# What is a realistic computational limit for a handtool-made mechanic computer?

This question here brought up interesting points on what kind of distribution we could expect for the increase in computational power of mechanical computers in a world relying solely on such non-electric computation devices. A related question is asking about theoretical limits to mechanical computing.

I am wondering on what realistic computational limits exist on mechanical computers given a certain level of mechanical expertise - i.e. how small can we make the actual gears/shafts/springs/cogs/...

What is the maximum amount of computational power we could expect from a mechanical computer?

Some limitations:

• Let's assume that the level of mechanical expertise is what we see in exquisite (and expensive) mechanical watches today - so in effect mechanics on a scale that a person can manufacture at with hand tools.
• As a size limit let's pick the size of some of the earliest large computers (maybe similar to ENIAC and consorts): the mechanical computer still needs to fit into a medium sized building.

As a measure of computational power I'm interested in FLOPS, i.e. floating point operations per second, which is still the standard in measuring computational strength of cluster systems nowadays. Exact numbers would of course be dependant on the system, but some rough order-of-magnitude estimation should be possible. For reference:

• Z4 reached about 0.27 FLOPS
• ENIAC reached about 500 FLOPS

Bonus: If possible I'd also be interested in the power consumption (in Watt) of such a computational machine, but this could also be hand waved.

• I think that the power consumption is not really a bonus. If you want the maximum performance the practical limiting factor will almost certainly turn out to be power density. You probably could get some kind of an estimate simply by comparison to equivalent electronic system. Metal components can sustain higher temperatures and conduct heat better than semiconductors so that is a plus. On the other hand energy per computational bit will be very much greater since moving mechanical parts requires more work than switching the state of a FET. – Ville Niemi Jan 24 at 9:15
• Related, possibly a duplicate: Just How Powerful Could a Mechanical Computer Be? – a CVn Jan 24 at 10:22
• @aCVn, I've seen the question. I'm more interested in a 'realistic'/current/... limit given the limitations I mentioned above as compared to the theoretical considerations in that question. Any idea on how I could change my title to differentiate my question from the other? – fgysin Jan 24 at 11:44
• If you limit the mechanical expertise to watchmaking you'll limit yourself a lot compared to what we can do mechanically today. Is that your goal? That is, do you purposefully ask about mechanics on that scale that a person can manufacture at home with hand tools? Because watchmaking is crude compared to MEMS technology used in every cellphone etc. – pipe Jan 24 at 12:28
• @fgysin The easiest way to do it might be to simply add a link to that question within yours, and basically incorporate your comment along with it. – a CVn Jan 24 at 12:38

## 1 Answer

Propagation of mechanical signals into solids is basically limited by the speed of sound in that solid.

Therefore, assuming that the length over which you want to transfer a mechanical signal is $$L$$ and the signal propagates with velocity $$s$$, neglecting inertial effect you cannot switch the signal before a time $$t_{min}=L/s$$, which gives a maximum operating frequency of $$F_{max}=1/t_{min}=s/L$$

Also here we see that reducing the dimension of the features is a good way to increase the frequency of the device.

Just to throw some numbers in, let's say the device is made of steel and the critical size is 1 cm, this means that the maximum frequency would be $$F_{max}=5900 [m/s]/0.01 [m]=590 kHz$$

Giving the equivalent in FLOPS goes beyond my capability, and I suspect the architecture of the device should be known, too.

• Somewhat related: phys.org/news/… - electromechanical computing elements. I know this question is not about electromechanical, but it shows how small mechanical computational elements can be built right now. Fun fact? It works at 500kHz, just about what your answer states. – Mołot Jan 24 at 11:59
• For comparison, a Zilog Z80 running at 4 MHz was capable of about 0.6 MIPS, or maybe 0.05 MFLOPS... I've used such a computer, in the old days. With CP/M and Turbo Pascal! – AlexP Jan 24 at 12:09
• MOS Technology 6502: 0.500 MIPS at 1 MHz. By using very sloppy math, then, 500 KHz might get you on the order of 0.25 MIPS. – rje Jan 24 at 15:07
• Hz is "cycles per second", so converting from kHz to FLOPS (FLoating point Operations Per Second) would require knowing how many cycles that particular device requires to perform a Floating Point Operation. So, you are right that the architecture of the device would be a necessity - even in modern CPUs it varies greatly – Chronocidal Jan 24 at 17:10
• @JBH, 343 m/s is the velocity of sound in air. In steel it is 5900 m/s. – L.Dutch Jan 27 at 23:55