Paradox: increased blood perfusion to the face <Emphasis Type="BoldItalic">enhances</Emphasis> protection against frostbite while it <Emphasis Type="BoldItalic">lowers</Emphasis> wind chill equivalent temperatures

A model of facial heat exchange in cold and windy environments is presented. The tissue is depicted as a hollow cylinder and the model includes heat conduction and heat transport by blood circulation from the warmer core. A steady-state solution facilitating the estimation of wind chill equivalent temperature (WCET) as a function of the effective wind velocity, air temperature and blood perfusion rate was obtained. The results quantify and demonstrate the elevation of skin temperatures caused by increased flow of warmer blood from the inner core to the face. Elevated facial temperatures, while enhancing protection against frostbite and other cold-related injuries, also increase heat loss to the colder environment. Paradoxically, such elevated facial temperatures cause WCETs, as estimated by the prevailing definition, to attain lower rather than higher values, indicating, in fact, increased risk of frostbite. The results of this study should be useful in understanding and quantifying the effects of blood perfusion in protection against cold-related injuries. They should also be considered in the re-evaluation and re-formulation of the concept of wind chill, which has been a useful cold weather indicator for decades.     

Modified wind chill temperatures determined by a whole body thermoregulation model and human-based facial convective coefficients

Wind chill equivalent temperatures (WCETs) were estimated by a modified Fiala’s whole body thermoregulation model of a clothed person. Facial convective heat exchange coefficients applied in the computations concurrently with environmental radiation effects were taken from a recently derived human-based correlation. Apart from these, the analysis followed the methodology used in the derivation of the currently used wind chill charts. WCET values are summarized by the following equation: $$ \mathrm{WCET}=12.87+0.5334\ast {T}_o-\left(12.66-0.4414\ast {T}_o\right)\ast {U}_{reported}{}^{0.1228} $$ Results indicate consistently lower estimated facial skin temperatures and consequently higher WCETs than those listed in the literature and used by the North American weather services. Calculated dynamic facial skin temperatures were additionally applied in the estimation of probabilities for the occurrence of risks of frostbite. Predicted weather combinations for probabilities of “Practically no risk of frostbite for most people,” for less than 5 % risk at wind speeds above 40 km h^?1, were shown to occur at air temperatures above ?10 °C compared to the currently published air temperature of ?15 °C. At air temperatures below ?35 °C, the presently calculated weather combination of 40 km h^?1/?35 °C, at which the transition for risks to incur a frostbite in less than 2 min, is less conservative than that published: 60 km h^?1/?40 °C. The present results introduce a fundamentally improved scientific basis for estimating facial skin temperatures, wind chill temperatures and risk probabilities for frostbites over those currently practiced.     

Wind-chill-equivalent temperatures: regarding the impact due to the variability of the environmental convective heat transfer coefficient

The wind-chill index (WCI), developed in Antarctica in the 1940s and recently updated by the weather services in the USA and Canada, expresses the enhancement of heat loss in cold climates from exposed body parts, e.g., face, due to wind. The index provides a simple and practical means for assessing the thermal effects of wind on humans outdoors. It is also used for indicating weather conditions that may pose adverse risks of freezing at subfreezing environmental temperatures. Values of the WCI depend on a number of parameters, i.e, temperatures, physical properties of the air, wind speed, etc., and on insolation and evaporation. This paper focuses on the effects of various empirical correlations used in the literature for calculating the convective heat transfer coefficients between humans and their environment. Insolation and evaporation are not included in the presentation. Large differences in calculated values among these correlations are demonstrated and quantified. Steady-state wind-chill-equivalent temperatures (WCETs) are estimated by a simple, one-dimensional heat-conducting hollow-cylindrical model using these empirical correlations. Partial comparison of these values with the published “new” WCETs is presented. The variability of the estimated WCETs, due to different correlations employed to calculate them, is clearly demonstrated. The results of this study clearly suggest the need for establishing a “gold standard” for estimating convective heat exchange between exposed body elements and the cold and windy environment. This should be done prior to the introduction and adoption of further modifications to WCETs and indices. Correlations to estimate the convective heat transfer coefficients between exposed body parts of humans in windy and cold environments influence the WCETs and need to be standardized.     

Comments on “Modified wind chill temperatures determined by a whole body thermoregulation model and human-based convective coefficients” by Ben Shabat,Shitzer and Fiala (2013) and “Facial convective heat exchange coefficients in cold and windy environments estimated from human experiments” by Ben Shabat and Shitzer (2012)

Ben Shabat et al. (Int J Biometeorol 56(4):639-51, 2013) present revised charts for wind chill equivalent temperatures (WCET) and facial skin temperatures (FST) that differ significantly from currently accepted charts. They credit these differences to their more sophisticated calculation model and to the human-based equation that it used for finding the convective heat transfer coefficient (Ben Shabat and Shitzer, Int J Biometeorol 56:639-651, 2012). Because a version of the simple model that was used to create the current charts accurately reproduces their results when it uses the human-based equation, the differences that they found must be entirely due to this equation. In deriving it, Ben Shabat and Shitzer assumed that all of the heat transfer from the surface of their cylindrical model was due to forced convection alone. Because several modes of heat transfer were occurring in the human experiments they were attempting to simulate, notably radiation, their coefficients are actually total external heat transfer coefficients, not purely convective ones, as the calculation models assume. Data from the one human experiment that used heat flux sensors supports this conclusion and exposes the hazard of using a numerical model with several adjustable parameters that cannot be measured. Because the human-based equation is faulty, the values in the proposed charts are not correct. The equation that Ben Shabat et al. (Int J Biometeorol 56(4):639-51, 2013) propose to calculate WCET should not be used.     

Facial convective heat exchange coefficients in cold and windy environments estimated from human experiments

Facial heat exchange convection coefficients were estimated from experimental data in cold and windy ambient conditions applicable to wind chill calculations. Measured facial temperature datasets, that were made available to this study, originated from 3 separate studies involving 18 male and 6 female subjects. Most of these data were for a −10°C ambient environment and wind speeds in the range of 0.2 to 6 m s⁻¹. Additional single experiments were for −5°C, 0°C and 10°C environments and wind speeds in the same range. Convection coefficients were estimated for all these conditions by means of a numerical facial heat exchange model, applying properties of biological tissues and a typical facial diameter of 0.18 m. Estimation was performed by adjusting the guessed convection coefficients in the computed facial temperatures, while comparing them to measured data, to obtain a satisfactory fit (r ² > 0.98, in most cases). In one of the studies, heat flux meters were additionally used. Convection coefficients derived from these meters closely approached the estimated values for only the male subjects. They differed significantly, by about 50%, when compared to the estimated female subjects' data. Regression analysis was performed for just the −10°C ambient temperature, and the range of experimental wind speeds, due to the limited availability of data for other ambient temperatures. The regressed equation was assumed in the form of the equation underlying the “new” wind chill chart. Regressed convection coefficients, which closely duplicated the measured data, were consistently higher than those calculated by this equation, except for one single case. The estimated and currently used convection coefficients are shown to diverge exponentially from each other, as wind speed increases. This finding casts considerable doubts on the validity of the convection coefficients that are used in the computation of the "new" wind chill chart and their applicability to humans in cold and windy environments.     

Convective and radiative components of wind chill in sheep: Estimation from meteorological records

Wind chill is defined as the excess of sensible heat loss over what would occur at zero wind speed with other conditions unchanged. Wind chill can be broken down into a part that is determined by air temperature and a radiative part that comprises wind-dependent effects on additional long-wave radiative exchange and on solar radiation (by reducing solar warming). Radiative exchange and gain from solar radiation are affected by changes that are produced by wind in both surface and fleece insulations. Coefficients are derived for (a) converting the components of sensible heat exchange (air-temperature-dependent including both convective and associated long-wave radiative, additional long-wave radiative and solar) into the components of the total heat loss that are associated with wind and (b) for calculating equivalent air temperature changes. The coefficients contain terms only in wind speed, wetting of the fleece and fleece depth; these determine the external insulation.Calculation from standard meteorological records, using Plymouth and Aberdeen in 1973 as examples, indicate that in April–September 1973 at Plymouth reduction in effective solar warming constituted 28% of the 24-h total wind chill, and 7% in the other months of the year combined; at Aberdeen the corresponding percentages were 25% and 6%. Mean hour-of-day estimates for the months of April and October showed that at midday reduction in solar warming due to wind rose to the order of half the air-temperature-dependent component of wind chill, with a much smaller effect in January. For about six hours at midday in July reduction in solar warming due to wind was similar in magnitude to the air-temperature-dependent component.It is concluded that realistic estimates of wind chill cannot be obtained unless the effect of solar radiation is taken into account. Failure to include solar radiation results not only in omitting solar warming but also in omitting the effects of wind in reducing that warming.The exchange of sensible (non-evaporative) heat loss between a homeothermic animal and its environment can be divided into two parts: one part is due to the temperature difference between the animal and the surrounding air, and the other part is due to additional long-wave radiative exchange between animal and environment and to solar radiation. Both parts of the heat exchange are determined in magnitude by the animal's thermal insulation, which is itself affected by windspeed and wetting. Wind diminishes as animal's external insulation, so increasing heat loss under all conditions when the air temperature is lower than the animal's surface temperature: this effect is termed wind chill. Wind chill has previously been investigated more commonly in relation to man (Burton an Edholm, 1955; Smithson and Baldwin, 1978; Mumford, 1979; Baldwin and Smithson, 1979). This paper is concerned with the separate contributions to wind chill calculated for sheep that can be associated with convective and radiative heat exchanges.     

The calculation from weather records of the requirement for clothing insulation

Standard meteorological measurements of dry bulb temperature, wind speed, sunshine, cloud cover and rainfall are used to calculate the clothing insulation required by man for thermal comfort under given weather conditions. The calculation is based on earlier work on the effect of weather on sensible (non-evaporative) heat loss from sheep, which used the relation between heat flow, thermal insulation and the difference between body and environmental temperatures.Clothing insulation for man is estimated in two ways: as clothing (I_c) that is impervious to the effects of wind and rain; and as the equivalent depth of sheep fleece (f_m), which is not impervious. This allows the assessment of wind chill for a range of clothing of varied penetration by wind instead of for only one type of garment.Results are given as daily means calculated from hourly measurements throughout 1973 for Plymouth (on the south coast of Britain) and Aberdeen (on the far northeast coast of Britain). Wind chill is estimated both by its effect on f_m requirement and by the fall in air temperature that would be needed to produce under still-air conditions the same demand for f_m that occurs in the actual environment. The monthly mean f_m requirement is reduced by about 40% when the effect of wind is removed. When wind chill is estimated as an equivalent fall in air temperature it approximates to 1 K per knot wind speed measured at the standard meteorological height of 10 m.     

Advances,shortcomings, and recommendations for wind chill estimation

This article discusses briefly the advances made and the remaining short-comings in the "new" wind chill charts adopted in the US and Canada in 2001. A number of indicated refinements are proposed, including the use of whole body models in the computations, verification of heat exchange coefficients by human experiments, reconsideration of "calm" wind conditions, reconsideration of frostbite threshold levels, the inclusion of cold-related pain and numbness in the charts, etc. A dynamic numerical model is applied to compare the effects of wind speeds, on the one hand, and air temperatures, on the other, on the steady-state exposed facial and bare finger temperatures. An apparent asymmetry is demonstrated, favoring the effects of wind speeds over those of air temperatures for an identical final facial temperature. This asymmetry is reversed, however, when SI unit changes in these quantities are considered.     

Thermal physiological ecology of Colias butterflies in flight

Summary As a comparison to the many studies of larger flying insects, we carried out an initial study of heat balance and thermal dependence of flight of a small butterfly (Colias) in a wind tunnel and in the wild.Unlike many larger, or facultatively endothermic insects, Colias do not regulate heat loss by altering hemolymph circulation between thorax and abdomen as a function of body temperature. During flight, thermal excess of the abdomen above ambient temperature is weakly but consistently coupled to that of the thorax. Total heat loss is best expressed as the sum of heat loss from the head and thorex combined plus heat loss from the abdomen because the whole body is not isothermal. Convective cooling is a simple linear function of the square root of air speed from 0.2 to 2.0 m/s in the wind tunnel. Solar heat flux is the main source of heat gain in flight, just as it is the exclusive source for warmup at rest. The balance of heat gain from sunlight versus heat loss from convection and radiation does not appear to change by more than a few percent between the wings-closed basking posture and the variable opening of wings in flight, although several aspects require further study. Heat generation by action of the flight muscles is small (on the order of 100 m W/g tissue) compared to values reported for other strongly flying insects. Colias appears to have only very limited capacity to modulate flight performance. Wing beat frequency varies from 12–19 Hz depending on body mass, air speed, and thoracic temperature. At suboptimal flight temperatures, wing beat frequency increases significantly with thoracic temperature and body mass but is independent of air speed. Within the reported thermal optimum of 35–39°C, wing beat frequency is negatively dependent on air speed at values above 1.5 m/s, but independent of mass and body temperature. Flight preference of butterflies in the wind tunnel is for air speeds of 0.5–1.5 m/s, and no flight occurs at or above 2.5 m/s. Voluntary flight initiation in the wild occurs only at air speeds 1.4 m/s.In the field, Colias fly just above the vegetation at body temperatures of 1–2°C greater than when basking at the top of the vegetation. These measurements are consistent with our findings on low heat gain from muscular activity during flight. Basking temperatures of butterflies sheltered from the wind within the vegetation were 1–2°C greater than flight temperatures at vegetation height.     

Face cooling by cold wind in walking subjects

The effects of low to moderate wind speeds on face temperature, thermal and pain sensations while subjects walked on a treadmill during cold exposure were studied in eight healthy men. The purpose of the study was to evaluate further the risk of frostbite at different activity levels. The walking speed was 2.8 km h(-1) and two inclination levels were used, 0 degrees and 6 degrees. The subjects were exposed to -10 degrees C and 0, 1 or 5 m s(-1) wind for 60 min dressed in cold-protective clothing with only the face unprotected. Results from previous experiments with the same subjects standing for 30 min were included in the analysis of the data. Each individual was exposed to all combinations of air velocity and activity level. The exposure to -10 degrees C and the highest wind speed used would carry no risk of frostbite according to the wind chill index. Cold lowered the skin temperature of the face significantly and wind further increased skin cooling. The activity level did not affect forehead and cheek temperatures, but the average nose skin temperature was higher and pain sensations were reduced at a higher work rate. The predicted risk of frostbite in the nose, based on average responses, would thus be less at a higher work rate. However, the results indicate that exercise does not necessarily protect all individuals from frostbite at moderate air speeds, since the nose skin temperature of 25% of the subjects dropped to 0 degrees C at 5 m s(-1) during both standing and walking. Thus the potential individual risk of frostbite in the nose is similar during light exercise and standing. Moreover, the risk of frostbite seems to be underestimated by the wind chill index under the conditions tested in this study.