Hudson's equation, also known as Hudson formula, is an equation used by coastal engineers to calculate the minimum size of riprap (armourstone) required to provide satisfactory stability characteristics for rubble structures such as breakwaters 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)[1][2] [3] The equation itself is: where:
This equation was rewritten as follows in the nineties: where: The armourstone may be considered stable if the stability number Ns = Hs / Δ Dn50 < 1.5 to 2, with damage rapidly increasing for Ns > 3.
Also it is not valid for breakwaters and shore protections with an impermeable core.
Therefore nowadays for armourstone the Van der Meer formula or a variant of it is used.