wind-chill factor

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A chart of wind chill temperatures for given air temperatures and wind speeds

Wind chill is the apparent temperature felt on exposed skin due to wind. The degree of this phenomenon depends on both air temperature and wind speed. The wind chill temperature (often popularly called the wind chill factor) is always lower than the air temperature for values where the wind chill formula is valid. In cases where the apparent temperature is higher than the air temperature, the heat index is used instead.

Explanation

The human body loses heat largely by evaporative cooling and convection^[1][2]. The rate of heat loss by a surface depends on the wind speed above that surface: the faster the wind speed, the more readily the surface cools. For inanimate objects, the effect of wind chill is to reduce any warmer objects to the ambient temperature more quickly. For most biological organisms, the physiological response is to maintain surface temperature in an acceptable range so as to avoid adverse effects. Thus, the attempt to maintain a given surface temperature in an environment of faster heat loss results in both the perception of lower temperatures and an actual greater heat loss increasing the risk to adverse effects such as frostbite and death.

Formulae and tables

The first wind chill formulae and tables were developed by Paul Allman Siple and Charles Passel working in the Antarctic before the Second World War, and were made available by the National Weather Service by the 1970s. It was based on the cooling rate of a small plastic bottle as its contents turned to ice while suspended in the wind on the expedition hut roof, at the same level as the anemometer. The so-called Windchill Index provided a pretty good indication of the severity of the weather. In the 1960s, wind chill began to be reported as a wind chill equivalent temperature (WCET), which is theoretically less useful. The author of this change is unknown, but it was not Siple and Passel as is generally believed. At first, it was defined as the temperature at which the windchill index would be the same in the complete absence of wind. This led to equivalent temperatures that were obviously exaggerations of the severity of the weather. Charles Eagan ^[3] realized that people are rarely still and that even when it was calm, there was some air movement. He redefined the absence of wind to be an air speed of 1.8 metres per second (4.0 mph), which was about as low a wind speed as a cup anemometer could measure. This led to more realistic (warmer-sounding) values of equivalent temperature.

Original model

Equivalent temperature was not universally used in North America until the 21st century. Until the 1970s, the coldest parts of Canada reported the original Wind Chill Index, a three or four digit number with units of kilocalories/hour per square meter. Each individual calibrated the scale of numbers personally, through experience. The chart also provided general guidance to comfort and hazard through threshold values of the index, such as 1400, which was the threshold for frostbite. The change in the 1970s to the metric system units in Canada changed all the numbers, making it confusing and requiring that everyone recalibrate their personal wind chill scale. It should never have had units in the first place, as Siple later pointed out ^[4] for it was not a measure of human heat loss but simply a number proportional to human heat loss.

The original formula for the index was:

^[5][6]

Where:

WCI = Wind chill index, kcal/m²/h

V = Wind velocity, m/s

T = Air temperature, °C

The general public seems to have been put off by the strange sounding units, either the old ones or the newer watts per square metre, and developed a strong preference for Equivalent Temperature, a deceptive simplification that only seems to be easier to understand. Even in the cold areas of Canada, broadcast media began to switch to the newer method of reporting after metrification.

New wind chill index

In November 2001 the National Weather Service implemented the new wind chill index, used by the U.S. and Canadian weather services, which is determined by iterating a model of skin temperature under various wind speeds and temperatures. The model used standard engineering correlations of wind speed and heat transfer rate. Heat transfer was calculated for a bare face in wind, facing the wind, while walking into it at 1.4 metres per second (3.1 mph). The model corrects the officially measured wind speed to the wind speed at face height, assuming the person is in an open field. ^[7] The results of this model may be approximated, to within one degree, from the following formula:

where is the wind chill index based on the Celsius scale, is the air temperature in °C, and is the air speed in km/h measured at 10 metres (33 ft), standard anemometer height).^[8]

The equivalent formula in US customary units is:

where and are measured in °F, and in mph.

Windchill Temperature is only defined for temperatures at or below 10 °C (50 °F) and wind speeds above 4.8 kilometres per hour (3.0 mph).^[9]

As the air temperature falls, the chilling effect of any wind that is present increases. For example, a 16 km/h (9.9 mph) wind will lower the apparent temperature by a wider margin at an air temperature of −20 °C (−4.0 °F), than a wind of the same speed would if the air temperature were −10 °C (14.0 °F).

Celsius Wind Chill Chart w/Frostbite information

Comparison of old and new values of Wind Chill at −15 °C (5.0 °F)

The method for calculating wind chill has been controversial because experts^[who?] disagree on whether it should be based on whole body cooling either while naked or while wearing appropriate clothing, or if it should be based instead on local cooling of the most exposed skin, such as the face. The internal thermal resistance is also a point of contention. It varies widely from person to person. Had the average value for the subjects been used, calculated WCET's would be a few degrees more severe.

The 2001 WCET is a steady state calculation (except for the time to frostbite estimates^[10]) There are significant time-dependent aspects to wind chill because cooling is most rapid at the start of any exposure, when the skin is still warm.

The exposure to wind depends on the surroundings and wind speeds can vary widely depending on exposure and obstructions to wind flow.

References

External links

• National Weather Service Wind Chill Temperature Index Table of Wind Chill temperatures
• National Science Digital Library - Wind Chill Temperature
• [1] Environment Canada's Wind Chill Calculator
• Weather Images Wind Chill Chart and Introduction
• An Introduction to Wind Chill A lesson plan on Wind Chill
• A Cold Wind Blowing An article on wind chill and tables in SI units
• Wind Chill and Humidex Criticism about the use of Wind chill and humidex
• Windows program for Heat Index, Wind Chill, etc
• An article about wind chill from The Canadian Encyclopedia
• Windchill Explanation by Frozen Owen
• Gorman, James (February 10, 2004). "Beyond Brrr: The Elusive Science of Cold". New York Times. http://www.nytimes.com/2004/02/10/science/beyond-brrr-the-elusive-science-of-cold.html. 

See also

• Cold wave
• Humidex