Carl Morey builds weather stations in his free time. He started with an indoor unit that could measure temperature, humidity, and air pressure and store the data on a memory card. When he decided to add an outside aspect to his setup, he had to decide how to measure wind speed. Typically people use a mechanical anemometer -- those little spinning things you see from time to time. However, Carl decided he wanted an ultrasonic anemometer, according to an Arduino Forum post.
His design uses four ultrasonic transducers. He's measuring the time of flight (ToF) between opposing units. If the wind is traveling against the direction of the signal, the ToF goes up. If the wind is traveling with the direction of the signal, the ToF goes down. By comparing the north/south and east/west ToF, he can figure out the speed of the wind.
See this example from his documentation.
He calculates a ToF without any wind at 1,044.3 microseconds by simply dividing the distance between the sensors by the speed of sound (at his local temperature). The north-to-south ToF measures at 1,043.5 microseconds, while the south-to-north ToF measures at 1,045.2 microseconds. This means that a 1kph wind will give him a difference of 0.8 or 0.9 microseconds in the ToF.
After 3 months of operation, Carl had the following to say about the unit:
"I cannot give accuracy in terms of % as I do not have access to a wind tunnel. I can only compare it with my WMR-100 weather station and there is very good correlation. Below 5kph the ultrasonic is much more accurate because of the limitations of the eggcup sensors.
It has been through rain and strong wind gusts and always gives accurate results. For my amateur requirements the sensor is a success."
Carl has gone above and beyond in his documentation, which you can download here. The files include his entire circuit design, which is shown as a schematic and explained in theory and implementation. He gives roughly 30 pages of details, including test measurements, physical construction, and reference links for each step in the design. He offers not only his original design, but also a couple of modified and updated ones.