Cool! This is some neat stuff. I once saw a video showcasing a mechanical calculator, it had a dizzying amount of levers and pivoting mechanisms. Figuring all that out is nothing short of miraculous!
Would it be accurate to say that most of mechanical computation is handled by gear ratios in various ways?
Weldo,
From my Fire Control Tech days (50 years ago), I can't recall any purely mechanical multiplication done by gear ratios. Our calculations required smooth, continuously-variable input and output values: i.e. real numbers rather than the discrete values of fixed gear ratios. Much of the mechanical action were related to inputs to the computation, or a way of outputting the results of computation.
The Fire Control System's Attack Director section, which does the Target Motion Analysis (TMA) is a good example. It has several electro-mechanical modules, e.g. Own Ships Course, Own Ship's Speed, Target Course, Target Speed, Target Bearing, Target Range are both inputs and output devices. The modules might receive an manual input via a handcrank, or by electronic input via a "synchro-servo", in either case this causes some shaft rotation driving a dial (like a compass rose) or mechanical counter (like an odometer) providing a visual ouput for display as well as turn a shaft geared to a precision variable resistor to be used in analog math calculations.
As a purely hypothetical example, a given shaft position in the Target Range module might equate to 8,200 yards and result in a 8.200 volt output from the resistor. So the voltage is analogous to the range and would be one of several inputs to a precision OpAmp (operational amplifier) that could be used to multiple the variable range by other variables and/or constants.
One place where purely mechanical computation is done is via a device known as a "ball-disc integrator." Rather than describe it myself, here is a link explaining the hardware and the mathematics involved.
Singer Librascope Ball and Disc Integrators. These devices are analogous to continuously-variable transmissions rather than manual gearboxes. Our submarines' fire control systems were built by Singer Corp's Librascope division. (Singer made more than sewing machines.]
Here's an article specific to "my"
Mk113 Mod 9 UWFCS (Actually, on our 594-class fast attack subs, we had the Mod 6 system. The Attack Director section is the top section of the wide stack on the left. You can see the six black hand knobs. When one is pulled out, automatic input is disabled and you can manually set a value, push it in and the knob is disconnected and the servo motors drive the module to an externally provided value (e.g. target bearing provided by sonar or from the periscope, or by the computed value (if in the dynamic "On Torpedoes Mode.")
Greg ex-submarine Fire Control Tech, FTG1(SS).