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# 1.3 Ground-level winds and air movements

Section 2.2 dealt mainly with the general picture of air movements in the main troposphere (meaning above about 1000 m altitude). These are known as the geostrophic winds or gradient winds. The lower sub-region below 1000 m comprises the atmospheric boundary layer. This has a complex wind profile in terms of wind speed versus height because of the variability of heating effects and geographic features. In this region, the wind speed is modelled from a reference wind speed at a ground level to reference height, , of 10 m. In this layer the flow is mixed and can be modelled as turbulent.

In engineering applications – for example, in the design of buildings and other external structures such as radio masts, or monitoring likely winds around airports – the profile is usually represented by a power model of the form:

Equation label:(Equation 9)

where is the required design wind speed at height , is the wind speed at the 10 m reference height , and the exponent is related to the surface roughness. Table 1 shows some values for .

## Table 1 Ground-level wind speed model exponents

Feature | Model exponent,
--- | ---
Flat lands and open water | 0.10
Open varied terrain | 0.15
Suburban | 0.25
City centres | 0.35

## Selecting design wind speeds

It is proposed to erect a 50.0 m tall radio mast in the flatlands of Norfolk where the reference wind speed at 10.0 m height is 23.0 m s-1. What would be the design wind speed for the top of the mast? Give your answer to 3 significant figures.

### Solution

The design wind speed can be found using equation (10):

First, identify the relevant values:

Rearranging equation (10), the design wind speed is

## Activity 7

What would be the design wind speed at the top of an offshore wind turbine of height 245 m? The reference wind speed at reference height 10.0 m is 25.0 m s−1. Give your answer to 3 significant figures.

### Answer

Considering equation (10),

So

Wind speeds and their effects have been categorised in the Beaufort wind force scale, which will be familiar to listeners of broadcast shipping and weather forecast bulletins (and students of previous modules). It is named after the Irish hydrographer Sir Francis Beaufort, (1774–1857). It is not an exact scale, being based originally on subjective visual observations noted from sailing ships at sea. Table 2 summarises its main features as applied now to effects on land and sea.

## Table 2 Beaufort scale and wind effects on land, adapted from Meteorological Office data

Beaufort scale number | Wind type | Wind speed limits | Effects on land | Effects out at sea
--- | --- | --- | --- | ---
|  | (m s−1) | (km h−1) |  |
0 | Calm | < 1 | < 3.6 | Smoke rises vertically | Flat mirror-like surface
1 | Light air | 1–2 | 3.6–7.2 | Smoke drifts, weather vanes not indicating | Ripples like scales, no foam crests visible
2 | Light breeze | 2–3 | 7.2–10.8 | Leaves rustle, weather vanes indicating, wind felt on face | Small wavelets not breaking
3 | Gentle breeze | 4–5 | 14.4–18.0 | Leaves and twigs moving, light flags extended | Large wavelets, a few beginning to break
4 | Moderate breeze | 6–8 | 21.6–28.8 | Dust raised, paper and small branches moved | Small longer waves, frequent ‘white horses’
5 | Fresh breeze | 9–11 | 32.4–39.6 | Small trees sway, crested wavelets on lakes | Moderate waves getting longer, some spray and many ‘white horses’
6 | Strong breeze | 11–14 | 39.6–50.4 | Large branches move, telegraph wires hum, umbrellas difficult to manage | Large waves, widespread longer-length foam crests
7 | Near gale | 14–17 | 50.4–61.2 | Whole trees sway, walking into wind difficult | Waves breaking, foam being blown, spindrift starting
8 | Gale | 17–21 | 61.2–75.6 | Twigs break off trees, walking into wind more difficult | High long waves, crests breaking into spindrift, prominent foam streaks
9 | Strong gale | 21–24 | 75.6–86.4 | Chimney pots, tiles breaking loose, walkers blown over | High waves, dense foam affecting visibility
10 | Storm | 25–28 | 90.0–100.8 | Trees uprooted, considerable structural damage | Very high waves, long overhanging crests, whole surface becoming white. Poor visibility
11 | Violent storm | 29–32 | 104.4–115.2 | Widespread damage | Exceptionally high waves hiding small ships, dense white foam
12 | Hurricane | 33+ | 118.8+ | Devastation | Air filled with foam and spray, sea completely white, very poor visibility

Referred to in the table, spindrift is spray blown from the cresting waves in the direction of the gale, while white horses is a colloquial term for short lengths of foaming white water.

Because the wind motion at ground level is in a turbulent boundary layer, the wind speed at any point varies erratically. The higher-gradient wind can also come into the picture at any time due to the ad hoc nature and development of large-scale weather events. Thus, when designing buildings and outdoor structures, the consideration of wind loads likely to be experienced has to rely on statistical methods using published data.

For buildings and other civil engineering works, these wind loads are covered by a British Standard (BSI, 2010) which in turn is based on a Eurocode (CEN, 2005) with a National Annex for the UK. The Eurocodes are Europe-wide standards for incorporation into national legislation, but because of the vagaries of weather and wind patterns (in particular, for example, the exposed nature of the UK), each country will have its own national specifications based on localised data.

The basic idea is to establish for a particular location a maximum value of mean wind velocity that is sustained for a 10-minute period, and that is only likely to occur with an annual probability of 0.02, i.e. once in every 50 years. This will be chosen from a wind speed map such as that in Figure 9. The wind speeds are shown on each contour in m s−1 and the grid squares labelled NA to TW are 100 km × 100 km each. For a location between contour lines, a value can be interpolated or the higher value of the two adjacent contours can be used. The process then is described in the standard as the calculation of characteristic values of overall wind actions. In brief, this can comprise more than 20 stages considering a number of issues, such as the location (distance from coast), the land terrain, the proximity of other buildings, the height of the building, the altitude of the building from sea level, the shape of the building, the orientation of the building, the proximity of any cliffs, ridges or escarpments, etc.

Figure 9 Wind map for the UK from British Standards (2010)

These considerations are quantified as individual factors and coefficients, which are then applied to the chosen worst-case mean wind velocity to determine a peak velocity pressure (usually written even though it is a pressure, with units of pascals) which can be used for design load cases. Equation 11 gives an example:

Equation label:(Equation 11)

where is the wind speed, is the altitude coefficient, is the direction coefficient, is the exposure coefficient and is a town location coefficient. Equation 11 is basically the equation for dynamic pressure in air of density = 1.225 kg m−3 i.e.

but with a series of correction factors for location. When designing real structures, the appropriate values for these factors must be determined from the original standards. As the load cases determined by this method are based on statistics and probability, there is always a possibility, however small, that they will be exceeded in an exceptional storm. There is, however, an optimum design where the cost of further construction for greater safety is not justifiable and the calculated failure probability is extremely small.

## Activity 8

Using the simple model in Equation 9 and the British Standards wind speed map (a larger PDF version can be found here), determine the wind speed in km h−1 allowed for in the design of a 30.0 m-high building in the centre of Carlisle. What would it be in the countryside surrounding the city, assuming that the countryside comprises open varied terrain? Give your answers to 3 significant figures.

### Answer

From the wind speed map shown in Figure 9, the wind speed for Carlisle is 24 m s−1.

From Equation 9 and Table 1

so

or

In the countryside

or

## Design wind speeds from wind maps

A notional design wind speed is obtained from official maps and then modified with factors to take account of local features and height.

If is the reference wind speed at a reference height of 10 m, is the height under consideration and is a factor related to local features as indicated in Table 1, the design wind speed can be obtained from equation (10):

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