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Inspired by many questions that make use of utility fog.

Utility fogs are not, as the name might suggest, fogs, but rather lattice solids.

Cells of the foam are pollen-like micrometer-scale machines physically connected to one another by robotic arms. When they run out of power, or are ripped off the lattice by force, the machines try to recover -- or fall to the ground.

Foglets are produced by some outside device. Once deployed, will eventually degrade to nothing as casual-use damage to the lattice accumulates.

Are they feasible? What can they do?

Here are the specs. Feel free to look here for additional material.

  • Body is 10 micrometers in diameter
  • Has up to twelve arms, 5 micrometers in diameter and 50 micrometers long giving a fully-extended reach of about 100 micrometers, and a fully-contracted volume of 10 micrometers per cell
  • Made or shrouded in aluminum oxide. Density of alumina allows ranges between 3,000 to 4,000 kg per cubic meter
  • Arms have a tensile strength of about 100,000 psia. Compressive strength is about 800,000 psia (from this source).
  • Hands (connecting nodes) has a tensile strength of 1,000 psia.
  • Sensors : best available with current technology
  • Processing : 100 million instructions per second, or best available
  • Power : best available with current technology (maybe supercapacitors).
  • Computational Power Consumption : best available (I found ~45 Watts per terahash on a Bitcoin mining site) and 1 hash $\approx$ 12,700 operations
  • Operating Mode : continuously on while deployed. Evaluating objects attempting to pass into the fog and adjusting shape as required.
  • Failure Mode : individual micromachines stow their arms and go inert when disconnected from the lattice and unable to re-attach. Micromachine nodes also stow and go inert when power failure is imminent.

Uses of utility fog :

  • As a seat belt alternative / safety restraint
  • On-demand construction of roads
  • On-demand furniture and non-consumable household goods
  • Moving objects, people
  • Solid telepresence or entertainment content

So, here's a few specific questions :

  • What is the minimum (stowed) volume of 1 kilogram of this utility fog?
  • What is the maximum (fully extended) volume of 1 kg of utility fog?

Would it be dangerous for a human being to be enveloped in this medium:

  • Are the 50-micrometer arms a physical injury hazard?
  • Is ingestion or inhalation a physical injury hazard?
  • Are "soft spots" (eyes) in danger from being enveloped in a utility fog?

How long could a utility fog stay in active operation before running out of power?

How much pressure can a 1kg utility fog exert on an enclosed space? Does the maximum utility fog force scale with the density of the utility fog? (think the answer is "yes" given the slender arms).

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    $\begingroup$ Is hard science the right tag? Since no utility fogs actually exist, I'm not sure that people can answer with meaningful scientific papers about them. $\endgroup$
    – Zxyrra
    Feb 19, 2020 at 23:32
  • $\begingroup$ There may be a better tag. I'd like to answer specific physical questions based on the stated physical properties in the spec (tensile strength and size). Leaving aside the practicality of construction, and looking at best available current power densities -- even if none of those are built to that scale currently. $\endgroup$ Feb 19, 2020 at 23:35
  • $\begingroup$ So... I think its a very good question, but I have one question: what exactly is utility fog used for? I see a bunch of stuff about "enveloping" and "danger to humans"; however, your question does not adequately explain the usage. $\endgroup$
    – The Daleks
    Feb 20, 2020 at 2:09
  • $\begingroup$ Added uses from the linked document $\endgroup$ Feb 20, 2020 at 13:00

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Stowed and Deployed Characteristics

Approximating the fog body as solid aluminum (3,000 $kg \over m^3$ ), 1 kilogram of stowed utility fog takes up a space of about 7 centimeters (~ 2.8 inches) on a side.

Deployed, the fog increases it's diameter by 10x from 10 micrometers to 100 micrometers. The deployed volume of 1 kilogram of utility fog is 70 centimeters (~ 2.5 feet) per side.

Lifespan

There are 343 billion micromachines in 1 kilogram of utility fog. Motion cueing systems for flight simulators update 1,000 times per second (ref). So 343 billion machines updating their position 1,000 times per second is 343 trillion calculations per second.

Using Bitcoin Miner power efficiencies of 45 Watts per tera (trillion) hashes (calculations). Each hash is 12,700 operations. The utility fog will consume 1 watt simply on computation.

Lithium-ion gets higher power densities than supercapacitors (100 $Wh \over m^3$). But, even if the whole volume of the micromachine node body (also called "foglet") is turned over to power, only 1 x $10^{-13}$ Watt-hours is available. However, converted to Joules (3,600 $seconds \over hour$) and multiplied by the 343 billion machines in the 1 kilogram utility fog, the total available energy is 123 Joules. Divide that by 1W = 1 $Joule \over second$ of computational power consumption and the lifespan of a utility fog is 123 seconds (or about 2 minutes).

Some alternatives : some sort of hydrogen fuel cell (33,000 $Wh \over m^3$) ~ 600 seconds (10 minutes) of operation. Also, reduce the update rate to 250 Hz ~ 40 minutes. Also, some near-future improvements on computing power consumption --- maybe 80 minutes of operating time.

Strength

Each arm is 5 micrometers thick and can handle up to 800,000 psia of pressure (or 0.00002 pounds-force per arm). Up to 4 of the 12 arms can be facing a load, each taking sin(45) ~ 0.707% of the total = 0.000056 pounds-force per machine.

Spread across the area of the machine, the compressive strength is 565,000 psia when just barely deployed, 5,656 psia when fully deployed, and 800,000 psia when fully stowed. One atmosphere of pressure is 14.7 psi. So the strength of the utility fog ranges from around 380 atmospheres to 38,000. Easily enough to flip over cars or break things.

Human Safety

Electrically, the whole thing is a single structure, always on the ground. it shoud, then, be electrically grounded.

At 10 micrometers for the body, these devices are about the same size as pollen. They might embed in the top layer of epidermis, get caught in mucus, but won't penetrate. At 0.6 millimeters thickness, even the middle layer of the human eyelid is six times the thickness of these devices. Arms might break off and penetrate further, but the body is always shedding these layers. Given a short exposure to the utility fog, any micromachines captured by the human body should be shed.

Living full, or most of the time, in a utility fog, some people may develop metal hypersensitivity or allergy requiring their removal from the fog.

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