# Re: Nano-Copters

From: hal@finney.org
Date: Fri Nov 24 2000 - 12:40:15 MST

Mike Lorrey writes:
> I was under the impression that the rotors being used have very broad
> chord blades, which replicate insect aerodynamics. At nanoscale, I would
> imagine that any propulsion device using rotors or wings would have to
> be able to work like the blades were tennis rackets, flying about in an
> environment of high speed ping-pong balls. If the fluid is dense enough,
> it should work.

Insects have two differences, first they are in air, and secondly they
are thousands to a million times bigger than what we are talking about.

In 9.4.2.1 of Nanomedicine, Freitas compares a human swimming underwater
with a bacterium. There are two forces, inertia and viscous drag.
For a human swimmer inertial force is 10 Newtons and viscous force is
.0001 Newtons, a ratio of 10^5. However for a bacterium the situation
is reversed. Viscous forces are 10^5 greater than inertial forces.

"The bacterium (or any micron-sized medical robot) lives in a world
dominated by viscosity, where, as an example, the phenomenon of 'coasting'
essentially ceases to exist. For enstance if motive power to a swimming
nanorobot with radius R = 1 micron and velocity v = 1 cm/sec is suddenly
stopped, then the nanorobot will 'coast' to a halt in time 0.1 microsec
and in a distance 1 nm."

He goes on, "Purcell notes that for a man to be swimming at the same
Reynolds number as his own sperm, he would have to be placed in a swimming
pool full of molasses and then be forbidden to move any part of his body
faster than 1 cm/min, roughly the speed of the minute-hand of a large
wall clock."

In this environment a better model than a propeller is a threaded screw,
which by rotating forces its way forward through the viscous medium.
This is essentially what the bacterial flagellum does.

Freitas discusses flying nanobots in section 9.5.3.1:

"Insects make use of both inertial and viscous forces, often employing
unusual wing flapping patterns and elastic energy storage systems to
remain aloft. The smallest known flying insect that can make any use
of aerodynamic lift (inertial) forces is the four-winged parasitic
chalcid wasp Encarsia formosa, which has a total wingspan of ~1.4 mm.
Aerobotic machines with wingspans smaller than 100 microns probably must
make almost exclusive use of viscous propulsive forces."

He concludes that flying nanobots would do better to propel themselves
using similar mechanisms to those used by bacteria in water, such as
corkscrew flagellar drives, rather than wings and jets.

> In my terraforming paper I wrote, I came up with the concept of a large
> buckeyball (C-360 or larger) molecule with no matter inside should be
> bouyant in a 1 bar atmosphere, as a nano-balloon (my CO2 sequestering
> nanites would have these on their bodies to float in the atmosphere
> above the point where the atmosphere was too hot for the carbon to not
> burn up).

>From a post on sci.nanotech by Robert Shimmin, nothing near C-360 will work.
Try C-100000000:
: For a purely back-of-envelope job:
: C-60 has a diameter of 1.2 nm. Assuming the C-C bond length remains constantish,
: a single buckyball ought to have a bulk density of about density [kg/m3] = 10200 /
: sqrt(# C atoms).
:
: This gives C60 a density of 1320 kg/m3, abou 60% that of graphite. To float in air
: (density ~1 kg/m3), you'd need a buckyball with at least 10^8 carbons in it. It would
: have a diameter of about 1.5 microns. No clue whether a fullerene this flat could
: withstand atmospheric pressure.

"What is the tiniest possible lighter-than-air balloon? J.S. Hall
notes that for a one-atom-thick graphene shell the out-of-plane bending
stiffness of the C-C bond is much lower than the in-plane stretching
stiffness. This is why hollow fullerenes of submicron diameter are
experimentally observed to collapse (and remain collapsed due to van
der Waals forces) even when their interiors are not evacuated."

Freitas goes on to analyze the weight of internal cross beams
sufficient to prevent collapse, and finds that they weigh too much.
No balloon of this design can float in air "although macroscale
geodesic trusswork-stabilized vacuum balloons cannot be ruled out".
His best approach is to fill the balloon with hydrogen or helium.
A helium filled 13.6 micron fullerene sphere can lift a payload of 1
cubic micron of water. Generally speaking, powered propulsion will be
superior, as gravitational forces are relatively small at the nanoscale.

BTW the complete text of the book is available online at
www.nanomedicine.com. This is an astonishingly complete resource for those
interested in the capabilities of nanomachines. The book is about far more
than medical applications.

Hal

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