How To Convert Wind Speed To Force

When talking about wind, many different images may come to mind. Wind takes many forms, from a balmy kite-flying summer breeze to a roof-ripping hurricane. An anemometer measures wind speed, but how does the speed of the wind translate into force?

Force, generally defined as a push or pull, can be calculated using the formula force equals mass times acceleration (F = ma). Wind also pushes and pulls, generally with greater force when moving faster. Pressure equals force divided by area. Essentially, wind applies force against an area like a wall, a roof or a person.

Anemometers measure wind. Although different types of anemometers exist, the one that's most commonly used turns with the wind. The rate of turns translates into wind speed and wind pressure. Because wind speed fluctuates, an average number of turns over a short time is used to calculate wind speed. Wind speed most commonly will be reported in miles per hour (mph), kilometers per hour (kph) or Beaufort scale, but it may also be reported as knots, feet per second (f/s) or meters per second (m/s). Several online programs will convert wind speed from one unit to another.

Calculating the force of wind requires the mass of air and acceleration of wind. The average density of a mass of air at sea level equals approximately 1.229 kilograms per cubic meter. The area the wind hits is measured, in this case, in square meters. The mass of air hitting a surface then equals air density times area. The acceleration (a) equals the square of the wind speed in meters per second (m/s).

Use the formula force (F) equals mass (m) times acceleration (a) to calculate the force in Newtons (N). One Newton equals one kilogram-meter per second squared (kg-m/s²).

Be sure to use the matching units. In this calculation, the average air density at sea level equals 1.229 kilograms per cubic meter (kg/m³). The area of air impact equals 1 square meter. To calculate the force of a 5-mile-per-hour wind, first convert the wind speed to meters per second. Using an online converter shows that 5 mph equals 2.24 m/s.

Filling in the formula force equals air mass (A_m) times wind speed squared:

\(F=A_m\timesd a^2\)

gives this calculation:

\(F = (1\text{ m}^2) \times (1.229\text{ kg/m}^3) \times (2.24\text{ m/s})^2=6.17\text{ N}\)

Completing the math shows that F = 6.17 kg-m/s² or 6.17 N. So, a breeze of 5 miles per hour would have just enough force to lift a standard kite.