The Wind Pressure Formula

In a posting on this blog, "The Air Pressure Vector", I pointed out that the fact that whitecaps form on waves when the wind speed reaches 22 kilometers per hour this means that wind at this speed must exert a force that is equal to the standard air pressure of 14 pounds per square inch or 9,863.6 kg per square meter.

In the weather report, wind is expressed as a velocity. But this does not tell how much force the wind exerts on an object.

Suppose you are building a sign and you are told that the sign must be able to withstand a wind of 35 kph. What exactly does this mean? It does not tell you how much force the wind will exert on your sign. There is the old Beaufort Scale of wind effects but this is just broken down into a scale of one to ten.

For an aircraft, this is not the case. Aircraft have both an air speed and a ground speed. The air speed is how fast the plane is being propelled by it's engines. The ground speed is how fast the aircraft is moving relative to the ground when the wind is factored in. For aircraft, the expression of wind is more useful in terms of velocity.

My proposal is that the conversion factors between velocity and force of the wind as revealed by the fact that whitecaps form at 22 kph (13.67 miles per hour) and standard atmospheric pressure is 10,356.78 kg/sq. meter (14.7 psi) should be kept handy. This will make it simple and easy to calculate the pressure that a wind of a given velocity will exert. Then, a sign or other structure can be pre-tested to withstand wind by putting it in a horizontal position and putting appropriate weights on it.

In estimating the pressure that wind will put on a structure, we should not try to be too accurate. The effect of wind on the base of a structure will depend on how it is mounted. If it is not perpendicular to the wind direction then trigonometric functions must be used. When a structure is based on the ground, the force of the wind on it is diminished somewhat by stationary air "piling up" against it and forming an invisible inclined plane along which the wind moves. It is well-known to fence builders that wind will just jump over a solid fence but will be broken up into eddies by one with pickets on alternating sides of the rails.

To calculate the wind pressure on a surface perpendicular to the wind direction, divide the speed of the wind in kph by 22, or miles per hour by 13.67. Then square the result and multiply it by the standard air pressure. To square a number, multiply it by itself. We must square the result of the division because we know that an object travelling twice as fast has twice the momentum and when dealing with a fluid, it will mean that the surface will be struck by twice as many atoms or molecules, thus increasing the force by a factor of two.