© 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/sec², r_particle ~ 1000 kg/m³, r_fluid = r_air and h = h_air, then terminal velocity v_t = 1.2 x 10⁸ R_nano² (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/m³. 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