Does "wind speed" depend on the density of air?

Our intuitive notion of "wind speed" is that it is the speed at which air molecules are moving at point.

Consider two situations where the velocity of the air molecules are the same but the densities are different.

Will an anemometer indicate the same wind speed in both situations?

How about when using a ribbon (using how it droops as an indication of wind speed)?

How about other air speed measuring devices -- such as a pitot-static system?

And what's the formal definition of "wind speed"? Is it:

• the momentum density divided by a standard value for the density of air
• the momentum density divided by the actual density of air at a point
• something else???

What definition do meteorologists use?

• There are many kinds of anemometers. Commented May 25, 2021 at 5:25

For something like a vane or cup anemometer that actually measures wind speed directly, I don't see why the anemometer would not indicate the same windspeed regardless of density with error due to friction (which would increase as air density or wind speed decreases). It would take longer to adjust to changes in wind speed if the air was less dense though.

Like two cars of the same mass both redlining at the same speed, one with low torque engine and one with a high torque engine. The fact one car puts out more torque just means it accelerates faster up to max speed but both are still limited by the fact that their wheels can't spin any faster. The high torque car might be able to push harder the same higher density air can push harder but it's not travelling any faster.

However, things like a pitot tube measure pressure and in that case you do have to compensate for air density if you want to know true air speed. In an airplane you don't really care about this compensation because what you really care about is that you are flying fast enough so you don't fall out of the sky for the air density you are flying in so the direct pressure from the pitot tube is what you want.

The ribbon also relies on how hard it is being pushed against gravity so would also give different readings for different air densities.

• My guess is that cup anemometers would be affected by air density since they work on the pressure difference between the concave and convex profiles of the cups in the air flow. Commented May 25, 2021 at 14:04
• @ErikR Oh that's a good point. I tend to think of them working more like a sail. But the wave you describe it is almost like a wing. Commented May 25, 2021 at 18:10

You might find it helpful to distinguish between actual wind speed and measured wind speed, since your question seems more about the latter than the former.

You should also bear in mind that even on a still day when there is no wind, the average speed of air molecules might still be around 1,000mph, so it is wrong to equate wind speed directly with the speed of molecules. We need to be clear that the wind speed we observe is an overall drift in the mass of air, which is superimposed on their faster random motions.

The density of the air will have an effect on the measured speed of wind- the quality of an anemometer can be considered to reflect how well it can report wind speed independent of changes in density.

For a given wind speed, a simple ribbon anemometer would exhibit far less movement in very rarefied air than it would in very dense air.

Cup anemometers too are calibrated for assumed range of air density- if an anemometer calibrated for use near sea level were taken to the top of Everest, say, it would need to be recalibrated owing to the reduced density of air at higher altitudes.

There are many different types of anemometer, such as ultrasound devices which measure propagation delays owing to the passage of air through the device.

However, all these factors relate to the measured speed. The actual speed remains the actual speed regardless of density.

• What do you mean by "actual wind speed"? Even though I said "speed" in my question, I really am interested in how a "wind velocity vector" might be determined. It seems it would be related to the combined momentum of air molecules in a small region of space. Commented May 25, 2021 at 13:23
• This is a distinction between mean speed and mean Velocity, of which the latter is understood to be meant in all meteorological and aircraft settings. Commented May 25, 2021 at 14:28
• You have a random motion combined with an overall drift. If you work with velocity instead of speed, the random contributions will tend to cancel out and what will remain if you average all the velocities will be a measure of the overall drift. The 'actual wind speed' in a region is magnitude of the average velocity of the air molecules moving through the region. Commented May 25, 2021 at 14:43