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A Thought…

Because in the end, you won’t remember the time you spent working in the office or mowing your lawn. Climb that goddamn mountain.

   — Jack Kerouac

Mechanical analog computers

Posted on 2017-Mar-27 at 15:27:02 by Phil
Last update on 2022-Jul-05 at 11:32:00 by Phil

In addition to the topic on Babbage’s Difference Engine and Analytic Engine, there have been mechanical analog computers since at least the early 20th century. These finely crafted devices were used, among other places, in naval gunnery directors to calculate where to point and elevate a gun to hit a distant target. Fire-control teams had to input ship and target headings and speeds, air temperature and humidity, wind speed and direction, and shell size and propellant charge (initial speed of the shell). Even the Coriolis Effect had to be taken into account at long ranges. In return, the machine would tell them the azimuth and altitude needed to hit the target.

The famed Norden Bombsight (as well as) also took many of these factors into account, to tell a bombardier how far ahead of the target to release the bombs (and how much to the side the bomber should be to allow for crosswinds). It was hardly top secret, being quite famous among the public, although aircraft crews were to make sure the device was destroyed before bailing out and saving themselves. The problem was, the Norden required a clear view of the target (difficult over Europe, with frequent clouds, ground smoke, and fog) and a knowledge of all the winds at various levels down to ground level. Thus, it rarely lived up to the hype about being able to put a bomb into a barrel. In addition, Norden insisted on hiring European craftsmen to build the things, and it turned out that several were Nazi agents who passed the plans along to Berlin before the US even entered the war! The Luftwaffe evaluated the Norden, but decided it wasn’t enough of an improvement over their existing bombsights, to build it themselves.

Discussion of other specialized mechanical calculating devices for specific purposes (as opposed to slide rules or small calculators) is welcome here. Circular slide rules with specialized scales (like the one used in Dr. Strangelove to calculate radiation exposure) aren’t all that interesting.

Posted on 2017-May-17 at 13:36:06 by Phil
Last update on 2023-Apr-06 at 12:53:00 by Phil

Let’s not forget the famed Antikythera Mechanism (1) and Antikythera Mechanism (2) a 2000 or so year old orrery/astronomical calculator.

This video, by Spencer Connor of Engineering Commons, gives a look at the operation of the Mechanism, possible designs for missing parts, and his improvements on the original design (he built an improved replica).

An article on Ars Technica about the internals of, and reconstructions of, the Antikythera Mechanism.

Posted on 2018-May-02 at 21:17:04 by Phil
Last update on 2022-Jun-19 at 21:56:00 by Phil

Another great analog computer was the US Navy Torpedo Data Computer for its submarines. A good documentary on Navy Fire Control computers in WWII, includes some material on the TDC (although it covers mechanical analog computing). As usual with analog computers, it was built to do one thing and do it well. It was not a general purpose computer like your laptop machine.

The TDC was shown in action in USS Cod SS 224, Part 2. USS Cod SS 224, Part 1 is available.

The History Guy, in a video on the development of the transistor (Transistors and Forgotten History), shows a TDC in more detail, but not the workings, except that they were electronically-assisted mechanical. He also shows Colossus at Bletchley Park, but mistakenly says it was for decoding Enigma (it was actually for “Fish”).

Some of the basic math problems to be solved by the TDC are shown in Drachinifel’s The Drydock #88. Click the link in the comments section to go to 4:09:32 WW2 Torpedo Fire Control for Submarines.

Posted on 2018-Nov-09 at 17:27:53 by Phil

I’m not sure if the Friden STW10 mechanical calculator is internally analog or digital, but here’s a fun video about trying to make it divide by zero, and going crazy. Now, what’s that “DIV STOP” button for? I would imagine it’s well-worn on some units!

Posted on 2019-Dec-22 at 12:50:10 by Phil
Last update on 2022-Sep-11 at 14:10:00 by Phil

An article on the Boeing B-29 Superfortress and its General Electric model 2CFR55B1 centralized fire-control system. Pretty amazing stuff for 1943 vintage. It was visually controlled (not by radar), but multiple gun turrets could be controlled from one of several control stations, for redundancy and flexibility. All a gunner had to do was keep the enemy fighter in the sights, and the computers did the rest of figuring exactly where to aim the guns.

A B-29 gunner’s training film shows that the gunner not only had to center the target in the sight; he also had to tell the range by inputting the target’s wingspan (once), and (continually) adjusting the reticle as the range changed. Here’s another video that shows more of the fire-control system.

Posted on 2019-Dec-22 at 13:21:26 by Phil
Last update on 2020-Jul-30 at 21:50:22 by Phil

There’s also the Curta calculator (article) that could fit in your hand and was quite popular until the advent of small electronic pocket-sized calculators. Note that this device was a calculator and not a programmable computer, but still a neat piece of gear. Be sure to watch Adam Savage’s presentation on a 3D printed replica. The story of its inventor, Curt Herzstark, is one of amazing survival in the Buchenwald concentration camp.

There are a number of videos on the construction and theory of the Curta, including this and this. I seem to recall an article in Smithsonian Magazine a few years back, but it doesn’t seem to be online, although much of the material is in the Wikipedia article.

Posted on 2021-May-10 at 14:47:57 by Phil

A thread on slide rules in general, with some digressions into other calculating devices.

Posted on 2021-Sep-18 at 18:21:29 by Phil

A presentation in Greg’s Airplanes and Automobiles on the FW-190’s Kommandogerät engine control computer for the BMW-801 radial engine. This is a hydraulic (oil) geared mechanical computer to control throttle, mixture, propeller pitch, tweaking ignition timing, and supercharger speed selection all from one control lever (go slow/go fast). This was a useful thing, as a fighter pilot who doesn’t have to pay so much attention to all the individual controls (found on other aircraft) can spend more time looking around the sky for targets or threats, and can be more effective (and more likely to survive).

Posted on 2023-May-09 at 15:47:00 by Phil

The video discusses a NASA competition for a mechanical computer that can function for a long period in the oven that is the surface of Venus. Current electronics (including all computer processors) soon fail when baked at those temperatures, although work has long been under way for processors that can survive such heat (e.g., for use in engines, re-entry vehicles, etc.). Much work so far as been on keeping electronics cool, such as by periodically lifting the package high into the cool atmosphere via a balloon, to cold-soak it. NASA isn’t forbidding the development of high temperature electronics, but would like to have an alternative in case such fail to materialize.

One thing that is still a big question mark is how to gather data without electronics, and transmit it off the surface. One suggestion is to have a semaphore-like system that could be read by radar beam from an orbiting spacecraft! How to take pictures and transmit them without more than very rudimentary electronics is still a problem.

Posted on 2023-May-28 at 16:57:00 by Phil
Last update on 2023-Oct-14 at 19:37:00 by Phil

US Navy WWII training films on the internals of shipboard fire-control computers. These are a glimpse of the mechanisms, not the specifics of using them to train and elevate the guns.

It’s frightening to think that almost any high school graduate could understand these concepts 80 years ago. Today, most college-bound AP students probably couldn’t understand it! On the other hand, it’s fascinating that simple, purely mechanical devices can add, subtract, multiply, divide, take logs, powers, roots, differentiate, and integrate (within reasonable input ranges of values, and limited precision).

A simple demonstration of integration using two discs: The Mechanical Integrator - a machine that does calculus.

What would be cool would be to get rid of the shafts and whatnot connecting the various mechanical adders, integrators, etc., and use electrical signals (or even air pressure or hydraulics) to transmit analog values from one to the other. I wonder if anyone ever built such a thing? Note that these are still analog machines (values are the amount of rotation or translation) rather than digital. There are some pretty massive analog computers built in the past that you ran patch cords from one processing unit to another — perhaps that’s exactly it?

A moderately complex relay logic electromechanical system in a Wurlitzer jukebox. This isn’t really computing, per se, but does illustrate some complex logic handling.

And here’s the complex relay logic within a 1970s pinball machine (before they became computerized).

We are not going to deeply cover mechanical and electromechanical calculators and adding machines. While these are interesting in their own right (and have many videos covering their design), they are not really more than the performance of single numerical operations, relying on the operator (person) to sequence operations and decide on branching.

Posted on 2023-Jul-12 at 13:23:00 by Phil

A quick look by Drachinifel at some of the innards of a battleship's electromechanical fire control computer aboard BB-64 USS Wisconsin, "The Wisky". Wisky? The only battleship where you can cross the state line from Wisconsin to Kentucky!

Posted on 2023-Jul-24 at 11:42:00 by Phil

The story of “Old Brass Brains” and the mechanical computers long used to predict tides: video. There is also a look at some other early mechanical computers developed over the centuries. One interesting aspect of this machine is the use of a series of pulleys on one long chain to (apparently) change various inputs when one or more other inputs are adjusted. A given pulley is moved up or down as the chain is adjusted, causing a change to a linear input device for part of the calculation.

Posted on 2023-Aug-28 at 21:12:00 by Phil
Last update on 2023-Dec-26 at 20:43:00 by Phil

Around the end of the 1890’s, Albert Michelson (of Speed of Light fame) designed a “Harmonic Analyzer”, to be built and sold by William Gaertner & Co. of Chicago, IL. The purpose is to generate arbitrary periodic waveforms specified by \(A = \sum_{n=1}^{20} a_n \cos(n (\phi_n + x))\). From further discussion in the video, it appears that phase angles can be set for each cosine wheel, giving sines or cosines, and potentially arbitrary phase angles (a sine wave is the same shape as a cosine wave, just starting 90 degrees earlier). A number of such machines were built in the early 20th Century, including a 20 cosine (20 gear) machine which ended up at the University of Illinois, Urbana-Champaign, where it is displayed today. It sums 20 cosines (up to 80 in some other models) at settable amplitudes (and phases), in fixed multiples of the crank speed.

Note that this is not a Fourier Analysis (decomposing a waveform into its components), but rather the synthesis of an arbitrary waveform from the sum of many cosines. Apparently, if you want to figure out what goes into some waveform of interest, it is possible to use this machine to sample a waveform and determine the amplitude settings!

There are some limitations to the machine as compared to an electronic computer, of course. There is a limit of 20 gears/cosines (although an arbitrary number can be disabled by setting their amplitude to 0). More expensive models boasted up to 80, and Michelson at one point wanted to build a 1000 gear unit! The gears (driving the cosine levers through cams) are driven at fixed speed ratios, and it is difficult to set arbitrary phases. Springs used to sum the overall output can weaken over time (the 20 individual springs are countered by a master spring), and even the angle of the pen against the paper can greatly affect the waveform shape. The various cranks and arms rocking back and forth introduce extra motions that may introduce error (many parts are very long to reduce this effect). Perhaps a more modern design and materials could overcome some of these issues, yet the machine remains a marvel for what it can do. Anyone up for a challenging Maker project? Perhaps something using a pin in a T-slot to get pure sinusoidal motion, with multipliers and differential adders to sum it all up?

And here is a nice presentation on digital signal processing, mentioning the high points of signal decomposition into a sum of sine waves, using a spectrum analyzer. It’s oriented more towards digital audio recording, but is a good starting point.

And here is another video, on the basics of the Fourier Transform, Discrete FT (working with discrete sample values), and Fast FT (widely used in digital signal processing). If C.F. Gauss had bothered to publish his FFT discovery in 1805, rather than letting it be rediscovered in the mid-1960s, the 1963 Partial Test Ban Treaty might well have been a Comprehensive Test Ban Treaty, and the Nuclear Club might have stayed at four.

Posted on 2024-Jan-18 at 11:08:00 by Phil

Part 5 of a multipart video series on the restoration of a Bendix MG-1 Central Air Data Computer from 1950’s and 1950’s US fighter jets. This is a mixed electrical and mechanical computer, where the actual mathematical functions (add, multiply, logs, powers, etc.) were performed with mechanical systems (gears, cams, differentials, etc.) and electronics glued it all together. Over a half century or more, most of the electronics had failed, while the mechanics still worked perfectly.

See also the entry on the MG-1’s electronic successor, the MP944-based CADC.


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