Measuring heat stress

Air temperature alone tells you little about heat stress. A worker in dry shade at 33 °C may be comfortable, while another at 30 °C in full sun, high humidity and no breeze may be heading for heat exhaustion. To judge heat stress properly, you need to account for four environmental factors, plus the work rate and the clothing. This lesson explains the main indices used to do that, how to measure them and what each is good for.

The four environmental factors

Lesson 2 showed that the body exchanges heat by convection, radiation and evaporation. The environment affects each of these through four measurable factors. Air temperature, measured with an ordinary shaded thermometer and called the dry bulb temperature, drives convection. Humidity, the amount of water vapor in the air, controls how fast sweat can evaporate. Radiant heat, from the sun or hot surfaces, is measured with a black globe thermometer. Air speed affects both convection and evaporation. Any good heat stress index must capture all four, either by measuring them or by assuming typical values.

Humidity is usually reported as relative humidity, the percentage of the maximum water vapor the air could hold at that temperature. Because warm air can hold much more water than cool air, the same relative humidity means much more moisture, and much less evaporation, on a hot day. The dew point, the temperature at which the air would become saturated, is a more direct measure of moisture: dew points above about 20 °C feel muggy, and above 24 °C oppressive.

Wet bulb globe temperature

The wet bulb globe temperature, or WBGT, is the index used by the ACGIH heat stress threshold limit values, by ISO 7243, by many Canadian and US regulators, and by militaries and sports bodies around the world. It combines three measurements. The natural wet bulb temperature, Tnwb, is read from a thermometer whose bulb is covered with a wet wick and exposed to natural air movement and radiation; it falls below air temperature as water evaporates from the wick, so it reflects humidity and air movement. The globe temperature, Tg, is read from a thermometer inside a hollow black copper sphere, traditionally 15 cm in diameter, which absorbs radiant heat. The dry bulb temperature, Tdb, is ordinary shaded air temperature.

Outdoors in sunlight, the three are combined as:

Indoors, or outdoors without solar load, the dry bulb term is dropped:

The heavy weighting of the natural wet bulb, 70 percent, reflects how important evaporation is to the body's heat balance. WBGT is always lower than air temperature in normal conditions, so a WBGT of 30 °C is a serious level of heat stress even though 30 °C air temperature might sound moderate. Do not compare WBGT values directly with air temperatures or with humidex.

Measuring WBGT properly

Electronic WBGT meters are now common and much easier to use than the traditional tripod of glass thermometers, but they must be used properly to give meaningful results. The instrument should be placed where the workers actually work, at about chest height, or at head, abdomen and ankle height averaged when conditions vary by height. It needs time to stabilize, typically 10 to 30 minutes for a full-size globe, less for smaller globes, which may read differently from the standard 15 cm globe in some conditions. Readings should be taken during the hottest part of the shift and whenever conditions change. Wet bulb wicks must be kept clean and wet with distilled water.

When work moves between areas with different conditions, such as a furnace area and a cooler break room, a time-weighted average WBGT is calculated over a representative hour or two. Some meters also log data continuously, which is useful for programs that adjust work-rest cycles during the day. Weather services and smartphone apps now provide estimated WBGT forecasts for outdoor locations, which are useful for planning, but they cannot account for local radiant sources or conditions in a specific work area.

# WBGT from three measured temperatures (degrees C)
def wbgt_out(tnwb, tg, tdb): return 0.7 * tnwb + 0.2 * tg + 0.1 * tdb
def wbgt_in(tnwb, tg):       return 0.7 * tnwb + 0.3 * tg

roof  = wbgt_out(tnwb=25.5, tg=52.0, tdb=33.0)    # sunny roof, humid afternoon
shade = wbgt_out(tnwb=24.0, tg=34.0, tdb=31.0)    # nearby shade, no direct sun
foundry = wbgt_in(tnwb=24.0, tg=55.0)             # indoor, near a furnace
print(f"Sunny roof:   WBGT = {roof:.1f} C")
print(f"Shade:        WBGT = {shade:.1f} C")
print(f"Foundry area: WBGT = {foundry:.1f} C")

# Time-weighted average when a worker moves between areas each hour
segments = [(foundry, 40), (wbgt_in(20.0, 24.0), 20)]   # (WBGT, minutes)
twa = sum(w * t for w, t in segments) / sum(t for _, t in segments)
print(f"TWA over the hour (40 min foundry, 20 min break room): {twa:.1f} C")

Sunny roof:   WBGT = 31.6 C
Shade:        WBGT = 26.7 C
Foundry area: WBGT = 33.3 C
TWA over the hour (40 min foundry, 20 min break room): 29.3 C

Radiant heat matters a great deal. Moving from the sunny roof into nearby shade, with air only 2 °C cooler, drops WBGT by about 5 °C, which can mean the difference between continuous work and long rest breaks. Near the furnace, the very high globe temperature drives the WBGT up even though humidity is moderate. The time-weighted average shows the benefit of a cool break area: spending 20 minutes of every hour in the break room brings the hourly average down by about 4 °C.

Humidex

Humidex is a Canadian index developed by Environment Canada in 1965 to describe how hot, humid weather feels to the average person. It combines air temperature and humidity, using the dew point, into a single number read as if it were a temperature in degrees Celsius. It is rarely used in the United States, where the National Weather Service's heat index plays a similar role, but you may see it on equipment or in guidance from Canadian parent companies.

Humidex is calculated from the air temperature T in degrees Celsius and the vapor pressure e in hectopascals, which is derived from the dew point Td:

Environment Canada describes humidex values of 30 to 39 as causing some discomfort, 40 to 45 as great discomfort where exertion should be avoided, and above 45 as dangerous, with heat stroke possible. For workers doing physical work, those general-public bands are not protective enough.

Heat index

The heat index, used by the National Weather Service, estimates how hot it feels in the shade from air temperature and relative humidity. It is calculated in degrees Fahrenheit using a regression equation developed by Lans Rothfusz, with adjustments for very low or very high humidity. The NWS uses it in its heat advisories and excessive heat warnings, and OSHA and NIOSH guidance has used it to set risk levels for outdoor work. Because it assumes shade and light wind, the NWS notes that full sun can raise the effective heat index by up to about 15 °F.

import math

def humidex(t_c, dewpoint_c):
    e = 6.11 * math.exp(5417.7530 * (1 / 273.16 - 1 / (273.15 + dewpoint_c)))
    return t_c + 0.5555 * (e - 10.0)

def heat_index_f(t_f, rh):
    """NWS heat index (Rothfusz regression with the simple formula below 80 F)."""
    simple = 0.5 * (t_f + 61.0 + (t_f - 68.0) * 1.2 + rh * 0.094)
    if (simple + t_f) / 2 < 80:
        return simple
    hi = (-42.379 + 2.04901523 * t_f + 10.14333127 * rh - 0.22475541 * t_f * rh
          - 6.83783e-3 * t_f**2 - 5.481717e-2 * rh**2 + 1.22874e-3 * t_f**2 * rh
          + 8.5282e-4 * t_f * rh**2 - 1.99e-6 * t_f**2 * rh**2)
    if rh < 13 and 80 <= t_f <= 112:
        hi -= ((13 - rh) / 4) * math.sqrt((17 - abs(t_f - 95)) / 17)
    elif rh > 85 and 80 <= t_f <= 87:
        hi += ((rh - 85) / 10) * ((87 - t_f) / 5)
    return hi

def dewpoint(t_c, rh):                      # Magnus approximation
    a, b = 17.62, 243.12
    g = math.log(rh / 100) + a * t_c / (b + t_c)
    return b * g / (a - g)

for t_c, rh in [(30, 40), (30, 70), (33, 55), (35, 30)]:
    td = dewpoint(t_c, rh)
    t_f = t_c * 9 / 5 + 32
    hi_f = heat_index_f(t_f, rh)
    print(f"{t_c} C, RH {rh:2d}%: dew point {td:4.1f} C, humidex {humidex(t_c, td):4.1f}, "
          f"heat index {hi_f:5.1f} F ({(hi_f - 32) * 5 / 9:4.1f} C)")

30 C, RH 40%: dew point 14.9 C, humidex 33.9, heat index  85.4 F (29.7 C)
30 C, RH 70%: dew point 23.9 C, humidex 41.2, heat index  95.1 F (35.0 C)
33 C, RH 55%: dew point 22.8 C, humidex 43.0, heat index 100.1 F (37.8 C)
35 C, RH 30%: dew point 14.8 C, humidex 38.9, heat index  94.4 F (34.7 C)

The comparison shows two things. First, humidity matters a great deal: at 30 °C, raising relative humidity from 40 to 70 percent raises the humidex by about 7 points. Second, humidex and heat index give different numbers. At 30 °C and 70 percent, the humidex is about 41 while the heat index is about 35 °C (95 °F). Neither is wrong; they are different scales. A workplace plan must say clearly which index it uses and set its action levels on that scale.

Comparing the indices

In practice, many workplaces use two levels. Weather-based indices such as humidex or heat index are used for daily planning and to trigger the heat plan, because they are forecast in advance and easy to communicate. WBGT measurements are used where conditions are severe, where radiant sources or protective clothing are involved, or where the employer needs to compare conditions with ACGIH screening criteria. Physiological monitoring is reserved for high-risk work, such as firefighting, hazmat response or work in encapsulating suits.

Physiological monitoring

Because the indices describe the environment, not the person, they cannot tell how a particular worker is coping. Physiological monitoring measures heat strain directly. The ACGIH guidance suggests that heat strain may be excessive if sustained heart rate exceeds about 180 beats per minute minus age, if core temperature exceeds 38.5 °C in medically selected, acclimatized workers or 38 °C in unselected or unacclimatized workers, if heart rate does not recover to about 120 beats per minute one minute after peak work, or if there are symptoms such as sudden fatigue, nausea, dizziness or light-headedness.

Wearable sensors now estimate core temperature from heart rate and skin temperature, and ingestible temperature pills give direct readings in research and some emergency response work. These tools can be valuable, but they raise questions of accuracy, privacy and who sees the data. They support, but do not replace, environmental assessment, good work planning and trained observation by workers and supervisors.