps was switched on, thereby irradiating the subject from three sides at an intensity of 0.15–0.71 g-cal/cm² per minute. From the fourth side, the subject was irradiated at the same intensity by a reflector stove. In the other chamber, predominantly convective meteorological conditions equivalent in thermal sensation were created.

In this series, calculation of the equivalent in terms of air temperature yielded a value of 5.4° per 0.1 g-cal/cm² per minute. Since the walls of the chamber in which the radiative conditions were created were heated by radiation from the lamps, corresponding corrections had to be introduced. These reduced the value of the equivalent to 4.9° per 0.1 g-cal.

No significant differences were found in skin temperature, increase in pulse rate, or increase in body heat content between convective and radiative conditions. The temperature of the warmed air, however, was higher under radiative conditions. The same was true of the temperature of the outer surface of the clothing: under radiative conditions it was higher by an average of 3.2° (2.2–4.3°).

Thus, in all four series of experiments, conditions equivalent in thermal sensation yielded objective measures that were similar but did not coincide entirely. In the first two series, exposure to radiation produced higher objective physiological measures; in the third, the measures of the personal microclimate were also higher; and in the fourth, only those of the personal microclimate were higher. Apparently, the increased heat load under radiation is moderated by factors acting in the opposite direction: the lower temperature of the inhaled air and of the air flowing over the exposed skin surfaces. It may also play some part that radiation, penetrating into the body, does not act directly on the skin receptors.

It follows that, under nonuniform irradiation, assessment by thermal sensation yields a lower equivalent for radiation than assessment by objective physiological measures. Uniform irradiation produces closer agreement between objective and subjective physiological measures.

It should be emphasized that meteorological conditions equivalent in thermal sensation produce sensations that are only similar, not identical. In stating that the conditions are equally

…equally warm or equally cool, two of the four subjects rated the radiant conditions as more pleasant. One of them emphasized the feeling of stuffiness under convective conditions, while the other noted the freshness of the air and the pleasant warmth of the radiant conditions (“pleasantly warming”). The other two subjects preferred the convective conditions as “calmer.” When the temperature under convective conditions was around 35°, all subjects preferred the radiant conditions. If the temperature under the latter fell below 15°, they became unpleasant because of cold feet; however, warming the legs with gaiters eliminated this sensation, and the subjects preferred the radiant conditions.

It is clear from the foregoing that the equivalents based on thermal sensation do not exaggerate, but rather underestimate, the thermal effect on a person of a unit of radiation, since objective physiological indicators, as well as indicators of the state of the personal microclimate, point to a higher equivalent.

A comparison of the equivalents from the first, second, and fourth series of experiments reveals a remarkably consistent relationship between the equivalent and the size of the irradiated surface.

Taking the equivalent for irradiation from both sides (1.8°) as 1, we obtain approximately 1.5 for irradiation of the back and sides, and may reasonably assume that irradiation of the torso from four sides would yield approximately 2.

If the effective surface area of the torso is taken to be approximately 70% of the total body surface area, we may assume that, under uniform exposure to meteorological conditions, the torso accounts for approximately 70% of the body’s overall heat balance, for which the equivalent as a whole should be approximately 3 units.

However, the relationship between the value of the equivalent and the area of the irradiated body surface should not be interpreted mechanically. For example, it would be wrong to calculate separate equivalents for the head and legs based solely on the area of the surface exposed to radiation. The specific characteristics of these body parts must be taken into account: the heightened sensitivity of the extremities to cold and of the head to radiation. Our study has by no means resolved this question.

In all the preceding discussion, we have left air humidity and movement out of account. In our experiments, relative humidity was 40–50% under radiant conditions and 30–40% under convective conditions; the corresponding mean absolute humidity values ranged from 7.2–8.7 and 9.6–9.8 g-cal per 1 m³ of air, respectively. Thus, despite the very similar absolute humidity, relative humidity was lower under convective conditions.

This raises the question of whether temperatures can legitimately be compared at different relative humidities and whether they should be converted to effective temperatures. We chose not to do so, believing that effective temperature under radiation cannot be calculated on the basis of the American effective-temperature scale. The reason is that the mean temperatures of the air beneath the clothing and of the clothing itself, which are decisive factors in the body’s heat loss, were higher under radiant conditions than under convective conditions. Under these circumstances, conversion using the American effective-temperature scale loses all practical meaning.

Considering that the equivalents are intended for hot workshops, where absolute humidity is usually constant and low, and that an increase in temperature always entails a reduc—

…humidity, we believe that it is possible to rely solely on the difference in temperatures. At the same time, however, it should be remembered that when air humidity substantially exceeds the levels observed in the radiation chamber during our experiments, the values of the equivalents become less accurate. As for air movement, it was greater under the radiation conditions, but even here it did not exceed the air velocities permissible in occupied rooms with properly functioning general ventilation: it averaged 0.21 m/sec, varying from 0.17 to 0.25 m/sec (as against 0.12, varying from 0.8 to 0.16 m/sec under the convection conditions). Allowing for air movement could have increased the equivalent only very slightly.

A comparison of the equivalents obtained by us and by other authors is undoubtedly of interest.

Bedford cites a study presenting numerical data on the comparative thermal effects of air and enclosure temperatures, on the one hand, and radiation, on the other.

Fichenden and Wilgress (1925) studied comfort under air heating and radiant heating produced by a gas flame and an electric heater. They took 18.3° as the comfortable temperature under air heating. When this was reduced by 2.8°, i.e., to 15.5°, unilateral irradiation at an intensity of 0.135 g-cal was required to achieve comfortable conditions. Thus, 0.135 g-cal is equivalent to 2.8°, or the equivalent for 0.1 g-cal is \(2.8 : 1.35 = 2.1°\). If the surface of the trunk is taken to constitute 70% of the effective body surface, then our experiments yield an equivalent for unilateral irradiation of the body of

\[ \frac{0.95 \cdot 100}{70}=1.36. \]

This means that the equivalent we obtained is 35% lower than that determined by Fichenden and Wilgress.

According to the experiments of the same authors, when the temperature of the air and enclosures was lowered to 12.5°, irradiation from all sides at an intensity of 0.11 g-cal was required to achieve comfort. This means that 0.11 g-cal corresponds to 5.8°, i.e., the equivalent is 5.3° per 0.1 g-cal. It differs from the value we obtained by less than 10%. If allowance is made for the fact that, under nonuniform irradiation, equivalents obtained on the basis of thermal sensation must be considered underestimated, the difference between our data and those of the authors mentioned is entirely understandable.

American studies conducted by the method of partial calorimetry (experiments by Gagge, Winslow, and Herrington) also present data on the equivalence of radiation and convection for a clothed person. The experiments were performed on two subjects. For one, a convection constant of 6.84 and a radiation constant of 8.82 were obtained; for the other, the corresponding values were 4.68 and 5.76. From these data, the ratio between the thermal effects of wall and air temperatures can be derived as 1.2–1.3. The corresponding calculations show that the equivalents we obtained in the fourth series are 26% lower than these values.

This discrepancy can be explained in part by the fact that in our experiments (irradiation from four sides), the effectively irradiated surface was somewhat smaller than in the experiments of the American investigators, who made their observations in a chamber equipped with devices permitting irradiation not only from the sides but also from above. However, since the equivalents derived from the work of Fichenden and Wilgress are also lower than those calculated from the experiments of the three American investigators named above, the discrepancy may arise from simplifications made in the calculation.

Conclusions

1. The method of subjective assessment can yield equivalents of radiant and convective heat that are sufficiently reliable to serve as approximate values in setting standards for meteorological conditions in hot workplaces.

2. On the basis of the experiments conducted, the following numerical values of the equivalents for 0.1 g-cal/cm² per minute may be proposed for the hygienic assessment of the thermal effect of radiation:

a) with continuous irradiation of the torso from both sides at an intensity of less than 1.0 g-cal, 1.8°;

b) with continuous irradiation of the torso from three sides (the sides and back), 2.8°;

c) with irradiation from all sides at an intensity of less than 0.5 g-cal, 5.0°;

d) with irradiation of the torso from one side at an intensity of less than 1.5 g-cal, with the radiation flux moving from one part of its surface to another, 0.6–0.8°;

e) under the same conditions for the whole body, 0.8–1.0°.

1. Meteorological conditions that are equivalent in terms of thermal sensation produce thermal effects and sensations that are similar, but not identical.