Scaling of speeds
Question: When it comes to macroscale style machinery at the nanoscale,
what is the most natural (optimal) scaling for speeds ascross scales?
Contents
Constant speeds as a very crude first approximation
A crude first approximation as a starting point seem to be "same relative deflections across scales". This leads to keeping speeds constant across scales and acccordingly to linearly rising frequencies.
Despite actual parctical systems will not adhere to this scaling, this is still good to look at first as it gives a clear-cut scaling law as a starting point for further thinking.
More realistically but less accurately - some slowdown
There is strong motivation to deviate from "keeping speeds constant across scales" coming from the desire to keep losses and heatup from dynamic friction low. Speeds at the macroscale do not incur much more friction with higher speeds. Rather deflections from accelerations are usually the limiting factor. Nanomachinery though incurs dynamic friction quadratically growing with speeds. Friction levels per area are quite significant at m/s scales. Thus proposed speeds for future gem-gum based advanced productive nanosystems are more down in the low mm/s range.
As a slowdown needs to be compensated with more machinery in order to keep the same throughput one only gains a linear drop in friction losses rather than a quadratic one. For details see: Lower friction despite higher bearing area. This tradeoff of more of nanomachitery for running it slower is enabled by the all important scaling law of higher throughput of smaller machinery.
As this is not a clear cut scaling law this is not a good starting point for thinking despite being much closer to actually proposed systems. The problem is that friction in nanoscale bearings and friction in macroscale bearings are quite different in scaling and it's difficult to reliably predict the transition. Or even the behaviour of future macroscale bearings based on gem-gum metamaterials.
The proposed slowdown is roughly a thosand x (from m/s to mm/s) aross a scale of a million x (from m to nm). This gives roughly/perhaps/maybe a scaling of speeds with the squareroot of scale. More insights may arise.
Scaling of speeds in natural systems
Note that as natural systems work quite differently, natural scaling laws (for speed across scales) differing from aboves consideration do not idicate that aboves considerations are wrong.
(wiki-TODO: Cover the below points in more detail eventually.)
- There is the scaling of the speed of insect wings.
- There is the scaling of speeds imparted by viscous drag when moving in liquids (which is much higher than dynamic friction in crystolecule bearings).
- There is the scaling of speeds in biological metabolism (which deviates notably from what is desctibed on the page higher throughput of smaller machinery).
- There is exploitation of diffusion transport (which is not free of energy dissipation!) (wiki-TODO: Derive the scaling law assuming both transport distance and block size being at the scale L. (pseudo)speeds should drop rapidly with scaleL). Unless charged ions in a field speeds cannot be accelerated here. Well, reduced dimensionality of transport can accelerate (pseudo)speeds.
