Bagnold Formula
Encyclopedia
The Bagnold formula, named after Ralph Alger Bagnold
, relates the amount of sand
moved by the wind to wind speed
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
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.
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
; 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 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 dunes, therefore, are not included.
Ralph Alger Bagnold
Brigadier Ralph Alger Bagnold, FRS OBE, was the founder and first commander of the British Army's Long Range Desert Group during World War II. He is also generally considered to have been a pioneer of desert exploration, an acclaim earned for his activities during the 1930s...
, relates the amount of sand
Sand
Sand is a naturally occurring granular material composed of finely divided rock and mineral particles.The composition of sand is highly variable, depending on the local rock sources and conditions, but the most common constituent of sand in inland continental settings and non-tropical coastal...
moved by the wind to wind speed
Wind speed
Wind speed, or wind velocity, is a fundamental atmospheric rate.Wind speed affects weather forecasting, aircraft and maritime operations, construction projects, growth and metabolism rate of many plant species, and countless other implications....
by saltation. It states that the mass transport of sand is proportional to the third power of the friction velocity
Log wind profile
The Log wind profile is a semi-empirical relationship used to describe the vertical distribution of horizontal wind speeds above the ground within the atmospheric surface layer...
. 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
Ralph Alger Bagnold
Brigadier Ralph Alger Bagnold, FRS OBE, was the founder and first commander of the British Army's Long Range Desert Group during World War II. He is also generally considered to have been a pioneer of desert exploration, an acclaim earned for his activities during the 1930s...
in 1936 and later published in his book The Physics of Blown Sand
The Physics of Blown Sand
The Physics of Blown Sand and Desert Dunes 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 sand dunes in the Libyan Desert...
and Desert Dunes in 1941. Wind tunnel
Wind tunnel
A wind tunnel is a research tool used in aerodynamic research to study the effects of air moving past solid objects.-Theory of operation:Wind tunnels were first proposed as a means of studying vehicles in free flight...
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.
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 airDensity of air
The density of air, ρ , is the mass per unit volume of Earth's atmosphere, and is a useful value in aeronautics and other sciences. Air density decreases with increasing altitude, as does air pressure. It also changes with variances in temperature or humidity...
; 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 velocityLog wind profile
The Log wind profile is a semi-empirical relationship used to describe the vertical distribution of horizontal wind speeds above the ground within the atmospheric surface layer...
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 dunes, therefore, are not included.
See also
- Bagnold numberBagnold NumberThe Bagnold number is the ratio of grain collision stresses to viscous fluid stresses in a granular flow with interstitial Newtonian fluid, first identified by Ralph Alger Bagnold.The Bagnold number is defined by...
- Saltation (geology)Saltation (geology)In geology, saltation is a specific type of particle transport by fluids such as wind or water. It occurs when loose material is removed from a bed and carried by the fluid, before being transported back to the surface...
- Aeolian processes
- Aeolian landformAeolian landformAeolian landforms are features of the Earth's surface produced by either the erosive or constructive action of the wind. This process is not unique to earth, and it has been observed and studied on other planets, including Mars.-Terminology:...
- DuneDuneIn physical geography, a dune is a hill of sand built by wind. Dunes occur in different forms and sizes, formed by interaction with the wind. Most kinds of dunes are longer on the windward side where the sand is pushed up the dune and have a shorter "slip face" in the lee of the wind...
- BarchanBarchanA barchan dune, also barkhan is an arc-shaped sand ridge, comprising well-sorted sand. This type of dune possesses two "horns" that face downwind, with the slip face at the angle of repose of sand, or approximately 35 degrees . The upwind side is packed by the wind, and stands at about 15 degrees...