Wind Chill and Other Meteorological Matters

Wind chill is one of those things that allow us to exaggerate how cold it really is! But is it real? Yes - but the "yes" needs to be qualified. The wind chill factor is a calculated temperature that represents the ‘feel’ of a wind on exposed human skin in terms of an equivalent temperature in still air. The concept is based on sound principals, but its application should only be in the context of exposed skin. While wind speed in the most important parameter in the calculation of wind chill, humidity and pressure also has some impact, but are generally ignored.

The chilling effect of wind comes from two sources:

1. The disturbance of the insulating boundary layer of warm air over the skin

2. The evaporative cooling effect of moisture loss from the skin.

In practice, wind can also cause drafts within clothing and hence heat loss, but this effect is not considered in the chill factor calculation because of its obvious variability.

Note: You cannot cool to a temperature much lower than that of the wind, but you can cool faster to that temperature. Depending on the humidity, it is possible to drop below the air temperature by a few degrees.

Measuring wind chill

The wind chill is commonly presented as a table of temperature versus wind speed. An example of a Celsius-kph table and a Fahrenheit-mph table are presented below:

   0   10   20   30   40   50   60   70   80

  20
  15
  10
   5
   0
 
  -5
 -10
 -15
 -20
 -25
 
 -30
 -35
 -40
 -45
 -50

  20   19   16   15   14   13   13   13   13
  15   13   10    8    7    6    5    5    5
  10    8    4    1   -1   -2   -2   -3   -3
   5    2   -3   -6   -8   -9  -10  -11  -11
   0   -3   -9  -13  -15  -17  -18  -18  -19
  
  -5   -8  -15  -20  -22  -24  -25  -26  -27
 -10  -14  -22  -27  -30  -32  -33  -34  -34
 -15  -19  -28  -34  -37  -39  -41  -42  -42
 -20  -25  -35  -40  -44  -47  -48  -49  -50
 -25  -30  -41  -47  -51  -54  -56  -57  -58
 
 -30  -36  -47  -54  -59  -62  -64  -65  -66
 -35  -41  -54  -61  -66  -69  -71  -73  -73
 -40  -47  -60  -68  -73  -77  -79  -81  -81
 -45  -52  -66  -75  -81  -84  -87  -88  -89
 -50  -58  -73  -82  -88  -92  -94  -96  -97

The case illustrated in the photograph above is a 190 kph wind. However, the tables do not extend to these speeds. However, it can be seen that at higher wind speeds the wind chill changes by only a small amount with a change in wind speed. At -15°C, the change between 60 and 80 kph is just 1°C, so it is reasonable to conclude at 190 kph the wind chill would be around -45°C.

   0    5   10   15   20   25   30   35   40   45

 45
 40
 35
 30
 25
 20
 
 15
 10
  5
  0
 -5
-10
 
-15
-20
-25
-30
-35
-40

  45   43   34   29   26   23   21   20   19   18
  40   37   28   23   19   16   13   12   11   10
  35   32   22   16   12    8    6    4    3    2
  30   27   16    9    4    1   -2   -4   -5   -6
  25   22   10    2   -3   -7  -10  -12  -13  -14
  20   16    3   -5  -10  -15  -18  -20  -21  -22
  
  15   11   -3  -11  -17  -22  -25  -27  -29  -30
  10    6   -9  -18  -24  -29  -33  -35  -37  -38
   5    0  -15  -25  -31  -36  -41  -43  -45  -45
   0   -5  -22  -31  -39  -44  -49  -52  -53  -54
  -5  -10  -27  -38  -46  -51  -56  -58  -60  -62
 -10  -15  -34  -45  -53  -59  -64  -67  -69  -70
 
 -15  -21  -40  -51  -60  -66  -71  -74  -76  -78
 -20  -26  -46  -58  -67  -74  -79  -82  -84  -85
 -25  -31  -52  -65  -74  -81  -86  -89  -92  -93
 -30  -36  -58  -72  -81  -88  -93  -97 -100 -102
 -35  -42  -64  -78  -88  -96 -101 -105 -107 -109
 -40  -47  -71  -85  -95 -103 -109 -113 -115 -117

A wind chill formula

For the mathematically minded, one formula in pseudo code for wind chill temperature t_c is

if s < 8 then
        c = -0.4488s
else
        c = 14.81 - 2.682s + 0.055041s² - 0.000575s³ + 0.000002402s⁴
t_c = t + c (33.3 - t) / 73.3 °C

Where s = the wind speed in kilometres per hour (kph, 0<s<80) and t = the air temperature in degrees Celsius (°C, -50<t<+20). The result is in degrees Celsius and is accurate (i.e. matches standard tables) to better than 1°C over most of the range. To use other units, appropriate conversions should be made or the equations modified appropriately.

The formula is also valid for high temperatures and hot wind heat stress, although the last line would more appropriately be modified to t_h = t + t (40 - t) / 80, to allow for the fact that the skin temperature is likely to be closer to 40°C than 33°C.

The following Calculator implements this algorithm for wind speeds up to 80kph:

The impact of wind chill on humans

As already mentioned wind chill is not an exact measurement and is not the only parameter that contributes to comfort in windy conditions. The warming effect of direct sunlight can provide some relief. Also there are characteristics that effect particular individuals. For example someone who is thin or someone wearing damp clothes will lose more heat and feel colder than someone who is not.

Wind chill should be taken very seriously. Wind chill below -50°C to an exposed forehead can be very painful and cause unconsciousness in minutes. If a significant percentage of skin is exposed, core temperature will drop rapidly and induce server hypothermia, coma and death within 10 to 15 minutes.

When the body’s core temperature is at -35°C, deep shivering will occur and recovery in a warm environment can take hours. At -34°C blood flow to the brain is impaired causing difficulty in walking, talking and sleepiness. Below 30°C the body no longer attempts to regulate temperature and coma in induced. At -25°C the heart stops. It iced water this occurs in less than 30 minutes.

The impact of wind chill is summarised in a table below.

What is the Wind Chill Factor?

In the above table an addition term is introduced: the Wind Chill Factor. Wind Chill Factor is a more scientific term for 'wind chill' and is expressed in watts per square meter. It is the total conductive heat flux from a heated surface exposed to a cold wind. Typically 33°C is chosen as the temperature of the heated surface as it reasonably representative of the human skin temperature in the cold. As a matter of interest, the human body generates 150 - 500 watts of heat, depending on exertion levels.

The Wind Chill Factor is a useful measure, as it may be used in conjunction with other mechanism of heat loss or gain to yield a net effect.

Is there a Sun Roast Factor ?

Is there an equivalent Sun Roast Factor at the other end of the scale? There should be, but there is not one in common use.

Absorption of the sun's radiant heat can increase the skin's temperature above ambient and above the bodies core temperature (37°C). The result can be server heat stress, hyperthermia and even death.

When the body’s temperature is at 42°C, heat stroke is likely to develop with dizziness, fainting. At 43°C abdominal distress, delirium and physical damage to body cells, especially those of the brain and possible death. The solution is to find shade, apply cooler material to skin (such as water or mud) and / or exploit the cooling effect of a breeze (i.e. wind chill!).

The intensity of the sun's radiation can also be expressed as a heat flux in watts per square meter. Typically the midday sun is 1100 watts per square meter although it may down to 700 watts per square meter at high latitudes. If this figure is subtracted from the Wind Chill Factor, it can significantly alter the comfort level of the environment.

Conversely to the warming effect of the sun, a clear night sky can have a cooling impact as heat is radiated into space. On a clear night the heat loss can be as high as 150 watts per square meter.

The human body has a very narrow range of operating temperature. The core temperature is the temperature of the main body cavity and is normally maintained at 37°C ±0.5°C. Excursions outside this range can be very serious.

Thankfully, however, the human body has evolved a most effective thermo-regulation system.