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For me, nothing beats the mechanical calculator used to calculate torpedo firing solutions in WWII. It was a sophisticated differential equation solver that kept a real-time updated firing solution using ... gears.

There's a whole maintenance and operations manual beautifully scanned here[1]. I've wanted to build one forever, but lack the time and expertise.

1. https://maritime.org/tech/tdc.htm

I am interested in differential analyzers too, especially after the anecdotes in Richard Hamming's Learning to Learn (aka Hamming on Hamming)[1] about re-purposing "gun directors" to solve engineering problems.

Some of the mechanisms involved are really elegant, like the torque amplifier[2] which wasn't invented until the 1920s. A tabletop demo of one is on my to-do list.

[1] https://www.youtube.com/playlist?list=PL2FF649D0C4407B30

[2] https://en.wikipedia.org/wiki/Torque_amplifier

The same sorts of things were built using analog electronics.

And even these have fallen by the wayside to digital electronics.

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