Development of effective cold stress indices has garnered significantly less attention than that of heat stress indices (see Part 4). Perhaps this is explained, at least in part, by the lesser threat to life posed by cold stress, as explained in Part 7. Whatever the reason, this difference does not indicate lesser importance. Cold stress and cold injuries are serious conditions that effect workers in many ways and have both short- and long-term consequences. Monitoring environmental conditions and worker well-being is as critical a responsibility in cold environments as it is in hot ones.
This installment of the “Thermal Work Environments” series parallels the discussion in Part 4, beginning with a widely-reported, if not widely-understood, index used in weather forecasting, followed by a discussion of application in industrial settings. Readers are encouraged to review the discussions of heat and cold indices in conjunction.
Several independent weather-forecasting organizations have developed versions of “feels like” temperature indices to convey the level of discomfort one can expect to experience in cold, windy conditions. Others simply defer to the National Weather Service (NWS) in the US or the Canadian Meteorological Service (MSC) in Canada, using the “New Improved Wind Chill Index” developed by an international consortium. This is a logical choice, as these national agencies are generally recognized as the experts in weather-related matters in North America. Outdated references may be encountered in resources that remain readily-available, such as websites and journal articles, however.
The likelihood of encountering obsolete material warrants a brief review of the history of the development of wind chill as a comfort index. Understanding input variables and calculation methods makes the variety of wind chill indices one may encounter more meaningful.
The concept of wind chill, as we know it today, originated in the Antarctic in 1945. Two explorers, Paul Siple and Charles Passel, measured the time required for a container of water to freeze at various temperatures and wind speeds. From the data gathered, Siple and Passel derived a formula for the rate of heat loss in cold, windy conditions:
where H is “wind chill” or rate of heat loss (kcal/m^2/hr), v is wind speed (m/s) and T is air temperature (°C).
This heat loss rate has little meaning outside the research community; therefore, conversion to a recognizable form is needed for practical use. This seminal work’s greatest contribution has been to inspire development of better indices.
To this end, further experiments were conducted, ultimately resulting in a revised formula for wind chill:
where WCI is the Wind Chill Index (W/m^2), v is wind speed (m/s), and T is ambient temperature (°C). WCI is converted to an apparent temperature with the following relation:
where Tch is the equivalent chilling temperature (°C) and WCI is the Wind Chill Index (W/m^2) calculated above.
In 1992, NWS published a wind chill index that came into wide use and public familiarity. This formulation calculates an apparent temperature, in a single step, according to the following:
where Twc is the apparent or “wind chill temperature” (°F), T is ambient temperature (°F), and v is wind speed (mph). Published wind chill tables are convenient; their widespread use makes them the most-likely references to this obsolete formulation to be encountered.
In 1998, Robert Quayle and Robert Steadman advocated for the Steadman Wind Chill to replace the existing index. Deficiencies of the NWS wind chill index cited by Quayle and Steadman include:
where TSF is the Steadman wind chill equivalent temperature (°F), v is wind speed (mph), and T is ambient temperature (°F). An alternate formulation, for use with metric units, was also developed:
where TSC is the Steadman wind chill equivalent temperature (°C), v is wind speed (m/s), and T is ambient temperature (°C).
The broader meteorological community was clearly aware of deficiencies in the existing wind chill index when, in 2000, an international consortium convened to update it. This effort resulted in “The New Improved Wind Chill Index.” The updated index was adopted by NWS and MSC in 2001 and continues to be cited in meteorological reports and forecasts across North America. In the US:
where Twc is the wind chill equivalent temperature (°F), T is ambient temperature (°F), and v is wind speed (mph). In Canada:
where Twc is the wind chill equivalent temperature (°C), T is ambient temperature (°C), and v is wind speed (km/hr or kph).
Though NWS and MSC did not simply adopt the Steadman equations for their improved indices, results are in much-greater alignment with Steadman’s than those of previous iterations. A comparison of wind chill equivalent temperature calculations is shown in Exhibit 1 for two hypothetical conditions. As conditions become extreme (i.e. very low temperature and high wind speed), discrepancies among the wind chill equivalent temperature calculations become more pronounced. The modern indices better reflect human physiology – the basis of Steadman’s arguments in the 1990s. Readers are encouraged to compare these values to those obtained by interpolating from wind chill index charts.
A wind chill index table remains the most-convenient resource, as precision is often unnecessary; the variability of human experience typically exceeds the error inherent in interpolation of tabulated values. NWS, MSC, and other national and independent organizations publish such tables. Going a step further, the supplement to this post, shown in Exhibit 2, provides a single reference for use with either US or metric units. Converted values are also included in the supplement tables to facilitate approximation of wind chill values when available measurements are in mixed units.
Wind chill equivalent temperatures are very useful for outdoor settings; however, significant shortcomings render them much less helpful in most indoor settings. Wind chill and heat index (see Part 4) are subject to a similar criticism: only two factors are included in calculations.
Wind chill calculations neglect the influence of radiation, though exposure to direct sunlight can increase the apparent temperature by 8 – 15° F (5 – 9° C). This can be accounted for with a wet bulb globe temperature (WBGT) measurement in hot conditions (see Part 4). However, most sources also conclude that humidity is not relevant to cold stress. This leaves only the dry bulb (ambient) temperature with no adjustment.
The ambient temperature alone may be sufficient for many indoor workplaces, where the air is calm (i.e. no appreciable air movement). In others, such as large freezer facilities, where significant air flows are necessary, the wind chill index provides a better assessment of conditions.
The required clothing insulation (IREQ) index incorporates aspects of human physiology to determine proper clothing for the existing work conditions. Two versions of the index have been defined:
Determining IREQ values requires complex calculations involving the heat balance equation (see Part 6). Therefore, these indices provide more value as conceptualizations of conditions than in direct application. The chart in Exhibit 3 visually reinforces the idea behind IREQ, though the index values remain abstract. Instituting the IREQ indices fully requires data collection and computation that are impractical in most occupational settings and, therefore, beyond the scope of this treatise.
While several practical options exist to assess potential heat stress (see Part 4), cold stress options are much more limited. In fact, simplicity being key to practical application in occupational settings renders all but wind chill infeasible. Some choice does remain, however. Wind chill should be cited in the scale (°F or °C) most familiar to the group effected. This may define the equation used or table referenced to determine the index. Though a “conservative” index may invite criticism for overprotection, an extra margin of safety reduces the risk inherent in the variability of human experience. Ultimately, it is individual experience, as subjective and unreliable as it may be, that must be the determining factor in many workplace decisions.
For additional guidance or assistance with Safety, Health, and Environmental (SHE) issues, or other 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).
[Link] Kodak's Ergonomic Design for People at Work. The Eastman Kodak Company (ed). John Wiley & Sons, Inc., 2004.
[Link] “Thermal Environment.” Student Manual, Occupational Hygiene Training Association; February 2016.
[Link] “Understanding Wind Chill.” University of Kentucky Weather Center.
[Link] “The Ridiculous History of Wind Chill.” Rachel Z. Arndt. Popular Mechanics; December 12, 2016.
[Link] “The Steadman Wind Chill: An Improvement over Present Scales.” Robert G. Quayle and Robert G. Steadman. Weather and Forecasting; December 1, 1998.
[Link] “The New Improved Wind Chill Index.” National Weather Service; November 1, 2001.
[Link] “Wind chill – text version.” Government of Canada; June 14, 2022.
[Link] “Wind Chill Calculator (Celsius).” CalcuNation; 2022.
[Link] “Calculate the wind chill.” Lenntech.
[Link] “Wind chill.” Wikipedia; July 13, 2023.
Jody W. Phelps, MSc, PMP®, MBA
JayWink Solutions, LLC
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