Is the force that the wind exerts on an object directly proportional to its speed?

Question

If for instance, the speed of the wind doubles will the force it exerts on - say - a tree or a wind turbine blade or a building simply double or increase by some other factor eg the square of the speed?

Answer 1

Good question. I presume that you'd like to know the reasons behind the different slow- and high-speed limits?

At slow speeds (or for very small objects), the dominant force is that due to viscosity, the "drag" provided by a relatively thin skin of air changing its velocity from zero to that of the ambient medium through which the object is passing. Because of the way that viscous forces behave, that makes the force exerted at slow speeds (and/or on very small objects) proportional to the velocity.


At high speeds (or for very large, particularly "bluff" bodies), a different effect tends to dominate, involving the pressure needed to "blast'' the obstructing volume of air out of the way and around the object. Pressure (force per unit area) and Energy Density (kinetic energy per unit volume) have the same dimensions. Because of that, ultimately, the force experienced by fast (and/or large) bodies tends to scale with the SQUARE of the speed, as you'd expect because that's the dependence present in kinetic energy.

Live long and prosper.

Answer 2

enable there be 2 bodies of hundreds m and M (m

Answer 3

For most large objects, air resistance takes the form of being directly proportional to the square of its velocity. For most smaller objects, air resistance is proportional to its velocity.