Thermal Work Environments – Part 4: A Measure of Comfort in Hot Environments

     Since the early 20th century, numerous methods, instruments, and models have been developed to assess hot environments in absolute and relative terms.  Many people are most familiar with the “feels like” temperature cited in local weather reports, though its method of determination can also vary.  Index calculations vary in complexity and the number of included variables.
     Despite the ever-improving accuracy and precision of instrumentation, heat indices remain models, or approximations, of the effects of hot environments on comfort and performance.  The models may also be applicable only in a narrow range of conditions.  When indices are routinely cited by confident “experts,” without qualifying information, those in the audience may attribute greater value to them than is warranted.
     Incorporating the range of possible environmental conditions and human variability requires an extremely complex model, rendering its use in highly-dynamic workplaces infeasible.  Though imperfect, there are models and methods that can be practically implemented for the protection of workers in hot environments.

     A comprehensive presentation of heat stress modeling is far beyond the scope of this series.  Instead, this installment presents two types of indices:
(1) indices that are familiar to most, such as those used in weather reports, and
(2) practical assessments of hot work places; i.e. indices derived from noninvasive measurement of environmental conditions.
 
Popular Meteorology
     Short-term weather forecasts are concerned, largely, with predicting levels of comfort.  Forecasters use temperature indices to convey what the combination of conditions “feels like” relative to a reference set of conditions (e.g. dry bulb temperature at 50% relative humidity).  Methods of calculation and individuals’ perceptions vary; thus, temperature indices are generally more reliable as temporal comparisons than geographical ones.
     The “apparent temperature” (AT) exemplifies the temporal utility and geographical futility of such indices.  AT has been defined in various ways, hindering meaningful aggregation of data.  This slip into generic use of the term also precludes a detailed discussion here; however, AT can still be a valuable reference in some applications.  If approximations are sufficient, a simple look-up table, such as that in Exhibit 1, can be used for rapid reference.

     As seen in the table, this formulation of apparent temperature accounts only for ambient temperature and relative humidity (RH).  Readers unfamiliar with meteorological instrumentation or terminology can interpret “dry bulb temperature,” Tdb, as “reading from standard thermometer.”
 
     Heat Index (HI), used by the National Weather Service (NWS), incorporates several variables in the calculation of apparent, or perceived, temperature.  Derived by multiple regression analysis (far beyond the scope of this series), calculation of HI has been simplified by choosing constant values for all variables except dry bulb temperature (Tdb) and relative humidity (RH).  To maintain brevity in this presentation, the selection of these values will not be discussed; practical application is not hampered by this omission.  Simplifications notwithstanding, calculation of Heat Index remains a multi-step process.
     First, the “simple” Heat Index equation is used:
     HI1 = 0.5 { Tdb + 61.0 + [(Tdb – 68.0) * 1.2] + (0.094 * RH)},
where Tdb is measured in degrees Fahrenheit (° F) and RH is given in percent (%).  If HI1 ≥ 80° F, the “full” Heat Index equation is used and required adjustments are applied.
     The full Heat Index equation incorporates the constant values selected for constituent variables.  Using temperatures measured on the Fahrenheit scale (subscript “F”),
     HIF = -42.379 + 2.04901523 * Tdb + 10.14333127 * RH – 0.22475541 * Tdb * RH – 0.00683783 * Tdb^2– 0.05481717 * RH^2 + 0.00122874 * Tdb^2 * RH + 0.00085282 * Tdb * RH^2 – 0.00000199 * Tdb^2 * RH^2 .
Using temperatures measured on the Celsius scale (subscript “C”),
     HIC = -8.78469476 + 64.4557644 * Tdb + 93.54195356 * RH – 233.78568 * Tdb * RH – 19.6929504 * Tdb^2 – 26.2797244 * RH^2 + 141.550848 * Tdb^2 * RH + 46.42944 * Tdb * RH^2 – 9.16992 * Tdb^2 * RH^2 .
     Under certain conditions, an adjustment to the calculated HI is needed.  When RH < 13% and 80 < Tdb (° F) < 112 [26.7 < Tdb (° C) < 44.5], the following adjustment factor is added to the calculated HI:
     Adj1F = -{[(13 – RH)/4] * SQRT([17 - | Tdb – 95|]/17)} or
     Adj1C = -{[(13 – RH)/7.2] * SQRT([17 - |1.8 *  Tdb – 63|]/17)} .
When RH > 85% and 80 < Tdb (° F) < 87 [26.7 < Tdb (° C) < 30.5], the following adjustment factor is added to the calculated HI:
     Adj2F = [(RH – 85)/10] * [(87 – Tdb)/5] or
     Adj2C = 0.02 * (RH – 85) * (55 – 1.8 * Tdb)/1.8 .
     Limitations of the Heat Index equation extend beyond complexity of computation.  For HI < 80° F or 26° C, the full equation loses validity; the simple formulation is more useful.  Its derivation via multiple regression yields an error of ± 1.3° F (0.7° C), though this accuracy is usually sufficient for weather forecasts, as the geographical variation may exceed this amount.  Exposure to direct sunlight (insolation) can increase HI values up to 15° F (8° C), though the actual amount in given conditions is indeterminate in this model.  Constants chosen for constituent variables may also limit utility of HI in real conditions, should they vary significantly from assumptions.
     The preceding presentation of HI was intended to develop some appreciation for the potential complexity and limitations of temperature indices.  In reality, practical application requires none of this.  NWS provides a simple interface to input Tdb and RH values and quickly obtain HI values.  It can be found at www.wpc.ncep.noaa.gov/html/heatindex.shtml.  Links to other information are also provided for interested readers.
 
     The Canadian Meteorological Service uses humidex to express apparent temperatures.  This “humidity index,” like HI, incorporates temperature and humidity; it is calculated as follows:
     Humidex = Tdb + 0.5555 * {6.11 * e^(5417.7530 * [1/273.16 – 1/ (Tdp + 273)]) - 10},
where Tdp is the dewpoint temperature (° C).  Alternatively,
     Humidex = Tdb + 0.5555 * (Pv – 10),
where Pv is the vapor pressure (hPa).  If vapor pressure data is available, calculation of humidex is obviously simpler; however, dewpoint temperatures are likely more readily attainable.
     Like their counterparts in the US, the Canadians save everyone the trouble of computing the index.  A humidex calculator is provided at weather.gc.ca/windchill/wind_chill_e.html.
 
Advanced Measures
     Presenting a detailed review of the numerous temperature indices and models would be contradictory to the objectives declared in Part 1.  The following discussion is limited to those with practical application to hot workplace environments.
     The most ubiquitous index is the Wet Bulb Globe Temperature (WBGT).  This index combines dry bulb (Tdb), wet bulb (Twb), and black globe (Tg) temperatures to compute an apparent temperature.  The component measurements represent ambient temperature, evaporative cooling, and radiant heat transfer, respectively.  The combination of measurements provides a better approximation of the effects of environmental conditions on the human body than is available from the meteorological indices discussed in the previous section.
     For outdoor environments with a solar load component,
     WBGTout = (0.7 * Twb) + (0.1 * Tdb) + (0.2 * Tg).
For environments with no solar load component (e.g. indoors), the calculation is reduced to
     WBGTin = (0.7 * Twb) + (0.3 * Tg).
Estimating WBGT, with adjustments for air movement and clothing, can be accomplished using the table and procedure described in Exhibit 2.

     For best results, an instrument that complies with a broadly-accepted standard, such as ISO 7243, should be used to maintain consistency and comparability of data.  The standard defines characteristics of the globe, proper bulb wetting, and other information needed to use the instrument effectively.
     WBGT has been criticized for being “overly conservative.”  That is, restrictions placed on work rates and schedules based on WBGT limits have been deemed more protective than necessary to maintain worker health to the detriment of productivity.  Such criticisms of WBGT have led some to advocate for its use only as a screening tool.  Research, judgment, and multiple indices can be used to make this determination for specific circumstances and establish appropriate policies and procedures.
 
     Wet Globe Temperature (WGT) is comparable to WBGT.  It uses a copper globe covered with a wetted black cloth, called a Botsball, in place of the separate instruments of the WBGT apparatus.  A conversion has been derived to obtain WBGT from Botsball measurements:
     WBGT = 1.044 * WGT – 0.187° C.
 
     The Thermal Work Limit (TWL) has gained acceptance in some industries, such as mining, and could become common in others.  In particular, it is useful in outdoor environments with a significant contribution to heat stress attributable to radiant sources.  Advocates claim that TWL addresses the deficiencies of WBGT and is, therefore, a more-reliable indicator of heat stress.
     The TWL is the maximum metabolic rate (W/m^2) that can be sustained while maintaining a safe core temperature [< 100.4° F (38° C)] and sweat rate [< 1.2 kg/hr (42 oz/hr)].  It is determined using five environmental factors:  Tdb, Twb, Tg, wind speed (va), and atmospheric pressure (Pa).  TWL is based on assumptions that individuals are euhydrated, clothed, and acclimated to the conditions.
     A series of calculations is needed to determine TWL.  Rather than derail this discussion with a lengthy presentation of equations, readers are encouraged to familiarize themselves by using a calculator, such as that provided by Cornett’s Corner.  Preliminary calculations can be made with estimated metabolic rates; a guideline is provided in Exhibit 3.

     Body surface area (Ab) is determined by the following calculation:
     Ab (m^2) = [weight (kg)]^0.425 * [height (cm)]^0.725 * 71.84 .
Finally, divide the metabolic rate by Ab and compare the result to TWL.  If TWL is exceeded, additional breaks in the work cycle are needed to maintain worker well-being.
 
     Other measures of heat stress and related risk are concerned with sweating and hydration.  Skin wittedness, predicted sweat loss, and required sweating determinations are more academic than practical.  Weight loss due to sweating of less than 1.5% of body weight indicates adequate hydration, but isolating the cause of weight variation in a workplace is not straightforward.
     The specific gravity of one’s urine is a more-reliable indication of a person’s hydration, but, again, collecting this data is not feasible in most workplaces.  The practical alternative is less scientific, less precise, but simple to implement on an individual basis.  The color of a person’s urine can warn of his/her worsening hypohydration and potential for heat illness (see Part 3).  A visual guideline for evaluation is provided in Exhibit 4.

Let’s Be Direct
     Three types of temperature or heat stress indices have been developed for various purposes.  Some are used to assess or predict comfort levels in noncritical environments, while others are used to protect workers from heat illness, extract maximum performance from an individual or battalion, or in pursuit of other consequential objectives.
     Rational indices are based on the heat balance equation (see Part 2).  These are the most accurate because they account for all mechanisms of heat transfer between the human body and its surroundings.  For the same reason, however, rational indices are also the most difficult to develop; the measurements required are infeasible outside a controlled research environment.  Their complexity and subsequent lack of practicality has excluded rational indices from this presentation.
     Two fatal flaws have excluded empirical indices from this presentation:  self-reported data and subjectivity of assessments.  Self-reported data is notoriously unreliable, as imperfect memory, motivated thinking, or other influences cause distortions in the record.  Subjective assessments have low repeatability that introduces large errors in results.  These flaws render empirical indices impractical for use in workplaces where consistent policies and procedures are required.
     Thus, we must rely on direct indices to assess workplace conditions.  Direct indices are derived from measurements of environmental parameters.  Such measurements are noninvasive; they do not interrupt workflows or require participation or attention from workers.
     Heat Index (HI), humidex, Wet Bulb Globe Temperature (WBGT), and Wet Globe Temperature (WGT) are direct indices of varying complexity.  The Thermal Work Limit (TWL) requires body dimensions, but these measurements need not be repeated frequently.  Metabolic work rates can be estimated, maintaining the noninvasive nature of the index.
 
     The indices presented in this installment are only a sample of a much wider array of heat stress models available.  Investigation of others may be necessary to develop confidence in the protection a chosen index affords workers.  Any effort to better understand the landscape of heat stress risks, evaluations, and countermeasures are worthwhile investments in worker safety.
 
     For additional guidance or assistance with Operations challenges, feel free to leave a comment, contact JayWink Solutions, or schedule an appointment.

     For a directory of “Thermal Work Environments” entries on “The Third Degree,” see Part 1:  An Introduction to Biometeorology and Job Design (17May2023).
 
References
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Jody W. Phelps, MSc, PMP®, MBA
Principal Consultant
JayWink Solutions, LLC
jody@jaywink.com