Temperature compensation for an Arduino ultrasonic distance sensor

161.3 cm

27.0°  347.7 m/s

Ultrasonic distance sensors can find the range out to 2-4 meters and are popular in e.g. robotics. Here I look at how the accuracy can be improved by compensating for the variation of speed of sound with temperature. It actually varies quite a lot in air and around 0 C it is:

      c = 331.3 + 0.606 * T

where c is in m/s and T is in C. The formula is good to up to at least +/-30 C. There is also a dependence of humidity, but as it is so small it is neglected here.

The equation can be analyzed for sensitivity (a little bit of differentation, you know). The result is that a two-way range measurement creates an error of 1.8 mm/C/m. That means that with a 4 degree C error, the deviation will be 14.4 mm at a range of 2 meters. Not a lot, but more than the wavelength which is 9 mm at 40 kHz. Considering how easy it is to compensate for, then why not give it a try?