Congratulations! You have just built an analog computer to use the Law of Cosines to solve for line segment AC. Non-dimensionalize your result and its a general LofC solver. A problem that (I suspect) would take the majority of modern day Eng undergrads a week to program without the use of the math lib[1], can be solved by any keen middle schooler.
Now build a robot that measures AC for you and you have an API for your analog computer.
Typically an analog computer is thought of as a set of opamps and diodes, whose currents and voltages solve a set of non-linear ODEs; but thats a very narrow view. An analog computer is, ultimately, any physics experiment whose model is known
Wind tunnel? Navier Stokes analog computer
Cold atoms traveling through a double slit in a magnetic field? Analog Quantum computer
RCL circuit? Analog computer solving the response of a car's suspension.
[1] code reuse and libraries are a big reason why digital computers are more popular to solve models nowadays. Cost, bandwidth, are another. Ostensibly so is reproducibility. But if CS scientists cannot get reproducible builds, what hope does a humble physicist hacking on C or Matlab have?
Oh oh oh! and also resistor/capacitor circuits! Great for integration or differentiation!
Integration and differentiation have interesting audio effects; maybe our ears might be one of the better analog computers.
An integrator is just a low-pass filter and a differentiator is just a high-pass filter, so you'll most likely get "boring" audio effects ;)
This line made me laugh out loud, but what an amazing explanation and set of examples. Thank you.
The original ECU in my 1980 Datsun ... is digital, right? I just never thought of the insane analog vacuum pot system that controls the cold start valve and the air conditioning selector and the cruise control to also be a "computer" but I guess it does compute things, in its humble way ;)
Does a 1980's Datsun have an ECU? That's not obvious to me. Even a 6502 would be an expensive add on at the time given car margins. Maybe a one bit controller?
But there are analog solutions to all these control situations. And you don't need vacuum tubes!
Measuring and adjusting the fuel-air mix is the carburetor's job. The carb doesnt just add fuel. It adds the right amount of fuel. Its needle calibrates it for different conditions (namely pressure).
The spark advance "computer" was super cool. Originally spark advance was a lever controlled by the user. Faster rpm -> adjust for more advance. Eventually the lever was attached to a governor (a set of balls attached to a spinning linkage and a stiff spring. It measures rpm) and the spark advance disappeared under the hood.
The automatic version of your car would have had a (very complicated) hydraulic circuit in the tranny pushing pistons that measure throttle, rpm, velocity and choose the gear accordingly.
The manual version had a vast organic neural network doing the same job but using just sound pitch of the engine. The manual transmission was cheaper because it didn't include the neural network shifter except on the very highest end cars - think RRs - and then only as a service (early SAS model).
German WW2 aircraft were fuel injected so they probably used a governor attached to the throttle wire and pressure gauge to guesstimate the mass flow and therefore the fuel to inject. There's a front page HN submission - the fuel control system of those engines or the original Mercedes Gull-wing!
All of the hydro-mechanical stuff described were slowly transistorized (but kept analog) in the 70s. In the late 80s to 90s everything became digital except the transmissions that took longer.
of course https://www.classiczcars.com/forums/topic/63812-1980-280zx-e...
picture https://www.electro-tech-online.com/attachments/4-ecu-full-s... a ton of Hitachi chips, big one on top seems to be some kind of ADC.
https://en.wikipedia.org/wiki/JECS build on BOSH license using Hitachi HD46802P (Motorola 6802 clone). Here reverse engineered https://github.com/eccs-reengineering/280ZX-Turbo-ECCS
Bosh shipped analog controlled d-jetronic in 1967 based on US patents/designs from fifties https://jetronic.org/index.php/en/d-jetronic/51-history.
Afaik first mass produced digital ECU was shipped by GM in 1978 (Motorola 6802 based). Ford also shipped some Toshiba ECUs in 1979. Bosh first fully digital ECU (Intel 8051 based) was https://en.wikipedia.org/wiki/Motronic in 1979 like Datsun/Nissan. Ford went full ECU in 1983 (https://en.wikipedia.org/wiki/Intel_8061)
Coupled together the embodied a mid sized equation (of the other way around), live and reactive as we'd say today.
Kinda blew my mind.
For example, you might decide that 0 volts is a logical 0 and 5 volts is a logical 1. If you get everyone to agree to this convention then you can build components that talk to each other. Unfortunately, it’s very difficult (impossible) to get to exactly 0 or exactly 5 volts. So instead you decide that anything less than 2 volts is a logical 0 and anything greater than 3 volts is a logical 1. This setup makes your circuits quite robust to noise.
To further improve things, you might decide that when you want to output a logical 0 you must produce a voltage less than 1 volt and if you want to output a logical 1 you must produce a voltage above 4 volts. This convention allows your system to continually correct voltages away from the undefined region (between 2 and 3 volts). A marginal input of 3.1 volts gets interpreted as a logical 1 and then output above 4 volts. This “self-correction” is what made digital computers the revolution they are.
Imagine a NxN matrix-matrix multiply. The computation part is (naively) N^3 multiplies. The conversion back to digital is only N^2 operations, and those operations may be much simpler than digital multipliers. If there’s a way to do the N^3 multiplies as analog, then we can potentially save a lot by converting to and from binary to enable the analog phase.