Notes on Underwater Ranging

The Speed of Sound

As our sensors are calibrated for in-air use, you will have to compensate for the different speed-of-sound in water as opposed to air. Our sensors calculate range using the speed-of-sound to determine the distance to a target based on the amount of time that passes before a sensor hears an echo bounce off a target. The speed-of-sound in air is different than it is underwater. For example, the speed-of-sound in air at 20 degrees Celsius is approximately 343 meters per second. At that same temperature, the speed-of-sound in water is much greater at approximately 1482 meters per second. This difference in speed causes our sensors to underestimate the true distance when underwater by a large factor. In this example, the underwater reading of a sensor calibrated for in-air use would be approximately 23 percent of the value reported in air.

Numerous factors are at play that affect the speed-of-sound in both air and water. We cannot always assume that the readings will be 23 percent of the true value. Temperature is one of the major factors affecting the ratio between the speed-of-sound in both water and air. However, pressure and chemical composition, as well as a host of other factors, play into the mix. Frosch (1964) found that the speed at which sound travels through water increases by 4.6 m/sec per one degree Celsius increase in temperature, it increases 0.16 meters per second with an increase in pressure of one kilogram per cubic centimeter, and 1.4 meters per second for each part per thousand increase in salinity above 35 parts per thousand (p. 890). Calculating the correct speed-of-sound for an underwater application can help ensure you receive accurate results.

Acoustic Differences

The speed-of-sound is not the only difference between the way sound behaves in water and in air. Vigoureux (2011) explains that the two greatest factors that differentiate in air and in water propagation of sound are differences in the characteristic impedance and absorption between sound and water (p. 49).

When you stand in the front row of a rock concert, you can feel the boom of the amplifiers rumble through your body. Typically, it is much easier to feel the bass line as opposed to the treble. This relates to acoustic impedance. Acoustic impedance relates how much sound pressure an acoustic flow creates at a given frequency. In the case of the rock concert, lower frequencies are generating more pressure than the higher frequencies, so you can feel them more easily. Vigoreux (2011) further notes that the characteristic impedance of water is greatly different than that of air being many times greater in water (p. 49). Absorption is the second large differentiating factor for in air and underwater sound propagation. Absorption is the process of sound energy being converted to heat energy as it travels through a material. Vigoreux (2011) states that water has about one thousandth the absorption of air (p. 49). These differences between air and water allow sound to travel much further and faster through water than it can through air at certain frequencies. In addition, the mismatch causes most sound to reflect and not pass between air and water (Vigoreux, 2011, p. 50). As sound will not pass well from water to air or vice versa, our sensors will not be able to detect passed the air water surface, but instead see that surface as a valid target. This, however, is not the end of the story. The ability of a sound to propagate or spread through a material is also related to frequency. Frosch (1964) explains that the propagation of high frequency sounds is highly limited, and sounds at frequencies over 10kHz may be limited for long range propagation (p. 889). All sensors released by MaxBotix Inc., at this time, 10/28/2015, utilize a 42kHz sound wave which is certainly a higher frequency than 10kHz. This limitation of high frequency propagation may be restrict long distance ranging in certain cases.

Underwater Challenges

Sound travels through water, and detection of targets happens as expected under controlled settings. In uncontrolled settings such as rivers, lakes, and oceans things may not always work out so well. Currents can shift temperature and carry larger objects that may negatively affect readings. Research by Weston et al., (1969) show underwater transmitted sounds can experience considerable changes and spreading of tonal frequency adding additional difficulties to underwater ranging (p. 568).

Pressure is certainly an uncontrollable challenge. Pressure affects how sound travels because sound itself is a traveling wave of changing pressure. In rare cases, underwater targets may even disappear. Avital and Miloh (2011) note it is possible for targets to have zero sound scattering, indicating acoustic invisibility using continuous distribution of oscillating pressure load to the target walls (p. 568). While this is not a typical or likely occurrence it may happen to a lesser degree and make underwater targets more unpredictable. It is no surprise that the deeper you go underwater, the more pressure you experience. As our sensors are calibrated for in air use, it is likely that you will experience more issues the deeper below the surface of the water you go. MaxBotix does not have any way to measure or compensate for changes in pressure in our sensors and this would be completely left up to the end user.

MaxBotix Inc., has not tested our sensors in underwater applications. There may be a number of unforeseen issues that may arise during testing. As we have not tested our components through these factors, we do not have a clear understanding of everything that will or will not happen.

Finding Solutions

While detecting a target underwater does present a number of challenges, they are not insurmountable. Problems with sound propagation can be fixed using a sensor with high output power and increased sensitivity. MaxBotix Inc., offers a number of high sensitivity sensors, but to determine which sensor works best, especially in an underwater setting, end user testing is required to verify performance in the final environment.

Adjusting for the difference in the speed-of-sound may well be one of the most important tasks for underwater ranging. One may wish to calibrate by placing targets a known distance away from the sensor and calculating a multiplicative factor that corrects for the majority of the error between the reported and observed distances. However, use of a more highly mathematical and scientific approach would certainly be possible. While underwater applications are not currently supported under warranty by MaxBotix Inc., there is certainly a potential to use ultrasonic sensors underwater rather than the more traditional sonar based location. If you choose to attempt such an application, we would love to hear about it. Your information could help guide other users to avoid certain pitfalls and create a successful underwater ranging application. You can review the results of a few end users that have published results regarding the use of our sensors underwater at the following links. Design Spark's Coconut Pi Individual Components Development for an AUV Waterproof Robot Sonar Tutorial

Works Cited

Avital, E. J., & Miloh, T.. (2011). Sound scattering by free surface piercing and fluid-loaded cylindrical shells. Philosophical Transactions: Mathematical, Physical and Engineering Sciences, 369(1947), 2852–2863. Retrieved from http://www.jstor.org/stable/23035835 Frosch, R. A.. (1964). Underwater Sound: Deep-Ocean Propagation. Science, 146(3646), 889–894. Retrieved from http://www.jstor.org/stable/1714368 Vigoureux, P.. (1960). Underwater Sound. Proceedings of the Royal Society of London. Series B, Biological Sciences,152(946), 49–51. Retrieved from http://www.jstor.org/stable/75361 Weston, D. E., Horrigan, A. A., Thomas, S. J. L., & Revie, J.. (1969). Studies of Sound Transmission Fluctuations in Shallow Coastal Waters. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 265(1169), 567–606. Retrieved from http://www.jstor.org/stable/73701