January 2006, Issue 186

Internet-Connected Sonic Anemometer

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SPEED OF SOUND IN AIR

The speed of sound in air depends mostly on the temperature. It depends slightly on humidity and the air’s actual mixture of gases. Luckily, you have to worry only about the temperature. Furthermore, if you’re only interested in the wind speed, you can just factor out these effects.

The standard speed of sound is usually determined by one of the following:

These are approximations, and they don’t account for humidity. A more precise instrument would use more elaborate models for the speed of sound in air.

How do you go about measuring the speed of sound? The most reliable methods involve ultrasound range measuring. Ultrasonic transducers, especially for the 40-kHz band, are readily available. I’ve seen them used in numerous robotics projects.

In an ultrasonic ranger, a short burst of ultrasound (8 to 16 cycles) is transmitted via a transducer. Another transducer then picks up the reflections of the sound. The delay between the transmitted burst and the received burst is called time of flight (TOF), which can be converted to distance if you know the speed of sound.



Although ultrasonic transducers are bidirectional devices (i.e., they function as transmit and receive transducers), they usually use a separate transmitter and receiver transducer. The transmit transducer has a tendency to ring for some time after the excitation waveform stops. This limits the short range of such a system.

Transducers can be optimized for transmitting or receiving. If you substitute one for the other, you’ll get reduced performance. Circuitry for rangers using separate transducers is available in many robotics publications and datasheets for transducers.

Measuring the actual speed of sound is easy if you have a calibrated distance. In sonic anemometers, the transducers are mounted in a fixture that fixes a direct distance between transducers. If you measure the direct time of flight between the transducers, you can compute the perceived speed.

This speed is the speed of sound in the air plus the speed the wind exerts.

If you determine the air temperature with a thermometer, you can compute the wind speed simply by applying one of the earlier expressions:

Now, here comes the clever part. If you measure the speed in both directions along the same path, you don’t need to know the temperature.

By combining the equations, you get:

You can also derive the current temperature:

Of course, the system needs to transmit and receive in both directions along the path. This requires the transceiving transducers or a set of transmit/receive transducers.

Ringing in the transmit transducer isn’t a big problem because the turnaround time is slow. The system waits for the burst to travel the distance to the other side before it switches direction. But the ring has a tendency to stretch the pulse by adding more cycles to it. This seems to work. Well, not quite. It only determines the wind speed along the path. When the wind blows from an angle, you can see only a portion of the wind speed. When the wind is orthogonal to the path, you can’t see any wind speed at all.

To fix this, you can configure the anemometer to measure in different paths. The cross (orthogonal) is a typical configuration. Use the same technique to measure the wind speed along each of the two paths (x and y). To compute the absolute wind speed, simply add the squares of each component and take the square root (magnitude equation):

You can also derive the wind direction:

Other configurations are also possible. I used a triangle (60°).

You might have noticed that you aren’t measuring the Doppler shift of the sound burst. A common misconception about using a sonic anemometer is that you can measure the wind speed by measuring the Doppler frequency shift of the ultrasonic signal.

Recall the high school physics experiment relating to train whistles changing pitch as they approach and recede from a stationary listener. Of course this is true, but in the sonic anemometer setup, both the listener and the train whistle appear to be moving at the same speed. So, it’s more like listening to the train whistle while you’re on a car in the back of the train (i.e., the pitch doesn’t change) even though the train may be moving at great speed.

The Doppler signal in a sonic anemometer measures the change in wind speed, which can give an indication of the wind speed’s stability at the moment it’s measured. You can use this to measure turbulence and fluctuations in wind speed. Of course, this involves being able to measure the changes in the received signal’s frequency. You can use a fast Fourier transform (FFT) to look at the purity of the spectrum. You may also need a transducer with a wide frequency range. Many ultrasonic transducers are tuned for a specific frequency and attenuate if the received sound frequency is out of the pass-band. Check the transducer’s datasheet.