wind speed and wind force

see also:

• Climate - Introduction 1 - atmosphere and temperature
• Climate - Introduction 2 - water and rain
• Climate - Introduction 3 - air & wind
• Climate - Introduction 4 - Climates
• beaches and sea waves
• thunderstorms and hail
• tents and the wind
• camping in strong winds

• the physics of wind is quite complicated and this page attempts to simplify it
• understanding wind and its forces is critical to ensuring a safe camping or outdoors experience
• gusts are often 50% stronger than average wind speeds
• winds averaging 50-60kph can have gusts to 100kph and these are generally labelled “damaging”
• winds averaging 70-90kph can have gusts to 130kph and these are generally labelled “destructive”
• peaks of Victoria's alps often have wind gusts 20-30% stronger than regional areas

• this scale was based on visual and subjective observation of a ship and of the sea - the wind speeds have later been added

• estimating ground wind speed from distance between isobars on a weather map:
  • assuming 2mb isobars at mid-latitudes such as Melbourne:
    • 2000km between isobars (ie. width of Australia) then < 2 knots
    • 1000km then 2-3 knots
    • 500km then 4-6 knots
    • 250km then 8-11 knots
    • 125km then 17-20 knots
  • wind speeds are generally faster near the equator for same pressure gradient
  • detailed calculation:
    • geostrophic wind speed  in m/sec = 77.5 x horizontal pressure gradient in mbar per metre / Coriolis parameter
    • Coriolis parameter = 2 x angular velocity of earth's rotation in radians per second x Sin(latitude)
    • angular velocity of earth's rotation = 7.29 x 10^-5 radians per second
  • you need to take into account local topographic effects, local fronts, storms, etc. as well.

• standard metereologic wind speed measurements are done at a height of 10m
• general relationship between wind speed and height from ground surface
  • the following are for heights 10m to 300m
  • above 300-600m, the wind velocity is generally no longer affected by the roughness of the earth's surface
• wind speed slowed by wind shear = wind speed at height h = v_o x (h / h_o)^α
  • v_o = wind speed (m/s) at height h_o in m
  • α = wind shear coefficient (open water = 0.1, smooth, level grass = 0.15, low bushes with few trees = 0.2, forests, hills or buildings = 0.25)
• compared to wind at 10m above ground, wind at 0.5m above ground is generally less than half, and may be close to 1/10th or less if there are numerous bushes or obstacles, and may be 70% of the wind speed at 2m elevation ¹⁾
• an alternate power law is Vz = k x z^1/a where Vz is velocity at height z and k and a are constants
  • for open country a = 7; for wooded countryside and urban outskirts, a = 3.5; for centres of large cities a = 2.5²⁾

• wind hitting a cliff:
  • the wind flow will be directed above the cliff at greater speed while a “bubble” region adjacent to the cliff face extending away from the cliff face by a distance of approx. half the cliff height will have turbulence and gusty winds which on average may be more into the wind direction rather than in the same direction - but don't rely on this reversal to stop your boats hitting rocks at the cliff face!
• wind flowing over land which ends as a cliff:
  • a separation bubble of increased turbulence with flow reversal will form for a distance beyond the cliff approx. 4 x the cliff height
• wind flowing over a small island (less than 100m high and 1km diameter):
  • a flow separation and reversal area with increased turbulence and higher wind gusts but lower average speed may form on the leeward side if the island is steep enough on the lee side for the given aerodynamic roughness of the island.
  • thus if the islet is covered by trees or bushes, separation will occur if the leeside slope is greater than about 20degrees, whereas it must be greater than about 30 degrees if it is covered by grass.
  • the potential wind gusts in the leeward region can be estimated approximately by the equation:
    • max. potential wind gust = (undisturbed wind speed at height 1/5th of islet height) x (1 + (7 x islet height/islet diameter))
  • the downwind extent of this reversal is usually no more than 3-4 x height of the islet but may extend to 10x height if the islet has a steep rocky crest. The average speed of the wind in this wake will have regained 90% of its original speed by some 10x islet diameter while the turbulence persists for a little further.
  • the wake disturbance also spreads out horizontally on either side of the islet.
• urban areas with housing
  • a wall can act as a windbreak or intensify airflow
  • the wind velocity profile generally falls the closer it is to the ground, and particularly when it is below the height of the building walls and trees (the interfacial layer) as a result of obstructions, although in certain circumstances channeling may actually increase wind speeds higher than this

• wind force (eg. on a sail)  = surface area of obstruction x air density x drag coefficient x (wind speed)² 
• air density is approx. 1.2 kg/m³ 
• thus every time wind speed doubles, the sail area needed must be reduced to a quarter, but in reality, what is done is reduce the force coefficient by changing the angle of the sail to the wind and adjusting the set of the sail. Also this depends on the aspect ratio of the sail - a tall one is more efficient than a short fat one, especially in strong winds - as wind speed increases with height - but a tall sail results in a greater “heeling moment” or tendency to pull the boat over sideways.

• drag coefficient (Cd) varies with shape of the obstruction and some very approximate values are:
  • concave surface (eg. wind blowing a tent wall inwards): Cd = 1.3-1.4
  • a flat non-deforming surface: Cd = 1
  • corner of cube into wind: Cd = 0.8
  • curved dome with peak facing into wind: Cd = 0.4
  • some highly streamlined tunnel tent shapes have a drag coefficient as low as 0.04
  • turbulence behind a short cylinder may result in Cd = 1.2 whereas the much less turbulence behind a long cylinder may result in Cd = 0.8
  • small tent fabric panels tension more and deform less than large ones and will may have lower Cd although there are a variety of other factors at play
  • the closer a panel is to vertical the more drag it has, and the more it will be impacted by wind, however, triangular panels with a wide base reduce this effect hence pyramid tents are quite aerodynamic

• when moving air (eg. wind) is stopped by a surface - the dynamic energy in the wind is transformed to pressure and the pressure acting the surface transforms to a force

wind pressure in Pascals = drag coefficient x air density x (velocity in m/sec)²

hence if Cd = 1, 100kph wind exerts 924Pa = 94kg/m² pressure, 90kph wind exerts 750Pa = 76kg/m² pressure 80kph wind exerts 591Pa = 60kg/ m² pressure

wind force in Newtons = wind pressure in Pascals x surface area of obstruction in m²

divide this by 9.8 to get wind force in kilograms