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Weight of the wind is a much used phrase - but is it a real effect?

The weight of the wind is an old saying that, perhaps unusually, has more than a grain of truth, although it is a fairly small grain. A simple question in meteorology rarely has a simple answer and it is all too easy to fall into the trap of making simplistic statements.

In dry air

The starting point is that the force on a sail or windmill blade varies directly with air density and as the square of the wind speed. Fairly obviously, cold air is denser than warm air and cold air will create a greater force than warm air at the same speed. It is easy to quantify this using Boyle’s law. For those without long memories, this simply says that, for a given pressure, the density of a gas varies inversely with the temperature where temperature is in °K (0°C = 273°K). In other words

(density at 0°C) divided by (density at 15°C) = 288/273

Therefore, with an air temperature of 0°C there will be 5% more force than with air at 15°C.

The effect of water vapour

The effect will be compounded by the fact that moist air is less dense than dry air. This is because water vapour is a relatively light gas compared to oxygen and nitrogen - the main constituents of the air. The chemical formula for water is H2O ie two molecules of hydrogen to one of oxygen. When water vapour content increases, the amount of oxygen and nitrogen in a given volume of air decreases.

The density of the air as a whole decreases because the mass decreases. Anyone wishing to do the sums can use Google (air density water vapour will probably do the trick) to find some rather frightening looking equations. For a fairly extreme example, in the tropics with a temperature of 32°C and 90% humidity, the air density is 1.14 kg/m3. In a northerly airstream around the UK, we might have temperatures of 10°C and 10% humidity giving an air density of 1.25 kg/m3. So with cold dry air, the force of the wind on a sail would be about 10% higher than with warm humid air at the same wind speed. For dry air at both temperatures there would be a 7% increase; the water vapour effect is fairly small.

A complicating factor and reality

However, the expectation may lead to some misinterpretation of what is actually happening. Remember that an increase in speed from 14 to 15 knots will give an increase in force on a sail of about 15%. In cold and unstable air, convection will result in mixing in the vertical up to heights of anything from 1000 to around 4000 metres. There will be stronger gusts than with warm stable air in which the mixing is much more restricted in depth. Compare the steady winds in the warm sector of a depression with the much more variable wind behind the cold front.

So, the reality is that there is “more weight” in cold dry air than in warm moist air. However, around the UK during the sailing season in one area the variation in the “weight” of the wind must be fairly small and masked by larger effects due to variations in wind speed and especially when there are convective gusts. The effect may only be detectable to a far better helmsman than I ever was. A practical corollary of the above is that wind turbines can generate more power at a given wind speed in cold climates than in warm ones.

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