HUDSON FORMULA
This is the Javascript version of the Hudson Formula for preliminary design of breakwaters.
Disclaimer: do not use these results for design purposes. This formula applies only to preliminary design. Your breakwater should be tested in a physical model before being built !

"Following work by Irribarren (1938, 1950), comprehensive investigations were made by Hudson (1953, 1959, 1961) at the U.S. Army Corps of Engineer Waterways Experiment Station (WES) and a formula was developed to determine the stability of armor units on rubble structures. The stability formula, based on the results of extensive small-scale model testing and some preliminary verification by large-scale model testing, is known by Hudson Formula". Shore Protection Manual, 1984.

1. Wave height, H: [m]
Design wave height at the structure site in meters or feet.
2. Unit weight of armor unit, Wr: [kN/m3]
Unit weight (saturated surface dry) of armor unit in N/m3 or lb/ft3. Note: substitution of rr, the mass density of armor material in kg/m3 or slugs/m3, will yeld W in units of mass (kilograms or slugs).
3. Unit weight of water, Ww: [kN/m3]
Unit weight of water: fresh water = 9.8 kN/m3 (62.4 lb/ft3) and sea water = 10.05 kN/m3.
4. Slope, m: [ ]
cotg q = m. q is the angle of structure slope measured from horizontal in degrees.
5. Breaking wave: breaking wave or nonbreaking wave.
The values of Kd for breaking and non-breaking waves refer to no-damage criteria and minor overtopping. These values were taken from table 7-8 of the Shore Protection Manual, 1984.
6. Select armor units:

 Armor Units n Placement Quarrystone smooth rounded 2 Random Quarrystone smooth rounded > 3 Random Quarrystone smooth angular 1 Random Quarrystone rough angular 2 Random Quarrystone rough angular > 3 Random Quarrystone rough angular 2 Special Quarrystone parallelepiped 2 Special Tetrapod 2 Random Quadripod 2 Random Tribar 2 Random Dolos 2 Random Modified cube 2 Random Hexapod 2 Random Toskane 2 Random Tribar 1 Uniform

7. Calc now.

8. Weight of an individual armor unit:

 Structure Trunk: [kN] = [tf] Kd = Structure Head: [kN] = [tf] Kd =

W - weight of an individual armor unit in the primary cover layer. When the cover layer is two quarry stones in tickness, the stones comprising the primary cover layer can range from about 0.75 W to 1.25 W with about 50% of the individual stones weighting more than W. The maximum weight of individual stones depends on the size or shape of the unit. The unit should not be of such a size as to extend an appreciable distance above the average level of the slope.

 Credit due to author: Carvalho, Ricardo Benoliel.