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Tide-Predicting Machines (TPMs) are analog computers which provide an accurate and efficient means of predicting the ocean tide. TPMs were invented in the late 19th century, but most of them were made in the first half of the 20th century, up until the time when digital computers consigned them to museums.
I love the mechanics of analog computers and LEGO is ideal to build, understand and run them. This project consists of a simplified version of a TPM and provides a thematic example of how most of them worked. The Tide-Predicting Machine No. 2 has around 750 parts and is 33 studs long, 16 studs deep, 18 studs high and weighs 0.6 kg.
Each TPM had its own architecture, however there were several features common to almost all of them. First a TPM had to have a driving mechanism to provide a circular motion with an angular frequency corresponding to that of a tidal constituent. Second, a TPM required a mechanism for converting that circular motion into sinusoidal motion and third it had to sum the individual sinusoidal motions to derive an overall sum. The Tide-Predicting Machine No. 2 is a fully working analog computer. See it in Action!
This project consists of three parts, a calculation block, an input/output unit and a display frame.
The calculation block is dedicated to the heart of the analog computer, the prediction of the ocean tide. The circular motion of a crank, with a pin fixed at the amplitude is converted into an up and down motion of the pulley wheel, thereby simulating the variation in water level due to that constituent.
Four of such pulley wheels can be geared to the main shaft. The pulley wheels for the height of the tide have the following properties (from front to rear):
• M2 (lunar) - amplitude: 5.0; sampled frequency: 12.5h; real frequency: 12.4h
• S2 (solar) - amplitude: 2.0; sampled frequency: 12.0h; real frequency: 12.0h
• K1 (lunar) - amplitude: 2.0; sampled frequency: 24.0h; real frequency: 23.9h
• O1 (lunar) - amplitude: 1.0; sampled frequency: 25.7h; real frequency: 25.7h
The right setting of the gears allows an accuracy of the frequencies of more than 99%.
This second generation TPM can simultaneously derive the height of the tide and its rate of change. This allows us to easily spot high and low tides (mathematically a local maximum/minimum when the first derivative is equal to zero).
The input/output unit holds the crank to run the machine. As the crank rotates, the gears align the frequency for the calculation block, the clock and the moon phase complication.
• Moon phase complication - sampled frequency: 720h; real frequency: 709h
The motions from the rise and fall of the pulley wheels are summed by using continuous bands. The bands are fixed at one end and wrap around the four pulley wheels. At their other ends they have a pointer which displays the results. A mechanism with a counterweight holds the band tight.
The display frame best replicates a tide prediction machine, including a clock, the moon phase complication, the pointers for the height of the tide (left side) and its rate of change (right side) as well as the wooden table to take notes. I have added stickers and other lively elements that I hope you will like.