**Nanomedicine,
Volume I: Basic Capabilities**

**©
1999 Robert A. Freitas Jr. All Rights
Reserved.**

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

**9.5.3.2 Nanoflight and
Gravity**

In addition to forward progression through the medium, atmospheric
flight requires active and continuous support against the pull of gravity. For
small spherical objects of radius R = R_{nano} in the laminar flow (low
N_{R}) regime, the rate of fall in a still medium is approximated by
Stokes Law for Sedimentation (Eqn. 3.10).* For
nanorobots near the Earth's surface that are falling in air, with g = 9.81 m/sec^{2},
r_{particle} ~ 1000 kg/m^{3}, r_{fluid}
= r_{air} and h
= h_{air}, then terminal velocity v_{t}
= 1.2 x 10^{8} R_{nano}^{2} (m/sec). An R_{nano}
= 1 micron nanorobot falls at v_{t} = 120 microns/sec; an R_{nano}
= 10 micron nanorobot falls at v_{t} = 1.2 cm/sec, requiring a rather
modest power expenditure of only P_{nano}/e% = (0.5 pW)/e% to remain
aloft (Eqn. 9.74).

* In sea level pressure dry air, particles
of 100 nm diameter will fall about twice as fast as estimated by Eqn.
3.10; 10-nm diameter particles fall about 12 times as fast as Stokes' sedimentation
formula predicts.^{1572}

Note also that in free atmosphere only the largest particles
ever settle out by gravity alone. Thermal and dynamic turbulence keeps most
of the smaller particles in suspension long beyond the period indicated by Eqn.
3.10. For example, nanorobot thermal velocity v_{thermal} (Eqn.
3.3) exceeds nanorobot terminal velocity v_{t} (Eqn.
3.10) for a nanorobot radius R_{nano} <~ 2 microns in sea level
air at 20°C with r_{nano} ~ 1000 kg/m^{3}.
The energy required to raise a 1-micron nanorobot a height of ~1 micron in a
1 g gravity field equals ~kT. Random indoor atmospheric eddies of 1-10 cm/sec
caused by the movements of people, animals, doors, and heating and air conditioning
systems equal or exceed the Stokes terminal velocity for particles of R <~
10-30 microns.

Last updated on 22 February 2003