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 blocks) 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) (see Shore Protection Manual and Rock Manual referenced below).

Initial equation

The equation itself is:

W =\frac{\gamma_r  H^3}{K_D \Delta^3\cot\theta}

where:

  • KD = around 3 for natural quarry rock
  • KD = around 10 for artificial interlocking concrete blocks

Updated equation

This equation was rewritten as follows in the nineties:

\frac{H_s}{\Delta D_{n50}}= \frac{(K_D cot\theta)^{1/3}}{1.27}


where:

  • KD = around 3 for natural quarry rock
  • KD = around 10 for artificial interlocking concrete blocks


The armour blocks may be considered stable if the stability number Ns = Hs / Δ Dn50 < 1.5 to 2, with damage rapidly increasing for Ns > 3.

Obviously, these equations may be used for preliminary design, but scale model testing (2D in wave flume, and 3D in wave basin) is absolutely needed before construction is undertaken.

See also

References

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