I have been told that the wind has more force on a yacht鈥檚 sail in conditions of high humidity, such as in the tropics, because the higher water content of the air increases its mass, and therefore the force, on the sail at any given wind speed. Is this true? If so, is there an equation I can use to calculate the increased force?
鈥� In fact, humid air exerts less wind force than dry air. At high speeds, the force exerted by a moving fluid is proportional to its density. There is a popular misconception that humid air is denser than dry air 鈥� probably because we feel more lethargic and tend to describe humid weather as 鈥渉eavy鈥� and oppressive. However, the opposite is actually the case.
鈥淭here is a misconception that humid air is denser than dry, probably because we describe it as 鈥榟eavy鈥欌��
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A water molecule, H2O, has a molecular weight of 18. Air consists of approximately 79 per cent nitrogen, N2, of molecular weight 28, and 21 per cent oxygen, O2, with a molecular weight of 32. So air鈥檚 effective average molecular weight is 28.84, much greater than water鈥檚 18.
From the ideal gas law, at a given pressure and temperature the number of molecules of gas in a given volume is constant, so if in humid air some of those molecules are water molecules, with their lower molecular weight, then humid air must have a lower density.
In fact, this lower density helps to drive the water cycle: the buoyant humid air rises to an altitude where it is cold enough to cause the water vapour to condense and fall back to earth as rain.
Although we might think of a gaseous water molecule as squeezing in between the air molecules and hence making the air denser, its actual effect is to force the air molecules apart to make space for itself. Only if the air were in a closed vessel would the evaporation of water cause it to become more dense, but then the pressure would rise too.
Conversely, it is easy to demonstrate how the volume and pressure drops when the water condenses back out again by shaking some warm water in a partly filled plastic bottle and then sealing the lid. As the water vapour cools and condenses, it will cause the air pressure to drop and the bottle will buckle inwards.
Of course, if the humid air contains fine droplets of water 鈥� as opposed to water vapour 鈥� then these will exert a large force as they impact on the sail.
Simon Iveson, School of Engineering, University of Newcastle, New South Wales, Australia
鈥� Air density decreases with rising humidity at typical sailing temperatures. At 25 掳C, air at 90 per cent relative humidity is about half a per cent less dense than at 30 per cent relative humidity. However, the effect of air density on a sailing boat is complex because density causes drag as well as lift, depending upon the boat鈥檚 鈥溾�� and sail plan.
Experiments using a velocity-prediction program developed for yachts suggest that humidity has a negligible overall effect upon boat speed for a modern America鈥檚 Cup-style yacht. (The software balances aerodynamic and hydrodynamic forces, which are derived from computational fluid dynamics models.)
鈥淗umidity has a negligible overall effect upon boat speed for a modern America鈥檚 Cup-style yacht鈥�
Nevertheless, the effect of temperature and barometric pressure on air density is significant. A boat sailing in 15 knots of wind during a hot, humid, low-pressure day off Valencia, Spain, could be 1 per cent faster than sailing on a cold, dry, high-pressure day in Auckland, New Zealand, due to decreased drag caused by 10 per cent less dense air.
It鈥檚 possible, though, that differences in wind shear and gradient between the locations would obscure this effect.
Christopher Miller, Kawau Island, New Zealand
鈥� It is possible that in some parts of the world there is a correlation between humid conditions and high barometric pressure, which would cause an increase in air density and hence a greater sail force for a given wind velocity.
High humidity may also cause the sail to become less 鈥渓eaky鈥� than in dry conditions, either by causing the fibres in the sail fabric to swell or, less likely, by the condensation of water onto the sail, partially blocking the pores in the fabric.
Ian Vickers, Harrison, Australian Capital Territory, Australia