Outside a building, air movement is referred to as wind speed. By international agreement, wind speed is measured in knots (though some nations favour m/s, but km/h is easier for most people to visualise). A knot is equal to 1.85 km/h, (0.514 m/s or 1.152 mph). The knot unit has its origins in naval history, where a knot is one nautical mile per hour. A nautical mile is one minute (one sixtieth of a degree) of latitude at the Earth's surface.

The Beaufort scale can also be used as a system for describing wind speeds. It was introduced in 1806 by Admiral Sir Francis Beaufort of the British navy to describe wind effects on a fully rigged man-of-war sailing ship. It was later extended to include descriptions of effects on land features as well. The following table relates the 12 classification of wind speeds with accompanying descriptions of the effects on surface features.

Wind speeds can fluctuate almost second-by-second. Whilst it is possible to take instantaneous measurements, they are not particularly meaningful unless looking for maximum speeds. To make them more meaningful, meteorological observations usually use the longer term mean wind speed, an average taken over the ten minutes preceding the time of observation.

A gust is a significant fluctuation above the mean typically lasting from a few seconds to a few minutes. Wind flow close to the ground is always turbulent due to the roughness of the Earth's surface. Gustiness is increased by the presence of buildings, trees and rocky country but, at the same time, the overall mean wind speed is decreased by friction. For this reason winds over the sea and lakes are usually much less gusty than over land.

For more information on our response to speeds within buildings, see the air movement topic in the comfort section.

Measuring Wind Speed

The measurement of wind speeds is usually done using a cup anemometer, such as the large one in the picture below. The cup anemometer has a vertical axis and three angled cups that capture the wind. The cups turn because the shape is such that the resistance to flow is asymmetric about each cup.

Figure 2 - A example of a cup anemometer, inset with a smaller propeller-based personal air movement meter more suitable for low-speed indoor measurements.

Instead of cups, anemometers may be fitted with propellers although this is not common. Other anemometer types include ultrasonic or laser anemometers which detect the phase shifting of sound or coherent light reflected from the air molecules. Hot wire anemometers detect the wind speed through minute temperature differences between wires placed in the wind and in the wind shade. The advantage of non-mechanical anemometers may be that they are less sensitive to icing. In practice, however, cup anemometers tend to be used everywhere, and special models with electrically heated shafts and cups may be used in arctic areas. The number of revolutions per minute is usually recorded electronically.

Anemometers are usually fitted with a wind vane to detect the wind direction. Wind direction is given as the direction the wind is coming from during the measurement and is given in degrees clockwise from true north.

The Power of Wind

The power of the wind ultimately derives from the power of the Sun, as discussed in the climate topic. Even though only about 1-2% of solar radiation incident on the Earth's surface ends up as wind energy, this is 50 to 100 times more than that converted into biomass by all plants on earth so it represents an enormous potential energy source.

Of course, winds have been known to blow things over. Thus it is important to know just how much power is in a gust of wind. The energy content of the wind varies with the third power (cube) of the average wind speed. If the wind speed is doubled, it will contain 2³ = 2x2x2 = 8 times as much energy.

Because air has mass which moves to form wind, it also has kinetic energy. You may remember from secondary school that:

kinetic energy (joules) = 0.5 x m x V²

where

V = velocity (meters/second) and
m = mass (kg)

Since energy = power x time and density is a more convenient way to express the mass of flowing air, the kinetic energy equation can be converted into a flow equation:

P = 0.5 x rho x A x V³

where

P = power in watts (W)
rho = air density (about 1.225 kg/m³ at sea level, less higher up)
A = Area exposed to the wind (m²)
V = wind speed in meters/sec

This yields the power in a free flowing stream of wind, if it were captured in a large sail or against a theoretical infinitely large surface such as a wall. For more practical purposes it is impossible to extract all the power from the wind as there is usually a spill around the surface due to pressure build-up or flow through a rotor blade. Thus, for a wind turbine for example, some additional terms are needed to get a practical equation:

P = 0.5 x rho x A x Cp x V³ x Ng x Nb

where: P = power in watts,
rho = air density (about 1.225 kg/m³ at sea level, less higher up)
A = rotor swept area, exposed to the wind (m²),
V = wind speed in meters/sec,
Cp = Coefficient of performance (.59 is the maximum theoretically possible, .35 for a good design),
Ng = Electricity generator efficiency (50% for car alternator, 80% or possibly more for a permanent magnet generator or grid-connected induction generator) and
Nb = gearbox/bearings efficiency (depends, could be as high as 95% if good).

The above information was taken from the American Wind Energy Association website.

Prevailing wind direction is important when siting wind turbines, since it is important to place them in areas with the least obstacles disturbing its flow patterns. However, local geography the urban landscape are also significant influences on local wind patterns, especially below 20m, making directions difficult to determine without exceptional local experience.

Wind Chill Factor

When the wind blows across the skin it removes the insulating layers of warm air molecules and replaces them with colder molecules. When all other factors are the same, the faster the wind blows, the greater the heat loss, and the colder we feel. The amount of cooling one feels due to the combination of wind and temperature is called wind chill.

Wind chill factors measure the effect of the combination of temperature and wind speed on human comfort for those exposed to the wind. These do not have the same effect on inanimate objects or humans who are sheltered from the wind. Wind chill factors are usually expressed as an equivalent temperature on the Celsius scale, or in units of power per unit area.

In Canada, wind chill factors are often reported as heat loss in watts per square metre.

Calculating Wind Chill

The formula the US National Weather Service uses to compute wind chill in imperial units is:

Twc = 0.0817(3.71sqrt(V) + 5.81 -0.25V)(T - 91.4) + 91.4

where Twc is the wind chill, V is in the wind speed in statute miles per hour (mph) and T is the temperature in degrees Fahrenheit.

To calculate a Celsius wind chill using V as the wind speed in kilometres per hour (km/h) and T in degrees Celsius, the formula can be rearranged to:

Twc = 0.045(5.27sqrt(V) + 10.45 - 0.28V) (T - 33) + 33

Several sources point out that these two formulas don't quite agree with each other due to round-off error in the constants. The following is an analysis of the problem I once found on the net but don't have a URL for.

Original source: Gene's Weather Pages - Wind Chill Factors

"The variations in various tables that have been published may be the result of use of different formulas for heat loss or different assumptions for skin temperature or calm wind speed, though many are round-off errors from conversions among the various units used along the way. As near as I can figure out, both the U.S. and Canada use an old wind chill formula developed by Paul Siple in the 1930s.

Start with a formula for heat loss, given the air temperature and wind speed. This is Siple's formula:

'H = (10.45 + 10×sqrt(v) - v)×(33 - t)

where:

''H = kilocalories per square metre-hour (kcal/(m²·h), and ''t = air temperature in degrees Celsius, and ''v = wind speed in metres per second, and the 33 °C factor is based on human skin temperature.

To convert this to the modern units of watts per square metre, which are used in Canada, multiply the result by 4184 J/kcal and 1 h/3600 s and 1 W s/J. (Note that 4184/3600 is about 1.162, and you can multiply by this number; the above shows where this number comes from.) Or, using the same units for t and v, change the formula to:

'H = (12.1452 + 11.6222×sqrt(v) -1.16222×v)×(33 - t)

where: H = Watts per metre squared exposed area (W/m²), t = Air temperature in degrees Celsius (°C), and v = wind speed in metres per second (m/s).

To get the equivalent temperature, the heat loss at the given temperature and wind speed is calculated and then the temperature is calculated which would give the same heat loss at a low (but not zero) wind speed. In the U.S. and Canada the speed used for this is 4 statute miles per hour (1.78816 m/s). A formula that will do this is the following, where s equals the skin temperature, either 33°C or the same temperature on the Fahrenheit scale 91.4°F, with the result in the same type of degrees:

 Tequiv = s - ((s - t)×(0.474266 + (b×sqrt(v)) + (c×v)))

where the constants b and c depend on the units in which the wind speed v is measured:

UNITS

B

C

m/s

0.453843

-0.0453843

km/h

0.239196

-0.0126067

kt

0.325518

-0.0233477

mi/h

0.303444

-0.0202886

I have carried my factors to 6 significant digits, which probably isn't really necessary, except to provide consistent results no matter what units are used for t, v, or H. These will most likely be used in a program or a spreadsheet anyway, so all the numbers won't have to be entered for each calculation. If you want to round the results to a whole number of degrees using an INT function, be careful how that function works with negative numbers; some round to the next lower number and some to the number closer to zero.

For example, to calculate equivalent temperature in the degrees used for t and for t in °C and v in km/h, use:

'teq = 33 - (33 - t)×(0.474266+0.239196×sqrt(v) - 0.0126067×v)

For t in °F and v in knots, use:

'teq = 91.4 - (91.4 - t)×(0.474266 + 0.325518×sqrt(v) - 0.0233477× v)

IMPORTANT NOTE: These wind chill formulas are not valid for wind speeds outside the range from 1.78816 m/s to 25 m/s (90 km/h, 55.9 mi/h, 48.6 kt). If you write a program to calculate wind chills, change all speeds higher than 25 m/s to 25 m/s and all speeds lower than 4 mi/h to 4 mi/h.

To convert between heat loss in watts per square metre and equivalent temperatures, use these formulas:

'H = 1300.3 - 14.227 teqF

''teqF = 91.4 - 0.0703 H

''H = 845.1 - 25.608 teqC

'teqC = 33 - 0.03905 H'

I hope that if my assumptions are incorrect, or if I have made an error in my calculations, someone will point that out to me."

Original author: Gene Nygaard

Related Links

Guided Tour on Wind Energy

http://www.windpower.dk/tour/index.htm

UK Wind Speed Database

http://www.britishwindenergy.co.uk/noabl/indexn.html

Wind Chill

Wind Chill - USA Today

http://www.usatoday.com/weather/windchil.htm

Environment Canada

http://www.tor.ec.gc.ca/comm/windchil.html