Analog Computers and Tides

In the 19th century, scientists were keen to solve the problem of predicting tides. Ships needed to know when to go to the port without running aground, and fishermen wanted to know when to catch fish. Variations in water level were measured using a mechanical device that plotted the height of the sea on graph paper. However, nobody knew how to use this data to predict tides and understand what exactly causes them. The story of tide prediction is absolutely fascinating and it led to a breakthrough in computing. It also features a young Lord Kelvin, right after the worked on laying the transatlantic telegraph cable when he developed a fascination for the sea. It is important to learn about analog computing since soon we might need to return to it in a more sophisticated form, in order to face the most difficult contemporary computing problems.

An image of a receding tide. Credit: SurferToday.

Since Newton, scientists knew that tides are caused by the gravitational tug of astronomical objects, such as the Moon and the Sun. In the 1770s, Laplace developed a system of partial differential equations that approximated tides based on the variations in the gravitational pull. Nevertheless, they were still a very rough approximation and it took until the 1860s to develop an ingenious way of predicting them.

A water level graph from Newport, RI in 2009. Credit: NOAA.

Tides come in cycles, so their pattern is a combination of sine and cosine functions. In order to decompose a complicated function, a Fourier transform developed in the early 19th century, could be used. William Thomson, later known as Lord Kelvin, decided to apply the Fourier transform to tidal waves. It was known that certain tidal patterns match up with the cycles in gravitational pull of the Sun and the Moon, but just how strong the impact each factor had, was up to debate. In order to find out, Thomson had to do tons of complicated multiplication and integration, therefore he decided to automate the process.

A mechanism for generating sinusoidal motion using circular motion. Credit: E. G. Fischer.

He knew that there was a mechanism used to convert circular motion to a sinusoidal graph. If he tuned a sufficient amount of these machines to the amplitude and frequency of each of the component functions, he could recreate the original function. Hence, this could be done in the opposite way and future tides could be predicted. He combined a few of these mechanisms together and with some clever calibration, one of the most successful analog computers of all time.

The 10 component tide predicting machine developed by Kelvin in the years 1872-1873. It is on display in the Science Museum in London. Credit: William M. Connolley.

Predicting tides not only proved useful for the fishing and transport industry, but it also helped beat the Nazis in WW2. Knowing when the tide would come on D-Day was crucial in order to avoid German defences on the beaches and allow the ships with soldiers to retreat. Analog tide prediction machines were in use till the 1960s and 1970s, until more powerful digital computers took over. The advantage of analog is that it allows for a continuous input and output rather than a string of 1s and 0s. However, since they are a mechanical system with continuous variables, tiny manufacturing uncertainty can completely invalidate the result. In digital machines an output of 0.95 is still classified as a 1, so manufacturers can be more lenient with precision.

What does this have to do with astrophysics? Computation is closely linked with modern research, as this is a field were direct observation is often difficult and simulations are required. Perhaps there are some future uses were analog machines in astronomy. More importantly, this is a story about understanding a physical phenomenon that has cosmic origins. It is another chapter in the story of using technology to decipher the universe and its impact on our daily life, in this case through gravitational fields. A lot of credit goes to Derek Muller at Veritasium for making a video about this topic. Its something I never even thought about and it sparked an ‘aha’ moment that made me write this post. Happy Holidays!


Hurricanes: Science and Society: Tides. (n.d.). Hurricanes: Science and Society.

Muller, [Veritasium]. (2021, December 21). The Most Powerful Computers You’ve Never Heard Of [Video]. YouTube.

Panos, K. (2015, October 8). How Analog Tide Predictors Changed Human History. Hackaday.

Tide Predicting Machines. (n.d.). Tide and Time.

Wikipedia contributors. (2021, July 4). Tide-predicting machine. Wikipedia.

Published by Mateusz Ratman

High school student from Warsaw, Poland. JHU Class of 2026.

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