Hudson's Equation, also known as Hudson's Formula, is an equation

Equation

An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign , for examplex + 3 = 5\,asserts that x+3 is equal to 5...

 used by coastal engineers

Coastal management

In some jurisdictions the terms sea defense and coastal protection are used to mean, respectively, defense against flooding and erosion...

 to calculate the minimum size of riprap

Riprap

Riprap — also known as rip rap, rubble, shot rock or rock armour or "Rip-rap" — is rock or other material used to armor shorelines, streambeds, bridge abutments, pilings and other shoreline structures against scour, water or ice erosion.It is made from a variety of rock types, commonly granite or...

 (rock armour) required to provide satisfactory stability characteristics for rubble

Rubble

Rubble is broken stone, of irregular size, shape and texture. This word is closely connected in derivation with "rubbish", which was formerly also applied to what we now call "rubble". Rubble naturally found in the soil is known also as brash...

 structures under attack from storm wave

Wave

In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...

 conditions.

The equation was developed by the United States Army Corps of Engineers

United States Army Corps of Engineers

The United States Army Corps of Engineers is a federal agency and a major Army command made up of some 38,000 civilian and military personnel, making it the world's largest public engineering, design and construction management agency...

, Waterways Experiment Station (WES), following extensive investigations by Hudson (1953, 1959, 1961a, 1961b).

Equation

The equation itself is:


where:

• W is the design weight of the riprap armour
• w_r is the unit weight of the armour
• H is the design wave height
• K_D is a dimensionless stability coefficient, calculated for different kinds of armour by laboratory experiment
• S_r is the specific gravity
  Specific gravity
  Specific gravity is the ratio of the density of a substance to the density of a reference substance. Apparent specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance. The reference substance is nearly always water for...
  
   of the armour, relative to the water at the structure i.e. S_r = (w_r / w_w)
• θ is the angle of revetment with the horizontal

See also

• Breakwater (structure)
  Breakwater (structure)
  Breakwaters are structures constructed on coasts as part of coastal defence or to protect an anchorage from the effects of weather and longshore drift.-Purposes of breakwaters:...
  
  
• Coastal erosion
  Coastal erosion
  Coastal erosion is the wearing away of land and the removal of beach or dune sediments by wave action, tidal currents, wave currents, or drainage...
  
  
• Coastal management
  Coastal management
  In some jurisdictions the terms sea defense and coastal protection are used to mean, respectively, defense against flooding and erosion...
  
  
• Riprap
  Riprap
  Riprap — also known as rip rap, rubble, shot rock or rock armour or "Rip-rap" — is rock or other material used to armor shorelines, streambeds, bridge abutments, pilings and other shoreline structures against scour, water or ice erosion.It is made from a variety of rock types, commonly granite or...