# Ultrasonic Anemometer Part 1 – Math Concepts

## Index

With the first stage of the weather station project nearing completion I’ve decided to explore building some additional sensors to collect more readings. One of the things that I’ve been very interested in measuring is wind speed and direction. A device that measures wind speed is called an anemometer. Wind direction is usually measured with a wind vane.

There are a few problems with traditional designs of these instruments, especially with anemometers. One of the biggest problems is that they usually have a minimum wind speed threshold. If the wind is below this threshold the device will not be able to measure it. This is usually because the wind is not strong enough to spin a propeller of some kind. To overcome the problem of low speed wind measurements I’ve decided to go with a solid-state (no moving parts) alternative. This alternative involves measuring the difference in <a href="https://en have a peek at this web-site.wikipedia.org/wiki/Time_of_flight” target=”_blank”>time-of-flight (TOF) of a sound wave across a known distance.

The overall approach to measuring the wind speed using this method will be:

1. Create a pulse of sound at point A
2. Measure the time it takes to arrive at point B
3. Create a pulse of sound at point B
4. Measure the time it takes to arrive at point A
5. Use the difference in the two times to determine wind speed

This method will determine the wind speed in along one axis. In order to get wind direction you must measure the wind speed along another axis, then use trigonometry to calculate overall speed and direction. To make these calculation easy we will measure the wind speed in the North-South direction and the East-West direction. In doing so the equation for overall speed is

Total Speed = SquareRoot(VNS2 + VEW2

where VNS is the wind speed in the North-South direction and VEW is the speed in the East-West direction. The formula is a direct application of the Pythagorean theorem. The equation for overall direction is

Angle = tan-1(VNS/VEW)

where tan-1 is the inverse tangent function. These equations are relatively simple because of the fact that we intend to make our wind speed measurements exactly 90 degrees apart. It would still be possible to calculate wind speed and angle if we had chosen another angel, but the math would not be as simple as this.

Now that the theory is out of the way, we will begin to actually implement this method in part 2 using some cool electronics and sensors.