How hard the wind pushes
Wind exerts a pressure on every surface it meets, and on a sign, a fence, a solar panel or a shade sail that pressure adds up to a large force. Estimating it helps you choose posts, footings and fasteners, or understand why a fence blew down in the last storm.
The formulas
The dynamic pressure of the wind is:
q = ½ × ρ × V²
with an air density ρ of about 1.225 kg/m³. In US units, with V in mph, this is about q = 0.00256 × V² psf.
The force on a flat surface of area A is:
F = q × Cf × A
where Cf is the force coefficient, about 1.2 for a flat sign, up to about 2 for long solid walls and less than 1 for round shapes. The overturning moment at the base, which the posts and footing must resist, is the force times the height of the center of the panel above the base.
Example
A 32 ft² sign in a 90 mph gust, with Cf = 1.2 and its center 8 ft above the ground:
- Wind pressure: 20.7 psf
- Pressure on the sign: 20.7 × 1.2 = 24.8 psf
- Force: about 795 lbf
- Moment at the base: about 6,360 ft·lb
At 45 mph, half the speed, the force drops to a quarter, about 200 lbf.
From estimate to design
Building codes such as ASCE 7 add factors that this simple calculation leaves out: the basic wind speed for your location, exposure category, height above ground, topography, gust effects and the risk category of the structure. Treat the results here as a first estimate, and have signs, fences, carports and structures over a few feet designed or checked to the local code.