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. In 1932, he staged the first recorded East-to-West crossing of the Libyan Desert. His work in the ...

, relates the amount of

sand Sand is a granular material composed of finely divided mineral particles. Sand has various compositions but is defined by its grain size. Sand grains are smaller than gravel and coarser than silt. Sand can also refer to a textural class of s ...

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 speed ...

by saltation. It states that the mass transport of sand is proportional to the third power of the

friction velocity Shear velocity, also called friction velocity, is a form by which a shear stress may be re-written in units of velocity. It is useful as a method in fluid mechanics to compare true velocities, such as the velocity of a flow in a stream, to a veloci ...

. 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 ''The Physics of Blown Sand and Desert Dunes'' (1941) is a science book, written by Ralph A. Bagnold. The book laid the foundations of the scientific investigation of the transport of sand by wind. It also discusses the formation and movement of ...

'' in 1941.

Wind tunnel Wind tunnels are large tubes with air blowing through them which are used to replicate the interaction between air and an object flying through the air or moving along the ground. Researchers use wind tunnels to learn more about how an aircraft ...

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: :

q = C \ \frac\ \sqrt u_*^3

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; ''

\rho

'' is the

density of air The density of air or atmospheric density, denoted '' ρ'', is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperature a ...

; ''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,

u_*

proportional to the square root of the shear stress 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, f ...

s, therefore, are not included.

References

External links

* Geomorphology Sedimentology {{geomorph-stub

See also

References

External links