Bagnold formula

TheBagnold formula,named afterRalph Alger Bagnold,relates the amount ofsandmoved by the wind towind speedbysaltation.It states that the mass transport of sand is proportional to the third power of thefriction velocity.Under steady conditions, this implies that mass transport is proportional to the third power of the excess of the wind speed (at any fixed height over the sand surface) over the minimum wind speed that is able to activate and sustain a continuous flow of sand grains.

The formula was derived by Bagnoldin 1936 and later published in his bookThe Physics of Blown Sand and Desert Dunesin 1941.Wind tunneland field experiments suggest that the formula is basically correct. It has later been modified by several researchers, but is still considered to be the benchmark formula.

In its simplest form, Bagnold's formula may be expressed as:

$q=C\ {\frac {\rho }{g}}\ {\sqrt {\frac {d}{D}}}u_{*}^{3}$

whereqrepresents the masstransportof sand across a lane of unit width;Cis a dimensionless constant of order unity that depends on the sand sorting;$\rho$is thedensity of air;gis the local gravitational acceleration;dis the reference grain size for the sand;Dis the nearly uniform grain size originally used in Bagnold's experiments (250 micrometres); and, finally,$u_{*}$isfriction velocityproportional to the square root of theshear stressbetween the wind and the sheet of moving sand.

The formula is valid in dry (desert) conditions. The effects of sand moisture at play in most coastaldunes,therefore, are not included.

See also

• Aeolian landform
• Aeolian process
• Bagnold number
• Barchan

External links

• The Bibliography of Aeolian Research