# Hudson's equation

Hudson's Equation, also known as Hudson's Formula, is an equation used by coastal engineers to calculate the minimum size of riprap (rock armour) required to provide satisfactory stability characteristics for rubble structures under attack from storm wave conditions.

The equation was developed by the United States Army Corps of Engineers, Waterways Experiment Station (WES), following extensive investigations by Hudson (1953, 1959, 1961a, 1961b).[citation needed]

## Equation

The equation itself is:

$W =\frac{\ w_r H^3}{K_D(S_r-1)^3\cot\theta}$

where:

• W is the design weight of the riprap armour
• wr is the unit weight of the armour
• H is the design wave height
• KD is a dimensionless stability coefficient, calculated for different kinds of armour by laboratory experiment
• Sr is the specific gravity of the armour, relative to the water at the structure i.e. Sr = (wr / ww)
• θ is the angle of revetment with the horizontal