Acoustics in Hydrographic Surveying

Math affects our lives in sometimes the simplest of ways. If you’ve ever rode on a boat you probably don’t think about the thousands of years of innovation that made it possible. Hydrographic surveying basically maps out the depth and floor of the ocean or any other body of water. It is very important to know the depths of the water a boat is sailing on so that they can safely pass. Ever since larger boats came in to use, depths were measured simply with sticks. Obviously this wasn’t very practical and eventually, as technology advanced, people progressed to what is called a lead line. This method has been used for the last thousand years, essentially it was a long rope with a piece of lead attached. The high density of lead ensured it would sink completely. After the lead hit the bottom, the rope would be measured. Measurements couldn’t encompass a large area, because like land the ocean floor has many mountains and valleys, so depths would have to be gathered about every half a mile and then would be put in a chart or map.

Most of these measurements, of various countries were gathered by the British, whose empire was very vast at the time. An example of one of these maps is Map A which is an Antique Nautical Navigation Chart, of Rockport Harbor in Massachusetts, this map was made in 1859. On the map there are various numbers scattered, each refers to the depth of the ocean at that particular spot measured using lead lines. Obviously it was a challenge, because they would have to sail to each spot and measure the depth and record it accurately, but at the time it was the only way to ensure safe sailing.

It wasn’t until World War I, when man started studying acoustic principles for war craft, that RADAR (RAdio Detection And Ranging) was discovered. Radar was developed for air only as a way to determine the distance of particular object or any surface. The same technology was then applied in water, and was critical to the use of submarines, and became what is known as SONAR (SOund Navigation And Ranging).

Sonar deals with the sound waves and acoustics branch of physics. Basically there is an instrument called a transducer that sits at the surface of the water, right above the desired measurement. This transducer sends out a longitudinal sound wave (a longitudinal sound wave looks like a pulse see Fig. A) at a very particular frequency that hits the floor of the body of water and reflects back to the transducer, which records the time from when it sent out the sound to the when it receives it back. This time has to be extremely accurate to get a correct reading and always records at the millisecond level. It is also very important to have a unique frequency that won’t be interfered with by naturally occurring sounds in the ocean, it is also usually a very high pitch that human ears cannot hear. The time is then plugged into a formula: Water Depth = Time2×Sound Velocity in Water

It’s a very simple formula, the reason the time is divided by 2 is because the time includes the depth down and back up. See example 1. However in order to get the Sound Velocity of Water a Sound velocimeter must be used. This device measures three environmental parameters that affect the sound velocity, temperature, salinity, and pressure. Salinity is measured on a scale of parts per thousand, this is how many salt molecules there are in every thousand water molecules. The denser the water is, the faster the sound wave moves because sound travels by vibrating molecules. Salinity is measured using an electric shock that goes between another instrument, the better it conducts, the higher the salinity, because salt conducts electricity. Pressure is measured by a much more complex instrument and it varies the entire depth. After those three factors are calculated, they are plugged into an equation, many of which are very complex, however one equation can be used in shallower water where pressure isn’t a large issue, Wilsons Equation for Sound in Water: c=1449.2+4.623T-0.0546T2+1.391×S-35

S = SalinityT = Temperaturec = Sound Velocity in Water

Once c is found it can be plugged into the formula for water depth. This can get much trickier because many factors vary as it gets deeper, temperatures get lower, pressures higher, and salinity varies, all of which affects the sound velocity in turn affecting the first equation. But that is much deeper into the topic and what is covered above is simply the basics, which is mostly done by computers now.

I chose this topic for many reasons but mostly because of my father, who works as a Hydrographic Surveyor. He works with the company Fugro and I even worked there as an office assistant. He also works some time out of the year for the NOAA (National Oceanographic Atmospheric Administration) on the Services Review Panel. Another reason is that this connects what I learned in Physics about sound waves to real life uses. This project helped me to really understand a concept that is not only used in oceanography, but many other things. Transducers are used in many way in our lives one of their most popular and everyday uses being ultrasounds. While most of this math is only used in specific Professions, the same math concepts can be used for various everyday things such as calculating how long it will take you to get to a destination at a specific speed. Although what fascinates me most is the amount of math used in everything we do, I would have never thought of all that goes into simply sailing a boat across a harbor.

Bibliography

Beemster, Cor, Tim Haycock, Peter Jansen, Huibert-Jan Lekkerkerk, Jelle Roders, Robert van der Velden, and Rein de Vries. Handbook of Offshore Surverying Volume 2. London: Skilltrade, 2006.
Carothers, Jeff. Personal interview. 20 May 2012.
United States. National Oceanographic Atmospheric Administration. 17 Nov. 2011. 22 May 2012 <http://oceanservice.noaa.gov/navigation/hydro/>.