The Bagnold formula, named after
Ralph Alger Bagnold
Brigadier Ralph Alger Bagnold, OBE, FRS, (3 April 1896 – 28 May 1990) was an English 20th-century desert explorer, geologist, and soldier.
Bagnold served in the First World War as an engineer in the British Army.
In 1932, he staged the ...
, relates the amount of
sand
Sand is a granular material composed of finely divided mineral particles. Sand has various compositions but is usually defined by its grain size. Sand grains are smaller than gravel and coarser than silt. Sand can also refer to a textural ...
moved by the wind to
wind speed
In meteorology, wind speed, or wind flow speed, is a fundamental atmospheric quantity caused by air moving from high to low pressure, usually due to changes in temperature. Wind speed is now commonly measured with an anemometer.
Wind spe ...
by
saltation. It states that the mass transport of sand is proportional to the third power of the
friction 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 Bagnold in 1936 and later published in his book ''
The Physics of Blown Sand and Desert Dunes'' in 1941.
Wind tunnel
A wind tunnel is "an apparatus for producing a controlled stream of air for conducting aerodynamic experiments". The experiment is conducted in the test section of the wind tunnel and a complete tunnel configuration includes air ducting to and f ...
and 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.
[Sørensen, M. 2004. On the rate of aeolian sand transport. Geomorphology 59:53-62.]
In its simplest form, Bagnold's formula may be expressed as:
:
where ''q'' represents the mass ''transport'' of sand across a lane of unit width; ''C'' is a dimensionless constant of order unity that depends on the sand sorting; ''
'' is the
density of air
The density of air or atmospheric density, denoted '' ρ'', is the mass per unit volume of Earth's atmosphere at a given point and time. Air density, like air pressure, decreases with increasing altitude. It also changes with variations in atmosph ...
; ''g'' is the local gravitational acceleration; ''d'' is the reference grain size for the sand; ''D'' is the nearly uniform grain size originally used in Bagnold's experiments (250 micrometres); and, finally,
is
friction velocity proportional to the square root of the
shear stress
Shear stress (often denoted by , Greek alphabet, Greek: tau) is the component of stress (physics), stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross secti ...
between 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 coastal
dune
A dune is a landform composed of wind- or water-driven sand. It typically takes the form of a mound, ridge, or hill. An area with dunes is called a dune system or a dune complex. A large dune complex is called a dune field, while broad, flat ...
s, therefore, are not included.
See also
*
Aeolian landform
Aeolian landforms, or Eolian landforms, are produced by either the erosion, erosive or deposition (geology), depositive aeolian processes, action of wind. These features may be built up from sand or snow, or eroded into rock, snow, or ice.
Aeolian ...
*
Aeolian process
*
Bagnold number
*
Barchan
References
External links
*
Geomorphology
Sedimentology
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